residual strength of corrosion-damaged reinforced concrete beams

8/11/2019 Residual Strength of Corrosion-Damaged Reinforced Concrete Beams

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40 ACI Materials Journal/January-February 2007

ACI MATERIALS JOURNAL TECHNICAL PAPER

ACI Materials Journal, V. 104, No. 1, January-February 2007.MS No. M-2006-003 received January 3, 2006, and reviewed under Institute publication

policies. Copyright 2007, American Concrete Institute. All rights reserved, including themaking of copies unless permission is obtained from the copyright proprietors. Pertinentdiscussion including authors closure, if any, will be published in the November-December2007ACI Materials Journalif the discussion is received by August 1, 2007.

In this work, an effort has been made to first observe the effect ofreinforcement corrosion on flexural behavior of reinforcedconcrete beams and then to develop a model based on the test datato predict their residual flexural strength. Test data were gathered

from the testing of 56 reinforced concrete beam specimens thatwere subjected to a varying degree of accelerated corrosion. It hasbeen observed that the product of corrosion current density andcorrosion period IcorrT is the most significant factor affecting the

flexural strength of a corroded beam. Based on the experimentaldata, a two-step approach is proposed to predict the residual

flexural strength of a corroded beam. First, the flexural strength iscalculated using the reduced area of corroded bars, and then thisvalue is multiplied by a correction factor that is formulated through a

regression analysis of test data to take into account bond, slip, andother applicable factors.

Keywords: deflection; flexural strength; reinforced concrete; reinforcementcorrosion.

INTRODUCTIONCorrosion of reinforcing steel is the single most dominant

causal factor for the premature deterioration of concretestructures. The basic problem associated with the deteriorationof reinforced concrete due to corrosion is not only that thereinforcing steel itself is reduced in mechanical strength, but alsothe products of corrosion exert stresses within the concrete thatcannot be supported by the limited plastic deformation of the

concrete, and the concrete therefore cracks. This leads to aweakening of the bond and anchorage between concrete andreinforcement, which directly affects the serviceability andultimate strength of concrete elements within a structure.1

A considerable amount of research has been devoted tocorrosion of reinforcement in reinforced concrete dealingwith various issues related to corrosion process, its initiation,damaging effects of corrosion, and the prediction of time-to-cover cracking of concrete due to corrosion.2-5These studiesindicate that it is possible to determine the time to corrosioninitiation if necessary data are available. The cover crackingdue to reinforcement corrosion, however, may not be consideredas an indication of the end of service life. The member withcracked cover may continue to be in service provided that theresidual strength of the structure is still sufficient enough toresist the loads within an acceptable margin of safety.

The effect of reinforcement corrosion on bond betweensteel and the concrete has been of great interest and this hasresulted in the proposition of several predictive models forwhich References 6 through 11 can be cited as representativesamples of work. These studies have found that the bondstrength increases with corrosion up to a certain level ofreinforcement corrosion, but with further increase in corrosion,the bond strength progressively declines. Even when there isextensive corrosion with considerable cracking of concrete,however, bond is not completely destroyed. This partially

explains the fact that structures with extensively corroded

reinforcement sometimes sustain considerable loads.11

Of the limited research that has been carried out in the area

of assessment of the flexural strength of corrosion damaged

reinforced concrete members, mention can be made of the

works of Tachibana et al.,12Rodriguez et al.,13Huang andYang,14 Mangat and Elgarf,15 Yoon et al.,16 and Jin and

Zhao.17Huang and Yang14studied the effect of the loss ofreinforcing steel area on the flexural behavior of reinforced

concrete beams. Tachibana et al.12and Yoon et al.16examined

the effect of reinforcement corrosion on the residual load

capacity of the concrete beams relating the residual flexuralcapacity with the percentage weight loss of reinforcing steel.

Rodriguez et al.13studied the effect of reinforcement corrosion

on the bending moment and the shear force of a reinforcedconcrete beam. Mangat and Elgarf15developed a relationship

between the degree of reinforcement corrosion and the

residual strength of flexural members. Jin and Zhao17

investigated the effect of reinforcement corrosion on the

bending strength of reinforced concrete beams. A structural

deterioration model in an exponential form has beenpresented by Li18as part of life-cycle modelling of corrosion-

affected members. Structural behavior of corroded flexural

members has been presented in Reference 19, which also

proposes a deterioration factor.

In this study, an attempt has been made to predict theresidual flexural strength of a corroded beam through the use

of conventional flexural formula by taking into account theloss of metal due to corrosion and an applicable correction

factor to account for the loss of bond. The correction factor

is a function of corrosion current density, corrosion time, and

the reinforcing bar diameter. The proposed strength predictionmodel is a two-step, easy-to-apply procedure that appears to

yield satisfactory results, as evidenced from the degree ofcorrelation with the experimental data.

