ACI MATERIALS JOURNAL
TECHNICAL PAPER
Title no. 104-M05
Residual Strength of Corrosion-Damaged Reinforced Concrete Beams by Abul K. Azad, Shamsad Ahmad, and Syed A. Azher In this work, an effort has been made to first observe the effect of reinforcement corrosion on flexural behavior of reinforced concrete beams and then to develop a model based on the test data to predict their residual flexural strength. Test data were gathered from the testing of 56 reinforced reinforced concrete concrete beam specimens that were subjected to a varying degree of accelerated corrosion. It has been observed that the product of corrosion current density and corrosion period IcorrT is the most significant factor affecting the flexural flexural strength strength of a corroded corroded beam. Based on the experimental data, a two-step approach is proposed to predict the residual flexural strength strength of a corroded corroded beam. beam. First, First, the flexural flexural strength strength is calculated using the reduced area of corroded bars, and then this value is multiplied by a correction factor that is formulated through a regression analysis of test data to take into account bond, slip, and other applicable factors. Keywords: deflection; flexural strength; reinforced concrete; reinforcement corrosion.
INTRODUCTION Corrosion of reinforcing steel is the single most dominant causal factor for the premature deterioration of concrete structures. The basic problem associated with the deterioration of reinforced concrete due to corrosion is not only that the reinforcing rei nforcing steel itself is reduced in mechanical strength, but also the products of corrosion exert stresses within the concrete that cannot be supported by the limited plastic deformation of the concrete, and the concrete therefore cracks. This leads to a weakening of the bond and anchorage between concrete and reinforcement, which directly affects the serviceability and ultimate strength of concrete elements within a structure. 1 A considerable amount of research has been devoted to corrosion of reinforcement in reinforced concrete dealing with various issues related to corrosion process, its initiation, damaging effects of corrosion, and the prediction of time-tocover cracking of concrete due to corrosion. 2-5 These studies indicate that it is possible to determine the time to corrosion initiation if necessary data are available. The cover cracking due to reinforcement corrosion, however, may not be considered as an indication of the end of service life. The member with cracked cover may continue to be in service provided that the residual strength of the structure is still sufficient enough to resist the loads within an acceptable margin of safety. The effect of reinforcement corrosion on bond between steel and the concrete has been of great interest and this has resulted in the proposition of several predictive models for which References 6 through 11 can be cited as representative samples of work. These studies have found that the bond strength increases with corrosion up to a certain level of reinforcement corrosion, but with further increase in corrosion, the bond strength progressively declines. Even when there is extensive corrosion with considerable cracking of concrete, however, bond is not completely destroyed. This partially
40
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., 12 Rodriguez et al.,13 Huang and Yang,14 Mangat and Elgarf, 15 Yoon et al.,16 and Jin and Zhao.17 Huang and Yang14 studied the effect of the loss of reinforcing steel area on the flexural behavior of reinforced concrete beams. Tachibana et al. 12 and Yoon et al.16 examined the effect of reinforcement corrosion on the residual load capacity of the concrete beams relating the residual flexural capacity with the percentage weight loss of reinforcing steel. Rodriguez et al. 13 studied the effect of reinforcement corrosion on the bending moment and the shear force of a reinforced concrete beam. Mangat and Elgarf 15 developed a relationship between the degree of reinforcement corrosion and the residual strength of flexural members. Jin and Zhao 17 investigated the effect of reinforcement corrosion on the bending strength of reinforced concrete beams. A structural deterioration model in an exponential form has been presented by Li18 as part of life-cycle modelling of corrosionaffected 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 the residual flexural strength of a corroded beam through the use of conventional flexural formula by taking into account the loss 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 prediction model is a two-step, easy-to-apply procedure that appears to yield satisfactory results, as evidenced from the degree of correlation with the experimental data.
RESEARCH SIGNIFICANCE This study aims to make a contribution in the area of prediction of the residual flexural strength of corroded reinforced concrete beam type members by suggesting a predictive model that has been developed through an extended experimental work on beams that were subjected to different 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 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 the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including authors’ closure, if any, will be published in the November-December November-December 2007 ACI Materials Materials Journal Journal if the discussion is received by August 1, 2007.
