highwayperformanceevaluationindexinsemiaridclimate ... · ation index pqi h20-2007 is composed of...

Research ArticleHighway Performance Evaluation Index in Semiarid ClimateRegion Based on Fuzzy Mathematics

Sanqiang Yang12 Meng Guo 3 Xinlei Liu1 Pidong Wang1 Qian Li1 and Haiqing Liu3

1Baoding City Road and Bridge Engineering Assembly Technology Key Laboratory College of Civil Engineering and ArchitectureHebei University Baoding Hebei 071002 China2Hebei Institute of Transportation Planning and Design Shi Jiazhuang Hebei 050011 China3e Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education Beijing University of TechnologyBeijing 100124 China

Correspondence should be addressed to Meng Guo mguoustbeducn

Received 27 February 2019 Revised 27 April 2019 Accepted 14 May 2019 Published 17 June 2019

Academic Editor Mohammad A Hariri-Ardebili

Copyright copy 2019 Sanqiang Yang 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

Accurate evaluation and analysis of expressway pavement performance is a prerequisite for determining the pavement designscheme and maintenance scheme Due to the fuzziness and randomness of many factors affecting the pavement performance thispaper relies on the reconstruction and expansion project of Xinglin section of the Taihang mountain expressway a method ofhighway pavement performance evaluation based on fuzzy mathematics is proposed +e results show the following① the studyuses the factor domain the comment level domain the fuzzy relationship matrix the evaluation factor full vector and the fuzzycomprehensive evaluation result vector five-step method +e method can be effectively combined with the multi-indexcomprehensive detection index used in the specification ② Based on the multi-index comprehensive test and evaluationadopted in the specification the performance grade of the old road surface was quantitatively evaluated by the iterative calculationof fuzzy mathematics that broke through the evaluation mode which was based on the traditional detection methods+e researchresults provide innovative theoretical methods for the accurate evaluation and analysis of highway pavement performance in thesemiarid climate region and also play a technical supporting role for the pavement design scheme and maintenance schemedecision-making in the semiarid climate region

1 Background

By the end of 2017 the total mileage of expressways in Chinais close to 130000 km among which the service period of5ndash10 years accounts for up to 45 +e performance evalu-ation of the old road surface and the design of the pavementmaintenance scheme will determine the investment budgetfor the reconstruction of the old road network [1]Pavementperformance evaluation is based on the collected pavementcondition data to judge the degree of pavement performancetomeet the requirements of use It is helpful to understand thepavement condition and the change rule of service perfor-mance making reasonable countermeasures and is the basisof making corresponding maintenance and reconstruction

measures [2] Pavement performance generally remains goodfor 1 to 5 years In 6 to 15 years pavement performance isdegraded due to natural environment factors traffic loadsand temperature changes A series of diseases such as ruts andcracks appear on the road surface Under the comprehensiveinfluence of various factors [3 4] the asphalt pavement ofexpressway needs a large area of maintenance for 5 to 8 yearsresulting in a large capital investment +erefore in order tomaintain the level of highway service delaying the decline ofroad performance reducing asset losses extending the servicelife of the road surface are the main tasks of highwaymaintenance management [5]

In recent years many experts and scholars at home andabroad have conducted a large number of theoretical studies

HindawiAdvances in Materials Science and EngineeringVolume 2019 Article ID 6708102 7 pageshttpsdoiorg10115520196708102

on pavement suitability evaluation and prediction Developedcountries engaged in this research earlier and its researchideas and methods have been mostly in the establishment ofthe road management system and road maintenance systemto achieve Among them a representative study has beendeveloped by the US Army Construction Engineering Re-search Institute of the PAVER system +e penalty methodwas first used to establish the pavement damage evaluationmodel by considering the road condition information con-dition evaluation and prediction +e method can accuratelycalculate and reduce overall damage caused by a variety ofdamage of pavement [6] +e Arizona management systemused the evenness and cracking data to evaluate thepavement performance [7]+e Milligan state road man-agement system management proposed the road perfor-mance attenuation curve the forecast road performance[8] In 2001 Prozzi from the University Of Californiaproposed a method to analyze and evaluate pavementperformance by combining field test data with experi-mental data [9] In the same year Nunoo from FloridaInternational University proposed to adopt the compositecomprehensive evaluation algorithm to optimize themultiyear integrated pavement maintenance plan for thenetwork pavement management and maintenance prob-lems [10] +e SHRP which began in 1987 considerspavement long-term performance (LTPP) research as a 10-year highway research project with the goal of providingthe means and assistance to ldquoimprove pavement perfor-mance and service liferdquo [11] In 2001 Hao from ChangrsquoanUniversity analyzed the necessity research plan and re-search strategy of carrying out long-term pavement per-formance research in his doctoral thesis ldquopavementperformance evaluation and analysis researchrdquo [12]

In terms of pavement performance evaluation there aregenerally two categories of evaluation indexes single indexand comprehensive index +e evaluation model mainlyincludes PSI [13] of AASHO in the United States CanadarsquosRCI [14] Japanrsquos MCI and Chinarsquos PQI and RQI+is paperrelies on the research carried out by the Chinese project sothe Chinese PCI and RQI models are selected

