md M

Design for durability of reinforced concrete elements in corrosive environment. Time-dependent correlation between rebar co Prediction of reduction of ultimate exural an Double development length needed for durab

s by ab

bility design procedure is illustrated with the help of a detailed design exam-

and introduce resistance or capacity reduction factors to accountfor the variation of material properties, member geometry anddetails, lack of quality control in design and construction practices,and load factors to consider the variations in applied loads.However, any decrease in resistance or stiffness of the membersdue to deterioration over the service life, because of aggressiveenvironmental inuences or other reasons, is not considered

vironmenttices and m

als contributed to the premature deterioration of the[4,18]. It follows from this and many other examples of unsatory structures around the world that to obtain satisfactorymance, the structure must be designed explicitly to ensure itssafety and serviceability over the entire service life. This wouldrequire adequate quality control during the design and construc-tion phases, along with regular maintenance throughout the sys-tem service life [19,20,28].

Corrosion of steel reinforcement due to chlorides has beennoted to be the most signicant threat to the existing reinforced

Corresponding author. Tel.: +1 514 398 6862.E-mail address: muhammad.ali2@mcgill.ca (M.S. Ali).

Construction and Building Materials 93 (2015) 317325

Contents lists availab

B

evvice life. Most national building codes require fulllment of therequirements of the ultimate and the serviceability limit states,

bridge showed that the inuence of the service enditions, poor quality control in construction prachttp://dx.doi.org/10.1016/j.conbuildmat.2015.05.0110950-0618/ 2015 Elsevier Ltd. All rights reserved.al con-ateri-bridgetisfac-perfor-ple. Analysis results show that because of corrosion the exural and shear strengths decrease by about80% and 52%, respectively, after the service life of 70 years.

2015 Elsevier Ltd. All rights reserved.

1. Introduction

Over the past few decades, many concrete structures, subjectedto aggressive environments, have performed unsatisfactorily, andhad to be decommissioned well before the end of their design ser-

[3,11,15]. A typical example was the Dickson Bridge in Montreal,which was constructed in 1959 and it was decommissioned in1994. The anticipated design service life of the bridge was about75 years, however, the bridge had to be decommissioned after aservice life of only 34 years. A detailed 3 year eld study on theService lifeMass loss

the service life of 70 yearsdesign. The proposed dura Decrease in exural and shear strength

a r t i c l e i n f o

Article history:Received 28 November 2014Received in revised form 16 March 2015Accepted 1 May 2015

Keywords:DurabilityCorrosionReinforced concreterrosion and its bond strength degradation.d shear strengths due to corrosion.ility design at the end of 70 year service life.out 80% and 52%, respectively.

a b s t r a c t

This paper presents a practice-oriented method for design of exural concrete members for a given ser-vice life in an aggressive environment. A time-dependent correlation between rebar corrosion level interms of mass loss and its bond strength degradation at the steelconcrete interface, and the ultimateexural and shear resistances of the reinforced concrete elements is evaluated using basic electrochem-istry and empirical relationships. The design development length is determined based on the mass lossprediction and the equation depicting loss of bond strength with mass loss due to corrosion. The resultsshow that the mass loss of rebars depends on several factors, such as the surface chloride concentration,cover thickness to rebar and concrete permeability, rebar size and ratio of the concrete cover thickness tothe rebar diameter (c/db ratio). The model results predict the required development length at the end of

to be more than twice that obtained from conventional reinforced concreteh i g h l i g h t sDurable design of reinforced concrete ele

M. Shafqat Ali , Chenhui Ji, M. Saeed MirzaMacdonald Engineering Building, Room 492, Department of Civil Engineering and Applie

Construction and

journal homepage: www.elsents against corrosion

echanics, McGill University, 817 Sherbrooke Street West, Montreal H3A0C3, Canada

le at ScienceDirect

uilding Materials

ier .com/locate /conbui ldmat

supply of oxygen and moisture is available to initiate and sustaincorrosion of steel bars. Sarja and Vesikari [31] reported atwo-step process of depassivation, followed by active corrosion(Fig. 1): the initiation stage and the propagation stage [35].During the initiation stage, steel gets depassivated; the chlorideions react with the iron in the passive layer on the steel bar andform soluble chlorides of iron which get diffused through thecover, leaving the bare steel surface exposed to moisture and oxy-gen, leading to the formation of rust. Corrosion reactions continueduring the propagation stage and the corrosion rate is controlledby the availability of oxygen (O2) and moisture, and the controllingenvironmental parameters: temperature (T) and relative humidity(RH).

uilding Materials 93 (2015) 317325concrete structures, such as bridges and marine facilities exposedto chloride-rich environments. The reinforcing steel in a concretebeam can corrode to different deterioration levels, dened by itsmass loss. A correlation can be developed between the level of cor-rosion, cracking, bond strength at the steelconcrete interface, andstiffness and strength of the structural element [8,12,13,17,21,22,29,30,32,36]. A prediction model for rebar mass loss for differentlevels of chloride ingress is developed based on corrosion electro-chemistry initially proposed by Niu et al. [24,25]; this informationis used to calculate the required rebar development length basedon the prevailing concepts of bond and to calculate the exuraland shear capacities at a given service life. A framework is pre-sented for the design of reinforced concrete exural members fordurability against corrosion of reinforcing steel.