ACI Materials Journal/January-February 2007
Abul K. Azad is 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 Ahmad is 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. Azher is a Graduate Student (Research Assistant) in the Department of Civil Engineering at KFUPM. He received his bachelor degree in civil engineering from Osmania University, Hyderabad, India. His research interests include durability of concrete materials and structural components with specific interest in corrosion of reinforcement in concrete, structural repair and rehabilitation of existing structures, and retrofitting using CFRP.
damage or to predetermine the maximum level of corrosion that can be tolerated for a specified service life.
EXPERIMENTAL INVESTIGATION The design variables used in this experimental program were two different bar diameters, 10 and 12 mm (3/8 and 1/2 in.); two different clear covers to the tension reinforcement, 25 and 40 mm (1 and 1.5 in.); two different levels of impressed corrosion current intensities, 2 and 3 mA/cm 2; and three different corrosion durations, 4, 6, and 8 days. A total of 56 reinforced concrete beam specimens were cast to include all variables. All tests were repeated twice, including those on the control specimens.
Specimen details and material strengths Rectangular reinforced concrete beam specimens 150 x 150 x 1100 mm (6 x 6 x 43 in.) were used for this study. All the beams were designed to fail in flexure by providing ample vertical shear reinforcement to exclude premature shear failure. The beam details are shown in Fig. 1. The vertical stirrups were double-legged 6 mm (0.25 in.) diameter bars spaced uniformly at 90 mm (3.5 in.) centers throughout the length of each beam. Deformed bars were used for all reinforcements. Two top 8 mm (0.31 in.) diameter bars with a clear cover of 36 mm (1.42 in.) were used to serve as stirrup-holders and were epoxy-coated to avoid corrosion. The stirrups were left uncoated so as to represent the practical case in which stirrups are also subjected to corrosion. All specimens were cast using concrete with a cement content of 350 kg/m 3 (590 lb/yd3) (ASTM Type I portland cement), coarse-fine aggregate ratio of 1.65 and effective water-cement ratio ( w / c) of 0.45. Two percent sodium chloride (NaCl) by weight of cement was added to the mixture to promote corrosion. Specimens were moist cured for 7 days followed by air curing at room temperature. The casting of 56 beams was carried out in 10 batches. For each batch of concrete mixture, three 75 x 150 mm (3 x 6 in.) cylinders were also cast to determine the compressive strength of the particular batch of concrete mixture. The beam specimens were divided into four groups, BT1 to BT4, based on the clear cover to the tension reinforcement and the reinforcing bar diameter. The beams that were not subjected to accelerated corrosion, referred to as the control beams, were designated as BT1-C (bar diameter D = 10 mm [3/8 in.] and clear cover C v = 25 mm [1 in.]), BT2-C ( D = 12 mm [1/2 in.] and C v = 25 mm [1 in.]), B T3-C ( D = 10 mm [3/8 in.] and C v = 40 mm [1.5 in.]), and BT4-C ( D = 12 mm [1/2 in.] and C v = 40 mm [1.5 in.]). The beams subjected to accelerated corrosion were designated to indicate the intensity
ACI Materials Journal/January-February 2007
and duration of the applied corrosion current. For example, Beam BT1-2-4 implies a beam in Group BT1 that was subjected to applied current intensity of 2 mA/cm 2 for a period of 4 days. The 28-day compressive strength of concrete f c′ for each mixture was determined as the average strength of three 75 x 150 mm (3 x 6 in.) cylinders cast from each batch mixture. It is observed that f c′ values varied from batch to batch, despite the use of same mixture proportions, same materials, and similar casting procedure. The measured values, taken as the average of three cylinder strengths, varied from a minimum of 33.4 MPa (4840 psi) to a maximum of 46.5 MPa (6740 psi) with a standard deviation of 4.95. The yield and ultimate tensile strength of tension bars used were as follows: for 10 mm (3/8 in.) diameter bars, yield strength and ultimate strength were 520 and 551 MPa (75.4 and 80 ksi), respectively, and for 12 mm (1/2 in.) diameter bars those values were 590 and 700 MPa (85.6 and 101.5 ksi), respectively.