Hebei Province is a typical semiarid climate region Atpresent the total length of expressways in Hebei Province is6531 km +e performance evaluation of old highwaypavement is especially difficult +e semiarid climate areahas less precipitation strong sunshine and sharp temper-ature change +e shrinkage deformation of highwaypavement in the semiarid climate area is particularlyprominent due to high temperature rutting in summer lowtemperature cracking in winter annual temperature dif-ference and diurnal temperature difference

In recent ten years researchers began to apply fuzzymathematics to highway performance evaluation index re-search Zhou et al proposed a prediction method ofpavement performance based on grey prediction theory andclustering analysis method [15] Chen established theevaluation model of highway asphalt pavement which iscreated on the basis of fuzzy evaluation grey relationshipand ameliorated artificial neutral network (ANN) [16] Inhighway pavement maintenance management decision-

making optimization Wen discussed highway pavementmaintenance project decision-making and maintenancefund allocation [17] Li put forward a method of expresswayasphalt pavement maintenance decision-making based onthe matter-element model +e model can greatly reduce thecalculation amount of the optimization analysis process ofeach maintenance section [18]

Based on the above background this paper relies on thereconstruction and expansion project of Xinglin section ofthe Taihang mountain expressway and a method of highwaypavement performance evaluation based on fuzzy mathe-matics is proposed

2 Climate Characteristics and EngineeringDescription of Semiarid Areas

+e semiarid climate zone refers to the zone whose meanannual precipitation is less than the evaporation [19] thedrought index AI (the ratio of annual precipitation and theannual evaporation) is in the range of 02 to 05 the pre-cipitation is commonly 200sim400mm the temperaturechanges sharply and the annual sunshine amount variesgreatly +e difference in sunshine is more than 30 degreesCelsius and the highest temperature can reach 75 degreesCelsius +e areas include the central and eastern InnerMongolia Hebei Yanbei in Shanxi northern region ofShanxi Xihaigu in the south of Ningxia Dingxi in GansuYuzhong Yushu in Qinghai Guoluo Lhasa in Tibet andother regions Rainfall is directly related to pavement waterresistance and temperature difference is directly related topavement high and low temperature performance Corre-lation analysis based on fuzzy mathematics can solvemultifactor problems better

+e XingtaindashLinqing expressway based on this study islocated in the south of Hebei Province with gentle to-pography and topographic forms of alluvial diluvial andlimnetic plain For the warm temperate semiarid monsoonclimate region weather is like in spring drought windysummer weather hot and rainy and winter weather coldand less snowy +e annual average temperature is 131degCthe average temperature is 269degC In July the extrememaximum temperature is 418degC the average temperaturefrom December to January is minus 35 degrees Celsiusand the extreme minimum temperature is minus216degC +eaverage annual precipitation is about 550mm+rough theinvestigation and analysis of road conditions it is foundthat the sections with high temperature rutting in summerare significantly distributed and the transverse and lon-gitudinal cracks of the road surface are widely distributed+e types of pavement diseases are closely related to thetemperature and precipitation in this area

3 Evaluation and Analysis of the ExistingStandard Indexes

In this study the highway from Xingtai to Linqing in thesemiarid climate region of Hebei Province was selected andthe pavement performance index (PCI) [20] road drivingquality index (RQI) and rutting depth evaluation (RDI)

2 Advances in Materials Science and Engineering

were used to analyze the change rules of various pavementperformance indexes from 2011 to 2016 Pavement struc-tural strength [21 22] was used to evaluate the variation rulesof deflection in 2015 and 2016 (Figures 1ndash6)

According to Figures 1ndash3 from 2011 to 2016 the overalltrend of the PCI index of pavement damage decreased yearby year +e road surface driving quality index (RQI) is allabove 90 points indicating that the road surface is in goodcondition +e rutting depth index (RDI) of the road surfaceshowed that the rutting depth index of the road surfacedecreased continuously with the increase of years and thedecay law of the road surface performance was obvious Itcan be concluded from the analysis that the rutting depthindex RDI affecting the road surface of this section is relatedto the quality of internal pavement material and pavementstructure as well as external climatic conditions and trafficconditions

+e bending and subsidence data of the Taihangmountain expressway from Xingtai to Linqing in thesemiarid climate region of Hebei Province in 2015 and 2016were selected for analysis and the strength variation ruleswere evaluated (Figures 4ndash6)

According to the analysis in Figures 4ndash6 SSI data of theroad surface from Xingtai to Linqing section of the Taihangmountain expressway in 2015 and 2016 show that with theincrease of the service period the overall strength of the roadsurface structure presents a downward trend +e mainfactors of intensity attenuation are heavy traffic largetemperature difference and other meteorological and en-vironmental factors

4 Comprehensive Evaluation of PavementPerformance Based on Fuzzy Mathematics

41 Analysis Steps

411 Determine the Factor Domain of the Evaluation Object+e evaluation fuzzy phenomenon first determines theevaluation factors and the collection of these factors con-stitutes the evaluation factors [23] +e theory of domain ofour countryrsquos current technical specification for the highwayasphalt pavement maintenance JTG comprehensive evalu-ation index PQI H20-2007 is composed of four indexesnamely the pavement damage index roughness rut andantisliding performance So the factors concerning domainU (PCI RQI RDI SRI)