RESEARCH SIGNIFICANCEThis study aims to make a contribution in the area of

prediction of the residual flexural strength of corrodedreinforced concrete beam type members by suggesting apredictive model that has been developed through an

extended experimental work on beams that were subjected todifferent degrees of corrosion damage. The proposed

strength prediction model can be used either to find the

residual flexural capacity of a beam that has suffered corrosion

Title no. 104-M05

Residual Strength of Corrosion-Damaged Reinforced

Concrete Beams

by Abul K. Azad, Shamsad Ahmad, and Syed A. Azher


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41ACI Materials Journal/January-February 2007

damage or to predetermine the maximum level of corrosionthat can be tolerated for a specified service life.

EXPERIMENTAL INVESTIGATIONThe design variables used in this experimental program

were two different bar diameters, 10 and 12 mm (3/8 and1/2 in.); two different clear covers to the tension reinforcement,25 and 40 mm (1 and 1.5 in.); two different levels ofimpressed corrosion current intensities, 2 and 3 mA/cm2;

and three different corrosion durations, 4, 6, and 8 days. Atotal of 56 reinforced concrete beam specimens were cast toinclude all variables. All tests were repeated twice, includingthose on the control specimens.

Specimen details and material strengthsRectangular reinforced concrete beam specimens 150 x

150 x 1100 mm (6 x 6 x 43 in.) were used for this study. Allthe beams were designed to fail in flexure by providingample vertical shear reinforcement to exclude prematureshear failure. The beam details are shown in Fig. 1. Thevertical stirrups were double-legged 6 mm (0.25 in.) diameterbars spaced uniformly at 90 mm (3.5 in.) centers throughoutthe length of each beam. Deformed bars were used for all

reinforcements. Two top 8 mm (0.31 in.) diameter bars witha clear cover of 36 mm (1.42 in.) were used to serve asstirrup-holders and were epoxy-coated to avoid corrosion.The stirrups were left uncoated so as to represent the practicalcase in which stirrups are also subjected to corrosion.

All specimens were cast using concrete with a cementcontent of 350 kg/m3(590 lb/yd3) (ASTM Type I portlandcement), coarse-fine aggregate ratio of 1.65 and effectivewater-cement ratio (w/c) of 0.45. Two percent sodium chloride(NaCl) by weight of cement was added to the mixture topromote corrosion. Specimens were moist cured for 7 daysfollowed by air curing at room temperature. The casting of56 beams was carried out in 10 batches. For each batch ofconcrete mixture, three 75 x 150 mm (3 x 6 in.) cylinderswere also cast to determine the compressive strength of theparticular batch of concrete mixture.

The beam specimens were divided into four groups, BT1to BT4, based on the clear cover to the tension reinforcementand the reinforcing bar diameter. The beams that were notsubjected to accelerated corrosion, referred to as the controlbeams, were designated as BT1-C (bar diameterD= 10 mm[3/8 in.] and clear cover Cv= 25 mm [1 in.]), BT2-C (D=12 mm [1/2 in.] and Cv= 25 mm [1 in.]), BT3-C (D= 10 mm[3/8 in.] and Cv= 40 mm [1.5 in.]), and BT4-C (D= 12 mm[1/2 in.] and Cv= 40 mm [1.5 in.]). The beams subjected toaccelerated corrosion were designated to indicate the intensity

and duration of the applied corrosion current. For example,Beam BT1-2-4 implies a beam in Group BT1 that wassubjected to applied current intensity of 2 mA/cm2 for aperiod of 4 days.

The 28-day compressive strength of concrete fc for eachmixture was determined as the average strength of three 75 x150 mm (3 x 6 in.) cylinders cast from each batch mixture. Itis observed thatfc values varied from batch to batch, despitethe use of same mixture proportions, same materials, andsimilar casting procedure. The measured values, taken as the

average of three cylinder strengths, varied from a minimumof 33.4 MPa (4840 psi) to a maximum of 46.5 MPa (6740 psi)with a standard deviation of 4.95. The yield and ultimatetensile strength of tension bars used were as follows: for10 mm (3/8 in.) diameter bars, yield strength and ultimatestrength were 520 and 551 MPa (75.4 and 80 ksi), respectively,and for 12 mm (1/2 in.) diameter bars those values were 590and 700 MPa (85.6 and 101.5 ksi), respectively.

Test setup for accelerated corrosion inductionand testing of beams

After completion of curing, the specimens were subjectedto accelerated corrosion by applying anodic current of specifiedintensity and time. This was achieved through a small DC

power supply with a built-in ammeter to monitor the current.The concrete specimens were partially immersed in 5%sodium chloride solution in a tank. The direction of thecurrent was adjusted so that the reinforcing steel became theanode and a stainless steel plate placed on the concretespecimen served as the cathode. The stainless steel plate wasplaced in the tank covering both sides of its specimenthroughout the length. This arrangement ensured a uniformdistribution of the corrosion current along the whole lengthof the longitudinal bars. A schematic representation of thetest setup is shown in Fig. 2. The total current required foreach type of beam specimen was calculated based on their

Abul K. Azadis a Professor in the Department of Civil Engineering at King Fahd

University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia. He received

his DEng from Concordia University, Montreal, Quebec, Canada. His research

interests include concrete durability, structural optimization, and damage assessment.