Test setup for accelerated corrosion induction and testing of beams After completion of curing, the specimens were subjected to accelerated corrosion by applying anodic current of specified intensity 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 the current was adjusted so that the reinforcing steel became the anode and a stainless steel plate placed on the concrete specimen served as the cathode. The stainless steel plate was placed in the tank covering both sides of its specimen throughout the length. This arrangement ensured a uniform distribution of the corrosion current along the whole length of the longitudinal bars. A schematic representation of the test setup is shown in Fig. 2. The total current required for each type of beam specimen was calculated based on their
Fig. 1—Details of test specimens and loading.
Fig. 2—Schematic presentation of accelerated corrosion test setup.
41
respective steel surface area. The current supplied to each concrete specimen was checked on a regular basis and any drift was corrected. All the beam specimens were tested in a four-point bend test under a universal testing machine, using the setup shown in Fig. 1. The load and midspan deflection data for each specimen were recorded using a computerized data acquisition system at predetermined load intervals till failure.
Gravimetric weight loss Following the flexure test on corroded beams, each beam was broken to remove the two corroded tension bars for measurement of the average weight loss of steel due to induced corrosion. The bars were cleaned to remove all rust products using Clarke solution and then they were weighed to find the net weight of steel. Preparation, cleaning, and evaluation of corrosion test specimens were carried out in accordance with ASTM G 1.20 Samples of corroded reinforcing bars after gravimetric test showed general corrosion along the length but reaffirmed the general perception that reinforcement corrosion in concrete, in general, is non-uniform along the length of the bar, as the loss of reinforcing bar at some sections was seen to be considerably higher than that at the other sections due to pitting corrosion.
RESULTS AND DISCUSSION Weight loss of bars and corrosion current density The measured weight loss of bars was used to calculate the instantaneous corrosion rate J r as follows weight loss J r = ------------------------------------------------------------------------------------------surface area of bar × corrosion period
(1)
From the calculated values of J r , the corrosion current density I corr was determined from the following expression 21 J r =
W - I corr ---F
(2)
where W equals the equivalent weight of steel and F equals the Faraday’s constant. With W = 27.925 g (0.062 lb) and F = 96,487 Coulombs (A-sec) in Eq. (2), the following simplified equation for calculating I corr from the value of J r is obtained as I corr = 0.1096 J r
(3)
where I corr is in mA/cm 2 and J r is in gm/cm2 /year. From Eq. (1) and (2), the weight loss of a bar can be expressed as
weight loss ⁄ surface area of bar
W = ----- I corr T F
(4)
= 0.289 I corr T where I corr is in mA/cm 2 and T is in seconds. The calculated values of I corr from Eq. (3) are shown collectively for all corroded beams in Table 1. It is observed that the I corr values established from gravimetric analysis are lower than the applied corrosion current density I app. The difference between I corr and I app is attributed to several
Table 1—Gravimetric test results and conversion of weight loss into I corr
42
I app, ρ, mA/cm2 T , days % weight loss
J r ,
I corr ,
I corr T ,
g/cm2 /year
mA/cm2
mA-days/cm2
5.40
9.37
1.03
4.12
4
14.20
24.83
2.72
10.88
6
15.20
17.96
1.97
11.82
3
6
21.40
25.00
2.74
16.44
10 (0.39)
2
8
21.50
19.94
2.18
17.44
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
Beam
D, mm (in.)
