effectofhybridsteel-basaltfiberonbehaviorsofmanufactured...
TRANSCRIPT
Research ArticleEffect of Hybrid Steel-Basalt Fiber on Behaviors of ManufacturedSand RPC and Fiber Content Optimization Using CenterComposite Design
Yunlong Zhang Jiahui Liu Jing Wang and Bin Wu
School of Transportation Science and Engineering Jilin Jianzhu University Changchun 130000 China
Correspondence should be addressed to Jiahui Liu 15584787755163com
Received 4 September 2020 Revised 18 November 2020 Accepted 23 November 2020 Published 11 December 2020
Academic Editor Jose Aguiar
Copyright copy 2020 Yunlong Zhang et al -is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
-e mechanical properties and workability of manufactured sand reactive powder concrete (RPC) mixed with steel and basaltfibers were studied using the response surface method -e central composite design was used to explore the 7-day and 28-daycompressive strength flexural strength and workability of different amounts of mixed fiber-manufactured sand RPC Resultsshowed that when the steel fiber content was less than 25 mixing basalt fibers can significantly improve the flexural strength andflexural-compressive ratio of RPC -e relationship equations of the two fibers with the 28-day compressive strength flexuralstrength and flexural-compressive ratio of the manufactured sand RPC were obtained through the response surface model -emodel proved to be reliable according to the analysis of variance -e content of the two fibers was optimized by multiobjectiveoptimization technology and the optimal content of the mixed fiber-manufactured sand RPC under standard curing conditionswas verified
1 Introduction
Reactive powder concrete (RPC) is a high-density cement-basedcomposite material with high strength high durability goodstability and broad application prospects developed in the 1990s[1 2] -e use of RPC in the structure can effectively reduce itssize and weight while saving more resources Existing studiesmostly use quartz sand and river sand to prepare RPC the use ofmanufactured sand to prepare RPC is still in its infancy [3]Using manufactured sand instead of quartz sand can lower thecost And if the river sand could be replaced by the manu-factured sand the damage to the river bed and dam could belessened -erefore manufactured sand RPC has importantresearch value In order to improve themechanical properties ofRPC and reduce the brittleness caused by its high strengthvarious fibers are usually added to RPC [4ndash7] However thereare few reports on the blending of fibers in manufactured sandRPC and how to blend fibers in manufactured sand RPC andthe ratio of fibers are the technical key to the application of
manufactured sand in RPC -erefore the research on addingfiber to manufactured sand RPC is very important
Currently the researches on the steel fiber are devel-oping faster than that of other fibers -e addition of steelfiber can significantly improve the tensile properties of RPCand hinder the development of cracks to improve theductility and toughness of RPC [8ndash10] A proper ratio ofmixing steel fiber can replace part of steel bars in structuresthereby reducing the difficulty and cost of construction [11]However the strength of RPC will not continue to increasewith the amount of steel fiber Blindly increasing the fibercontent not only increases the self-weight of the structurebut also causes the poor workability of concrete because ofthe agglomeration of steel fiber [3] Basalt fiber as a newenvironmental-friendly material in the 21st century hasexcellent mechanical properties corrosion resistance hightemperature resistance and electrical insulation propertiesIn recent years it has been widely used in the reinforcementof concrete materials [12] Compared with steel fiber basalt
HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8877750 17 pageshttpsdoiorg10115520208877750
fiber has higher tensile strength smaller size andmore fibersin the same volume And the addition of basalt fiber im-proves the initial cracking strength of concrete underbending load which effectively inhibits the generation ofmicrocracks [13] Basalt fiber has better workability whenadded to concrete but its effect of enhancing the com-pressive strength is not as obvious as tensile strength andflexural strength [14] -erefore steel fiber and basalt fiberhave a certain degree of synergy and complementarity interms of size and reinforcement mechanism So somescholars have mixed basalt fiber and steel fiber into ordinaryconcrete and found that it exhibits a good positive hybrideffect [15] Compared with single blended fiber the flexuralstrength of blended steel-basalt fiber is more significantlyimproved but the compressive strength will be reducedwhen the blending fiber content is high [16] Under ap-propriate blending amount the shear strength axial tensilestrength four-point bending strength splitting tensilestrength and energy dissipation capacity could be improvedsignificantly [17] However most of the studies are on theeffect of steel-basalt fiber mixing on ordinary concrete -einteraction between steel-basalt fiber in manufactured sandRPC and how to acquire the best mixing effect has not beensystematically analyzed -erefore the compressive strengthand flexural strength of the steel-basalt fiber-manufacturedsand RPC were tested to facilitate the preparation ofmanufactured sand RPC that meets actual engineeringneeds
In summary this article uses the content of steel fiberand basalt fiber as the influencing factors through the centralcomposite design to study the influence of the interactionbetween steel fiber and basalt fiber on the mechanicalproperties and workability of manufactured sand RPCEmploying the response surface method the compressivestrength flexural strength and flexural-compressivestrength ratio of manufactured sand RPC under the inter-action of steel fiber and basalt fiber are analyzed and aresponse surface model is established to obtain the rela-tionship between the two fibers and the mechanical strength-e response surface fitting formula can be used to obtainthe steel-basalt fiber content corresponding to the RPC ofmanufactured sand with different strengths so as to preparethe manufactured sand RPC that can meet different re-quirements -e response surface method is used to opti-mize the design of steel-basalt fiber-manufactured sandRPC and the results are verified by experiments whichprovides the necessary theoretical basis for the promotionand application of manufactured sand RPC
2 Materials and Methods
21 Raw Material PII525 cement by Jilin Yatai Cement(Changchun China) was used for the test -e cementinspection report (Table 1) complies with the GeneralPortland Cement Testing Standard (GB175-2007) [18]Silica fume produced by Dongyue Silicone Material (ZiboChina) fly ash manufactured by Datang Second -ermalPower (Changchun China) and S95-grade mineral pow-der produced by Longze Water Purification Materials
(Gongyi China) were used -e test reports are presentedin Tables 2ndash4-ese materials were used in accordance withthe technical specifications of the application of mineraladmixtures (GBT510032014) [19] -e superplasticizerused was an HSC polycarboxylic acid high-performancewater-reducing agent produced by Borida Building Ma-terials (Chongqing China) -e test report is shown inTable 5 -e fine aggregate was made from manufacturedsand produced by Jiusheng Industry (Changchun China)and a photo is presented in Figure 1 -e sand screeningtest results are provided in Table 6 and according to theStandard for Technical Requirements and Test Method ofSand and Crushed Stone for Ordinary Concrete (JGJ 52-2006) [20] the manufactured sand distribution is shown inFigure 2 -e steel fibers were made from copper-platedsteel fibers manufactured by Ruke Steel Fiber Industry(Yongkang China) -e specifications and performanceindices are shown in Table 7 Figure 3 presents a picture ofthe steel fibers -e basalt fibers were made from copper-plated steel fibers produced by Anjie Composite MaterialFactory (Haining China) -e specifications and perfor-mance indices are listed in Table 8 and a picture is shownin Figure 4
22 Test Preparation and Curing First the cement silicafume fly ash mineral powder and manufactured sand werepoured into a mixer and dry mixed for 2min Second asmixing continued steel and basalt fibers were sprinkledthrough a sieve When the fibers were added they scatteredafter 2min of dry mixing -ird a mixture of 80 super-plasticizer and water was added slowly and stirred for 4minFinally the remaining superplasticizer agent was added andstirred for 2min
In this test the curing method was standard curing(temperature 20degCplusmn 2degC humidity 95) After the RPCwas installed the specimens were placed immediately in thecuring room After 24 h the specimens were separated fromthe mold and placed once again in the curing room forcuring until the test days as shown in Figure 5
23 Testing Procedure
231 Mix Proportion -e mix proportion used in the ex-periment is shown in Table 9 -e mix proportion is theoptimal mix ratio determined by the orthogonal test ofZhong et al [3] taking the water-binder ratio sand-binderratio silica fume and fly ash as factors and analyzingcompressive strength -e amount of HSC polycarboxylicacid superplasticizer added in this experiment was 12 ofthe cementing material quality
232 Testing Program According to the GBT31387-2015[21] a 100mmtimes 100mmtimes 100mm cube specimen wasselected as the test specimen for pressure resistance An SYE-3000B hydraulic press (Hydraulic Press of New TestingMachine Co Ltd Changchun China) was used for loading-e loading rate for the compressive test was kept between
2 Advances in Civil Engineering
12MPas and 14MPas -e flexural strength test utilized a100mmtimes 100mmtimes 400mm prism specimen and used aWAW-1000B electrohydraulic servo universal materialtesting machine (Hydraulic Press of New Testing MachineCo Ltd Changchun China) for loading -e loading rate
was maintained at approximately 008MPas and 01MPas-emean values of the three measured compressive strengthand flexural strength values were taken as the test resultsSlump and slump flow were measured according to GBT50080-2002 [22]
Table 2 Physical and chemical properties of silica fume
Properties Standard value Actual value
Physical properties Specific surface area (m2kg) ge15 20Pozzolanic activity index () ge85 116
Chemical properties
SiO2 () ge850 95Loss on ignition () le60 195
Clminus () le002 002Moisture content () le30 12
Water demand ratio () le125 118
Table 1 Physical and chemical properties of cement
Properties Standard value Actual value
Physical propertiesSpecific surface area (m2kg) ge300 363
Initial set (min) ge45 128Final set (min) le390 183
Compressive strength 3 days (MPa) ge230 3157 days (MPa) ge525 596
Flexural strength 3 days (MPa) ge40 617 days (MPa) ge70 90
Chemical properties
Stability Qualified QualifiedLoss on ignition () le35 127
MgO () le50 079SO3 () le35 240
Insolubles () le15 101Clminus () le006 0009
Table 3 Chemical properties of fly ash
Properties Standard value Actual value
Chemical properties
Water demand ratio () le95 91Loss on ignition () le50 28Moisture content () le10 01
SO3 () le30 20CaO3 () le10 016MgO () le50 108Clminus () le002 001
Table 4 Physical and chemical properties of mineral powder
Properties Standard value Actual value
Physical propertiesSpecific surface area (m2kg) ge400 429
Liquidity ratio () ge95 102Density () ge28 28
Chemical properties
Moisture content () le10 10Loss on ignition () le30 30
Pozzolanic activity index () 7 daysge 75 8328 daysge 95 98
Advances in Civil Engineering 3
233 CCD -e RSM is a combination of statistical andmathematical techniques which is widely used in variousfields for modeling and analysis Compared with otherexperimental methods the advantage of the RSM is that therelationship between response and various factors can befound through a small number of experiments [23] In thisstudy the CCD in the RSM was adopted -e CCD is themost common experimental designmethod in RSM research[24] -e specific process involves obtaining a combinationof numerous test data through the CCD for the test todetermine the response value and establishing the functionalrelationship between the influencing parameter and re-sponse value through an undetermined coefficient methodthereby attaining a highly accurate response surface modelIn addition the analysis of variance (ANOVA) was used to
Table 5 Physical and chemical properties of superplasticizer
Properties Standard value Actual value
Physical propertiesWater reduction rate ge25 28Gas content () le60 29Bleeding rate () le60 37
Chemical propertiesClminus () le01 002OHminus () le3 2Na2SO4 le05 02
Figure 1 Manufactured sand
Table 6 Manufactured sand screening test results
PropertiesSieve size (mm)
Sieve bottom236 118 06 03 015
Sieve residue (g) 85 145 107 55 925 155Submeter () 17 29 214 11 185 31Cumulative () 17 46 674 784 969 100
5 4 3 2 1 00
20
40
60
80
100
Perc
ent p
assin
g (
)
Sieve size (mm)
Upper limitManufactured sand gradationLower limit