Shamsad Ahmadis an Assistant Professor in the Department of Civil Engineering at

KFUPM. He received his PhD from the Indian Institute of Technology (IIT), Delhi,

India . His research interests include durability of concrete material s and structures,

mainly corrosion of reinforcement in concrete; diagnosis; service life prediction;

and preventive measures.

Syed A. Azheris a Graduate Student (Research Assistant) in the Department of CivilEngineering at KFUPM. He received his bachelor degree in civil engineering from

Osmania University, Hyderabad, India. His research interests include durability ofconcrete materials and structural components with specific interest in corrosion of

reinforcement in concrete, structural repair and rehabilitation of existing structures,

and retrofitting using CFRP.

Fig. 1Details of test specimens and loading.

Fig. 2Schematic presentation of accelerated corrosiontest setup.


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respective steel surface area. The current supplied to eachconcrete specimen was checked on a regular basis and anydrift was corrected.

All the beam specimens were tested in a four-point bendtest under a universal testing machine, using the setup shownin Fig. 1. The load and midspan deflection data for eachspecimen were recorded using a computerized data acquisitionsystem at predetermined load intervals till failure.

Gravimetric weight loss

Following the flexure test on corroded beams, each beamwas broken to remove the two corroded tension bars formeasurement of the average weight loss of steel due toinduced corrosion. The bars were cleaned to remove all rustproducts using Clarke solution and then they were weighedto find the net weight of steel. Preparation, cleaning, andevaluation of corrosion test specimens were carried out inaccordance with ASTM G 1.20Samples of corroded reinforcingbars after gravimetric test showed general corrosion alongthe length but reaffirmed the general perception that rein-forcement corrosion in concrete, in general, is non-uniformalong the length of the bar, as the loss of reinforcing bar atsome sections was seen to be considerably higher than that atthe other sections due to pitting corrosion.

RESULTS AND DISCUSSIONWeight loss of bars and corrosion current density

The measured weight loss of bars was used to calculate theinstantaneous corrosion rateJras follows

(1)Jrweight loss

surface area of bar corrosion period-------------------------------------------------------------------------------------------=

From the calculated values of Jr, the corrosion currentdensityIcorrwas determined from the following expression

21

(2)

where Wequals the equivalent weight of steel and Fequalsthe Faradays constant.

With W= 27.925 g (0.062 lb) and F= 96,487 Coulombs

(A-sec) in Eq. (2), the following simplified equation forcalculatingIcorrfrom the value ofJris obtained as

Icorr= 0.1096Jr (3)

whereIcorris in mA/cm2andJris in gm/cm

2/year.

From Eq. (1) and (2), the weight loss of a bar can beexpressed as

(4)

= 0.289IcorrT

whereIcorris in mA/cm2and Tis in seconds.

The calculated values of Icorr from Eq. (3) are showncollectively for all corroded beams in Table 1. It is observedthat theIcorrvalues established from gravimetric analysis arelower than the applied corrosion current density Iapp. Thedifference between Icorr and Iapp is attributed to several

JrW

F-----

Icorr=

weight loss surface area of bar WF-----

IcorrT=

Table 1Gravimetric test results and conversion of weight loss into Icorr

BeamD,

mm (in.)

Iapp,

mA/cm2 T, days,

% weight loss

Jr,

g/cm2/year

Icorr,

mA/cm2IcorrT,

mA-days/cm2

BT1-2-4 10 (0.39) 2 4 5.40 9.37 1.03 4.12BT1-3-4 10 (0.39) 3 4 14.20 24.83 2.72 10.88

BT1-2-6 10 (0.39) 2 6 15.20 17.96 1.97 11.82

BT1-3-6 10 (0.39) 3 6 21.40 25.00 2.74 16.44

BT1-2-8 10 (0.39) 2 8 21.50 19.94 2.18 17.44

BT1-3-8 10 (0.39) 3 8 31.00 27.33 2.99 23.92

BT2-2-4 12 (0.47) 2 4 5.50 11.40 1.25 5.00

BT2-3-4 12 (0.47) 3 4 8.80 17.92 1.96 7.84

BT2-2-6 12 (0.47) 2 6 20.10 27.35 2.99 17.94

BT2-3-6 12 (0.47) 3 6 14.00 19.07 2.09 12.54

BT2-2-8 12 (0.47) 2 8 22.90 23.53 2.58 20.64

BT2-3-8 12 (0.47) 3 8 25.50 23.88 2.62 20.96

BT3-2-4 10 (0.39) 2 4 8.00 13.88 1.52 6.08

BT3-3-4 10 (0.39) 3 4 9.10 15.75 1.73 6.92

BT3-2-6 10 (0.39) 2 6 10.10 11.72 1.28 7.68

BT3-3-6 10 (0.39) 3 6 17.60 20.18 2.21 13.26

BT3-2-8 10 (0.39) 2 8 21.40 18.41 2.02 16.16

BT3-3-8 10 (0.39) 3 8 34.80 28.54 3.13 25.04

BT4-2-4 12 (0.47) 2 4 7.90 15.81 1.74 6.96

BT4-3-4 12 (0.47) 3 4 10.90 22.69 2.49 9.96

BT4-2-6 12 (0.47) 2 6 13.40 18.52 2.03 12.18

BT4-3-6 12 (0.47) 3 6 18.60 25.60 2.80 16.80

BT4-2-8 12 (0.47) 2 8 18.00 19.01 2.08 16.64

BT4-3-8 12 (0.47) 3 8 20.70 21.60 2.37 18.96


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ACI Materials Journal/January-February 2007 43