BT1-2-4
10 (0.39)
2
4
BT1-3-4
10 (0.39)
3
BT1-2-6
10 (0.39)
2
BT1-3-6
10 (0.39)
BT1-2-8 BT1-3-8
ACI Materials Journal/January-February 2007
factors among which mention can be made of the concrete cover around the bars, quality of concrete, nonuniform corrosion rate along the length of the bars, and the diameter of bars. It is interesting to note that for beams with 10 mm (3/8 in.) diameter bars (BT1 and BT3 series), the apparent discrepancy between I corr and I app is significantly less than that observed for beams with 12 mm (1/2 in.) diameter bars (Beam BT2 and BT4 series). Similar observations have also been reported by others. 22-23
Load-deflection plots and mode of failure of beams The midpoint deflections of all beams tested were recorded in a data logger. A typical plot of load versus deflection shown in Fig. 3 portrays the expected results that the corroded beams had higher deflection than the corresponding control beams at same load level due to degrading stiffness of the beams. For example, at a load of approximately 42 kN (9.44 kip), Beam BT1-3-8 ( I corr T = 24 mA-days/cm 2) recorded a maximum mid-span deflection of approximately 4.6 mm (0.18 in.) compared with 3 mm (0.12 in.) for the control Beam BT1-C. Figure 3 also shows that load-deflection plots after cracking are virtually linear up to approximately 70% of the ultimate load and that the degradation or loss of stiffness of beams increases with increasing corrosion activity. Apart from the loss of flexural capacity, reinforcement corrosion also produces higher deflection that may lead to serviceability problems. Both strength and serviceability, major concerns for a corroding beam, get progressively impaired with increasing I corr T . Flexure-shear type failure was observed in all beams. The flexure-shear cracks advanced towards the top with new cracks emerging. Failure was assumed to occur when the applied load on beam began to drop, with increasing midspan deflection. The vertical shear reinforcement provided throughout the length of the specimens served its purpose by safeguarding against any unwanted premature shear failure. As the tension bars were anchored w ell at ends, no premature slip of bars occurred.
Flexural capacity of beams Experimental value of the ultimate moment capacity M ex,uc for each control beam (BT1 to BT4) was calculated simply from statics as M ex,uc = 350P kN-mm (0.26P ft-kip), where P is the load applied in kN (kip) (Fig. 1) at failure. For each control beam, the average of two test results was taken as the representative value of M ex,uc. The values of M ex,uc, for the four control beams having different C v and D, are presented in Table 2. The theoretical values of the ultimate moment capacity of the control beams M th,uc shown in Table 2 were calculated using conventional strength theory based on strain-compatibility analysis, as the location of the top 8 mm (0.31 in.) bars was found to be within the tension zone and 10 mm (3/8 in.) bars showed nonlinear stress-strain relationship after the proportional limit. For calculation of M th,uc values, the values of f c′ for the beams obtained from the cylinder tests (Table 2) were used. Strain-compatibility analysis used to calculate the ultimate moment capacity of the beam specimens consisted of the following steps: 1) first an initial value of the neutral axis depth d is assumed; 2) the strains in tension bars and in hanger bars are calculated based on a linear strain distribution with the maximum concrete compressive strain of 0.003 at the top face; 3) the corresponding stresses in the
ACI Materials Journal/January-February 2007
reinforcement and the forces in the tension and hanger bars are computed; 4) the compressive force in concrete is calculated for the assumed neutral axis depth on the basis of a uniform stress of 0.85 f c′ over a depth of 0.8 d ; 5) if the total tensile force, T s and the compressive force, C are not equal, steps 1) through 4) are repeated with a new value of d , until C = T s; and 6) once the correct value of d is established, the moment capacity is calculated by taking moment from the corresponding internal forces. For corroded beam specimens, the computed residual diameters as presented later were considered to calculate the effective area of the tension reinforcement. The results show that the ratio of M ex,uc / M th,uc, designated as C c, is close to 1.0 for beams with 12 mm (1/2 in.) diameter bars (BT2-C and BT4-C), indicating a high degree of accuracy for 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 C c exceed 1.0 by over 10%, implying that the theoretical predictions were somewhat smaller than the actual strength. The experimentally determined values of flexural strength of the corroded beams M ex,c, calculated in the same manner as for the control beams (that is, M ex,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 corroded M ex,uc times 100. The beams as R, which is the ratio of M ex,c / values of f c′ , as determined from different batch mixtures, showed that corroded beams had values of f c′ somewhat different from the corresponding control beams. For calculation of R, however, the experimentally determined moment capacity for a control beam is assumed to be the same for all beams in the same group (Table 3).