Figure 2 Gradation of manufactured sand used in this study
Table 7 Physical properties of steel fibers
Index Diameter(mm)
Length(mm)
Aspectratio
Tensile strength(MPa)
Unitvalue 02 13 65 2850
4 Advances in Civil Engineering
examine the interaction between the various variables andimpact on the response and to optimize the model to find theoptimal solution
Each influencing factor in the CCD was set to five levels-e test consisted of three parts that is the factorial test at thecube point the repeated test at the center point and the starpoint test at the axial point -e distribution of two-factor CCD test points is shown in Figure 6 [25] with 2kfactorial points where k represents the number of factors and2k represents axial points -e axial point distance from thecenter point is 2k4-e center point in the CCD is determinedby the average value of the factorial point -e number ofexperiments required for the CCD is determined by thefollowing equation [26]
N 2k+ 2k + CP (1)
where k is the number of factors and Cp is the number ofcentral points
A quantitative mathematical relationship (quadraticpolynomial linear equation) was obtained by establishing theresponse surface model to reflect the relationship betweenthe factors and response and the optimal condition of theresponse can be determined as shown in the followingequation
y β0 + 1113944k
i1βixi + 1113944
k
i1βiix
2i + 1113944
i
1113944j
βijxixj + ε (2)
where y is the predictive response xi and xj are the codevalues of factor variables i is the linear coefficient j is thequadratic coefficient β is the regression coefficient k is thenumber of factors for experimental research and optimi-zation and ε is the random error [24 25]
In this study the Design-Expert 8reg software was used forthe CCD mathematical modeling and variable analysis andoptimization In addition ANOVA was employed to study
Figure 3 Steel fibers
Table 8 Physical properties of basalt fibers
Index Length (mm) Diameter (mm) Density (gcm3) Elastic modulus (GPa) Tensile strength (MPa) Elongation at fracture ()Unit value 12 7ndash15 265 91sim110 3000sim4800 15sim32
Figure 4 Basalt fibers
Figure 5 Standard curing
Advances in Civil Engineering 5
the interaction between the variables and the influence of eachparameter on the response Steel fiber content (A) and basaltfiber content (B) were taken as factor variables and the unitwas percentage -e 28-day compressive strength (R1) 28-day flexural strength (R2) and 28-day flexural-compressiveratio (R3) were the responses According to the literature theselected factor range is 1ndash4 [3 17] for steel fibers and0ndash035 for basalt fibers [12 15 17] Table 10 shows the codevalues of five levels and the responses of the two factors -ehigh and low levels of each factor were coded as minus1 and +1 thecenter point was coded as 0 and the axis point was coded asminusα and +α In addition α was 1414 under the two factors
-e two-factor five-level CCD test design consisted offour sets of factorial tests four sets of star point tests and fivesets of center repeat tests-e factor variable code values andtest results of 13 experimental CCD groups in this study areshown in Table 11 in which H9ndashH13 are five repeated centertest groups for evaluating the stability of the model -e H0group without fibers but with the same mix ratio was addedas the reference group
3 Results and Discussion
31Workability of RPC Workability is significantly reducedafter the RPC blending In the slump test the overlap of thehybrid fibers increases the integration of the RPC Filling theslump cylinder during the tamping process is difficult -especific surface area of the steel and basalt fibers is large andthe basalt fibers have a rough surface and high frictioncoefficient which increase internal friction resistance and
worsen the fluidity of the mixture A large amount of cementpaste is attached to the surface of the hybrid fibers and thecement paste wrapped around the manufactured sand isreduced [8] thereby increasing the viscosity of the mixtureand decreasing workability With the same amount of steelfibers (A) slump is slightly reduced as the amount of thebasalt fibers (B) increases -is result is caused by the ex-istence of hybrid fiber which hinder the relative slip betweenthe particles Moreover owing to their obvious hydrophi-licity the basalt fibers are mixed into the mixture anddispersed into a large number of very fine flocculent fiberfilaments which absorb part of the free water therebyweakening the fluidity of the manufactured sand RPC
32 Analysis of Mechanical Properties of Steel-BasaltFiber-Manufactured Sand RPC
321 Compressive Strength -e 7-day and 28-day com-pressive strength of 14 sets of cube specimens are tested andthe test results are presented in Figure 7 Compared with thereference group the compressive strength of the sand RPCmixed with hybrid fibers is significantly better -e additionof hybrid fibers improves integrity and the bonding forcebetween the hybrid fibers and RPC matrix plays a satis-factory role in enhancing compressive strength during theloading process In the compression process the sound ofpulling fibers can be heard in the RPC test block Moreoverthe RPC test block does not burst like the fiberless RPC butgradually drops fragments and retains a relatively completeshape after the test When the test block is removed hybridfiber bridges are observed in the concrete matrix alongcracks as shown in Figure 8 -e steel fiber content of theH8 central (H9ndashH13) and H7 groups is 25 but the basaltfiber content differs Compared with the reference group the7-day compressive strength of the three groups increases by1989 2911 and 1672 and their 28-day compressivestrength increases by 2961 3164 and 2462When thesteel fiber content is 25 with an increase in the basalt fibercontent the 7-day and 28-day compressive strength show aninitial increasing and then decreasing trend Compared withthe reference group the 7-day compressive strength of theH3 and H1 groups increases by 466 and minus249 re-spectively and the 28-day compressive strength increases by
Table 9 Mix proportion
Waterbinder ratio Cement () Silica fume () Fly ash () Mineral powder () Sandbinder ratio Superplasticizer ()018 62 13 20 5 07 12
(0 0)
(+1 +1)
(+1 ndash1)(ndash1 ndash1)
(ndash1 +1)
(ndashα 0) (α 0)
(0 ndashα)
(0 α)
x1
x2
Figure 6 Two-factor CCD
Table 10 Code levels
Symbol Factors Actual values Code values
ASteel fibercontent()
1 144 25 356 4 minusα minus1 0 +1 α
B
Basaltfiber
content()
0 005 0175 03 035 minusα minus1 0 +1 α
6 Advances in Civil Engineering
Tabl
e11E
xperim
entalfactors
andresults
ofCCD
matrixdesig
n
Mix
number
Cod
elevel
ofvariables
Workability
7-daystandard
curing
(MPa
)28-day
standard
curing
(MPa
)
AB
Slum
p(m
m)
Slum
pflo
w(m
m)
Com
pressiv
estreng
thFlexural
streng
thCom
pressiv
estreng
thFlexural
streng
thH0
265
360
8217
753
10359
975
H1
minus1
minus1
245
320
8012
1002
12071
1558
H2
1minus1
190
220
11418
1734
14115
2312
H3
minus1
1255
310
861141
1302
1767
H4
11
225
290
10945
1623
13954
2234
H5
minusα
0190
255
8501
1004
11951
1452
H6
α0
245
270
11849
1716
14408
2316
H7
0minusα
230
255
9591
1405
12909
1956
H8
0α
265
350
9851
1496
13426
2115
H9
00
260
315
10694
161
13647
2196
H10
00
250
280
10609
1597
13581
2142
H11
00
245
325
10504
1576
13719
2136
H12
00
245
305
10559
1533
13516
2128
H13
00
250
325
10658
1579
13637
2114
Advances in Civil Engineering 7
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
fiber has higher tensile strength smaller size andmore fibersin the same volume And the addition of basalt fiber im-proves the initial cracking strength of concrete underbending load which effectively inhibits the generation ofmicrocracks [13] Basalt fiber has better workability whenadded to concrete but its effect of enhancing the com-pressive strength is not as obvious as tensile strength andflexural strength [14] -erefore steel fiber and basalt fiberhave a certain degree of synergy and complementarity interms of size and reinforcement mechanism So somescholars have mixed basalt fiber and steel fiber into ordinaryconcrete and found that it exhibits a good positive hybrideffect [15] Compared with single blended fiber the flexuralstrength of blended steel-basalt fiber is more significantlyimproved but the compressive strength will be reducedwhen the blending fiber content is high [16] Under ap-propriate blending amount the shear strength axial tensilestrength four-point bending strength splitting tensilestrength and energy dissipation capacity could be improvedsignificantly [17] However most of the studies are on theeffect of steel-basalt fiber mixing on ordinary concrete -einteraction between steel-basalt fiber in manufactured sandRPC and how to acquire the best mixing effect has not beensystematically analyzed -erefore the compressive strengthand flexural strength of the steel-basalt fiber-manufacturedsand RPC were tested to facilitate the preparation ofmanufactured sand RPC that meets actual engineeringneeds
In summary this article uses the content of steel fiberand basalt fiber as the influencing factors through the centralcomposite design to study the influence of the interactionbetween steel fiber and basalt fiber on the mechanicalproperties and workability of manufactured sand RPCEmploying the response surface method the compressivestrength flexural strength and flexural-compressivestrength ratio of manufactured sand RPC under the inter-action of steel fiber and basalt fiber are analyzed and aresponse surface model is established to obtain the rela-tionship between the two fibers and the mechanical strength-e response surface fitting formula can be used to obtainthe steel-basalt fiber content corresponding to the RPC ofmanufactured sand with different strengths so as to preparethe manufactured sand RPC that can meet different re-quirements -e response surface method is used to opti-mize the design of steel-basalt fiber-manufactured sandRPC and the results are verified by experiments whichprovides the necessary theoretical basis for the promotionand application of manufactured sand RPC
2 Materials and Methods
21 Raw Material PII525 cement by Jilin Yatai Cement(Changchun China) was used for the test -e cementinspection report (Table 1) complies with the GeneralPortland Cement Testing Standard (GB175-2007) [18]Silica fume produced by Dongyue Silicone Material (ZiboChina) fly ash manufactured by Datang Second -ermalPower (Changchun China) and S95-grade mineral pow-der produced by Longze Water Purification Materials
(Gongyi China) were used -e test reports are presentedin Tables 2ndash4-ese materials were used in accordance withthe technical specifications of the application of mineraladmixtures (GBT510032014) [19] -e superplasticizerused was an HSC polycarboxylic acid high-performancewater-reducing agent produced by Borida Building Ma-terials (Chongqing China) -e test report is shown inTable 5 -e fine aggregate was made from manufacturedsand produced by Jiusheng Industry (Changchun China)and a photo is presented in Figure 1 -e sand screeningtest results are provided in Table 6 and according to theStandard for Technical Requirements and Test Method ofSand and Crushed Stone for Ordinary Concrete (JGJ 52-2006) [20] the manufactured sand distribution is shown inFigure 2 -e steel fibers were made from copper-platedsteel fibers manufactured by Ruke Steel Fiber Industry(Yongkang China) -e specifications and performanceindices are shown in Table 7 Figure 3 presents a picture ofthe steel fibers -e basalt fibers were made from copper-plated steel fibers produced by Anjie Composite MaterialFactory (Haining China) -e specifications and perfor-mance indices are listed in Table 8 and a picture is shownin Figure 4
22 Test Preparation and Curing First the cement silicafume fly ash mineral powder and manufactured sand werepoured into a mixer and dry mixed for 2min Second asmixing continued steel and basalt fibers were sprinkledthrough a sieve When the fibers were added they scatteredafter 2min of dry mixing -ird a mixture of 80 super-plasticizer and water was added slowly and stirred for 4minFinally the remaining superplasticizer agent was added andstirred for 2min
In this test the curing method was standard curing(temperature 20degCplusmn 2degC humidity 95) After the RPCwas installed the specimens were placed immediately in thecuring room After 24 h the specimens were separated fromthe mold and placed once again in the curing room forcuring until the test days as shown in Figure 5
23 Testing Procedure
231 Mix Proportion -e mix proportion used in the ex-periment is shown in Table 9 -e mix proportion is theoptimal mix ratio determined by the orthogonal test ofZhong et al [3] taking the water-binder ratio sand-binderratio silica fume and fly ash as factors and analyzingcompressive strength -e amount of HSC polycarboxylicacid superplasticizer added in this experiment was 12 ofthe cementing material quality
232 Testing Program According to the GBT31387-2015[21] a 100mmtimes 100mmtimes 100mm cube specimen wasselected as the test specimen for pressure resistance An SYE-3000B hydraulic press (Hydraulic Press of New TestingMachine Co Ltd Changchun China) was used for loading-e loading rate for the compressive test was kept between