factors among which mention can be made of the concretecover around the bars, quality of concrete, nonuniformcorrosion rate along the length of the bars, and the diameterof bars. It is interesting to note that for beams with 10 mm(3/8 in.) diameter bars (BT1 and BT3 series), the apparentdiscrepancy betweenIcorrandIappis significantly less thanthat observed for beams with 12 mm (1/2 in.) diameter bars(Beam BT2 and BT4 series). Similar observations have alsobeen reported by others.22-23

Load-deflection plots and modeof failure of beamsThe midpoint deflections of all beams tested were

recorded in a data logger. A typical plot of load versusdeflection shown in Fig. 3 portrays the expected resultsthat the corroded beams had higher deflection than thecorresponding control beams at same load level due todegrading stiffness of the beams. For example, at a load ofapproximately 42 kN (9.44 kip), Beam BT1-3-8 (IcorrT=24 mA-days/cm2) recorded a maximum mid-span deflectionof approximately 4.6 mm (0.18 in.) compared with 3 mm(0.12 in.) for the control Beam BT1-C. Figure 3 also showsthat load-deflection plots after cracking are virtually linearup to approximately 70% of the ultimate load and that the

degradation or loss of stiffness of beams increases withincreasing corrosion activity. Apart from the loss of flexuralcapacity, reinforcement corrosion also produces higherdeflection that may lead to serviceability problems. Bothstrength and serviceability, major concerns for a corrodingbeam, get progressively impaired with increasingIcorrT.

Flexure-shear type failure was observed in all beams. Theflexure-shear cracks advanced towards the top with newcracks emerging. Failure was assumed to occur when theapplied load on beam began to drop, with increasing mid-span deflection. The vertical shear reinforcement providedthroughout the length of the specimens served its purpose bysafeguarding against any unwanted premature shear failure.As the tension bars were anchored well at ends, no premature

slip of bars occurred.

Flexural capacity of beamsExperimental value of the ultimate moment capacity

Mex,ucfor each control beam (BT1 to BT4) was calculatedsimply from statics asMex,uc= 350P kN-mm (0.26P ft-kip),where Pis the load applied in kN (kip) (Fig. 1) at failure. Foreach control beam, the average of two test results was takenas the representative value of Mex,uc. The values of Mex,uc,for the four control beams having different Cv and D, arepresented in Table 2.

The theoretical values of the ultimate moment capacity ofthe control beams Mth,ucshown in Table 2 were calculatedusing conventional strength theory based on strain-compatibilityanalysis, as the location of the top 8 mm (0.31 in.) bars wasfound to be within the tension zone and 10 mm (3/8 in.) barsshowed nonlinear stress-strain relationship after theproportional limit. For calculation of Mth,uc values, thevalues offc for the beams obtained from the cylinder tests(Table 2) were used. Strain-compatibility analysis used tocalculate the ultimate moment capacity of the beam specimensconsisted of the following steps: 1) first an initial value of theneutral axis depth is assumed; 2) the strains in tension barsand in hanger bars are calculated based on a linear straindistribution with the maximum concrete compressive strainof 0.003 at the top face; 3) the corresponding stresses in the

d

reinforcement and the forces in the tension and hanger barsare computed; 4) the compressive force in concrete is calculatedfor the assumed neutral axis depth on the basis of a uniformstress of 0.85fc over a depth of 0.8d; 5) if the total tensileforce, Tsand the compressive force, Care not equal, steps 1)through 4) are repeated with a new value of d, until C = Ts;and 6) once the correct value of dis established, the momentcapacity is calculated by taking moment from the correspondinginternal forces. For corroded beam specimens, the computedresidual diameters as presented later were considered to calculate

the effective area of the tension reinforcement.The results show that the ratio ofMex,uc/Mth,uc, designated

as Cc, is close to 1.0 for beams with 12 mm (1/2 in.) diameterbars (BT2-C and BT4-C), indicating a high degree of accuracyfor the theoretical predictions. For beams with 10 mm (3/8 in.)diameter bars as the tension reinforcement (BT1-C and BT3-C),however, the values of Ccexceed 1.0 by over 10%, implyingthat the theoretical predictions were somewhat smaller thanthe actual strength.

The experimentally determined values of flexural strengthof the corroded beamsMex,c, calculated in the same manneras for the control beams (that is, Mex,c= 350P kN-mm[0.26P ft-kip]), are shown collectively for all beams in Table 3.These values are the average of two test results. Table 3 also

shows the percentage residual strength of the corrodedbeams asR, which is the ratio ofMex,c/Mex,uctimes 100. Thevalues of fc , as determined from different batch mixtures,showed that corroded beams had values of fc somewhatdifferent from the corresponding control beams. For calculationof R, however, the experimentally determined momentcapacity for a control beam is assumed to be the same for allbeams in the same group (Table 3).