2. Steel bar mass loss chloride-induced corrosion

The reinforcing steel bar mass loss is dened as the loss of themetal relative to the original mass of the reinforcement. Thisresearch program aims to establish a prediction model for the levelof corrosion of the steel rebars in the concrete due to chloride ioningress into the concrete.

2.1. Chloride ingress and reinforcing steel corrosion

Chloride ions from seawater, or deicing salt can penetratethrough the pores in the hydrated cement paste (hcp) to the inte-rior of the concrete. The main factors inuencing the chlorideingress into the concrete are the surface chloride concentration,environmental conditions, such as humidity and temperature, con-crete permeation properties and chloride binding capacity of thepore walls, and the chemical reactions [2,6,23,28]. It is generallyagreed that chloride ions are transported totally, or partly inwater-lled pores by diffusion and/or by capillary absorptionmechanisms, depending on the prevailing exposure conditions.The CEB [7] reported that limestone has chemical and physicalbinding capacity for chloride ions, depending on the chloride con-centration of the pore water. The chloride ions in the concrete canexist either in the free or bound form. There also exists a dissolu-tion equilibrium between bound and free chloride ions in the porewater, and only the free chloride ions can participate in promotingcorrosion of the steel rebars. The complex interaction of physicsand chemistry of concrete, and the environmental conditions makethe entire transport process extremely complex, which cannot bemodeled accurately by a representative analytical model. Fickssecond law of diffusion is often used for the prediction of ionic dif-fusion through a porous medium and it has yielded acceptableresults; it assumes that the ingress of the chloride ions into theconcrete relies mainly on diffusion characteristics of the concrete,and the chloride concentration at the concrete surface, but it ismodied to account for the chloride binding capacity at the poresurface. The fundamental process of diffusion is represented bythe equation:

Cx:t CC0 CS CC0 1 erf x=2DCt

p

h i1

where Cx,t is the concentration of chlorides at a distance x from thesurface at time t, CCo is initial concentration of chlorides within theconcrete, Cs is concentration of chlorides at the concrete surface, erfis the error function and Dc is the apparent coefcient of diffusion ofconcrete for chlorides.

Although the high alkalinity (pH > 13) of the concrete cover pro-vides a protective chemical barrier, against corrosion of steel rein-

318 M.S. Ali et al. / Construction and Bforcement, the presence of chloride ions in concrete in excess ofthe threshold level can cause depassivation of the layer of protec-tive oxides and hydroxides of iron layer, provided that an adequate2.1.1. Basic assumptionsThe following assumption were made to model the corrosion

process:

1. The reinforcing steel corrosion occurs only after depassivationof the rebar surface due to chloride ingress, with the chloridelevel at the rebar surface equalling or exceeding the thresholdlevel.

2. The oxygen diffusion in concrete follows Ficks rst law ofdiffusion.

3. Enough water is present in the hydrated cement paste for cor-rosion of rebars to occur when the environmental relativehumidity exceeds the critical level of humidity for corrosion.It acts as an electrolyte with low resistivity.

3. Prediction of reinforcing steel corrosion in concrete

In chemical corrosion, a continuous oxide lm is formed on thesurface of the metal. Diffusion of oxygen through a lm duringmetal oxidation occurs according to Ficks rst law. As the lmthickness increases, diffusion rate decreases with time.

Assuming for simplicity that oxygen diffusion in concreteoccurs at a constant rate following Ficks rst law, the concentra-tion gradient of oxygen in the lm (Fig. 2) is given by:

dCx=dx C0 COS=d1 2

where C(x) = oxygen concentration in the concrete at a distance xfrom the free surface of the lm in the direction of diffusion(mol/mm3); C0 = oxygen concentration on the external concretesurface, assumed to be 8:93 109mol=mm3; COS oxygen concen-tration on the surface of the concrete at its interface with the rebar(mol/mm3); d1 = chloride ion ingress depth (mm), and x = distanceof the lm from the free surface in the direction of diffusion.Fig. 1. Corrosion model for steel in concrete, consisting of initiation and propaga-tion stages [35].

where dMs is mass of the corrosion products produced during timeinterval ds (g), M is atomic mass of iron (55.8 g/mol) and na is elec-tric charge of the iron ion. Because the corrosion products are a mix-ture of Fe2O3 and Fe3O4; the value of na is dependent on theproportion of the two products. In the absence of appropriate exper-imental data, the two products can be assumed to have the samemol value (na) of 2.8 [15]. Aa is the reinforcement surface areawhere corrosion occurs at time s and ia (s) is the current in the ano-dic process which is equal to the current in the cathodic process [ia(s)] since the corrosion process is controlled by the amount of oxy-gen available at the cathode [15].