412 Domain the Evaluation Grade eory Domain theevaluation grade theory divides the evaluation objects intoseveral levels generally from 4 levels to 9 levels [24] In thispaper the evaluation is divided into five grades namely theevaluation theory of field V= (excellent good mediumsecondary bad) = (A B C D E)

413 Establish the Fuzzy Relation Matrix After the hier-archical fuzzy subset is constructed the evaluated objectsshould be quantified from each factor one by one that is themembership degree of the evaluated objects to the

2011 2012 2013 2014 2015 20160

20

40

60

80

100

PCI

Year

Figure 1 Continuous chart of the road condition index

Year2011 2012 2013 2014 2015 2016

0

20

40

60

80

100

RQI

Figure 2 Continuous statistics of the driving quality index chart

Year2011 2012 2013 2014 2015 2016

0

20

40

60

80

100

RDI

Figure 3 Continuous chart of the rutting depth index

K23 K24 K25 K26 K27 K28 K29 K30 K31 K32 K33 K34 K35 K36 K37

11

12

13

14

15

16

Pile

Def

lect

ion

(00

1mm

)

Figure 4 Trend of pavement deflection in 2015

Advances in Materials Science and Engineering 3

hierarchical fuzzy subset from the perspective of a singlefactor [25] +e attribute measure function of each evalu-ation index is shown in the following table

As can be seen from Table 1 the attribute measurementfunctions of the four evaluation indicators are the same+en the membership functions of PCI RQI RDI and SRIare as follows

rE

1 85lt rle 100

rminus 7085minus 70

70lt rle 85

0 0lt rle 75

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

rG

100minus r

100minus 85 85lt rle 100

1 70lt rle 85

rminus 5570minus 55

55lt rle 70

0 0lt rle 55

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rM

0 85lt rle 100

85minus r


1 55lt rle 70

rminus 4055minus 40

40lt rle 55

0 0lt rle 40

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rS

0 70lt rle 100

70minus r


1 40lt rle 55

rminus 2540minus 25

25lt rle 40

0 0lt rle 25

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rB

0 55lt rle 100

55minus r


1 25lt rle 40

rminus 1025minus 10

10lt rle 25

0 0lt rle 10

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

PileK23 K24 K25 K26 K27 K28 K29 K30 K31 K32 K33 K34 K35 K36 K37

12

13

14

15

16

17

18

Def

lect

ion

(00

1mm

)



13

14

15

16

17

18

19

20

SSI

Pile

IN2015 SSIIN2016 SSI

Figure 6 SSI comparison in 2015 and 2016

Table 1 Road surface performance

Indicators Excellent Good Medium Secondary BadPCI [85 100) [70 85) [55 85) [40 55) [0 40)RQI [85 100) [70 85) [55 85) [40 55) [0 40)RDI [85 100) [70 85) [55 85) [40 55) [0 40)SRI [85 100) [70 85) [55 85) [40 55) [0 40)


414 Determine the Total Vector of Evaluation Factors+e vector coefficient W in the weight vector reflects theinfluence of each index on the object under evaluation [26]In this paper the analytic hierarchy process is adopted todetermine the weight vector When the importance of PCI ofpavement damage is 1 it is considered that the importanceof rut is 12 the importance of flatness is 2 the importance ofantislip is 1 and the importance of structural strength is 3After constructing the judgment matrix C to find its max-imum eigenvalue and eigenvector and normalizing it theweight coefficient of each index is obtained asω1ω2ω3 and ω4

C cij1113872 1113873

c11 c12 middot middot middot c1j


middot middot middot middot middot middot middot middot middot middot middot middot

ci1 ci2 middot middot middot cij

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)

For the consistency test on matrix C taking the con-sistency index

CI λmax minus n

nminus 1 (3)

+e randomness index RI is shown in Table 2For the consistency test for matrix C using equation (3)

if CRlt 01 then judge matrix C has good consistencyOtherwise matrix C needs to be readjusted

CR CIRI

(4)

415 Result Vector of Fuzzy Comprehensive EvaluationAccording to this formula bi is the i-th membership degreecalculated by combining all factors of W and R According tothe principle of maximum membership let d0 max[bi]and then consider the i-th comment level in the commentdomain V

D di1113858 1113859 W middot R ω1ω2ω3 ωm1113858 1113859 middot

r11 middot middot middot r1n

middot middot middot middot middot middot middot middot middot

rm1 middot middot middot rmn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

b1 b2 bn1113858 1113859

(5)

42 Example Analysis Taking the K23+000-K33+000upbound line of the XingtaindashLinqing expressway in HebeiProvince as an example the performance evaluation indexesof each item were calculated +e test results are shown inTable 3

Since PCI 6883 the membership function values at theoptimal good medium secondary and bad levels werecalculated respectively according to the above calculationformula and obtained after normalization

PCI 6883 r1 [rE rG rM rS rB] [r11 r12 r13 r14

r15] [0 0922 1 0078 0]

RQI 9384 r2 [r21 r22 r23 r24 r25] [1 0411 0 0 0]

RDI 7939 r3 [r31 r32 r33 r34 r35] [0626 1 0374

0 0]

SRI 7388 r4 [r41 r42 r43 r44 r45] [0259 1 0741

0 0]

To sum up the matrix is obtained R([Vij])

Rvij1113858 1113859( 1113857

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)