Effect of chosen variables on reinforcement corrosionThe variables chosen in this study includeIapp,T,D, and Cv.

For computations, the values of Icorr as determined through

Fig. 3Typical load-deflection plot (1 kN = 0.225 kip).

Table 2Moment capacity of control beams

Beam fc, MPa (psi)Mex,uc,

kN-m (ft-kip)

Mth, uc,

kN-m (ft-kip)

Cc=Mex,uc/

Mth,uc

BT1-C 45.8 (6641) 11.64 (8.59) 10.48 (7.73) 1.11

BT2-C 36.3 (5264) 14.80 (10.92) 14.02 (10.34) 1.06

BT3-C 46.5 (6743) 11.76 (8.67) 10.15 (7.49) 1.16

BT4-C 46.1 (6685) 13.13 (9.68) 13.40 (9.88) 0.98


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gravimetric weight loss were used. From Eq. (4), it is noted thatthe weight loss of a bar is directly proportional to the productIcorrT, implying that a higher corrosion current density for alesser period of corrosion would be as damaging as a lesser valueofIcorrfor a longer corrosion period in terms of metal loss of acorroding bar. The product IcorrT, termed as the corrosionactivity index, is therefore the most significant factor for theweight loss of a corroding reinforcing bar.

The percentage weight loss of metal due to induced corrosionfor each corroded beam is shown as in Table 1. Using the

values of andIcorrT from Table 1, Fig. 4 is drawn for fourgroups of beams with respect toDand Cvto show the variationof withIcorrT. For a givenIcorrT, for a beam with 12 mm(1/2 in.) diameter bars is lesser than that of 10 mm (3/8 in.)diameter bars. This implies that, percentage-wise, metal losswill be smaller for higher diameter bars at a given value ofIcorrT. The effect of cover Cv on percentage weight lossappears to be negligible for the test beams.

Effect of corrosion activity index on residualstrength of corroded beams

The values of percentage residual strengthRfrom Table 3are plotted with respect toIcorrTfrom Table 1 in Fig. 5 foreach group of beams. Figure 5 shows thatRdecreases with

increasing IcorrT as expected. With increasing IcorrT, themetal loss will be higher, and this inevitably will reduce theresidual flexural strength. As an example, for beams withD= 10 mm (3/8 in.) and Cv= 25 mm (1 in.), the value ofRdecreased from 92 to 56% whenIcorrTincreased from 4.12to 23.92 mA-days/cm2. A comparison of the two plots for

Group 1 and 2 and those for Group 3 and 4 shows that the

values of Rare not significantly affected by Cv, within the

range of Cvconsidered, whenIcorrTexceeds 12 mA-days/cm2.

Flexural strength of corroded beamsbased on metal loss

The flexural strength of a corroded beam at a given value

of IcorrT is predominately affected by the following two

phenomena: 1) loss of metal due to corrosion; and 2) degradation

of bond between reinforcement and concrete due to corrosion.

While the former reduces the moment capacity of a beamdue to reduced steel area, past research6-11has shown that

reinforcement corrosion also leads to degradation of bond,

following a small increase in strength at the early stage of

corrosion, and the loss of bond strength adversely affects the

moment capacity of a corroded beam.

The flexural capacity of a corroded beam was first calculated

in the same manner as the control beams but using a reduced

diameter of tension bars Ddue to corrosion in place ofthe original diameter D. Any adverse implication of

possible impairment of bond between reinforcement and

concrete from corrosion on moment capacity was ignored

for this calculation.

The reduced diameterDis calculated from the well-knownformula for metal loss rate or penetration rate Prgiven as

21

(5)PrW

Fst---------Icorr

Jr

st-----= =

Fig. 4Percentage weight loss versus IcorrTplots.

Fig. 5Variation of percentage residual strength withIcorrT.