2 Advances in Civil Engineering
12MPas and 14MPas -e flexural strength test utilized a100mmtimes 100mmtimes 400mm prism specimen and used aWAW-1000B electrohydraulic servo universal materialtesting machine (Hydraulic Press of New Testing MachineCo Ltd Changchun China) for loading -e loading rate
was maintained at approximately 008MPas and 01MPas-emean values of the three measured compressive strengthand flexural strength values were taken as the test resultsSlump and slump flow were measured according to GBT50080-2002 [22]
Table 2 Physical and chemical properties of silica fume
Properties Standard value Actual value
Physical properties Specific surface area (m2kg) ge15 20Pozzolanic activity index () ge85 116
Chemical properties
SiO2 () ge850 95Loss on ignition () le60 195
Clminus () le002 002Moisture content () le30 12
Water demand ratio () le125 118
Table 1 Physical and chemical properties of cement
Properties Standard value Actual value
Physical propertiesSpecific surface area (m2kg) ge300 363
Initial set (min) ge45 128Final set (min) le390 183
Compressive strength 3 days (MPa) ge230 3157 days (MPa) ge525 596
Flexural strength 3 days (MPa) ge40 617 days (MPa) ge70 90
Chemical properties
Stability Qualified QualifiedLoss on ignition () le35 127
MgO () le50 079SO3 () le35 240
Insolubles () le15 101Clminus () le006 0009
Table 3 Chemical properties of fly ash
Properties Standard value Actual value
Chemical properties
Water demand ratio () le95 91Loss on ignition () le50 28Moisture content () le10 01
SO3 () le30 20CaO3 () le10 016MgO () le50 108Clminus () le002 001
Table 4 Physical and chemical properties of mineral powder
Properties Standard value Actual value
Physical propertiesSpecific surface area (m2kg) ge400 429
Liquidity ratio () ge95 102Density () ge28 28
Chemical properties
Moisture content () le10 10Loss on ignition () le30 30
Pozzolanic activity index () 7 daysge 75 8328 daysge 95 98
Advances in Civil Engineering 3
233 CCD -e RSM is a combination of statistical andmathematical techniques which is widely used in variousfields for modeling and analysis Compared with otherexperimental methods the advantage of the RSM is that therelationship between response and various factors can befound through a small number of experiments [23] In thisstudy the CCD in the RSM was adopted -e CCD is themost common experimental designmethod in RSM research[24] -e specific process involves obtaining a combinationof numerous test data through the CCD for the test todetermine the response value and establishing the functionalrelationship between the influencing parameter and re-sponse value through an undetermined coefficient methodthereby attaining a highly accurate response surface modelIn addition the analysis of variance (ANOVA) was used to
Table 5 Physical and chemical properties of superplasticizer
Properties Standard value Actual value
Physical propertiesWater reduction rate ge25 28Gas content () le60 29Bleeding rate () le60 37
Chemical propertiesClminus () le01 002OHminus () le3 2Na2SO4 le05 02
Figure 1 Manufactured sand
Table 6 Manufactured sand screening test results
PropertiesSieve size (mm)
Sieve bottom236 118 06 03 015
Sieve residue (g) 85 145 107 55 925 155Submeter () 17 29 214 11 185 31Cumulative () 17 46 674 784 969 100
5 4 3 2 1 00
20
40
60
80
100
Perc
ent p
assin
g (
)
Sieve size (mm)
Upper limitManufactured sand gradationLower limit
Figure 2 Gradation of manufactured sand used in this study
Table 7 Physical properties of steel fibers
Index Diameter(mm)
Length(mm)
Aspectratio
Tensile strength(MPa)
Unitvalue 02 13 65 2850
4 Advances in Civil Engineering
examine the interaction between the various variables andimpact on the response and to optimize the model to find theoptimal solution
Each influencing factor in the CCD was set to five levels-e test consisted of three parts that is the factorial test at thecube point the repeated test at the center point and the starpoint test at the axial point -e distribution of two-factor CCD test points is shown in Figure 6 [25] with 2kfactorial points where k represents the number of factors and2k represents axial points -e axial point distance from thecenter point is 2k4-e center point in the CCD is determinedby the average value of the factorial point -e number ofexperiments required for the CCD is determined by thefollowing equation [26]
N 2k+ 2k + CP (1)
where k is the number of factors and Cp is the number ofcentral points
A quantitative mathematical relationship (quadraticpolynomial linear equation) was obtained by establishing theresponse surface model to reflect the relationship betweenthe factors and response and the optimal condition of theresponse can be determined as shown in the followingequation
y β0 + 1113944k
i1βixi + 1113944
k
i1βiix
2i + 1113944
i
1113944j
βijxixj + ε (2)
where y is the predictive response xi and xj are the codevalues of factor variables i is the linear coefficient j is thequadratic coefficient β is the regression coefficient k is thenumber of factors for experimental research and optimi-zation and ε is the random error [24 25]
In this study the Design-Expert 8reg software was used forthe CCD mathematical modeling and variable analysis andoptimization In addition ANOVA was employed to study
Figure 3 Steel fibers
Table 8 Physical properties of basalt fibers
Index Length (mm) Diameter (mm) Density (gcm3) Elastic modulus (GPa) Tensile strength (MPa) Elongation at fracture ()Unit value 12 7ndash15 265 91sim110 3000sim4800 15sim32
Figure 4 Basalt fibers
Figure 5 Standard curing
Advances in Civil Engineering 5
the interaction between the variables and the influence of eachparameter on the response Steel fiber content (A) and basaltfiber content (B) were taken as factor variables and the unitwas percentage -e 28-day compressive strength (R1) 28-day flexural strength (R2) and 28-day flexural-compressiveratio (R3) were the responses According to the literature theselected factor range is 1ndash4 [3 17] for steel fibers and0ndash035 for basalt fibers [12 15 17] Table 10 shows the codevalues of five levels and the responses of the two factors -ehigh and low levels of each factor were coded as minus1 and +1 thecenter point was coded as 0 and the axis point was coded asminusα and +α In addition α was 1414 under the two factors
-e two-factor five-level CCD test design consisted offour sets of factorial tests four sets of star point tests and fivesets of center repeat tests-e factor variable code values andtest results of 13 experimental CCD groups in this study areshown in Table 11 in which H9ndashH13 are five repeated centertest groups for evaluating the stability of the model -e H0group without fibers but with the same mix ratio was addedas the reference group
3 Results and Discussion
31Workability of RPC Workability is significantly reducedafter the RPC blending In the slump test the overlap of thehybrid fibers increases the integration of the RPC Filling theslump cylinder during the tamping process is difficult -especific surface area of the steel and basalt fibers is large andthe basalt fibers have a rough surface and high frictioncoefficient which increase internal friction resistance and
worsen the fluidity of the mixture A large amount of cementpaste is attached to the surface of the hybrid fibers and thecement paste wrapped around the manufactured sand isreduced [8] thereby increasing the viscosity of the mixtureand decreasing workability With the same amount of steelfibers (A) slump is slightly reduced as the amount of thebasalt fibers (B) increases -is result is caused by the ex-istence of hybrid fiber which hinder the relative slip betweenthe particles Moreover owing to their obvious hydrophi-licity the basalt fibers are mixed into the mixture anddispersed into a large number of very fine flocculent fiberfilaments which absorb part of the free water therebyweakening the fluidity of the manufactured sand RPC
32 Analysis of Mechanical Properties of Steel-BasaltFiber-Manufactured Sand RPC
321 Compressive Strength -e 7-day and 28-day com-pressive strength of 14 sets of cube specimens are tested andthe test results are presented in Figure 7 Compared with thereference group the compressive strength of the sand RPCmixed with hybrid fibers is significantly better -e additionof hybrid fibers improves integrity and the bonding forcebetween the hybrid fibers and RPC matrix plays a satis-factory role in enhancing compressive strength during theloading process In the compression process the sound ofpulling fibers can be heard in the RPC test block Moreoverthe RPC test block does not burst like the fiberless RPC butgradually drops fragments and retains a relatively completeshape after the test When the test block is removed hybridfiber bridges are observed in the concrete matrix alongcracks as shown in Figure 8 -e steel fiber content of theH8 central (H9ndashH13) and H7 groups is 25 but the basaltfiber content differs Compared with the reference group the7-day compressive strength of the three groups increases by1989 2911 and 1672 and their 28-day compressivestrength increases by 2961 3164 and 2462When thesteel fiber content is 25 with an increase in the basalt fibercontent the 7-day and 28-day compressive strength show aninitial increasing and then decreasing trend Compared withthe reference group the 7-day compressive strength of theH3 and H1 groups increases by 466 and minus249 re-spectively and the 28-day compressive strength increases by
Table 9 Mix proportion
Waterbinder ratio Cement () Silica fume () Fly ash () Mineral powder () Sandbinder ratio Superplasticizer ()018 62 13 20 5 07 12
(0 0)
(+1 +1)
(+1 ndash1)(ndash1 ndash1)
(ndash1 +1)
(ndashα 0) (α 0)
(0 ndashα)
(0 α)
x1
x2
Figure 6 Two-factor CCD
Table 10 Code levels
Symbol Factors Actual values Code values
ASteel fibercontent()
1 144 25 356 4 minusα minus1 0 +1 α
B
Basaltfiber
content()
0 005 0175 03 035 minusα minus1 0 +1 α
6 Advances in Civil Engineering
Tabl
e11E
xperim
entalfactors
andresults
ofCCD
matrixdesig
n
Mix
number
Cod
elevel
ofvariables
Workability
7-daystandard
curing
(MPa
)28-day
standard
curing
(MPa
)
AB
Slum
p(m
m)
Slum
pflo
w(m
m)
Com
pressiv
estreng
thFlexural
streng
thCom
pressiv
estreng
thFlexural
streng
thH0
265
360
8217
753
10359
975
H1
minus1
minus1
245
320
8012
1002
12071
1558
H2
1minus1
190
220
11418
1734
14115
2312
H3
minus1
1255
310
861141
1302
1767
H4
11
225
290
10945
1623
13954
2234
H5
minusα
0190
255
8501
1004
11951
1452
H6
α0
245
270
11849
1716
14408
2316
H7
0minusα
230
255
9591
1405
12909
1956
H8
0α
265
350
9851
1496
13426
2115
H9
00
260
315
10694
161
13647
2196
H10
00
250
280
10609
1597
13581
2142
H11
00
245
325
10504
1576
13719
2136
H12
00
245
305
10559
1533
13516
2128
H13
00
250
325
10658
1579
13637
2114
Advances in Civil Engineering 7
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
12MPas and 14MPas -e flexural strength test utilized a100mmtimes 100mmtimes 400mm prism specimen and used aWAW-1000B electrohydraulic servo universal materialtesting machine (Hydraulic Press of New Testing MachineCo Ltd Changchun China) for loading -e loading rate
was maintained at approximately 008MPas and 01MPas-emean values of the three measured compressive strengthand flexural strength values were taken as the test resultsSlump and slump flow were measured according to GBT50080-2002 [22]
Table 2 Physical and chemical properties of silica fume
Properties Standard value Actual value
Physical properties Specific surface area (m2kg) ge15 20Pozzolanic activity index () ge85 116
Chemical properties
SiO2 () ge850 95Loss on ignition () le60 195
Clminus () le002 002Moisture content () le30 12
Water demand ratio () le125 118
Table 1 Physical and chemical properties of cement
Properties Standard value Actual value
Physical propertiesSpecific surface area (m2kg) ge300 363
Initial set (min) ge45 128Final set (min) le390 183
Compressive strength 3 days (MPa) ge230 3157 days (MPa) ge525 596
Flexural strength 3 days (MPa) ge40 617 days (MPa) ge70 90
Chemical properties
Stability Qualified QualifiedLoss on ignition () le35 127
MgO () le50 079SO3 () le35 240
Insolubles () le15 101Clminus () le006 0009
Table 3 Chemical properties of fly ash
Properties Standard value Actual value
Chemical properties
Water demand ratio () le95 91Loss on ignition () le50 28Moisture content () le10 01
SO3 () le30 20CaO3 () le10 016MgO () le50 108Clminus () le002 001
Table 4 Physical and chemical properties of mineral powder
Properties Standard value Actual value
Physical propertiesSpecific surface area (m2kg) ge400 429
Liquidity ratio () ge95 102Density () ge28 28
Chemical properties
Moisture content () le10 10Loss on ignition () le30 30
Pozzolanic activity index () 7 daysge 75 8328 daysge 95 98
Advances in Civil Engineering 3