The value of Aa for a unit length (1 mm) of the steel bar is givenby (Fig. 3):

Aa 2r arccos r c d1r

db arccos db 2c 2d1db

mm2

9

uilding Materials 93 (2015) 317325 319Assuming a continuous oxide lm of thickness, d1, on the sur-face of reinforcement being corroded, the quantity of oxygen dif-fusing in the concrete, dn (in mols) is:

dn D0 A dCxdx dt

where D0 is diffusion coefcient of concrete for oxygen (mm2/year),A is surface area of the oxide lm on the steel rebar surface, throughwhich oxygen diffusion occurs (mm2), dCx=dx is concentrationgradient in mol/mm3/mm, and dt is diffusion period in years.

Niu et al. [26] developed the following empirical relationshipbetween the diffusion coefcient of oxygen into the concrete andits compressive strength:

D0 0:0132:15=f cu 0:44mm2=sec 3where f cu is the specied compressive strength of concrete obtainedfrom 150 150 150 mm cubes at an age of 28 days, wheref 0c 0:79f cu [33], and f 0c the specied compressive strengthobtained from 150 mm diameter by 300 mm high cylinders at anage of 28 days.

Then, the rate of oxygen diffusion per unit area, Jcs; at time, s,is:

Jcs dn

A dt D0dCxdx

D0 C0 COSd1 4

Assuming that the oxidation reaction commences immediately,instead of accumulating on the surface of reinforcement, Cos = 0, itfollows from Eq. (4) that:

Jcs D0C0=d1 5

x

Fig. 2. Diffusion of oxygen through a lm during metal oxidation [34].

M.S. Ali et al. / Construction and BThe cathodic current of the reinforcement corrosion cell is alinear function of the quantity of oxygen diffusing to the electrode,giving:

ics Jcs n0 F 6where ics is the current density at the cathode at time s in

Cmm2 year

, Jcs = the rate of oxygen diffusion per unit

cross-sectional area at time s molmm2 year

, n0 = the number of electrons

assimilated at the cathode by one molecule of oxygen = 4,

F = Faradays constant 9:6486 104C:mol1Substituting from Eq. (5) into Eq. (6) gives:

ics n0FD0C0=d1 7Therefore, according to Faradays Law, the mass of the corrosionproducts produced between time s and (s ds) is:

dMs iasnaF MAads icsnaF

MAads 8where d1, r, c and db are chloride ion ingress depth (mm), rebarradius (mm), concrete cover thickness (mm) and rebar diameter(mm), respectively.

3.1. Mass loss

When t < t0, the initiation time for corrosion according to FicksSecond Law of Diffusion is given by the equation [31]:

Cth Cs 1 erf c= 2Dct012

h i10

where t0, Cth, Cs, and Dc are the time to initiation of corrosion(years), critical chloride threshold level (%), chloride concentrationat the concrete surface (%) and chloride diffusion coefcient of theconcrete (m2/s), respectively, and erf x = error function = 2pp R x0 e

t2dt.From Eq. (10), the time t0 to initiation of corrosion is:

t0 c2=4Dcerf11 Cth=Cs2 11When t < t0, the percentage of mass loss due to reinforcement

corrosion:

q 0 12For t0 6 t < t1;

t1 c db2=4Dcerf11 Cth=Cs2 13where t1 time when all of the reinforcement surface is corroded.

d =

2r

C d

uncorroded reinforcement

corroded reinforcementchl

orid

e in

gres

s de

pth

cove

r thi

ckne

ssin

forc

emen

t dia

met

er

cl - concrete

-

Cs

bre

Fig. 3. Area of steel bar exposed to corrosion.

D0 are diffusion coefcients at time t and t0, respectively.

3.2.3. Corrosion threshold levelThe chloride threshold value, Cth, is the free chloride content

reaching the rebar surface that will cause depassivation of the pro-tective layer on the steel surface. Also, when the chloride contentexceeds the threshold value, corrosion will normally initiate. Fordesign purposes, the threshold value should be selected in therange appropriate for the associated risk of corrosion. Many stan-dards require threshold value not higher than 0.4% (Cl) by themass of cement for reinforced concrete and 0.2% for prestressed

uildiAlso, the chloride ingress depth at time, s; is given by:

d1 2Dcs0:5erf11 Cth=Cs 14From Eqs. (7) and (8), the mass loss, dMs; for a unit length of the

steel rebar, is given by

dMs icsnaF MAadsn0FD0C0=d1

naFM db cos1 db 2c2d1db

ds1

n0D0C02naDcs0:5erf11 CthCS

M

db cos1db 2c4Dcs0:5erf11 CthCS

db

!ds1 15

For one mm length of the uncorroded rebar, with a density of7.8 103 g/mm3, the mass M0 is given by:

M0 0:25pd2b 7:8 103 1 16The mass of the rebar corrosion products, Mt ; is given by:

Mt aPRHZ tt0

dMs 17

where a is correction coefcient for the mass of the rebar corrosionproducts due to the oxygen solubility. Assuming that only oxygendissolved in water can take part in the corrosion reaction, thena 0:028 (oxygen solubility in the water) can be used as the correc-tion coefcient and PRH correction coefcient for the mass of therebar corrosion products due to the relative humidity [24,25].Assuming that the steel reinforcement will corrode only when theenvironmental relative humidity exceeds the critical relativehumidity for rebar corrosion, one obtains from Eqs. (14)(16):

dMs n0D0C02naDcs0:5erf1 1 CthCS

M db

arccosdb 2c 4Dcs0:5erf1 1 CthCS

db

ds 1 18

Therefore, the percentage mass loss, q; at time t (t0 6 t < t1) isgiven by:

q MtM0

100% aPRHR tt0 dWs

14pD

21 7:8 103

100% 19

When t P t1;Aa pdb and d1 c db:

Mt aPRHZ t1t0

dMs Z tt1dM0s

20

Here,

dM0s icsnaF

MAads n0FD0C0=d1naF MAads n0D0C0dbpnac db Mds 1

21Therefore, the percentage mass loss for t P t1; is given by:

q MtM0

100% aPRH

R tt0 dMs

R tt1 dM

0s

14pD

21 7:8 103

100% 22

Eq. (22) can be used to calculate the total percentage mass lossof rebars embedded in concrete from the corrosion initiation timeto any stage of service life.

3.2. Input parameters

320 M.S. Ali et al. / Construction and B3.2.1. Notional surface chloride levelDiffusion of chlorides occurs because of the difference in the

chloride concentration between the outer concrete surface, andthat within the hydrated cement paste (hcp) pores. The surfacechloride level, Cs, depends not only on the environmental condi-tions, but also on the ability of the hydration products in the con-crete with different compositions to adsorb chlorides on the porewalls. The value of Cs is not always constant; however, over a longtime, the chloride source stabilizes to a near constant value in thetidal zone, splash zone, underwater zone, bridge decks, tunnelwalls, etc. Therefore, it is reasonable to assume that the surfacechloride concentration remains constant over time for such struc-tures. The surface chloride level Cs for marine structures, tunnelsand bridges decks can be assumed as shown in Table 1 [28].

3.2.2. Apparent diffusion coefcientThe value of the apparent diffusion coefcient depends on the

concrete composition, structure and distribution of pores in hcp,degree of hydration and other environmental factors such as tem-perature [14,15]. Most published values of the apparent diffusioncoefcient are of the order of 1012 m2/s for Portland cement con-crete [28], and 1013 m2/s for concrete mixtures with y ash andground granulated blast furnace slag. Siemes et al. [32]used a dif-fusion coefcient value of 1.5 1012 m2/s for dense Portlandcement concrete, 0.75 1012 m2/s for a concrete with high blastfurnace slag content cement and 0.3 1012 m2/s for a high qualityy ash cement concrete. Amleh [5] reported diffusion coefcientvalues ranging from 0.934 to 8.65 1012 m2/s (coefcient of vari-ation = 86%) in the severely deteriorated 34 year old DicksonBridge in Montreal; the high diffusion coefcient value was dueto the severity of the environment and physical exposure, andinadequate concrete strength and cover thickness because of thepoor quality of workmanship. The value of the concrete diffusioncoefcient decreases with time, and when hydration is completedafter a certain period, the value of the diffusion coefcient becomesnearly constant. Maage et al. [16] reported that the decrease in thediffusion coefcient is given by:

Dt=D0 t0=ta 23where the parameter a is determined by a regression analysis oftest results, which is summation of the parameters b and c, repre-senting the effect of continuing hydration, and the pore blockingeffect at the surface layer of magnesium and potassium ionexchange between sea water and concrete, respectively. D(t) and

Table 1Surface chloride levels.

Location Cs (by percentage of themass of cement)

Tidal and splash zone 56%Spray zone and marine atmospheric zone 35%Tunnel exposed to saline groundwater 34%Bridge deck (subjected to de-icing salt at an

average annual dosage rate of 250 g/m2)24%

ng Materials 93 (2015) 317325concrete [28].From Eq. (11), the reinforcement corrosion initiation time, t0; is

given by:

t0 c2=4Dcerf11 Cth=Cs2 24

The time, t1; for corrosion of the entire rebar surface is given by:

t1 c db2=4Dcerf11 Cth=Cs2 25

and the depth of the chloride ingress at time, s; is given by:

d1 2Dcs0:5erf11 Cth=Cs 26Typical results for corrosion initiation time t0 and propagation

time t1 for a 20 M bar (bar diameter = 19.5 mm) for a service life of100 years, concrete cover thicknesses varying from 25 mm to75 mm and Cs = 1 to 6%, are calculated and are summarized inFigs. 4 and 5, respectively. The time t1 for corrosion of the entirerebar surface can be calculated using Eq. (25), assuming

signicantly with any further increase in the surface chloridelevels. Therefore, surface chloride level of 2% is an important indexof potential damage due to chlorides in design for durability; how-ever, at chloride level higher than 2%, the rebar corrosion is quitesevere.

3.4. Variability of reinforcement corrosion mass loss with concretecover thickness

0

20

25 30 35 40 45 50 55 60 65 70Cover thickness (mm)

Fig. 5. Corrosion propagation time (t1) for 20 M bars.