Technical indexes of the Xinglin expressway asphaltpavement performance are C1-PCI C2-RDI C3-RQI andC4-SRI +e judgment matrix is constructed by equation (2)

C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ijtake4

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)

For maximum eigenvalues and eigenvectors

1113944

4

j1c1j 1 times 2 times 1 times 3 6 w1 1113944

4

c1j1113888 1113889

14

614 1565

1113944

4

j1c2j

12

times 1 times12

times 2 12 w2 1113944

4

c2j1113888 1113889

14

12

1113874 111387514

0841

1113944

4


4

c3j1113888 1113889

14

614 1565

1113944

4

j1c4j

13

times12

times13

times 1 118

w4 11139444

c4j1113888 1113889

14

118

1113874 111387514

0845

(8)

Normalize the eigenvector w (w1 w2 w3 w4)T

(1565 0841 1565 0485)T

w1 wi

11139364j1wj

i 1 2 3 4 j 1 2 3 4 11139444

j1wj 4456

(9)

Table 2 Randomness index RI

n 1 2 3 4 5 6RI 0 0 059 09 112 124

Table 3 Section K23-K33 performance evaluation indexes

Test results PCI RQI RDI SRIK23-K33 (uplink) 6883 9384 7939 7388


So

w1 15654456

0351

w2 08414456

0189

w3 15654456

0351

w4 04854456

0109

CW

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

0351

0189

0351

0109

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

λmax 1113944n

i1

(c middot w)i

n middot wi

1407

4 times 0351+

07584 times 0189

+1407

4 times 0351

+0437

4 times 0109 401

(10)

Inspection CI (λmax minus n)(nminus 1) (401minus 4)(4minus1) 00035 and CR CIRI 00035090 00038lt 01 Itis consistent +erefore w1 w2 w3 and w4 are 0351 03510189 and 0109 respectively +e weight vectorw (w1 w2 w3 w4)

T synthesis of the fuzzy comprehensiveevaluation result vector by formula (3)

D w middot R [0351 0351 0189 0109]

middot

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(11)

+e resulting D [0497 0765 0502 0027 0]According to the principle of maximum membership wheni 2 D0 max[di] 0765 +e corresponding rating isldquogoodrdquo

Similarly performance evaluation results of uplink canbe obtained based on the above model as shown in Table 4

It can be seen from Table 4 that based on the multi-index comprehensive detection and evaluation adopted bythe specification the performance grade of the old roadsurface is quantitatively evaluated by using the iterativecalculation of fuzzy mathematics and the evaluation scoreof each kilometer is more quantitatively intuitive Ithighlights the idea of expert evaluation based on traditionaldetection methods weakens subjective judgment high-lights objective quantitative evaluation and breaks throughthe evaluation mode based on traditional detectionmethods +e research results provide an innovative the-oretical method for the accurate evaluation and analysis ofhighway pavement performance in semiarid climateregions

5 Conclusions

+is paper uses fuzzy mathematics to comprehensivelyevaluate the pavement performance of Xingtai to Linqingsection of Taihang mountains expressway in the semiaridclimate zone of Hebei Province Based on the multi-indexcomprehensive detection and evaluation adopted by thespecification fuzzy mathematics is used to iteratively cal-culate and evaluate the performance grade of the old road+e research puts forward the feasibility of the fuzzymathematics method in highway pavement performanceevaluation and obtains the following research conclusions

(1) +is paper statistically analyzes the meteorologicaland hydrological characteristics of semiarid climatezones combined with engineering case investigationand analysis +e results show that the types anddistribution characteristics of highway pavementdiseases are closely related to rainfall extremetemperature and temperature difference in semiaridclimate areas

(2) +e study uses the factor domain the comment leveldomain the fuzzy relationship matrix the evaluationfactor full vector and the fuzzy comprehensiveevaluation result vector five-step method +emethod can be effectively combined with the multi-index comprehensive detection index used in thespecification

Table 4 Road performance evaluation results of K23simK33 section

Stake Excellent Good Medium Secondary Bad Evaluation PQI evaluationK23-K24 0555 0723 0444 0157 0 Good GoodK24-K25 0466 0803 0534 0073 0 Good GoodK25-K26 0446 0668 0554 0091 0 Good MediumK26-K27 0535 0823 0464 0058 0 Good GoodK27-K28 0563 0777 0437 0077 0 Good GoodK28-K29 0646 0879 0488 0 0 Good GoodK29-K30 0259 0596 0670 0318 0 Medium MediumK30-K31 0715 0900 0285 0 0 Good GoodK31-K32 0472 0534 0528 0271 0 Good MediumK32-K33 0624 0879 0376 0 0 Good Good


(3) Based on the multi-index comprehensive test andevaluation adopted in the specification the perfor-mance grade of the old road surface was quantita-tively evaluated by iterative calculation with fuzzymathematics which broke through the evaluationmode based on the traditional detection methods+e research results provide an innovative theoret-ical method for the accurate evaluation and analysisof highway pavement performance in semiarid cli-mate regions

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by Hebei Provincial NaturalScience Foundation Funded Project (E2018201106) HebeiProvincial Department of Education Research Program KeyProject (ZD2016073) Hebei Province High-Level TalentsFunding Project (B2017005024) and National NaturalScience Foundation of China (51808016)