233 CCD -e RSM is a combination of statistical andmathematical techniques which is widely used in variousfields for modeling and analysis Compared with otherexperimental methods the advantage of the RSM is that therelationship between response and various factors can befound through a small number of experiments [23] In thisstudy the CCD in the RSM was adopted -e CCD is themost common experimental designmethod in RSM research[24] -e specific process involves obtaining a combinationof numerous test data through the CCD for the test todetermine the response value and establishing the functionalrelationship between the influencing parameter and re-sponse value through an undetermined coefficient methodthereby attaining a highly accurate response surface modelIn addition the analysis of variance (ANOVA) was used to
Table 5 Physical and chemical properties of superplasticizer
Properties Standard value Actual value
Physical propertiesWater reduction rate ge25 28Gas content () le60 29Bleeding rate () le60 37
Chemical propertiesClminus () le01 002OHminus () le3 2Na2SO4 le05 02
Figure 1 Manufactured sand
Table 6 Manufactured sand screening test results
PropertiesSieve size (mm)
Sieve bottom236 118 06 03 015
Sieve residue (g) 85 145 107 55 925 155Submeter () 17 29 214 11 185 31Cumulative () 17 46 674 784 969 100
5 4 3 2 1 00
20
40
60
80
100
Perc
ent p
assin
g (
)
Sieve size (mm)
Upper limitManufactured sand gradationLower limit
Figure 2 Gradation of manufactured sand used in this study
Table 7 Physical properties of steel fibers
Index Diameter(mm)
Length(mm)
Aspectratio
Tensile strength(MPa)
Unitvalue 02 13 65 2850
4 Advances in Civil Engineering
examine the interaction between the various variables andimpact on the response and to optimize the model to find theoptimal solution
Each influencing factor in the CCD was set to five levels-e test consisted of three parts that is the factorial test at thecube point the repeated test at the center point and the starpoint test at the axial point -e distribution of two-factor CCD test points is shown in Figure 6 [25] with 2kfactorial points where k represents the number of factors and2k represents axial points -e axial point distance from thecenter point is 2k4-e center point in the CCD is determinedby the average value of the factorial point -e number ofexperiments required for the CCD is determined by thefollowing equation [26]
N 2k+ 2k + CP (1)
where k is the number of factors and Cp is the number ofcentral points
A quantitative mathematical relationship (quadraticpolynomial linear equation) was obtained by establishing theresponse surface model to reflect the relationship betweenthe factors and response and the optimal condition of theresponse can be determined as shown in the followingequation
y β0 + 1113944k
i1βixi + 1113944
k
i1βiix
2i + 1113944
i
1113944j
βijxixj + ε (2)
where y is the predictive response xi and xj are the codevalues of factor variables i is the linear coefficient j is thequadratic coefficient β is the regression coefficient k is thenumber of factors for experimental research and optimi-zation and ε is the random error [24 25]
In this study the Design-Expert 8reg software was used forthe CCD mathematical modeling and variable analysis andoptimization In addition ANOVA was employed to study
Figure 3 Steel fibers
Table 8 Physical properties of basalt fibers
Index Length (mm) Diameter (mm) Density (gcm3) Elastic modulus (GPa) Tensile strength (MPa) Elongation at fracture ()Unit value 12 7ndash15 265 91sim110 3000sim4800 15sim32
Figure 4 Basalt fibers
Figure 5 Standard curing
Advances in Civil Engineering 5
the interaction between the variables and the influence of eachparameter on the response Steel fiber content (A) and basaltfiber content (B) were taken as factor variables and the unitwas percentage -e 28-day compressive strength (R1) 28-day flexural strength (R2) and 28-day flexural-compressiveratio (R3) were the responses According to the literature theselected factor range is 1ndash4 [3 17] for steel fibers and0ndash035 for basalt fibers [12 15 17] Table 10 shows the codevalues of five levels and the responses of the two factors -ehigh and low levels of each factor were coded as minus1 and +1 thecenter point was coded as 0 and the axis point was coded asminusα and +α In addition α was 1414 under the two factors
-e two-factor five-level CCD test design consisted offour sets of factorial tests four sets of star point tests and fivesets of center repeat tests-e factor variable code values andtest results of 13 experimental CCD groups in this study areshown in Table 11 in which H9ndashH13 are five repeated centertest groups for evaluating the stability of the model -e H0group without fibers but with the same mix ratio was addedas the reference group
3 Results and Discussion
31Workability of RPC Workability is significantly reducedafter the RPC blending In the slump test the overlap of thehybrid fibers increases the integration of the RPC Filling theslump cylinder during the tamping process is difficult -especific surface area of the steel and basalt fibers is large andthe basalt fibers have a rough surface and high frictioncoefficient which increase internal friction resistance and
worsen the fluidity of the mixture A large amount of cementpaste is attached to the surface of the hybrid fibers and thecement paste wrapped around the manufactured sand isreduced [8] thereby increasing the viscosity of the mixtureand decreasing workability With the same amount of steelfibers (A) slump is slightly reduced as the amount of thebasalt fibers (B) increases -is result is caused by the ex-istence of hybrid fiber which hinder the relative slip betweenthe particles Moreover owing to their obvious hydrophi-licity the basalt fibers are mixed into the mixture anddispersed into a large number of very fine flocculent fiberfilaments which absorb part of the free water therebyweakening the fluidity of the manufactured sand RPC
32 Analysis of Mechanical Properties of Steel-BasaltFiber-Manufactured Sand RPC
321 Compressive Strength -e 7-day and 28-day com-pressive strength of 14 sets of cube specimens are tested andthe test results are presented in Figure 7 Compared with thereference group the compressive strength of the sand RPCmixed with hybrid fibers is significantly better -e additionof hybrid fibers improves integrity and the bonding forcebetween the hybrid fibers and RPC matrix plays a satis-factory role in enhancing compressive strength during theloading process In the compression process the sound ofpulling fibers can be heard in the RPC test block Moreoverthe RPC test block does not burst like the fiberless RPC butgradually drops fragments and retains a relatively completeshape after the test When the test block is removed hybridfiber bridges are observed in the concrete matrix alongcracks as shown in Figure 8 -e steel fiber content of theH8 central (H9ndashH13) and H7 groups is 25 but the basaltfiber content differs Compared with the reference group the7-day compressive strength of the three groups increases by1989 2911 and 1672 and their 28-day compressivestrength increases by 2961 3164 and 2462When thesteel fiber content is 25 with an increase in the basalt fibercontent the 7-day and 28-day compressive strength show aninitial increasing and then decreasing trend Compared withthe reference group the 7-day compressive strength of theH3 and H1 groups increases by 466 and minus249 re-spectively and the 28-day compressive strength increases by
Table 9 Mix proportion
Waterbinder ratio Cement () Silica fume () Fly ash () Mineral powder () Sandbinder ratio Superplasticizer ()018 62 13 20 5 07 12
(0 0)
(+1 +1)
(+1 ndash1)(ndash1 ndash1)
(ndash1 +1)
(ndashα 0) (α 0)
(0 ndashα)
(0 α)
x1
x2
Figure 6 Two-factor CCD
Table 10 Code levels
Symbol Factors Actual values Code values
ASteel fibercontent()
1 144 25 356 4 minusα minus1 0 +1 α
B
Basaltfiber
content()
0 005 0175 03 035 minusα minus1 0 +1 α
6 Advances in Civil Engineering
Tabl
e11E
xperim
entalfactors
andresults
ofCCD
matrixdesig
n
Mix
number
Cod
elevel
ofvariables
Workability
7-daystandard
curing
(MPa
)28-day
standard
curing
(MPa
)
AB
Slum
p(m
m)
Slum
pflo
w(m
m)
Com
pressiv
estreng
thFlexural
streng
thCom
pressiv
estreng
thFlexural
streng
thH0
265
360
8217
753
10359
975
H1
minus1
minus1
245
320
8012
1002
12071
1558
H2
1minus1
190
220
11418
1734
14115
2312
H3
minus1
1255
310
861141
1302
1767
H4
11
225
290
10945
1623
13954
2234
H5
minusα
0190
255
8501
1004
11951
1452
H6
α0
245
270
11849
1716
14408
2316
H7
0minusα
230
255
9591
1405
12909
1956
H8
0α
265
350
9851
1496
13426
2115
H9
00
260
315
10694
161
13647
2196
H10
00
250
280
10609
1597
13581
2142
H11
00
245
325
10504
1576
13719
2136
H12
00
245
305
10559
1533
13516
2128
H13
00
250
325
10658
1579
13637
2114
Advances in Civil Engineering 7
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
233 CCD -e RSM is a combination of statistical andmathematical techniques which is widely used in variousfields for modeling and analysis Compared with otherexperimental methods the advantage of the RSM is that therelationship between response and various factors can befound through a small number of experiments [23] In thisstudy the CCD in the RSM was adopted -e CCD is themost common experimental designmethod in RSM research[24] -e specific process involves obtaining a combinationof numerous test data through the CCD for the test todetermine the response value and establishing the functionalrelationship between the influencing parameter and re-sponse value through an undetermined coefficient methodthereby attaining a highly accurate response surface modelIn addition the analysis of variance (ANOVA) was used to
Table 5 Physical and chemical properties of superplasticizer
Properties Standard value Actual value
Physical propertiesWater reduction rate ge25 28Gas content () le60 29Bleeding rate () le60 37
Chemical propertiesClminus () le01 002OHminus () le3 2Na2SO4 le05 02
Figure 1 Manufactured sand
Table 6 Manufactured sand screening test results
PropertiesSieve size (mm)
Sieve bottom236 118 06 03 015
Sieve residue (g) 85 145 107 55 925 155Submeter () 17 29 214 11 185 31Cumulative () 17 46 674 784 969 100
5 4 3 2 1 00
20
40
60
80
100
Perc
ent p
assin
g (
)
Sieve size (mm)
Upper limitManufactured sand gradationLower limit
Figure 2 Gradation of manufactured sand used in this study
Table 7 Physical properties of steel fibers
Index Diameter(mm)
Length(mm)
Aspectratio
Tensile strength(MPa)
Unitvalue 02 13 65 2850
4 Advances in Civil Engineering
examine the interaction between the various variables andimpact on the response and to optimize the model to find theoptimal solution
Each influencing factor in the CCD was set to five levels-e test consisted of three parts that is the factorial test at thecube point the repeated test at the center point and the starpoint test at the axial point -e distribution of two-factor CCD test points is shown in Figure 6 [25] with 2kfactorial points where k represents the number of factors and2k represents axial points -e axial point distance from thecenter point is 2k4-e center point in the CCD is determinedby the average value of the factorial point -e number ofexperiments required for the CCD is determined by thefollowing equation [26]
N 2k+ 2k + CP (1)
where k is the number of factors and Cp is the number ofcentral points
A quantitative mathematical relationship (quadraticpolynomial linear equation) was obtained by establishing theresponse surface model to reflect the relationship betweenthe factors and response and the optimal condition of theresponse can be determined as shown in the followingequation
y β0 + 1113944k
i1βixi + 1113944
k
i1βiix
2i + 1113944
i
1113944j
βijxixj + ε (2)
where y is the predictive response xi and xj are the codevalues of factor variables i is the linear coefficient j is thequadratic coefficient β is the regression coefficient k is thenumber of factors for experimental research and optimi-zation and ε is the random error [24 25]
In this study the Design-Expert 8reg software was used forthe CCD mathematical modeling and variable analysis andoptimization In addition ANOVA was employed to study
Figure 3 Steel fibers
Table 8 Physical properties of basalt fibers
Index Length (mm) Diameter (mm) Density (gcm3) Elastic modulus (GPa) Tensile strength (MPa) Elongation at fracture ()Unit value 12 7ndash15 265 91sim110 3000sim4800 15sim32
Figure 4 Basalt fibers
Figure 5 Standard curing
Advances in Civil Engineering 5
the interaction between the variables and the influence of eachparameter on the response Steel fiber content (A) and basaltfiber content (B) were taken as factor variables and the unitwas percentage -e 28-day compressive strength (R1) 28-day flexural strength (R2) and 28-day flexural-compressiveratio (R3) were the responses According to the literature theselected factor range is 1ndash4 [3 17] for steel fibers and0ndash035 for basalt fibers [12 15 17] Table 10 shows the codevalues of five levels and the responses of the two factors -ehigh and low levels of each factor were coded as minus1 and +1 thecenter point was coded as 0 and the axis point was coded asminusα and +α In addition α was 1414 under the two factors