460 mm

300 mm

15M@200

4-20M

40 mm

15M Stirruph/2

135 Standard stirrup hook c = 40mm

Vs= Vs1 + Vs2

Vs

(b)(a)

Fig. 6. Beam cross-section: (a) Reinforcement detail (b) free body diagram for shearanalysis.

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

Mas

s Los

s(%

)

Time(year)

Cs=0.6%Cs=0.7%Cs=0.8%Cs=0.9%Cs=1%Cs=2%Cs=3%Cs=4%Cs=5%Cs=6%

Fig. 7. Mass loss of 20 M rebar due to chloride-induced corrosion over 100 yearsservice life for different surface chloride concentrations (Cs).

M.S. Ali et al. / Construction and BuildiDc = 3.0 1013 m2/s for calculation purposes. If the concrete coveris assumed to be 40 mm for exposure classes (C-1, C-2) in the CSAStandard A23.304, the corrosion initiation time t0 would be lessthan 10 years for surface chloride concentrations varying from 2 to6% and propagation time t1 would be less than 20 years. As aresult of these conditions, the entire 20 M rebar surface would startcorroding within 30 years of its service life.

3.3. Rebar mass variation loss with concrete surface chloride density

To understand the effect of chloride concentration, concretecover thickness and rebar size on its mass loss during the servicelife of a reinforced concrete element, a beam cross-section wasselected as shown in Fig. 6. For illustration purposes, this beam isassumed to be designed for a service life of 100 years, reinforcedwith 420 M bars, clear cover thickness = 40 mm; the concretecompressive strength, fc = 30 MPa; steel yield strengthfy = 400 MPa. The beam is subjected to different surface chloridelevels varying from 0.6 to 6%, the corrosion threshold level isassumed to be 0.4% (Cl) by mass of cement. AssumeDc = 1.5 1012 m2/s.

The rebar mass loss due to chloride-induced corrosion can becalculated using Eqs. (12), (19) and (22). Typical results for themass loss of a 20 M bar (bar diameter = 19.5 mm) for a service lifeof 100 years are summarized in Fig. 7. The results show that, asexpected, the mass loss increases with time. Also, the mass lossincreases with an increase in the surface chloride level, with theother parameter remaining constant. The results show that therebar mass loss could be as high as 10% within 50 years of its ser-vice life when the chloride concentration level is about 4%.

Fig. 7 also shows that when the chloride concentration on theconcrete surface is over 2% (the surface chloride level on the bridgedecks when subjected to de-icing salt at an annual dosage rate ofover 250 g/m2), the increase in the rebar mass loss decreases

0

10

20

30

40

50

60

70

80

90

25 30 35 40 45 50 55 60 65 70

Tim

e (y

ears

)

Cs=1%Cs=2%Cs=3%Cs=4%Cs=5%Cs=6%Cover Thickness (mm)

Fig. 4. Corrosion initiation time (t0) for 20 M bars.40

60

80

100

120

140

Tim

e (y

ears

)

Cs=1%Cs=2%Cs=3%Cs=4%Cs=5%Cs=6%

ng Materials 93 (2015) 317325 321The mass loss for 20 M rebar due to corrosion over a service lifeof 100 years, for concrete cover thickness varying from 25 mm to75 mm (Dc 1:5 1012m2=s;Cs 3% and Cth 0:4%) by the

mass of cement) is calculated using Eqs. (12), (19) and (22) and theresults are plotted in Fig. 8.

Fig. 8 shows that, if all other parameters remain constant, anincrease in the cover thickness of an appropriate quality (relativeimpermeability) causes a signicant decrease in the rebar massloss. Therefore, the service life of a structural member can beincreased considerably by appropriately increasing the thicknessof the concrete cover [7], and by enhancing its quality in termsof permeability of concrete. However, an excessive cover thicknesswill increase the risk of its cracking, which can result in an increasein chloride ingress and in an increased rebar mass loss and pittingcorrosion locally in the vicinity of the crack, which can also causeloss of rebar ductility.

If the same beam is to be designed using different bar sizes, the

rebars. The exural bond stress was omitted from the subsequentACI Codes and CSA A23.3 Standards and was replaced with designrequirements for the rebar development length, ld, calculated asld f ydb=4uwhere fy is the yield strength of steel rebars, with diam-eter, db. Initially, the development length, ld, was based on the per-missible bond stress values in the 1963 ACI Code [1]. To preventbrittle failures in bar development lengths and splices, the requireddevelopment lengths were increased by a factor of 1.2. However,these equations did not include parameters, such as the concretecover thickness, clear spacing between bars, and the effect of trans-verse reinforcement, which inuence the development length, orthe bond stress, u, at steel rebar-concrete interface. Orangun et al.[27] analyzed the results of over 500 development and splice testsand developed the following equation in Imperial units:

322 M.S. Ali et al. / Construction and Buildirebar mass loss can be similarly calculated (Fig. 9(a)) for bar sizesranging from 10 to 45 M. It can be noted that the percentage ofrebar mass loss decreases with an increase in the rebar diameter,therefore, it is useful to select a larger bar size for an increased ser-vice life. It should be noted that the rebar mass loss increases witha decrease in the ratio of concrete cover thickness to rebar diame-ter (c/db ratio) (Fig. 9(b)). The increase in the rebar mass loss due tocorrosion will greatly decrease the service life of the structure,therefore, it is useful to select a larger c/db ratio for an increasedservice life.