References

[1] Q R Li Z Y Guo Y J Wang Evaluation of freeway asphaltpavement performance based on PCAmdashSVMrdquo Journal ofBeijing University of Technology Naturnal Science Eitionvol 44 no 2 pp 283ndash288 2018

[2] J Zhao Performance evaluation and prediction model of as-phalt pavement PhD thesis Dalian University of Technol-ogy Dalian China 2008

[3] (FHWA)US Department of Transportation Federal HighwayAdministration Office of Management Asset ManagementOverview (FHWA) Washington DC USA 2007

[4] M Guo and Y Q Tan ldquoInteraction between asphalt andmineral fillers and its correlation to masticsrsquo viscoelasticityrdquoInternational Journal of Pavement Engineering 2019

[5] R Hass W R Huston and J Zaniewshi Modern PavementManagement Malabar Florida Krieger Publishing CompanyMalabar FL USA 1994

[6] M Y Shahin ldquoPavement managementmdashPAVER updaterdquo inProceedings of the Annual Meeting of the TransportationResearch Board (TRB) National Research Council Wash-ington DC USA 1999

[7] K C P Wang J Zaniewsk and G Way ldquoProbabilistic be-havior of pavementsrdquo Journal of Transportation Engineeringvol 120 no 3 pp 358ndash375 1994

[8] B R Kulkarni and W R Miller ldquoPavement ManagementSystems Past Present and Futurerdquo Transportation ResearchBoard vol 1853 no 1 pp 65ndash71 2003

[9] J L Prozzi Modeling pavement performance by combiningfield and experimental data PhD thesis University of Cal-ifornia Oakland CA USA 2001

[10] C Nunoo Optimization of Pavement Maintenance and Re-habilitation Programming Using Shuffled Complex EvolutionAlgorithm Florida International University University ParkFL USA 2001

[11] W O Hadley SHRP-LTTP Overview Five-Year ReportSHRP-P-416 Washington DC USA 1994

[12] D L Hao Evaluation and Analysis of Pavement PerformanceChangrsquoan University Xirsquoan China 2000

[13] R K Kher and M I Darter Probabilistic Concept and eirApplication to AASHO Interim Guide for Design of RigidPavements HRB 466 Washington DC USA 1973

[14] Pavement Desing and Evalauation Committee Roads andTransportation Association of Canada ldquoOutput measurementfor pavement management studies in canadardquo in Proceedingsof the ird International Conference on the Structural Designof Asphalt Pavements (ICSDAP) University of Michigan AnnArbor MI USA 1972

[15] H Zhou K Xie and H M Hu ldquoEvaluation and pavementmodel of expressway to pavement performancerdquo Engineeringand Construction vol 115 no 1 pp 66ndash69 2018

[16] T Chen Research on Performance Evaluation Technology andReinforcement Design Method of Expressway Asphalt Pave-ment Changrsquoan University Xirsquoan China 2003

[17] S Q Wen Research on Expressway Pavement MaintenanceDecision Based on Combination Prediction and Fuzzy Opti-mization Dalian University of Technology Dalian China2009

[18] H M Li Research on Maintenance Decision of AsphaltPavement of Network Expressway Based on Matter-ElementModel Southeast university Dhaka Bangladesh 2017

[19] J P Huang M X Ji and Y Z Liu ldquoAn overview of arid andsemi-arid climate changerdquo Progressus Inquisitiones DEMutatione Climatis vol 9 no 1 pp 09ndash14 2013

[20] C Ling L Zhou and F Gu ldquo+e application of extensiontheory on pavement performance evaluationrdquo AdvancedMaterials Research vol 168ndash170 pp 111ndash115 2010

[21] S Q Yang N Li and S Zhang ldquoAnalysis of design index andstructural mechanics of durable asphalt pavement in desertareardquo Journal of Hebei University Naturnal Science Editionvol 36 no 6 pp 574ndash582 2016

[22] S Q YangW XWu andN Li ldquoAnsys simulation analysis ofcement concrete pavement bearing capacity under extra heavyloadrdquo Journal of Hebei University Naturnal Science Editionvol 37 no 6 pp 561ndash566 2017

[23] S W Qi and F Q Wu ldquoSurrounding rockmass qualityclassification of tunnel cut by TBM with fuzzy mathematicsmethodrdquo Chinese Journal of Rock Mechanics and Engineeringvol 30 no 6 pp 1225ndash1229 2011

[24] J Bao Y Zhang X Su and R Zheng ldquoUnpaved road de-tection based on spatial fuzzy clustering algorithmrdquo EURASIPJournal on Image and Video Processing vol 26 no 12018

[25] J X Tang and X Y Li ldquoOn the stability evaluation of the deepsubway foundation pit based on the fuzzy mathematicaltheoryrdquo Journal of Safety and Environment vol 18 no 6pp 2135ndash2140 2018

[26] X Li X W Yang and J Huang ldquoComprehensive evaluationsystem of cement pavement performance based on fuzzymathematicsrdquo Journal of Lanzhou University Naturnal Sci-ence Edition vol 45 no S1 pp 88ndash92 2009