-e two-factor five-level CCD test design consisted offour sets of factorial tests four sets of star point tests and fivesets of center repeat tests-e factor variable code values andtest results of 13 experimental CCD groups in this study areshown in Table 11 in which H9ndashH13 are five repeated centertest groups for evaluating the stability of the model -e H0group without fibers but with the same mix ratio was addedas the reference group
3 Results and Discussion
31Workability of RPC Workability is significantly reducedafter the RPC blending In the slump test the overlap of thehybrid fibers increases the integration of the RPC Filling theslump cylinder during the tamping process is difficult -especific surface area of the steel and basalt fibers is large andthe basalt fibers have a rough surface and high frictioncoefficient which increase internal friction resistance and
worsen the fluidity of the mixture A large amount of cementpaste is attached to the surface of the hybrid fibers and thecement paste wrapped around the manufactured sand isreduced [8] thereby increasing the viscosity of the mixtureand decreasing workability With the same amount of steelfibers (A) slump is slightly reduced as the amount of thebasalt fibers (B) increases -is result is caused by the ex-istence of hybrid fiber which hinder the relative slip betweenthe particles Moreover owing to their obvious hydrophi-licity the basalt fibers are mixed into the mixture anddispersed into a large number of very fine flocculent fiberfilaments which absorb part of the free water therebyweakening the fluidity of the manufactured sand RPC
32 Analysis of Mechanical Properties of Steel-BasaltFiber-Manufactured Sand RPC
321 Compressive Strength -e 7-day and 28-day com-pressive strength of 14 sets of cube specimens are tested andthe test results are presented in Figure 7 Compared with thereference group the compressive strength of the sand RPCmixed with hybrid fibers is significantly better -e additionof hybrid fibers improves integrity and the bonding forcebetween the hybrid fibers and RPC matrix plays a satis-factory role in enhancing compressive strength during theloading process In the compression process the sound ofpulling fibers can be heard in the RPC test block Moreoverthe RPC test block does not burst like the fiberless RPC butgradually drops fragments and retains a relatively completeshape after the test When the test block is removed hybridfiber bridges are observed in the concrete matrix alongcracks as shown in Figure 8 -e steel fiber content of theH8 central (H9ndashH13) and H7 groups is 25 but the basaltfiber content differs Compared with the reference group the7-day compressive strength of the three groups increases by1989 2911 and 1672 and their 28-day compressivestrength increases by 2961 3164 and 2462When thesteel fiber content is 25 with an increase in the basalt fibercontent the 7-day and 28-day compressive strength show aninitial increasing and then decreasing trend Compared withthe reference group the 7-day compressive strength of theH3 and H1 groups increases by 466 and minus249 re-spectively and the 28-day compressive strength increases by
Table 9 Mix proportion
Waterbinder ratio Cement () Silica fume () Fly ash () Mineral powder () Sandbinder ratio Superplasticizer ()018 62 13 20 5 07 12
(0 0)
(+1 +1)
(+1 ndash1)(ndash1 ndash1)
(ndash1 +1)
(ndashα 0) (α 0)
(0 ndashα)
(0 α)
x1
x2
Figure 6 Two-factor CCD
Table 10 Code levels
Symbol Factors Actual values Code values
ASteel fibercontent()
1 144 25 356 4 minusα minus1 0 +1 α
B
Basaltfiber
content()
0 005 0175 03 035 minusα minus1 0 +1 α
6 Advances in Civil Engineering
Tabl
e11E
xperim
entalfactors
andresults
ofCCD
matrixdesig
n
Mix
number
Cod
elevel
ofvariables
Workability
7-daystandard
curing
(MPa
)28-day
standard
curing
(MPa
)
AB
Slum
p(m
m)
Slum
pflo
w(m
m)
Com
pressiv
estreng
thFlexural
streng
thCom
pressiv
estreng
thFlexural
streng
thH0
265
360
8217
753
10359
975
H1
minus1
minus1
245
320
8012
1002
12071
1558
H2
1minus1
190
220
11418
1734
14115
2312
H3
minus1
1255
310
861141
1302
1767
H4
11
225
290
10945
1623
13954
2234
H5
minusα
0190
255
8501
1004
11951
1452
H6
α0
245
270
11849
1716
14408
2316
H7
0minusα
230
255
9591
1405
12909
1956
H8
0α
265
350
9851
1496
13426
2115
H9
00
260
315
10694
161
13647
2196
H10
00
250
280
10609
1597
13581
2142
H11
00
245
325
10504
1576
13719
2136
H12
00
245
305
10559
1533
13516
2128
H13
00
250
325
10658
1579
13637
2114
Advances in Civil Engineering 7
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
examine the interaction between the various variables andimpact on the response and to optimize the model to find theoptimal solution
Each influencing factor in the CCD was set to five levels-e test consisted of three parts that is the factorial test at thecube point the repeated test at the center point and the starpoint test at the axial point -e distribution of two-factor CCD test points is shown in Figure 6 [25] with 2kfactorial points where k represents the number of factors and2k represents axial points -e axial point distance from thecenter point is 2k4-e center point in the CCD is determinedby the average value of the factorial point -e number ofexperiments required for the CCD is determined by thefollowing equation [26]
N 2k+ 2k + CP (1)
where k is the number of factors and Cp is the number ofcentral points
A quantitative mathematical relationship (quadraticpolynomial linear equation) was obtained by establishing theresponse surface model to reflect the relationship betweenthe factors and response and the optimal condition of theresponse can be determined as shown in the followingequation
y β0 + 1113944k
i1βixi + 1113944
k
i1βiix
2i + 1113944
i
1113944j
βijxixj + ε (2)
where y is the predictive response xi and xj are the codevalues of factor variables i is the linear coefficient j is thequadratic coefficient β is the regression coefficient k is thenumber of factors for experimental research and optimi-zation and ε is the random error [24 25]
In this study the Design-Expert 8reg software was used forthe CCD mathematical modeling and variable analysis andoptimization In addition ANOVA was employed to study
Figure 3 Steel fibers
Table 8 Physical properties of basalt fibers
Index Length (mm) Diameter (mm) Density (gcm3) Elastic modulus (GPa) Tensile strength (MPa) Elongation at fracture ()Unit value 12 7ndash15 265 91sim110 3000sim4800 15sim32
Figure 4 Basalt fibers
Figure 5 Standard curing
Advances in Civil Engineering 5
the interaction between the variables and the influence of eachparameter on the response Steel fiber content (A) and basaltfiber content (B) were taken as factor variables and the unitwas percentage -e 28-day compressive strength (R1) 28-day flexural strength (R2) and 28-day flexural-compressiveratio (R3) were the responses According to the literature theselected factor range is 1ndash4 [3 17] for steel fibers and0ndash035 for basalt fibers [12 15 17] Table 10 shows the codevalues of five levels and the responses of the two factors -ehigh and low levels of each factor were coded as minus1 and +1 thecenter point was coded as 0 and the axis point was coded asminusα and +α In addition α was 1414 under the two factors
-e two-factor five-level CCD test design consisted offour sets of factorial tests four sets of star point tests and fivesets of center repeat tests-e factor variable code values andtest results of 13 experimental CCD groups in this study areshown in Table 11 in which H9ndashH13 are five repeated centertest groups for evaluating the stability of the model -e H0group without fibers but with the same mix ratio was addedas the reference group
3 Results and Discussion
31Workability of RPC Workability is significantly reducedafter the RPC blending In the slump test the overlap of thehybrid fibers increases the integration of the RPC Filling theslump cylinder during the tamping process is difficult -especific surface area of the steel and basalt fibers is large andthe basalt fibers have a rough surface and high frictioncoefficient which increase internal friction resistance and
worsen the fluidity of the mixture A large amount of cementpaste is attached to the surface of the hybrid fibers and thecement paste wrapped around the manufactured sand isreduced [8] thereby increasing the viscosity of the mixtureand decreasing workability With the same amount of steelfibers (A) slump is slightly reduced as the amount of thebasalt fibers (B) increases -is result is caused by the ex-istence of hybrid fiber which hinder the relative slip betweenthe particles Moreover owing to their obvious hydrophi-licity the basalt fibers are mixed into the mixture anddispersed into a large number of very fine flocculent fiberfilaments which absorb part of the free water therebyweakening the fluidity of the manufactured sand RPC
32 Analysis of Mechanical Properties of Steel-BasaltFiber-Manufactured Sand RPC
321 Compressive Strength -e 7-day and 28-day com-pressive strength of 14 sets of cube specimens are tested andthe test results are presented in Figure 7 Compared with thereference group the compressive strength of the sand RPCmixed with hybrid fibers is significantly better -e additionof hybrid fibers improves integrity and the bonding forcebetween the hybrid fibers and RPC matrix plays a satis-factory role in enhancing compressive strength during theloading process In the compression process the sound ofpulling fibers can be heard in the RPC test block Moreoverthe RPC test block does not burst like the fiberless RPC butgradually drops fragments and retains a relatively completeshape after the test When the test block is removed hybridfiber bridges are observed in the concrete matrix alongcracks as shown in Figure 8 -e steel fiber content of theH8 central (H9ndashH13) and H7 groups is 25 but the basaltfiber content differs Compared with the reference group the7-day compressive strength of the three groups increases by1989 2911 and 1672 and their 28-day compressivestrength increases by 2961 3164 and 2462When thesteel fiber content is 25 with an increase in the basalt fibercontent the 7-day and 28-day compressive strength show aninitial increasing and then decreasing trend Compared withthe reference group the 7-day compressive strength of theH3 and H1 groups increases by 466 and minus249 re-spectively and the 28-day compressive strength increases by
Table 9 Mix proportion
Waterbinder ratio Cement () Silica fume () Fly ash () Mineral powder () Sandbinder ratio Superplasticizer ()018 62 13 20 5 07 12
(0 0)
(+1 +1)
(+1 ndash1)(ndash1 ndash1)
(ndash1 +1)
(ndashα 0) (α 0)
(0 ndashα)
(0 α)
x1
x2
Figure 6 Two-factor CCD
Table 10 Code levels
Symbol Factors Actual values Code values
ASteel fibercontent()
1 144 25 356 4 minusα minus1 0 +1 α
B
Basaltfiber
content()
0 005 0175 03 035 minusα minus1 0 +1 α
6 Advances in Civil Engineering
Tabl
e11E
xperim
entalfactors
andresults
ofCCD
matrixdesig
n
Mix
number
Cod
elevel
ofvariables
Workability
7-daystandard
curing
(MPa
)28-day
standard
curing
(MPa
)
AB
Slum
p(m
m)
Slum
pflo
w(m
m)
Com
pressiv
estreng
thFlexural
streng
thCom
pressiv
estreng
thFlexural
streng
thH0
265
360
8217
753
10359
975
H1
minus1
minus1
245
320
8012
1002
12071
1558
H2
1minus1
190
220
11418
1734
14115
2312
H3
minus1
1255
310
861141
1302
1767
H4
11
225
290
10945
1623
13954
2234
H5
minusα
0190
255
8501
1004
11951
1452
H6
α0
245
270
11849
1716
14408
2316
H7
0minusα
230
255
9591
1405
12909
1956
H8
0α
265
350
9851
1496
13426
2115
H9
00
260
315
10694
161
13647
2196
H10
00
250
280
10609
1597
13581
2142
H11
00
245
325
10504
1576
13719
2136
H12
00
245
305
10559
1533
13516
2128
H13
00
250
325
10658
1579
13637
2114
Advances in Civil Engineering 7
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
the interaction between the variables and the influence of eachparameter on the response Steel fiber content (A) and basaltfiber content (B) were taken as factor variables and the unitwas percentage -e 28-day compressive strength (R1) 28-day flexural strength (R2) and 28-day flexural-compressiveratio (R3) were the responses According to the literature theselected factor range is 1ndash4 [3 17] for steel fibers and0ndash035 for basalt fibers [12 15 17] Table 10 shows the codevalues of five levels and the responses of the two factors -ehigh and low levels of each factor were coded as minus1 and +1 thecenter point was coded as 0 and the axis point was coded asminusα and +α In addition α was 1414 under the two factors
-e two-factor five-level CCD test design consisted offour sets of factorial tests four sets of star point tests and fivesets of center repeat tests-e factor variable code values andtest results of 13 experimental CCD groups in this study areshown in Table 11 in which H9ndashH13 are five repeated centertest groups for evaluating the stability of the model -e H0group without fibers but with the same mix ratio was addedas the reference group
3 Results and Discussion
31Workability of RPC Workability is significantly reducedafter the RPC blending In the slump test the overlap of thehybrid fibers increases the integration of the RPC Filling theslump cylinder during the tamping process is difficult -especific surface area of the steel and basalt fibers is large andthe basalt fibers have a rough surface and high frictioncoefficient which increase internal friction resistance and