In summary, the mass loss of the embedded reinforcing bardepends on many factors, such as the chloride density on the con-crete surface, the concrete cover thickness and its permeability, thereinforcing bar size and the ratio of the concrete cover thickness tothe rebar diameter. If the surface chloride level is over 2%, the rebarin the concrete can be subjected to severe corrosion over a periodof 25 years. Increased concrete cover thickness and lower concretepermeability can help to decrease the rebar mass loss.

3.5. Variations for rebar mass loss prediction

To validate the prediction model for rebar mass loss due to cor-rosion, more carefully planned laboratory work is needed alongwith the data from long-term eld tests; coefcient, u, can beintroduced in the equations for evaluation of the rebar mass lossto account for the variation between the eld corrosion behaviorof steel rebars from that in controlled laboratory tests.

u q=q 27where q is the mass loss from in-situ tests and q is the rebar massloss value obtained from controlled laboratory tests under similarconditions.

Substituting Eq. (27) into Eqs. (12), (19) and (22), gives:For t < t0,

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60 70 80 90 100

Mas

s Los

s(%

)

C=25mmC=30mmC=35mmC=40mmC=45mmC=50mmC=55mmC=60mmC=65mmC=70mmC=75mm

Service Life Fig. 8. Variation of mass loss of 20 M steel rebar over a service life of 100 years fordifferent cover thicknesses.q 0For t0 6 t < t1;

q /MtM0

100% aPRH

R tt0dMs

14pd

2b 7:8 103

100% 28a

For t > t1;

q /MtM0

100% aPRH

R tt0dMs

R tt1dM0s

14pd

2b 7:8 103

100% 28b

where

dMs n0D0C02naDcs0:5erf1 1 CthCS

M

D1 arccosdb 2c 4Dcs0:5erf1 1 CthCS

db

ds 1 28c

and

dM0s n0D0C0dbpnac db Mds 1 28d

The ACI Code-1963 and the earlier versions of CSA StandardA23.3 emphasized exural bond, which was dened as the bondstress (u) at the steelconcrete interface resisting the rate ofchange of bending moment over a unit length of a beam which isthe shearing force at the cross-section; this bond stress u wasexpressed as:

u V jdX

0 .

29

where V is the shearing force at the section with an internalmoment resistance arm jd, and

P0 is the perimeter of tension

(a) (b)

0

2

4

6

8

10

10 15 20 25 30 35 40 45

Mas

s Los

s(%

)

Rebar Size (mm)

0

2

4

6

8

10

1.7 2.0 2.3 2.7 3.0 3.3 3.7 4.0 4.3 4.7

Mas

s Los

s(%

)

c/db Ratio

Fig. 9. (a) Relationship between rebar mass loss and rebar size for a service life of100 years (b) relationship between rebar mass loss and ratio of concrete coverthickness and rebar diameter (c/db ratio) at age of 100 years.

ng Materials 93 (2015) 317325uf c

p 1:2 3cdb

50dbls

Atrf ytr500sdb

30

uildiwhere ls is the splice length, Atr is the cross-sectional area of thetransverse reinforcement at spacing, s, on centers, with yieldstrength, fytr, crossing the splitting crack.

The histogram of the ratio of the measured bond stress form the500 tests to the value calculated using Eq. (30), demonstrated anaverage value of around 1.0 with a relatively small coefcient ofvariation.

With no splices or transverse reinforcement in Amlehs tests,Eq. (30) reduces to

u A Bc=dbf 0c

q31

where A and B are constants determined from experimental data.The measured bond stress value was observed to decrease linearlywith the rebar mass loss, which would modify Eq. (31) as:

u A Bc=dbf 0c

q DML 32

For the normal Portland cement concrete mixtures, without anyaddition, the following empirical equations determined [5]:

u 0:35 0:3c=dbf 0c

q 0:42ML for w=c ratio 0:32

33

u 0:35 0:3c=dbf 0c

q 0:34ML for w=c ratio 0:42

34where ML is the percentage of rebar mass loss due to corrosion.

4. Illustrative example

A reinforcement concrete beam is designed for a service life of70 years, using concrete with compressive strength, fc = 30 MPa(w/c ratio = 0.42, chloride diffusion coefcient Dc = 1.5 1012 m2/s) and 420 M steel bars with a yield strengthfy = 400 MPa (Fig. 6). The beam is subjected to a surface chlorideconcentrated of 3% and the corrosion threshold level (Cth) isassumed to be 0.4% by the mass of cement. Assume 15 M stirrupsand a clear cover to the stirrup of 40 mm. Determine the designdevelopment length for the corroded bars at the end of the 70 yearservice life.