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Submit your manuscripts atwwwhindawicom

on pavement suitability evaluation and prediction Developedcountries engaged in this research earlier and its researchideas and methods have been mostly in the establishment ofthe road management system and road maintenance systemto achieve Among them a representative study has beendeveloped by the US Army Construction Engineering Re-search Institute of the PAVER system +e penalty methodwas first used to establish the pavement damage evaluationmodel by considering the road condition information con-dition evaluation and prediction +e method can accuratelycalculate and reduce overall damage caused by a variety ofdamage of pavement [6] +e Arizona management systemused the evenness and cracking data to evaluate thepavement performance [7]+e Milligan state road man-agement system management proposed the road perfor-mance attenuation curve the forecast road performance[8] In 2001 Prozzi from the University Of Californiaproposed a method to analyze and evaluate pavementperformance by combining field test data with experi-mental data [9] In the same year Nunoo from FloridaInternational University proposed to adopt the compositecomprehensive evaluation algorithm to optimize themultiyear integrated pavement maintenance plan for thenetwork pavement management and maintenance prob-lems [10] +e SHRP which began in 1987 considerspavement long-term performance (LTPP) research as a 10-year highway research project with the goal of providingthe means and assistance to ldquoimprove pavement perfor-mance and service liferdquo [11] In 2001 Hao from ChangrsquoanUniversity analyzed the necessity research plan and re-search strategy of carrying out long-term pavement per-formance research in his doctoral thesis ldquopavementperformance evaluation and analysis researchrdquo [12]

In terms of pavement performance evaluation there aregenerally two categories of evaluation indexes single indexand comprehensive index +e evaluation model mainlyincludes PSI [13] of AASHO in the United States CanadarsquosRCI [14] Japanrsquos MCI and Chinarsquos PQI and RQI+is paperrelies on the research carried out by the Chinese project sothe Chinese PCI and RQI models are selected

Hebei Province is a typical semiarid climate region Atpresent the total length of expressways in Hebei Province is6531 km +e performance evaluation of old highwaypavement is especially difficult +e semiarid climate areahas less precipitation strong sunshine and sharp temper-ature change +e shrinkage deformation of highwaypavement in the semiarid climate area is particularlyprominent due to high temperature rutting in summer lowtemperature cracking in winter annual temperature dif-ference and diurnal temperature difference

In recent ten years researchers began to apply fuzzymathematics to highway performance evaluation index re-search Zhou et al proposed a prediction method ofpavement performance based on grey prediction theory andclustering analysis method [15] Chen established theevaluation model of highway asphalt pavement which iscreated on the basis of fuzzy evaluation grey relationshipand ameliorated artificial neutral network (ANN) [16] Inhighway pavement maintenance management decision-

making optimization Wen discussed highway pavementmaintenance project decision-making and maintenancefund allocation [17] Li put forward a method of expresswayasphalt pavement maintenance decision-making based onthe matter-element model +e model can greatly reduce thecalculation amount of the optimization analysis process ofeach maintenance section [18]

Based on the above background this paper relies on thereconstruction and expansion project of Xinglin section ofthe Taihang mountain expressway and a method of highwaypavement performance evaluation based on fuzzy mathe-matics is proposed

2 Climate Characteristics and EngineeringDescription of Semiarid Areas

+e semiarid climate zone refers to the zone whose meanannual precipitation is less than the evaporation [19] thedrought index AI (the ratio of annual precipitation and theannual evaporation) is in the range of 02 to 05 the pre-cipitation is commonly 200sim400mm the temperaturechanges sharply and the annual sunshine amount variesgreatly +e difference in sunshine is more than 30 degreesCelsius and the highest temperature can reach 75 degreesCelsius +e areas include the central and eastern InnerMongolia Hebei Yanbei in Shanxi northern region ofShanxi Xihaigu in the south of Ningxia Dingxi in GansuYuzhong Yushu in Qinghai Guoluo Lhasa in Tibet andother regions Rainfall is directly related to pavement waterresistance and temperature difference is directly related topavement high and low temperature performance Corre-lation analysis based on fuzzy mathematics can solvemultifactor problems better

+e XingtaindashLinqing expressway based on this study islocated in the south of Hebei Province with gentle to-pography and topographic forms of alluvial diluvial andlimnetic plain For the warm temperate semiarid monsoonclimate region weather is like in spring drought windysummer weather hot and rainy and winter weather coldand less snowy +e annual average temperature is 131degCthe average temperature is 269degC In July the extrememaximum temperature is 418degC the average temperaturefrom December to January is minus 35 degrees Celsiusand the extreme minimum temperature is minus216degC +eaverage annual precipitation is about 550mm+rough theinvestigation and analysis of road conditions it is foundthat the sections with high temperature rutting in summerare significantly distributed and the transverse and lon-gitudinal cracks of the road surface are widely distributed+e types of pavement diseases are closely related to thetemperature and precipitation in this area

3 Evaluation and Analysis of the ExistingStandard Indexes

In this study the highway from Xingtai to Linqing in thesemiarid climate region of Hebei Province was selected andthe pavement performance index (PCI) [20] road drivingquality index (RQI) and rutting depth evaluation (RDI)