worsen the fluidity of the mixture A large amount of cementpaste is attached to the surface of the hybrid fibers and thecement paste wrapped around the manufactured sand isreduced [8] thereby increasing the viscosity of the mixtureand decreasing workability With the same amount of steelfibers (A) slump is slightly reduced as the amount of thebasalt fibers (B) increases -is result is caused by the ex-istence of hybrid fiber which hinder the relative slip betweenthe particles Moreover owing to their obvious hydrophi-licity the basalt fibers are mixed into the mixture anddispersed into a large number of very fine flocculent fiberfilaments which absorb part of the free water therebyweakening the fluidity of the manufactured sand RPC
32 Analysis of Mechanical Properties of Steel-BasaltFiber-Manufactured Sand RPC
321 Compressive Strength -e 7-day and 28-day com-pressive strength of 14 sets of cube specimens are tested andthe test results are presented in Figure 7 Compared with thereference group the compressive strength of the sand RPCmixed with hybrid fibers is significantly better -e additionof hybrid fibers improves integrity and the bonding forcebetween the hybrid fibers and RPC matrix plays a satis-factory role in enhancing compressive strength during theloading process In the compression process the sound ofpulling fibers can be heard in the RPC test block Moreoverthe RPC test block does not burst like the fiberless RPC butgradually drops fragments and retains a relatively completeshape after the test When the test block is removed hybridfiber bridges are observed in the concrete matrix alongcracks as shown in Figure 8 -e steel fiber content of theH8 central (H9ndashH13) and H7 groups is 25 but the basaltfiber content differs Compared with the reference group the7-day compressive strength of the three groups increases by1989 2911 and 1672 and their 28-day compressivestrength increases by 2961 3164 and 2462When thesteel fiber content is 25 with an increase in the basalt fibercontent the 7-day and 28-day compressive strength show aninitial increasing and then decreasing trend Compared withthe reference group the 7-day compressive strength of theH3 and H1 groups increases by 466 and minus249 re-spectively and the 28-day compressive strength increases by
Table 9 Mix proportion
Waterbinder ratio Cement () Silica fume () Fly ash () Mineral powder () Sandbinder ratio Superplasticizer ()018 62 13 20 5 07 12
(0 0)
(+1 +1)
(+1 ndash1)(ndash1 ndash1)
(ndash1 +1)
(ndashα 0) (α 0)
(0 ndashα)
(0 α)
x1
x2
Figure 6 Two-factor CCD
Table 10 Code levels
Symbol Factors Actual values Code values
ASteel fibercontent()
1 144 25 356 4 minusα minus1 0 +1 α
B
Basaltfiber
content()
0 005 0175 03 035 minusα minus1 0 +1 α
6 Advances in Civil Engineering
Tabl
e11E
xperim
entalfactors
andresults
ofCCD
matrixdesig
n
Mix
number
Cod
elevel
ofvariables
Workability
7-daystandard
curing
(MPa
)28-day
standard
curing
(MPa
)
AB
Slum
p(m
m)
Slum
pflo
w(m
m)
Com
pressiv
estreng
thFlexural
streng
thCom
pressiv
estreng
thFlexural
streng
thH0
265
360
8217
753
10359
975
H1
minus1
minus1
245
320
8012
1002
12071
1558
H2
1minus1
190
220
11418
1734
14115
2312
H3
minus1
1255
310
861141
1302
1767
H4
11
225
290
10945
1623
13954
2234
H5
minusα
0190
255
8501
1004
11951
1452
H6
α0
245
270
11849
1716
14408
2316
H7
0minusα
230
255
9591
1405
12909
1956
H8
0α
265
350
9851
1496
13426
2115
H9
00
260
315
10694
161
13647
2196
H10
00
250
280
10609
1597
13581
2142
H11
00
245
325
10504
1576
13719
2136
H12
00
245
305
10559
1533
13516
2128
H13
00
250
325
10658
1579
13637
2114
Advances in Civil Engineering 7
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
Tabl
e11E
xperim
entalfactors
andresults
ofCCD
matrixdesig
n
Mix
number
Cod
elevel
ofvariables
Workability
7-daystandard
curing
(MPa
)28-day
standard
curing
(MPa
)
AB
Slum
p(m
m)
Slum
pflo
w(m
m)
Com
pressiv
estreng
thFlexural
streng
thCom
pressiv
estreng
thFlexural
streng
thH0
265
360
8217
753
10359
975
H1
minus1
minus1
245
320
8012
1002
12071
1558
H2
1minus1
190
220
11418
1734
14115
2312
H3
minus1
1255
310
861141
1302
1767
H4
11
225
290
10945
1623
13954
2234
H5
minusα
0190
255
8501
1004
11951
1452
H6
α0
245
270
11849
1716
14408
2316
H7
0minusα
230
255
9591
1405
12909
1956
H8
0α
265
350
9851
1496
13426
2115
H9
00
260
315
10694
161
13647
2196
H10
00
250
280
10609
1597
13581
2142
H11
00
245
325
10504
1576
13719
2136
H12
00
245
305
10559
1533
13516
2128
H13
00
250
325
10658
1579
13637
2114
Advances in Civil Engineering 7
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
2569 and 1653 respectively -e steel fiber content ofboth groups is 144 but the basalt fiber content of the H3group increases by 025 compared with that of the H1group thereby showing a relatively higher compressivestrength Compared with the reference group the 7-daycompressive strength of the H4 and H2 groups increases by3321 and 3896 respectively and the 28-day compres-sive strength increases by 347 and 3626 respectively-e basalt fiber content of the H4 group increases by 025compared with that of the H2 group but its 7-day and 28-day compressive strength decrease It can be found thatwhen the content of steel fiber is small with the increase ofthe content of basalt fiber the compressive strength of 7dand 28d are significantly improved and when the steel fiberamount is high the effect of the basalt fibers on the com-pressive strength of the manufactured sand RPC is verysmall -is finding is observed because the size of the basaltfibers is smaller than that of the steel fibers When the steelfiber amount is small the appropriate amount of basalt fiberscan be distributed evenly among the steel fibers to play abridging role and inhibit the expansion of cracks When thesteel fiber amount is high the incorporation of basalt fibersleads to fiber agglomeration an increase in internal defectsand a reduction of compressive strength In summarycompressive strength is not consistently enhanced with theincrease of hybrid fiber content and proper fiber content
will exert a positive mixing effect Excessive amounts of fiberwill only waste resources and strength improvement is notobvious
322 Flexural Strength A total of 84100mmtimes 100mmtimes 400mm prism samples from the 14groups are tested for their 7-day and 28-day flexuralstrength -e flexural strength test results are shown inFigure 9 Compared with the nonfiber RPC the flexuralstrength of the mixed RPC is improved obviously becausethe main factor affecting flexural strength is the bondingforce between the fibers and the matrix In the loadingprocess because the fibers demonstrate roughness andunevenness the fibers slip with the matrix under tension andproduce adhesion stress which plays a bridging role andhinders the development of cracks [8] thereby substantiallyenhancing flexural strength Given that the RPC hydrationreaction at 7 days is incomplete and the bond between thefibers and thematrix is not at its maximum pulling the fibersout during the bending resistance experiment is easyHowever after 28 days the hydration reaction is completeand the bond between the fibers and the matrix is satis-factory thereby considerably increasing the bendingstrength compared with that at 7 days As shown in Fig-ure 10 the antibending specimen demonstrates obviousdeformation during compression First several microcracksappear at the bottom area between the two loading headsand the main crack gradually expands with debris observedin the crack gap During the test the sound of fiber ex-traction can be heard and the cracks extend to achievemaximum flexural strength after a certain degree -e steelfibers in the cracks are extracted from the RPC matrix andthe basalt fibers are mostly pulled As shown in Figure 9 theH3 group has the same steel fiber content of 144 as the H1group but the basalt content is 025 higher Comparedwith the reference group the 7-day flexural strength of thetwo groups increases by 5153 and 3307 and the 28-dayflexural strength increases by 8123 and 5979 -e steelfiber content of the H7 central (9ndash13) and H8 groups is25 and the basalt fiber content is 0 0175 and 035respectively Compared with the reference group the 7-dayflexural strength of the three groups increases by 86591093 and 9867 and the 28-day flexural strength in-creases by 10062 11908 and 11692 It can be seenthat when the steel fiber content is small the increase ofbasalt fiber content has a good increase in flexural strength-e 7-day flexural strength of the H4 and H2 groups in-creases by 11554 and 13028 respectively comparedwith that of the reference group and the 28-day flexuralstrength increases by 12913 and 13713 respectively-esteel fiber content of the H4 and H2 groups is 356 but asthe basalt fiber content increases flexural strength decreasesWhen the steel fiber content is excessive the addition ofbasalt fibers will not increase the flexural strength of themanufactured sand RPC -is finding is observed becausethe steel fibers form a network structure in the mixturewhereas the basalt fibers are small in volume but large inquantity-e appropriate amount of basalt fibers is scattered
H6 H2 H4 H11 H9 H13 H10 H12 H8 H3 H7 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
Steel fiberBasalt fiber
0
20
40
60
80
100
120
140
160
Com
pres
sive s
tren
gth
(MPa
)
7-day compressive strength28-day compressive strength
Figure 7 Compressive test result
Figure 8 Failure condition of compressive specimens
8 Advances in Civil Engineering
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
among the steel fibers which helps the steel fibers pull andincreases the probability of bridging the inner cracks of theRPC However when the steel fibers increase further theywill cross into the group with basalt fibers the dispersion ofthe hybrid fibers in the matrix will not be uniform thecontact area with the cement mortar will be reduced and theadhesion between the fibers and thematrix will be weakenedthereby resulting in the reduction of flexural strength -uswhen the manufactured sand RPC steel fiber content issmall the influence of increased basalt content on flexuralstrength is obvious When the steel fiber content is too highthe negative hybrid effect will occur when the basalt fibercontent is likewise excessive
323 Flexural-Compressive Ratio Flexural-compressiveratio is the ratio of concrete flexural strength to com-pressive strength used as a parameter to test the rela-tionship between concrete compressive strength andflexural strength the degree of influence on the two kindsof strength after mixing fiber can be seen by the flexural-compressive ratio that is when the flexural strength isincreased significantly the flexural-compressive ratio willincrease But if the compressive strength is increased moresignificantly and the flexural-compressive ratio will de-crease -e 7-day and 28-day flexural-compressive ratios
in this experiment are shown in Figure 11 and the 28-dayflexural-compressive ratio is generally higher than the 7-day flexural-compressive ratio -e H3 group has 025more basalt content than the H1 group and the steel fibercontent of both groups is 144 -e 7-day flexural-compressive ratio of the H3 and H1 groups increases by4476 and 3657 respectively and the 28-day flexural-compressive ratio increases by 4431 and 3719 re-spectively compared with those of the reference group-e steel fiber content of the H7 central (9ndash13) and H8groups is 25 and the basalt fiber content is 0 0175and 035 respectively Compared with the referencegroup the 7-day flexural-compressive ratio of the threegroups increases by 5993 6245 and 6812 and their28-day flexural-compressive ratio increases by 616652 and 6738 and the mixed basalt fiber will in-crease the flexural-compressive ratio -e proportion ofthe H8 group is 025 higher than that of the central group(9ndash13) and the flexural-compressive ratio changes slightly-erefore when the steel fiber content is small the ap-propriate basalt fiber mixture can significantly improve theflexural-compressive ratio of the manufactured sand RPC-e main reason for this finding is because the basalt fibersplay a small role in the compression process and the basaltfibers along the length of the specimen are evenly dis-tributed between the steel fibers in the bending test andplay a bridging role with the steel fibers throughout thebending process In addition the basalt fibers assist inpulling the manufactured sand RPC thereby helping itplay a substantial role -us the manufactured sandRPC mixed with steel-basalt fibers has a higher flexural-compressive ratio than the manufactured sand RPC withsteel fibers -e steel fiber amount of the H4 and H2 groupsis 356 but the basalt fiber amount of the H4 groupincreases by 025 compared with that of the H2 groupHowever the 28-day flexural-compressive ratio is reduced-erefore when the steel fiber content is too high theaddition of basalt fibers has a negative mixing effect on theflexural-compressive ratio According to the aforemen-tioned findings when the steel fiber content is largethe addition of basalt fibers has little influence on theflexural strength of the manufactured sand RPC -usthe bending pressure ratio does not increase -e 28-dayflexural-compressive ratio of ordinary concrete is generallybetween 7 and 8 [27] whereas the 28-day flexural-compressive ratio of the steelndashbasalt fiber-manufacturedsand RPC is between 12 and 16 In other words thesteel-basalt fiber mixing enhanced RPCrsquos flexural strengthmore obviously than its compressive strength By selectingthe appropriate flexural-compressive ratio the road flex-ural strength could be effectively improved which is ofgreat significance to road engineering