Effect of chosen variables on reinforcement corrosion The variables chosen in this study include I app , T , D, and C v. For computations, the values of I corr as determined through
Table 2—Moment capacity of control beams Beam
M ex , uc, M th, uc, f c′, MPa (psi) kN-m (ft-kip) kN-m (ft-kip)
C c = M ex ,uc / M th,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
Fig. 3—Typical load-deflection plot (1 kN = 0.225 kip).
43
gravimetric weight loss were used. From Eq. (4), it is noted that the weight loss of a bar is directly proportional to the product I corr T , implying that a higher corrosion current density for a lesser period of corrosion would be as damaging as a lesser value of I corr for a longer corrosion period in terms of metal loss of a corroding bar. The product I corr T , termed as the corrosion activity index, is therefore the most significant factor for the weight loss of a corroding reinforcing bar. The percentage weight loss of metal due to induced corrosion for each corroded beam is shown as ρ in Table 1. Using the values of ρ and I corr T from Table 1, Fig. 4 is drawn for four groups of beams with respect to D and C v to show the variation of ρ with I corr T. For a given I corr T , ρ 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 loss will be smaller for higher diameter bars at a given value of I corr T . The effect of cover C v on percentage weight loss appears to be negligible for the test beams.
Effect of corrosion activity index on residual strength of corroded beams The values of percentage residual strength R from Table 3 are plotted with respect to I corr T from Table 1 in Fig. 5 for each group of beams. Figure 5 shows that R decreases with increasing I corr T as expected. With increasing I corr T , the metal loss will be higher, and this inevitably will reduce the residual flexural strength. As an example, for beams with D = 10 mm (3/8 in.) and C v = 25 mm (1 in.), the value of R decreased from 92 to 56% when I corr T increased from 4.12 to 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 R are not significantly affected by C v, within the range of C v considered, when I corr T exceeds 12 mA-days/cm2.
Flexural strength of corroded beams based on metal loss The flexural strength of a corroded beam at a given value of I corr T 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 beam due to reduced steel area, past research 6-11 has 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 D′ due to corrosion in place of the 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 diameter D′ is calculated from the well-known formula for metal loss rate or penetration rate Pr given as21 J W P r = --------- I corr = -----r F γ st γ st
(5)
Table 3—Experimental moment capacity of corroded beams f c′
M ex,c
M ex,uc
psi
kN-m
ft-kip
kN-m
M ex c R = ------------- M e x u c × 100 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
,
,
Beam
Fig. 4—Percentage weight loss versus IcorrT plots.
Fig. 5—Variation of percentage residual strength with IcorrT.
44
MPa
ACI Materials Journal/January-February 2007
where W equals the equivalent weight of steel = 27.9 g (0.062 lb); F equals Faraday’s constant = 96487 A-sec; and γst equals density of steel = 7.85 g/cm 3 (0.28 lb/in.3). The reduction in bar diameter due to a steady-state corrosion current density I corr for a corrosion period of T is 2Pr T and D) times the percentage reduction in diameter of bar is (2 Pr T / 100. The reduced net diameter of a corroded bar D′ is then written as 2 P r T D ′ = D 1 – ----------- D
(6)
In terms of cross-sectional area, Eq. (6) can be recast for calculating the reduced cross-sectional area As′ as As′ = As(1 – α)2
(7)
where As is the original cross-sectional area of the bar D, defined as the metal loss factor. From and α = 2Pr T / Eq. (4) and (5), the percentage weight loss ρ can be shown to be equal to (2 α ) times 100. In other words, the ratio of weight loss to the original weight of a bar equals 2 α or twice the metal loss factor. Using As′ in place of As, M th,c values of all corroded beams were calculated using strain compatibility analysis. The calculated values of M th,c are presented in Table 4 along with the experimentally measured values of moment capacity of corroded beams M ex,c and values of C f , which is the ratio of M ex,c / M th,c. Two important observations can be made from