41 Analysis Steps




2011 2012 2013 2014 2015 20160

20

40

60

80

100

PCI

Year


Year2011 2012 2013 2014 2015 2016

0

20

40

60

80

100

RQI


Year2011 2012 2013 2014 2015 2016

0

20

40

60

80

100

RDI



11

12

13

14

15

16

Pile

Def

lect

ion

(00

1mm

)





rE

1 85lt rle 100

rminus 7085minus 70

70lt rle 85

0 0lt rle 75

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

rG

100minus r


1 70lt rle 85

rminus 5570minus 55

55lt rle 70

0 0lt rle 55

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rM

0 85lt rle 100

85minus r


1 55lt rle 70

rminus 4055minus 40

40lt rle 55

0 0lt rle 40

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rS

0 70lt rle 100

70minus r


1 40lt rle 55

rminus 2540minus 25

25lt rle 40

0 0lt rle 25

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rB

0 55lt rle 100

55minus r


1 25lt rle 40

rminus 1025minus 10

10lt rle 25

0 0lt rle 10

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)


12

13

14

15

16

17

18

Def

lect

ion

(00

1mm

)



13

14

15

16

17

18

19

20

SSI

Pile







C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)


CI λmax minus n

nminus 1 (3)



CR CIRI

(4)






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

b1 b2 bn1113858 1113859

(5)




r15] [0 0922 1 0078 0]

RQI 9384 r2 [r21 r22 r23 r24 r25] [1 0411 0 0 0]

RDI 7939 r3 [r31 r32 r33 r34 r35] [0626 1 0374

0 0]

SRI 7388 r4 [r41 r42 r43 r44 r45] [0259 1 0741

0 0]


Rvij1113858 1113859( 1113857

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ijtake4

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


1113944

4


4

c1j1113888 1113889

14

614 1565

1113944

4

j1c2j

12

times 1 times12

times 2 12 w2 1113944

4

c2j1113888 1113889

14

12

1113874 111387514

0841

1113944

4


4

c3j1113888 1113889

14

614 1565

1113944

4

j1c4j

13

times12

times13

times 1 118

w4 11139444

c4j1113888 1113889

14

118

1113874 111387514

0845

(8)


(1565 0841 1565 0485)T

w1 wi

11139364j1wj

i 1 2 3 4 j 1 2 3 4 11139444

j1wj 4456

(9)


n 1 2 3 4 5 6RI 0 0 059 09 112 124




So

w1 15654456

0351

w2 08414456

0189

w3 15654456

0351

w4 04854456

0109

CW

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

0351

0189

0351

0109

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

λmax 1113944n

i1

(c middot w)i

n middot wi

1407

4 times 0351+

07584 times 0189

+1407

4 times 0351

+0437

4 times 0109 401

(10)



D w middot R [0351 0351 0189 0109]

middot

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(11)




5 Conclusions








Data Availability




Acknowledgments


References






























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









41 Analysis Steps




2011 2012 2013 2014 2015 20160

20

40

60

80

100

PCI

Year


Year2011 2012 2013 2014 2015 2016

0

20

40

60

80

100

RQI


Year2011 2012 2013 2014 2015 2016

0

20

40

60

80

100

RDI



11

12

13

14

15

16

Pile

Def

lect

ion

(00

1mm

)





rE

1 85lt rle 100

rminus 7085minus 70

70lt rle 85

0 0lt rle 75

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

rG

100minus r


1 70lt rle 85

rminus 5570minus 55

55lt rle 70

0 0lt rle 55

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rM

0 85lt rle 100

85minus r


1 55lt rle 70

rminus 4055minus 40

40lt rle 55

0 0lt rle 40

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rS

0 70lt rle 100

70minus r


1 40lt rle 55

rminus 2540minus 25

25lt rle 40

0 0lt rle 25

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rB

0 55lt rle 100

55minus r


1 25lt rle 40

rminus 1025minus 10

10lt rle 25

0 0lt rle 10

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)


12

13

14

15

16

17

18

Def

lect

ion

(00

1mm

)



13

14

15

16

17

18

19

20

SSI

Pile







C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)


CI λmax minus n

nminus 1 (3)



CR CIRI

(4)






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

b1 b2 bn1113858 1113859

(5)




r15] [0 0922 1 0078 0]

RQI 9384 r2 [r21 r22 r23 r24 r25] [1 0411 0 0 0]

RDI 7939 r3 [r31 r32 r33 r34 r35] [0626 1 0374

0 0]

SRI 7388 r4 [r41 r42 r43 r44 r45] [0259 1 0741

0 0]


Rvij1113858 1113859( 1113857

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ijtake4

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


1113944

4


4

c1j1113888 1113889

14

614 1565

1113944

4

j1c2j

12

times 1 times12

times 2 12 w2 1113944

4

c2j1113888 1113889

14

12

1113874 111387514

0841

1113944

4


4

c3j1113888 1113889

14

614 1565

1113944

4

j1c4j

13

times12

times13

times 1 118

w4 11139444

c4j1113888 1113889

14

118

1113874 111387514

0845

(8)


(1565 0841 1565 0485)T

w1 wi

11139364j1wj

i 1 2 3 4 j 1 2 3 4 11139444

j1wj 4456

(9)


n 1 2 3 4 5 6RI 0 0 059 09 112 124




So

w1 15654456

0351

w2 08414456

0189

w3 15654456

0351

w4 04854456

0109

CW

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

0351

0189

0351

0109

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

λmax 1113944n

i1

(c middot w)i

n middot wi

1407

4 times 0351+

07584 times 0189

+1407

4 times 0351

+0437

4 times 0109 401

(10)