Table 3Experimental moment capacity ofcorroded beams

Beam

fc Mex,c Mex,uc

100MPa psi kN-m ft-kip kN-m ft-kip

BT1-2-4 38.91 5643 10.68 7.88 11.64 8.59 92

BT1-3-4 36.89 5350 10.15 7.49 11.64 8.59 87

BT1-2-6 45.77 6638 10.46 7.72 11.64 8.59 90

BT1-3-6 46.45 6737 9.15 6.75 11.64 8.59 79

BT1-2-8 33.40 4844 7.82 5.77 11.64 8.59 67

BT1-3-8 46.45 6737 6.48 4.78 11.64 8.59 56

BT2-2-4 39.94 5793 12.76 9.41 14.80 10.92 86

BT2-3-4 35.68 5175 11.97 8.83 14.80 10.92 81

BT2-2-6 44.45 6447 10.43 7.69 14.80 10.92 71

BT2-3-6 44.21 6412 10.55 7.78 14.80 10.92 71

BT2-2-8 44.69 6482 8.88 6.55 14.80 10.92 60

BT2-3-8 37.66 5462 8.49 6.26 14.80 10.92 57

BT3-2-4 40.18 5828 10.92 8.05 11.76 8.67 93

BT3-3-4 35.68 5175 10.19 7.52 11.76 8.67 87

BT3-2-6 33.40 4844 9.88 7.29 11.76 8.67 84

BT3-3-6 44.21 6412 9.28 6.84 11.76 8.67 79

BT3-2-8 33.40 4844 9.12 6.73 11.76 8.67 78

BT3-3-8 33.40 4844 6.60 4.87 11.76 8.67 56

BT4-2-4 36.89 5350 12.03 8.87 13.13 9.68 92

BT4-3-4 46.49 6743 10.93 8.06 13.13 9.68 83

BT4-2-6 46.49 6743 10.02 7.39 13.13 9.68 76

BT4-3-6 40.94 5938 8.98 6.62 13.13 9.68 68

BT4-2-8 40.94 5938 9.00 6.64 13.13 9.68 69

BT4-3-8 37.66 5462 7.57 5.58 13.13 9.68 58

RMex c,

Me x u c,--------------=


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where W equals the equivalent weight of steel = 27.9 g(0.062 lb); F equals Faradays constant = 96487 A-sec; and

stequals density of steel = 7.85 g/cm3 (0.28 lb/in.3).

The reduction in bar diameter due to a steady-state corrosioncurrent densityIcorrfor a corrosion period of Tis 2PrTandthe percentage reduction in diameter of bar is (2PrT/D) times100. The reduced net diameter of a corroded barDis thenwritten as

(6)

In terms of cross-sectional area, Eq. (6) can be recast forcalculating the reduced cross-sectional areaAsas

As =As(1 )2 (7)

where As is the original cross-sectional area of the barand = 2PrT/D, defined as the metal loss factor. FromEq. (4) and (5), the percentage weight loss can be shownto be equal to (2) times 100. In other words, the ratio ofweight loss to the original weight of a bar equals 2or twice

the metal loss factor.UsingAsin place ofAs,Mth,cvalues of all corroded beams

were calculated using strain compatibility analysis. Thecalculated values ofMth,care presented in Table 4 along withthe experimentally measured values of moment capacity ofcorroded beamsMex,cand values of Cf, which is the ratio ofMex,c/Mth,c. Two important observations can be made from

the trend of the values of Cffor beams. First, the Cfvalueprogressively declines with increasingIcorrTfor each type ofBeam BT1 to BT4. This implies that the prediction of flexuralstrength, based only on the use of reduced cross-sectional areaof steel reinforcementAs, calculated from Eq. (6), would notyield satisfactory results for higher values of IcorrT, that is,with higher degree of corrosion or metal loss. HigherIcorrTwill cause more corrosion damage that would result in lossof bond between steel and concrete. The moment capacity ofa corroded beam, therefore, cannot be calculated simply on

the basis of Asalone at a higher IcorrT, for which furtherimpairment due to bond effect must be taken into account.Second, it is also observed that Cfvalues at lower IcorrT

(Table 4) are closer to 1.0, or greater than 1.0 for beamsreinforced with 10 mm (3/8 in.) diameter bars (BT1 and BT3groups). This observation lends support to the postulationthat moment capacity of a corroded beam at a low value ofIcorrT can be calculated with an acceptable degree ofaccuracy using only As from Eq. (7) and ignoring anyimplication of bond. This is consistent with the prevailingnotion that at the early stage of corrosion, bond loss isminimal or there may be a small increase in bond strength.

The values of CfandIcorrTfrom Table 4 are plotted inFig. 6 for each group of beams to show the decline in Cf

values with IcorrT. The comparison of two plots of beamGroups BT1 and BT3 (beams having 10 mm (3/8 in.)diameter bars) and of the plots for beam groups BT2 andBT4 (beams having 12 mm [1/2 in.] diameter bars) showsthat the effect of cover Cv does not have appreciableeffect on Cfvalues within the range of IcorrTbetween 8and 20 mA-days/cm2.

D D 12PrT

D------------ =

Table 4D, Mex,c, Mth,c, and Cffor 24 corroded beams

Beam

Cv,

mmD,mm

IcorrT

(mA-days/cm2)

fc ,

MPa

D(Eq. (6)),

mm

Mth, c,

kN-m

Mex,c,

kN-m Cf=Mex,c/Mth, cValue of (Eq. (10))