33 Establishment and Analysis of Response Surface Model
331 Establishment and Verification of RSM In this studythree quadratic polynomial models of 28-day compressionstrength (R1) 28-day flexural strength (R2) and 28-day
H6 H2 H4 H9 H10 H11 H12 H8 H13 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
5
10
15
20
25
Flex
ural
stre
ngth
(MPa
)
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 9 Flexural test results
Figure 10 Failure condition of flexural specimens
Advances in Civil Engineering 9
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
flexural-compressive ratio (R3) are established using theDesign-Expert 10reg software based on multiple regressionanalysis as shown in (3)ndash(5)-emodels are generated fromactual values and the confidence level is maintained at 5statistical significance to evaluate and verify the models-rough ANOVA the interaction and relationship betweenthe steel fiber content (A) the basalt fiber content (B) andresponses R1 R2 and R3 are obtained and the accuracy ofthe models is verified according to statistical parameters-eresults of the ANOVA are shown in Table 12 When the P
value of the parameter is less than 005 it is significant andthe parameter items with P value gt005 are removed toimprove the model significance Table 12 shows that the P
values of the three models are lt005 thereby indicating thatthey have statistical significance at the 5 significance levelIn addition lack of fit can be used tomeasure the degree of fitbetween the models and the data Contrary to the P value ofthe parameter when the lack of fit (Plt 005) indicates thatthe fitting difference is large an insignificant lack of fit(Pgt 01) is what we want and the insignificant fitting isunsatisfactory -e lack of fit of the three models that is R1R2 and R3 is not significant thereby indicating that theycan better reflect the relationship between the factors andresponses
R1 13620 + 807 middot A + 190 middot B minus 277 middot A middot B
minus 191 middot A2
minus 197 middot B2
(3)
R2 2143 + 305 middot A + 04448 middot B minus 07175 middot A middot B
minus 128 middot A2
minus 05185 middot B2
(4)
R3 1574 + 143 middot A + 01436 middot B minus 026 middot A middot B
minus 0828 middot A2
minus 0158 middot B2
(5)
-e statistical results of variance show that the R2 of R1R2 and R3 is 09872 09943 and 09928 respectively asshown in Table 13 R2 is the absolute coefficient that is usedto measure the reliability of a model -e closer the R2 valueto 1 the more reliable the model -e R2 value of the threemodels is significantly close to 1 which further indicates
their quality Meanwhile the predicted R2 (09289 0983609733) and adjusted R2 (09780 09903 09877) of the threemodels are very close thereby indicating a good fit -eadequate precision (3301 468517 417526) of the threemodels is greater than 4 proving that the accuracy of thethree models is sufficient and that they can be used in thenavigation design space -e coefficient of variation (COV)is obtained by (6) which is used to indicate the credibilityand accuracy of the models and the unit is percentageWhen the COV is less than 10 the test result is reliableAccording to Table 13 the COV of the three responsemodels is less than 10 thereby indicating that they arereliable and have good repeatability
COV 100lowast (stddev)
(mean) (6)
Figure 12 presents the normal distribution of the re-siduals of R1 R2 and R3 which can further determinemodel satisfaction -e larger the residual value the worsethe regression fitting effect and the farther the deviation lineof the points in the figure -e farther the point the largerthe deviation from the straight line Figure 12 shows the dataon the residual normal distribution maps of models R1 R2and R3 which basically fall near the distribution fitting linethat is the residual value is small and the fit is good whichfurther prove that the models can be used in the navigationdesign space Moreover the models can better describe therelationship between the three responses and two factors andprovide highly accurate predictions
332 Interaction between Factors and Impact on ResponseFigure 13 illustrates the perturbation graph of each model-e perturbation graph in the RSM design reveals significantparameters by showing the change in the response valuecaused by the movement of each factor from the referencepoint which is the zero coded level of each factor [28] Asone factor changes the other factors remain unchanged atthe reference value In the three models factor A is steeperthan factor B thereby indicating that the compressivestrength and flexural strength of the manufactured sandRPC are highly sensitive to the steel fiber content As thesteel fiber content (A) increases the three responses likewiseincrease However as the basalt fiber content (B) increasesthe three responses increase slowly and then decrease Anoptimal content point exists which also proves the aboveconclusion that only appropriate basalt fiber content canimprove the compressive strength and flexural strength ofthe manufactured sand RPC rather than the more the better
Figure 14 demonstrates the contour and 3D graphs of theeffects of the two factors of the steel fiber content (A) and thebasalt fiber content (B) on the three responses that is R1R2 and R3 In model R1 the contour ofA is denser than thatof B and the 3D graph is steep as shown in Figure 14(a)thereby indicating that the influence of factor A on responseR1 is more obvious than that of factor B which is the same asthe previous conclusion-e bending degree of the 3D graphcan represent the significant degree of interaction betweenthe factors-emore curved the 3D graph the more obvious
H2 H6 H4 H9 H8 H13 H11 H10 H12 H7 H3 H1 H5 H000
05
10
15
20
25
30
35
40
45
Fibe
r con
tent
()
0
2
4
6
8
10
12
14
16
18
Flex
ural
-com
pres
sive r
atio
()
Steel fiberBasalt fiber
7-day compressive strength28-day compressive strength
Figure 11 Flexural-compressive ratio results
10 Advances in Civil Engineering
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
the interaction In model R1 the significant degree of in-teraction between A and B is relatively high When the steelfiber content (A) is 144 R1 increases with the increase ofthe basalt fiber content (B) When the steel fiber content (A)is 356 R1 first increases and then slowly decreases withthe increase of the basalt fiber content (B) As shown inFigure 14(b) in model R2 the contour of A is denser thanthat of B the 3D graph is steep and the interaction betweenA and B is relatively significant When the steel fiber content(A) is lower than 25 the increase of the basalt fiber content(B) significantly improves R2 When the steel fiber content(A) is high the increase of the basalt fiber content (B) haslittle effect on R2 As shown in Figure 14(c) the contour lineof A is denser than that of B the 3D graph is steep and thecontour lines are approximately parallel that is the inter-action between A and B is generally significant When thesteel fiber content (A) is lower than 25 the increase of the
basalt fiber content (B) significantly improves R3 When thesteel fiber content is high the basalt fiber content (B) haslittle influence on R3 -ese results can be attributed to thefact that when the steel fiber content is low the small andmultirooted basalt fibers are more likely to be evenly dis-persed in various parts of the internal structure of the RPCreducing the center spacing between the fibers and filling thegap between the steel fibers which greatly increases theprobability of bridging the internal cracks of RPC hindersthe generation of microcracks and forms a better spatialnetwork structure together with steel fibers so the me-chanical properties of RPC especially the flexural perfor-mance are significantly improved When the steel fibercontent is high the excessive incorporation of basalt fiberwill cause unfavorable phenomena such as entanglementand agglomeration of fibers resulting in a reduction in thecontact area between fiber and cementitious material and
Table 12 ANOVA results for response surface quadratic model parameters
Responses Source SOS DF MS F-value P value R
28-day compressive strength (R1)
Model 62652 5 12530 10756 lt00001 SignA 52047 1 52047 44678 lt00001 SignB 2885 1 2885 2476 00016 SignAB 3080 1 3080 2644 00013 SignA2 2541 1 2541 2181 00023 SignB2 2703 1 2703 2320 00019 Sign
Residual 815 7 116Lack of fit 584 3 195 336 01360 Not signPure error 232 4 05789
28-day flexural strength (R2)
Model 9044 5 1809 24566 lt00001 SignA 7460 1 7460 101312 lt00001 SignB 158 1 158 2150 00024 SignAB 206 1 206 2797 00011 SignA2 1133 1 1133 15383 lt00001 SignB2 187 1 187 2540 00015 Sign
Residual 05154 7 00736Lack of fit 01229 3 00410 04176 07505 Not signPure error 03925 4 00981
28-day flexural-compressive ratio (R3)
Model 2159 5 432 1938 lt00001 SignA 1637 1 1637 73268 lt00001 SignB 01649 1 01649 738 00299 SignAB 02704 1 02704 1210 00103 SignA2 477 1 477 21346 lt00001 SignB2 01737 1 01737 777 00270 Sign
Residual 01564 7 00223Lack of fit 00607 3 00202 08452 05365 Not signPure error 00957 4 00239
SOS sum of squares DF degree of freedom MS mean square R remark Sign significant
Table 13 Model validation for both responses
Statistical parameters 28-day compressive strength (R1) 28-day flexural strength (R2) 28-day flexural-compressive ratio (R3)R2 09872 09943 09928Adjusted R2 09780 09903 09877Predicted R2 09289 09836 09733Adeq precision 330126 468517 417526Std dev 108 02713 01495Mean 13381 2033 1513COV () 08066 133 09880
Advances in Civil Engineering 11
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
Studentized residuals
Nor
mal
p
roba
bilit
yNormal plot of residuals
ndash300 ndash200 ndash100 000 100 200
1
51020305070809095
99
(a)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(b)
Studentized residuals
Nor
mal
p
roba
bilit
y
Normal plot of residuals
ndash200 ndash100 000 100 200 300
1
51020305070809095
99
(c)
Figure 12 Normal distribution of residuals (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressive ratio (R3)
ndash1000 ndash0500 0000 0500 1000
115
120
125
130
135
140
145
A
A
B
B
Perturbation
Deviation from reference point (coded units)
28-d
ay co
mpr
essiv
e str
engt
h (M
Pa)
(a)
ndash1000 ndash0500 0000 0500 1000
14
16
18
20
22
24
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay fl
exur
al st
reng
th (M
Pa)
(b)
Figure 13 Continued
12 Advances in Civil Engineering
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
the weakening of the bond between fiber and matrix af-fecting the compactness of the RPC matrix increasing in-ternal defects reducing the effective internal bearing area ofthe material and being detrimental to the improvement ofthe mechanical properties of RPC In summary basalt fibermainly plays a role in inhibiting the beginning of micro-cracks when the steel fiber hinders the development ofcracks Appropriate ratio of fiber mixing has a significantimpact on the mechanical properties of manufactured sandRPC and increases the flexural-compressive ratio
4 Optimization of Fiber Content
41 Content of the Two Fibers Optimized by RSMObtaining the maximum compressive strength flexuralstrength and flexural ratio simultaneously is difficult-erefore this study adopts multiobjective optimizationtechnology to optimize multiple responses at the same timeIn this study compromise optimization is conducted for the28-day compressive strength (R1) flexural strength (R2)and flexural-compressive ratio (R3) As mentioned abovethe steel fiber content (A) and basalt fiber content (B) are theindependent variables and R1 R2 and R3 are the dependentvariables -e RSM is adopted to find the optimal content ofthe two fibers to maximize the three response values -isstudy employs the process optimization function in theDesign-Expert 8reg software -e definitions of factors andresponses during the optimization process are shown inTable 14 Each factor and response use the same importantlevel Based on the multiobjective optimization process ninerelatively close solutions are obtained which meet thepredetermined upper and lower limits Desirability refers tothe closeness of a response to a desired value and the closerthe value to 1 the better Figure 15 shows the changes in thedesirability function based on the multiobjective optimi-zation process -e desirability values are approximately0976 which is close to 1 thereby indicating that the RSM