D w middot R [0351 0351 0189 0109]

middot

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(11)




5 Conclusions








Data Availability




Acknowledgments


References






























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






rE

1 85lt rle 100

rminus 7085minus 70

70lt rle 85

0 0lt rle 75

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

rG

100minus r


1 70lt rle 85

rminus 5570minus 55

55lt rle 70

0 0lt rle 55

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rM

0 85lt rle 100

85minus r


1 55lt rle 70

rminus 4055minus 40

40lt rle 55

0 0lt rle 40

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rS

0 70lt rle 100

70minus r


1 40lt rle 55

rminus 2540minus 25

25lt rle 40

0 0lt rle 25

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

rB

0 55lt rle 100

55minus r


1 25lt rle 40

rminus 1025minus 10

10lt rle 25

0 0lt rle 10

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)


12

13

14

15

16

17

18

Def

lect

ion

(00

1mm

)



13

14

15

16

17

18

19

20

SSI

Pile







C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)


CI λmax minus n

nminus 1 (3)



CR CIRI

(4)






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

b1 b2 bn1113858 1113859

(5)




r15] [0 0922 1 0078 0]

RQI 9384 r2 [r21 r22 r23 r24 r25] [1 0411 0 0 0]

RDI 7939 r3 [r31 r32 r33 r34 r35] [0626 1 0374

0 0]

SRI 7388 r4 [r41 r42 r43 r44 r45] [0259 1 0741

0 0]


Rvij1113858 1113859( 1113857

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ijtake4

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


1113944

4


4

c1j1113888 1113889

14

614 1565

1113944

4

j1c2j

12

times 1 times12

times 2 12 w2 1113944

4

c2j1113888 1113889

14

12

1113874 111387514

0841

1113944

4


4

c3j1113888 1113889

14

614 1565

1113944

4

j1c4j

13

times12

times13

times 1 118

w4 11139444

c4j1113888 1113889

14

118

1113874 111387514

0845

(8)


(1565 0841 1565 0485)T

w1 wi

11139364j1wj

i 1 2 3 4 j 1 2 3 4 11139444

j1wj 4456

(9)


n 1 2 3 4 5 6RI 0 0 059 09 112 124




So

w1 15654456

0351

w2 08414456

0189

w3 15654456

0351

w4 04854456

0109

CW

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

0351

0189

0351

0109

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

λmax 1113944n

i1

(c middot w)i

n middot wi

1407

4 times 0351+

07584 times 0189

+1407

4 times 0351

+0437

4 times 0109 401

(10)



D w middot R [0351 0351 0189 0109]

middot

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(11)




5 Conclusions








Data Availability




Acknowledgments


References






























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)


CI λmax minus n

nminus 1 (3)



CR CIRI

(4)






⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

b1 b2 bn1113858 1113859

(5)




r15] [0 0922 1 0078 0]

RQI 9384 r2 [r21 r22 r23 r24 r25] [1 0411 0 0 0]

RDI 7939 r3 [r31 r32 r33 r34 r35] [0626 1 0374

0 0]

SRI 7388 r4 [r41 r42 r43 r44 r45] [0259 1 0741

0 0]


Rvij1113858 1113859( 1113857

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


C cij1113872 1113873





⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

ijtake4

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(7)


1113944

4


4

c1j1113888 1113889

14

614 1565

1113944

4

j1c2j

12

times 1 times12

times 2 12 w2 1113944

4

c2j1113888 1113889

14

12

1113874 111387514

0841

1113944

4


4

c3j1113888 1113889

14

614 1565

1113944

4

j1c4j

13

times12

times13

times 1 118

w4 11139444

c4j1113888 1113889

14

118

1113874 111387514

0845

(8)


(1565 0841 1565 0485)T

w1 wi

11139364j1wj

i 1 2 3 4 j 1 2 3 4 11139444

j1wj 4456

(9)


n 1 2 3 4 5 6RI 0 0 059 09 112 124




So

w1 15654456

0351

w2 08414456

0189

w3 15654456

0351

w4 04854456

0109

CW

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

0351

0189

0351

0109

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

λmax 1113944n

i1

(c middot w)i

n middot wi

1407

4 times 0351+

07584 times 0189

+1407

4 times 0351

+0437

4 times 0109 401

(10)



D w middot R [0351 0351 0189 0109]

middot

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(11)




5 Conclusions








Data Availability




Acknowledgments


References






























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




So

w1 15654456

0351

w2 08414456

0189

w3 15654456

0351

w4 04854456

0109

CW

1 2 1 3

12 1 12 2

1 2 1 3

13 12 13 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

0351

0189

0351

0109

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

λmax 1113944n

i1

(c middot w)i

n middot wi

1407

4 times 0351+

07584 times 0189

+1407

4 times 0351

+0437

4 times 0109 401

(10)



D w middot R [0351 0351 0189 0109]

middot

0 0922 1 0078 0

1 0411 0 0 0

0626 1 0374 0 0

0259 1 0741 0 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(11)




5 Conclusions








Data Availability




Acknowledgments


References






























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Data Availability




Acknowledgments


References






























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




highwayperformanceevaluationindexinsemiaridclimate ... · ation index pqi h20-2007 is composed of...

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