BT1-2-4 25 10 4.12 38.91 9.74 9.69 10.68 1.10 1.00

BT1-3-4 25 10 10.88 36.89 9.31 8.95 10.15 1.13 1.00

BT1-2-6 25 10 11.82 45.77 9.25 9.38 10.46 1.11 1.00

BT1-3-6 25 10 16.44 46.45 8.95 9.00 9.15 1.01 0.97

BT1-2-8 25 10 17.44 33.4 8.89 8.17 7.82 0.95 0.96

BT1-3-8 25 10 23.92 46.45 8.47 8.35 6.48 0.77 0.91

BT2-2-4 25 12 5.00 39.94 11.68 13.65 12.76 0.93 0.96

BT2-3-4 25 12 7.84 35.68 11.50 13.04 11.97 0.92 0.90

BT2-2-6 25 12 17.94 44.45 10.85 12.40 10.43 0.84 0.79

BT2-3-6 25 12 12.54 44.21 11.20 13.02 10.55 0.81 0.84

BT2-2-8 25 12 20.64 44.69 10.69 12.13 8.88 0.73 0.78

BT2-3-8 25 12 20.96 37.66 10.67 11.69 8.49 0.72 0.78

BT3-2-4 40 10 6.08 40.18 9.61 9.32 10.92 1.17 1.00

BT3-3-4 40 10 6.92 35.68 9.56 8.83 10.19 1.15 1.00BT3-2-6 40 10 7.68 33.4 9.51 8.54 9.88 1.15 1.00

BT3-3-6 40 10 13.26 44.21 9.15 8.96 9.28 1.03 0.99

BT3-2-8 40 10 16.16 33.4 8.97 8.04 9.12 1.13 0.97

BT3-3-8 40 10 25.04 33.4 8.41 7.55 6.60 0.87 0.91

BT4-2-4 40 12 6.96 36.89 11.56 11.92 12.03 1.01 0.92

BT4-3-4 40 12 9.96 46.49 11.37 12.54 10.93 0.87 0.87

BT4-2-6 40 12 12.18 46.49 11.22 12.33 10.02 0.81 0.84

BT4-3-6 40 12 16.8 40.94 10.93 11.46 8.98 0.78 0.80

BT4-2-8 40 12 16.64 40.94 10.94 11.48 9.00 0.78 0.80

BT4-3-8 40 12 18.96 37.66 10.79 10.98 7.57 0.69 0.79

Note: 25.4 mm = 1 in.; 1 MPa = 145 psi; 1 kN-m = 0.7376 kip-ft.


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PREDICTION OF RESIDUAL FLEXURALSTRENGTH OF CORRODED BEAMS

An attempt has been made to use the experimental datagathered in this study in proposing a predictive model for theestimation of the residual flexural strength of beams that aresubjected to reinforcement corrosion.

Basis of modelA prediction model for the residual flexural strength of

corroded beams was carried out on the basis of the following

observations, as discussed previously: 1) degree of corrosionincreases with increasing value of corrosion activity index,IcorrTand, consequently, the flexural strength of a corrodedbeam decreases with increasing IcorrT; 2) for a constantIcorrT, the percentage loss of metal cross-sectional area issmaller for a large diameter bar compared to that of a smallerdiameter bar; 3) the effect of reinforcement cover, within therange considered in this study, has small effect on metal lossat a givenIcorrT; and 4) the values of Cf, determined on thebasis of the theoretical moment capacity, calculated usingreduced cross-sectional areaAsfrom Eq. (7), shows that suchtheoretical prediction would be inaccurate at higherIcorrT, if theadverse implication of loss of bond is not addressed.

The accumulated corrosion damage can be viewed as the

manifestation of two simultaneously developing corrosiondamage factors, as stated earlier: metal loss and degradation ofbond. In proposing an analytical approach, these two corrosionphenomena have, however, been considered separately withdeterioration factors to capture the sustained loss of strength.

Strength prediction modelA two-step procedure is proposed to predict the residual

strength of a corroded beam for which cross-sectionaldetails, materials strengths, corrosion activity index,IcorrT,and diameter of reinforcing bar D are known. First, themoment capacity Mth,c is calculated using reduced cross-sectional area of tension reinforcement Asfrom Eq. (7) inthe conventional manner and then the computed value of

Mth,c is multiplied by a correction factor to obtain thepredicted residual strength of the beamMres, as follows

Mres= Mth,c (8)

The value of is assumed to represent the combined effect ofthe bond loss and factors pertaining to loss of flexural strength

other than the reduction of the metal area. The correlationbetweenMresandMth,ccan then be expressed, for simplicity,through the single factor . The proposed value of is taken as afunction of the two important variables, namelyIcorrTandD.Based on the experimental observations and discussionpresented earlier, the final empirical form of is taken as

(9)

where mand nare constants andAis a dimensional constant.This form captures the observation that Cf is inverselyrelated toIcorrTandD(refer to Table 4).

The values of the constants are determined through amulti-level regression analysis of test data for Cfpresented inTable 4, as A = 14.7, m = 0.15, and n = 1.0. Thus, theproposed equation for the correction factor is

(10)

whereD is the diameter of the reinforcing bar in mm,Icorr is

the corrosion current density in mA/cm2, and Tis the duration ofcorrosion in days.

The values of for all the 24 corroded beams, calculatedby substitutingIcorrTandDvalues in Eq. (10), are shown inTable 4. It can be seen from Table 4 that a high degree ofcorrelation exists between the values of as calculated andthe values of Cf, lending support to the empirical formula-tion of . The residual flexural strengthMres, can be calcu-lated from Eq. (8) using the values of andMth,c.