From Fig. 7, the rebar mass loss after 70 years, ML = 15%. Here,the cover to the 20 M bar, c = 40 + 16 56 mm. Therefore, by com-bining Eq. (33)with required bond strength relation, the designdevelopment length is:

ld:design 0:462 f y db=0:35 0:3c=db1:425f 0c

q 0:34ML

0:462 400 19:5=0:35 0:356=19:5

1:425 30

p 0:34 15

1277mm 65dbIn a corrosion free environment, this development length would

be 520 mm (= 26.6db) [9].The ultimate moment resistance, Mr; is governed by the yield

force, T, in the tension reinforcement, provided that the bar devel-opment length is adequate.

As the steel bars continue to corrode, at some stage becauseof deterioration at the steel rebar-concrete interface, the devel-opment resistance may not be adequate to cause the steel barsto yield, in which case, the moment resistance will be dependenton the maximum bond resistance generated along the barlength.

M.S. Ali et al. / Construction and BSubstituting Eq. (34) into Eq. (28a-d), the critical rebar mass losswhere the bond resistance governs the moment resistance is givenby:MLcritical 0:35 0:3c=db1:425f 0c

q f ydb=4ld=0:34

0:35 0:356=19:51:425 30

p 4001=

4 26:6=0:34 12%When the mass loss exceeds (ML)critical, the force in the tension

reinforcement depends on the available bond resistance of the cor-roded bars, and for ML > 12%, it is given by:

T 4u pdbld 4 0:35 0:3c=db

1:425f 0c

q 0:34ML pdbld

4 0:35 0:356=19:51:425 30

p 0:34ML p

19:5 520 127:4 7:92 0:34ML kNThe moment resistance, Mr, of the beam with corroded bars is

given by

M T d a=2 0:127 7:92 0:34MLd a=2 kN m 35With a decrease in the value of T due to the rebar mass loss, the

section moment resistance will also decrease almost linearly.However, if additional bar length is available beyond ld, the valueof Mr will be governed by the rebar tensile yield force, until thecritical mass loss is reached for the available development length.The value of Mr will then decrease based on the reducedcross-sectional area. This available rebar length can be representedas ld/db to examine its effect on the value of Mr. The moment resis-tance of the beam cross-section was calculated for four differentdevelopment lengths minimum required development length(ld,min = 26.6db), development length at critical mass loss (65db),1.5 ld,min (=39.9db), 2 ld,min (=53.2db), and 3 ld,min (=80db) anda summary of calculated moment resistances is presented inFig. 10.

Depending on the length of the bar available from the locationof the maximum bending moment to the point of contraexure,the capacity of the beam can be evaluated for different levels ofcorrosion after any period of exposure. A reverse process can beused in design of a beam; for a given length of bar available fordevelopment, and rebar corrosion level over a given period of timein a given environment, the reduced rebar tensile strength and thereduced Mr capacity can be calculated.

The results show that when the corrosion level is smaller thanthe critical corrosion level, the rebars has adequate bond strengthwith the concrete, and the exural strength will decrease slightlyas a result of an increase of corrosion level. When the corrosionlevel exceeds the critical corrosion level in terms of mass loss,which about 12% in this case, the exural strength will decreaseconsiderably because of debonding between the reinforcementand the concrete.

4.1. Inuence of corrosion on shear strength

Corrosion of stirrups is generally more serious than the corro-sion of the longitudinal reinforcement because the stirrups aregenerally smaller in size and closer to the concrete surface thanthe longitudinal reinforcement. Any brittle failure of the corrodedstirrups can be quite dangerous. Therefore, an appropriate modelfor the inuence of stirrup corrosion on shear strength of rein-forced concrete member needs to be developed.

Based on the simplied method for shear strength from the CSAA23.304, the factored shear resistance can be determined using

ng Materials 93 (2015) 317325 323the equation [10]:

Vr Vc VS 36

8ar M

diff

uildi0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 2 4 6

Mom

ent R

esis

tanc

e R

educ

tion

Rat

io

Reb

Fig. 10. Reduction in moment resistance of beam due to corrosion for

1

1.1

o

324 M.S. Ali et al. / Construction and Bwhere Vr, Vc, and Vs are the factored shear resistance provided bythe concrete section, factored shear resistance attributed to the con-crete, and the factored shear resistance provided by the shear rein-forcement, respectively.where

Vc 0:18k/cf 0c

qbwd 37

and

Vs /snV 0s 38where n is the number of stirrups crossing an inclined crack whichis equal to = d.coth/s and Vs0 is tensile force develop in a stirrup,which is a product of cross-sectional area Av and the stress fs inthe stirrup; h is an angle of inclination of diagonal compressivestresses to the longitudinal axis of the member. Here, Av is the areaof shear reinforcement perpendicular to the axis of the memberwithin a distance s, which is spacing of shear reinforcement, mea-sured parallel to the longitudinal axis of the member.