the trend of the values of C f for beams. First, the C f value progressively declines with increasing I corr T for each type of Beam BT1 to BT4. This implies that the prediction of flexural strength, based only on the use of reduced cross-sectional area of steel reinforcement As′, calculated from Eq. (6), would not yield satisfactory results for higher values of I corr T , that is, with higher degree of corrosion or metal loss. Higher I corr T will cause more corrosion damage that would result in loss of bond between steel and concrete. The moment capacity of a corroded beam, therefore, cannot be calculated simply on the basis of As′ alone at a higher I corr T , for which further impairment due to bond effect must be taken into account. Second, it is also observed that C f values at lower I corr T (Table 4) are closer to 1.0, or greater than 1.0 for beams reinforced with 10 mm (3/8 in.) diameter bars (BT1 and BT3 groups). This observation lends support to the postulation that moment capacity of a corroded beam at a low value of I corr T can be calculated with an acceptable degree of accuracy using only As′ from Eq. (7) and ignoring any implication of bond. This is consistent with the prevailing notion that at the early stage of corrosion, bond loss is minimal or there may be a small increase in bond strength. The values of C f and I corr T from Table 4 are plotted in Fig. 6 for each group of beams to show the decline in C f values with I corr T . The comparison of two plots of beam Groups BT1 and BT3 (beams having 10 mm (3/8 in.) diameter bars) and of the plots for beam groups BT2 and BT4 (beams having 12 mm [1/2 in.] diameter bars) shows that the effect of cover C v does not have appreciable effect on C f values within the range of I corr T between 8 and 20 mA-days/cm 2.
Table 4—D , M ex ,c , M th ,c , and C f for 24 corroded beams ′
Beam
C v, mm
I corr T D, mm (mA-days/cm2)
f c′ , MPa
D′ (Eq. (6)), mm
M th, c, kN-m
M ex , c, kN-m
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
1.00
BT3-2-6
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
Value of β C M th, c (Eq. (10)) f = M ex,c /
Note: 25.4 mm = 1 in.; 1 MPa = 145 psi; 1 kN-m = 0.7376 kip-ft.
ACI Materials Journal/January-February 2007
45
PREDICTION OF RESIDUAL FLEXURAL STRENGTH OF CORRODED BEAMS An attempt has been made to use the experimental data gathered in this study in proposing a predictive model for the estimation of the residual flexural strength of beams that are subjected to reinforcement corrosion.
other than the reduction of the metal area. The correlation between M res and M th,c can then be expressed, for simplicity, through the single factor β. The proposed value of β is taken as a function of the two important variables, namely I corr T and D. Based on the experimental observations and discussion presented earlier, the final empirical form of β is taken as
Basis of model A 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 corrosion increases with increasing value of corrosion activity index, I corr T and, consequently, the flexural strength of a corroded beam decreases with increasing I corr T ; 2) for a constant I corr T , the percentage loss of metal cross-sectional area is smaller for a large diameter bar compared to that of a smaller diameter bar; 3) the effect of reinforcement cover, within the range considered in this study, has small effect on metal loss at a given I corr T ; and 4) the values of C f , determined on the basis of the theoretical moment capacity, calculated using reduced cross-sectional area As′ from Eq. (7), shows that such theoretical prediction would be inaccurate at higher I corr T , if the adverse implication of loss of bond is not addressed. The accumulated corrosion damage can be viewed as the manifestation of two simultaneously developing corrosion damage factors, as stated earlier: metal loss and degradation of bond. In proposing an analytical approach, these two corrosion phenomena have, however, been considered separately with deterioration factors to capture the sustained loss of strength.