The proposed strength prediction model can be used to findthe residual flexural capacity of a beam that has sufferedcorrosion damage, and also to find the limit of Icorrfor a givencorrosion period Tthat can be permitted for a beam at a lowestlevel of compromised safety or to predict the useful service life,

based on the lowest acceptable residual flexural strength of thebeams subjected to a given Icorr. The utility of the proposedstrength prediction model is explained by the following example.

ExampleSpecify the permissible limit of Icorrso that the flexural

strength of a beam (effective depth = 250 mm [9.84 in.],breadth = 200 mm [7.87 in.],As= 4 bars of 12 mm [1/2 in.]each, fc = 40 MPa [5.8 ksi], and fy= 500 MPa [72.5 ksi])would not fall below 85% due to reinforcement corrosionduring a corrosion period of 50 years.

T= 50 years = 18,250 days;D= 12 mm (1/2 in.);R= 85%;andAs = 4 /4(12)

2= 452.4 mm2 (0.7 in.2).M

th,uc

= 52.78 106N-mm = 52.78 kN-m (38.93 ft-kip);R= 85%, henceMres= 0.85 52.78 = 44.86 kN-m (33.1 ft-kip).From Eq. (5), Pr= 0.03185 Icorr(mm/day), whereIcorrisin mA/cm2; therefore = 2 PrT/D= 96.877Icorr.

WithIcorr= 0.0103, = 0.5585/0.15, Mth,c= 80.32 10

6

0.15,As = 452.4 (1 )2mm2[0.7(1 )2in.2], Mth,calso

equals [56.55 106(1 )2 3.76 106(1 )4].The value of is determined from trial and error as

0.0382, givingIcorr= 0.393 A/cm2.

CONCLUSIONSBased on the results of this study, the following conclusions

are drawn:

A

IcorrT( )mD

n-----------------------------=

14.7

D IcorrT( )0.15

------------------------------- 1.0=

Fig. 6Variation of Cfwith IcorrTand D.


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1. Measured values of the corrosion current density, Icorrare less than the applied current density Iappdue to theresistance and the electrolytic properties of concretesurrounding the reinforcing bars;

2. The corrosion activity indexIcorrTis the key measure ofcorrosion damage. The percentage metal loss and the loss offlexural strength increase with increasingIcorrT;

3. The effect of reinforcement cover on degree of corrosionat a constant value ofIcorrTis found to be small. The loss ofmetal is smaller for a large diameter bar compared to that for

a smaller diameter bar at a constantIcorrT;4. At a lower value ofIcorrT, the residual flexural strengthof a corroded beam can be predicted with a reasonable accuracyby considering only the reduced cross-sectional area oftension reinforcementAsfrom Eq. (7). At a higher value ofIcorrT, however, the increasing adverse effect of bond cannotbe ignored in determining the residual flexural capacity;

5. Based on the experimental data, an approach has beenproposed to predict the residual flexural strength of acorroded beam for which IcorrT, D, cross-sectional details,and material strengths are known. The proposed two-stepapproach requires determination of a correction factor thatshould be applied to correct the theoretical moment capacityof a corroded beam, calculated on the basis of reduced cross-

sectional areaAs. This approach appears to produce satisfactoryresults within the range ofIcorrTused in this study; and6. A corroded beam shows higher deflection than an

uncorroded one because of the degradation in flexural stiffnessdue to corrosion that increases with increasingIcorrT.

ACKNOWLEDGMENTSThe authors gratefully acknowledge the financial support received from

King Fahd University of Petroleum and Minerals (KFUPM), Dhahran,Saudi Arabia, under the research Grant SABIC-2002/2. The support of theDepartment of Civil Engineering at KFUPM is also acknowledged.

NOTATIONAs = cross-sectional area of corroded reinforcementAs = cross-sectional area of uncorroded reinforcement

C = compressive force in concreteCc = Mex,uc/Mth,ucratioCf = Mex,c/Mth,cratioCv = concrete cover thickness

D = diameter of corroded reinforcing barD = diameter of uncorroded reinforcing bar

= neutral axis depthF = Faradays constant (96487 A-sec)

fc = 28-day compressive strength of concretefy = yield strength of reinforcing barIapp = applied corrosion current densityIcorr = corrosion current densityIcorrT = corrosion activity indexJr = instantaneous corrosion rate (mass of metal lost/surface area/time)Mex,c = experimental ultimate moment capacity of corroded beamMex,uc = experimental ultimate moment capacity of uncorroded beamMres = residual ultimate moment capacity of corroded beam

Mth,c = theoretical ultimate moment capacity of corroded beamMth,uc = theoretical ultimate moment capacity of uncorroded beamm, n, A = empirical constantsP = load applied on beamPr = penetration rate (penetration depth/time)

R = percentage residual strength(Mex,c100/Mex,uc)T = corrosion duration in daysTs = total tensile force in steelW = equivalent weight of steel (27.9 g) = metal loss factor = 2PrT/D = correction factorst = density of steel (7.85 g/cm

3) = percentage weight loss of metal due to induced corrosion

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residual strength of corrosion-damaged reinforced concrete beams

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