From Eq. (33), mass loss and required bond strength relation,the design development length at yielding of stirrups is 413 mm:

ld:design 0:462 400 16=0:35 0:340=161:425 30

p

0:3415 1413 mmIn a corrosion free environment this development length would

be 420 mm. With a standard 135 hook, the length of the attachedstraight length to cause the hooked stirrup to yield is [9] is292 mm:

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 2 3 4 5 6 7 8

Shea

r Stre

ngth

Red

uctio

n R

ati

Mass

Fig. 11. Variation of shear resistance at different corrosion levels10 12 14 16 18ass Loss (%)

26.6d39.9d53.2d65d80d

erent development lengths (ld = 26.6db, 39.9db, 53.2db, 65db and 80db).

ng Materials 93 (2015) 317325ldh 100db=f 0c

q 100 16=

30

p 292 mm

However, the available length from the end of the hook to thecritical stirrup section (h/2) is 190 mm (Fig. 6(b)). Consequently,the stirrup does not yield. The shear force resisted by a stirrup,Vs, is governed by the tensile force, Vs0, developed in the stirrup,provided that the bar development length is adequate. In this case,the tensile force, Vs0, can be divided into the force resisted due tothe bond strength along the 190 mm length of the stirrup leg(V 0s1) and the force resisted by the anchorage due to the hook(V 0s2). Assuming that the stirrup continues to corrode, at somestage, the resistance developed will continue to decrease. Thechange in the shear resistance attributed to the concrete Vc dueto concrete deterioration is assumed to be relatively small, whichcan be ignored. The shear strength is inuenced only by the corro-sion deterioration of the shear reinforcement, and can be calcu-lated using Eq. (36) and (38).

Substituting Eq. (34) into Eq. (28a-d), the critical stirrup massloss, which was about 10%, where the shear resistance (Vs0) governsthe shear resistance by the anchorage due to hook at the end (V 0s2).With a decrease in the value of Vs0 due to the stirrup mass loss, thesection shear resistance will decrease almost linearly, until thecritical mass loss is reached for the available development length.The value of Vs0 will then become equal to V

0s1, which will then

decrease based on the reduced cross-sectional area. The factored

9 10 11 12 13 14 15 16 17 Loss (%)

for 15 M shear reinforcement during service life of 70 years.

shear resistances at different levels of stirrup mass loss due to cor-rosion are calculated and plotted in Fig. 11, which illustrates a con-siderable degradation of the shear resistance (about 52%) with themass loss of the stirrup reinforcement, which is more serious thanthe degradation of the exural resistance due to corrosion of theexural reinforcement (82%).

5. Summary and conclusions

The time-dependent behavior of the resistance of concrete

crete structures due to the ingress of the various aggressive sub-

[7] CEB Bulletin dinformation No. 182. Durable Concrete Structures, CEB DesignGuide, CEB; 1989.

[8] Choi YS, Yi S-T, Kim MY, Jung WY, Yang EI. Effect of corrosion method of thereinforcing bar on bond characteristics in reinforced concrete specimens.Constr Build Mater 2014;54:1809.

[9] Concrete design handbook. 3rd ed., Ottawa, Canada: Cement Association ofCanada; 2006.

[10] CSA Standard A23.3-04. Design of concrete structures. Mississauga, Ontario,Canada: Canadian Standard Association; 2004.

[11] Fazio R. Flexural behaviour of corroded reinforced concrete beams [M.Eng.thesis], Montreal: Department of Civil Engineering and Applied Mechanics,McGill University; 1996.

[12] Han S-J, Lee DH, Kim KS, Seo S-Y, Moon J, Monteiro PJM. Degradation of

M.S. Ali et al. / Construction and Building Materials 93 (2015) 317325 325stances, especially chlorides, over a long time period are needed.

References

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A model for prediction of exural capacity of reinforced con-crete beam at a given design service life shows that the embed-ment length of the reinforcement can inuence thetime-dependent exural behavior of reinforced concrete beams.When the corrosion level exceeds the critical level, the exuraland shear strength decreases considerably because of the loss ofbond between the reinforcement and the concrete.

6. Future research

More experimental and analytical work is needed to considerthe effect of different parameters, such as reinforcing bar diameter,type of loading, concrete cover thickness, concrete strength andsteel yield strength on the behavior of reinforced concrete beamssubjected to corrosion. Collection of long-term data on corrosionof reinforced concrete beams and study of the deterioration of con-exural strength in reinforced concrete members caused by steel corrosion.Constr Build Mater 2014;54:57283.

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Durable design of reinforced concrete elements against corrosion1 Introduction2 Steel bar mass loss chloride-induced corrosion2.1 Chloride ingress and reinforcing steel corrosion2.1.1 Basic assumptions

3 Prediction of reinforcing steel corrosion in concrete3.1 Mass loss3.2 Input parameters3.2.1 Notional surface chloride level3.2.2 Apparent diffusion coefficient3.2.3 Corrosion threshold level

3.3 Rebar mass variation loss with concrete surface chloride density3.4 Variability of reinforcement corrosion mass loss with concrete cover thickness3.5 Variations for rebar mass loss prediction

4 Illustrative example4.1 Influence of corrosion on shear strength

5 Summary and conclusions6 Future researchReferences