optimization technique is feasible -e largest group ofdesirability values is taken as the optimal group and theoptimal steel fiber content (A) and basalt fiber content (B)are 3561 and 0142 respectively -e predicted com-pressive strength flexural strength and flexural-compres-sive ratio are 11951MPa 2325MPa and 1636respectively as shown in Table 15 -e steel fiber contentreaches 3561 because the steel fiber content is the maininfluencing factor of each response of the manufacturedsand RPC -e addition of steel fibers can inhibit the de-velopment of cracks and improve the mechanical propertiesof the manufactured sand RPC However the basalt fibercontent is 0142 Excessive basalt fiber content is notconducive to the overlap of steel fibers to cracks and will notimprove the compressive strength and flexural strength ofthe manufactured sand RPC -us the optimized basaltcontent is not excessive Furthermore additional tests areconducted to verify the theoretical response results -reeadditional tests are conducted using the same mix ratio andtwo optimized fiber content to determine whether the op-timized fiber content could provide improved compressivestrength flexural strength and flexural-compressive ratioTable 15 compares the average value of the three sets ofexperimental results with the theoretical response value -eresults show that the average error between the theoreticalresponse and actual response is 137 which is consistentAnd through the slump test it has been found that itsworkability is good In other words the above model can beused for practical prediction and the optimal fiber contentobtained by the RSM optimization process is accurate
-e compressive strength flexural strength and com-pression ratio obtained from the additional tests are14437MPa 2309MPa and 1602 compared with those ofthe H6 test group the steel fiber content is reduced by 044the basalt fiber content is reduced by 0033 the compressivestrength flexural strength and flexural-compressive ratio aresimilar and the enhancement effect is obvious -is finding is
ndash1000 ndash0500 0000 0500 1000
12
13
14
15
16
17
A
A
BB
Perturbation
Deviation from reference point (coded units)
28-d
ay b
end-
pres
s rat
io (
)
(c)
Figure 13 Perturbation plot for (a) 28-day compressive strength (R1) (b) 28-day flexural strength (R2) (c) 28-day flexural-compressiveratio (R3)
Advances in Civil Engineering 13
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d compressive strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
125
130 135
1405
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
115
120
125
130
135
140
145
28d
com
pres
sive s
treng
th (M
Pa)
A steel fiber (
)B basalt fiber ()
(a)
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d flexural strength (MPa)
A steel fiber ()
B b
asal
t fibe
r (
)
16
1820
225
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
14
16
18
20
22
24
28d
flexu
ral s
treng
th (M
Pa)
A steel fiber ()B basalt fiber ()
(b)
Figure 14 Continued
14 Advances in Civil Engineering
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
observed because the basalt fibers are mixed into the RPC anddispersed into very fine fiber filaments which can be wellinserted into the steel fibers in the mixture However once thesteel fiber content becomes too large staggered agglomeration
occurs Evenly distributing the basalt fibers between the steelfibers to work together is difficult and the agglomeratedmixed fibers tend to adsorb a large amount of cement mortarthereby resulting in decreased strength
143934 196967 25 303033 35606600512563
0113128
0175
0236872
029874428d bend-press ratio ()
A steel fiber ()
B b
asal
t fibe
r (
)
14 15 165
00512563 0113128
0175 0236872
0298744
143934196967
25303033
356066
12
13
14
15
16
17
28d
flexu
ral-c
ompr
essiv
e rat
io (
)
A steel fiber ()B basalt fiber ()
(c)
Figure 14 Contour and 3D plots (a) R1 (b) R2 (c) R3
Table 14 Definitions of factors and responses in the multiobjective optimization process
Factors and responses Goal Lower limit Upper limit ImportanceSteel fiber () In range 144 356 3Basalt fiber () In range 005 03 3Compressive strength (MPa) Maximize 11951 14408 3Flexural strength (MPa) Maximize 1452 2316 3Flexural-compressive ratio () Maximize 1215 1638
005125630113128
01750236872
0298744
143934196967
25303033
356066
0000
0200
0400
0600
0800
1000
Des
irabi
lity
A steel fiber (
)B basalt fiber ()
0976
Figure 15 Variation in desirability function based on the multiobjective optimization process
Advances in Civil Engineering 15
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
5 Conclusions
Based on the CCD in the RSM this study conducts ex-perimental research on the compressive strength flexuralstrength and workability of manufactured sand RPC mixedwith steel and basalt fibers and draws the followingconclusions
(i) It is feasible to use manufactured sand instead ofquartz sand and river sand to prepare RPC and its7-day and 28-day compressive strength and flexuralstrength are good under standard curing -e ad-dition of steel fiber and basalt fiber slightly reducesthe working performance of machine-made sandRPC but its strength is improved which can be usedin actual engineering
(ii) -e mechanical properties of manufactured sandRPCmixed with steel and basalt fibers are improvedsubstantially compared with those of manufacturedsand RPC without fibers When the steel fibercontent is lower than 25 the influence of in-creasing the basalt content on flexural strength andflexural-compressive ratio is obvious When thesteel fiber content is too high the addition of basaltfibers will have a negative mixing effect -e flex-ural-compressive ratio of steel-basalt fiber-manu-factured sand RPC is much higher than that ofordinary concrete
(iii) -ree response surface models of 28-day compres-sive strength (R1) 28-day flexural strength (R2) and28-day flexural-compressive ratio (R3) are estab-lished ANOVA verifies that the three models havesufficient accuracy and steel fibers are more signif-icant than basalt fibers in improving the mechanicalproperties of machine-made sand RPC In additionthe relationship equations between the three re-sponses and the steel fiber content (A) and basaltcontent (B) are obtained to help select the desiredsteel and basalt fiber content of the manufacturedRPC according to different actual conditions
(iv) Based on the multiobjective optimization technol-ogy of the RSM the optimal steel fiber content (A) is3561 and the optimal basalt fiber content (B) is0142 -e predicted eclectic optimal 28-daycompressive strength 28-day flexural strength and28-day flexural-compressive ratio are 14245MPa2325MPa and 1636 respectively Additionaltests verify that the optimal content obtained byRSM multiobjective optimization is reliable
Data Availability
-e data that supports the findings of this study are availablewithin the article
Conflicts of Interest
-e authors declare no conflicts of interest
Authorsrsquo Contributions
Y Zhang and J Liu contributed to conceptualization andmethodology J Wang and J Liu contributed to validationand formal analysis Y Zhang and J Wang contributed toinvestigation and writingmdashreview and editing J Liu and BWu contributed to writingmdashoriginal draft preparation JWang contributed to project administration
Acknowledgments
-is research was funded by the Science Technology De-partment Program of Jilin Province (Grant no20190303138SF) and the Science and Technology Project ofEducation Department of Jilin Province (Grant nosJJKH20190875KJ and JJKH20190870KJ)
References
[1] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement and Conssssscrete Researchvol 25 no 7 pp 1501ndash1511 1995
[2] M Cheyrezy V Maret and L Frouin ldquoMicrostructuralanalysis of RPC (reactive powder concrete)rdquo Cement andConcrete Research vol 25 no 7 pp 1491ndash1500 1995
[3] C Zhong M Liu Y Zhang and J Wang ldquoStudy on mixproportion optimization of manufactured sand RPC anddesign method of steel fiber content under different curingmethodsrdquo Materials vol 12 no 11 p 1845 2019
[4] Y-S Tai H-H Pan and Y-N Kung ldquoMechanical propertiesof steel fiber reinforced reactive powder concrete followingexposure to high temperature reaching 800degCrdquo Nuclear En-gineering and Design vol 241 no 7 pp 2416ndash2424 2011
[5] C H Dong and X W Ma ldquoExperimental research on me-chanical properties of basalt fiber reinforced reactive powderconcreterdquo Advanced Materials Research vol 893 pp 610ndash613 2014
[6] Saloma Hanafiah and F N Putra ldquo-e effect of polypro-pylene fiber on mechanical properties of reactive powderconcreterdquoAIP Conference Proceedings vol 1885 no 1 ArticleID 020093 2017
[7] Y Ju L Wang H Liu and G Ma ldquoExperimental investi-gation into mechanical properties of polypropylene reactive
Table 15 Results of theoretical responses and additional experimental responses of optimal mix design
Factors and responses Model predictive value Actual test value Error ()Steel fiber () 3561Basalt fiber () 0142Compressive strength (MPa) 14245 14437 135Flexural strength (MPa) 2325 2309 069Flexural-compressive ratio () 1636 1602 208Desirability 0976
16 Advances in Civil Engineering
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17
powder concreterdquo ACI Materials Journal vol 115 no 1pp 21ndash32 2018
[8] Y Zhang B Wu J Wang M Liu and X Zhang ldquoReactivepowder concrete mix ratio and steel fiber content optimi-zation under different curing conditionsrdquo Materials vol 12no 21 p 3615 2019
[9] H M Al-Hassani W I Khalil and L S Danha ldquoMechanicalproperties of reactive powder concrete with various steel fiberand silica fume contentsrdquo Acta Technica Corvininesis-Bulletinof Engineering vol 7 no 1 2014
[10] K ZMa A Que and C Liu ldquoAnalysis of the influence of steelfiber content on mechanical properties of reactive powderconcreterdquo Journal of Advanced Concrete Technology vol 3pp 76ndash83 2016
[11] F Minelli and G A Plizzari ldquoOn the effectiveness of steelfibers as shear reinforcementrdquo ACI Structural Journalvol 110 no 3 pp 379ndash389 2013
[12] H Liu S Liu S Wang X Gao and Y Gong ldquoEffect of mixproportion parameters on behaviors of basalt fiber RPC basedon box-behnken modelrdquo Applied Sciences vol 9 no 10p 2031 2019
[13] J Branston S Das S Y Kenno and C Taylor ldquoMechanicalbehaviour of basalt fibre reinforced concreterdquo Constructionand Building Materials vol 124 pp 878ndash886 2016
[14] T Ayub N Shafiq and M F Nuruddin ldquoMechanicalproperties of high-performance concrete reinforced withbasalt fibersrdquo Procedia Engineering vol 77 pp 131ndash139 2014
[15] W Liu ldquoExperimental study on basic mechanical propertiesand strengthening mechanism of steel fiber mixed basalt fiberreinforced cement mortarrdquo Journal of Advanced ConcreteTechnology vol 12 pp 125ndash128 2013
[16] Y Wu L Chen and W Li ldquoExperimental study on me-chanical properties of steel-basalt hybrid fiber pavementconcreterdquo International Journal of Science Technology andEngineering vol 15 pp 232ndash238 2015
[17] Z-X Li C-H Li Y-D Shi and X-J Zhou ldquoExperimentalinvestigation on mechanical properties of hybrid fibre rein-forced concreterdquo Construction and Building Materialsvol 157 pp 930ndash942 2017
[18] GB175-2007 Standard for Common Portland Cement Chi-nese Standard Beijing China 2007
[19] GBT510032014 Technical Code for Application of MineralAdmixture Chinese Standard Beijing China 2014
[20] JGJ 52-2006 Standard for Technical Requirements and TestMethod of Sand and Rrushed Stone (or Gravel) for OrdinaryConcrete Ministry of Construction of the Peoplersquos Republic ofChina Beijing China 2015
[21] GBT31387-2015 Standard for Reactive Powder ConcreteChinese Standard Beijing China 2015
[22] GBT50080-2002 Standard Test Methods for Performance ofOrdinary Concrete Mixtures Chinese Standard BeijingChina 2007
[23] N Biglarijoo M Nili S M Hosseinian M RazmaraS Ahmadi and P Razmara ldquoModelling and optimisation ofconcrete containing recycled concrete aggregate and wasteglassrdquo Magazine of Concrete Research vol 69 no 6pp 306ndash316 2017
[24] M A A Aldahdooh N M Bunnori and M A M JoharildquoEvaluation of ultra-high-performance-fiber reinforced con-crete binder content using the response surface methodrdquoMaterials amp Design (1980ndash2015) vol 52 pp 957ndash965 2013
[25] D C Montgomery Design and Analysis of Experiments JohnWiley amp Sons Hoboken NJ USA 2017
[26] M Barbuta E Marin S M Cimpeanu et al ldquoStatisticalanalysis of the tensile strength of coal fly ash concrete withfibers using central composite designrdquo Advances in MaterialsScience and Engineeringvol 2015 Article ID 486232 7 pages2015
[27] L Jiang and J Yin ldquoA brief discussion on the factors affectingconcrete bend-press ratiordquo Journal of Ready-Mixed Concretevol 7 pp 51ndash55 2018
[28] T F Awolusi O L Oke O O Akinkurolere andA O Sojobi ldquoApplication of response surface methodologypredicting and optimizing the properties of concrete con-taining steel fibre extracted from waste tires with limestonepowder as fillerrdquo Case Studies in Construction Materialsvol 10 Article ID e00212 2019
Advances in Civil Engineering 17