Strength prediction model A two-step procedure is proposed to predict the residual strength of a corroded beam for which cross-sectional details, materials strengths, corrosion activity index, I corr T, and diameter of reinforcing bar D are known. First, the moment capacity M th,c is calculated using reduced crosssectional area of tension reinforcement As′ from Eq. (7) in the conventional manner and then the computed value of M th,c is multiplied by a correction factor β to obtain the predicted residual strength of the beam M res, as follows M res = β M th,c
(8)
The value of β is assumed to represent the combined effect of the bond loss and factors pertaining to loss of flexural strength
β
A = ----------------------------( I corr T ) m Dn
(9)
where m and n are constants and A is a dimensional constant. This form captures the observation that C f is inversely related to I corr T and D (refer to Table 4). The values of the constants are determined through a multi-level regression analysis of test data for C f presented in Table 4, as A = 14.7, m = 0.15, and n = 1.0. Thus, the proposed equation for the correction factor β is
β
14.7 = ------------------------------- ≤ 1.0 0.15 D ( I corr T )
(10)
where D is the diameter of the reinforcing bar in mm, I corr is the corrosion current density in mA/cm 2, and T is the duration of corrosion in days. The values of β for all the 24 corroded beams, calculated by substituting I corr T and D values in Eq. (10), are shown in Table 4. It can be seen from Table 4 that a high degree of correlation exists between the values of β as calculated and the values of C f , lending support to the empirical formulation of β. The residual flexural strength M res, can be calculated from Eq. (8) using the values of β and M th,c. The proposed strength prediction model can be used to find the residual flexural capacity of a beam that has suffered corrosion damage, and also to find the limit of I corr for a given corrosion period T that can be permitted for a beam at a lowest level of compromised safety or to predict the useful service life, based on the lowest acceptable residual flexural strength of the beams subjected to a given I corr . The utility of the proposed strength prediction model is explained by the following example.
Example Specify the permissible limit of I corr so 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, f c′ = 40 MPa [5.8 ksi], and f y = 500 MPa [72.5 ksi]) would not fall below 85% due to reinforcement corrosion during a corrosion period of 50 years. T = 50 years = 18,250 days; D = 12 mm (1/2 in.); R = 85%; and As = 4 × π /4(12)2 = 452.4 mm2 (0.7 in.2). Mth,uc = 52.78 × 106 N-mm = 52.78 kN-m (38.93 ft-kip); R = 85%, hence M res = 0.85 × 52.78 = 44.86 kN-m (33.1 ft-kip). From Eq. (5), Pr = 0.03185 × I corr (mm/day), where I corr is D = 96.877 I corr . in mA/cm2; therefore α = 2 Pr T / With I corr = 0.0103α, β = 0.5585/ α0.15, Mth,c = 80.32 × 106 α0.15, As′ = 452.4 (1 – α)2 mm2 [0.7(1 – α)2 in.2], Mth,c also equals [56.55 × 106(1 – α)2 – 3.76 × 106(1 – α)4]. The value of α is determined from trial and error as 0.0382, giving I corr = 0.393 µA/cm2.
CONCLUSIONS Fig. 6—Variation of Cf with IcorrT and D.
46
Based on the results of this study, the following conclusions are drawn:
ACI Materials Journal/January-February 2007
1. Measured values of the corrosion current density, I corr are less than the applied current density I app due to the resistance and the electrolytic properties of concrete surrounding the reinforcing bars; 2. The corrosion activity index I corr T is the key measure of corrosion damage. The percentage metal loss and the loss of flexural strength increase with increasing I corr T ; 3. The effect of reinforcement cover on degree of corrosion at a constant value of I corr T is found to be small. The loss of metal is smaller for a large diameter bar compared to that for a smaller diameter bar at a constant I corr T ; 4. At a lower value of I corr T , the residual flexural strength of a corroded beam can be predicted with a reasonable accuracy by considering only the reduced cross-sectional area of tension reinforcement As′ from Eq. (7). At a higher value of I corr T , however, the increasing adverse effect of bond cannot be ignored in determining the residual flexural capacity; 5. Based on the experimental data, an approach has been proposed to predict the residual flexural strength of a corroded beam for which I corr T , D, cross-sectional details, and material strengths are known. The proposed two-step approach requires determination of a correction factor β that should be applied to correct the theoretical moment capacity of a corroded beam, calculated on the basis of reduced crosssectional area As′. This approach appears to produce satisfactory results within the range of I corr T used in this study; and 6. A corroded beam shows higher deflection than an uncorroded one because of the degradation in flexural stiffness due to corrosion that increases with increasing I corr T .
ACKNOWLEDGMENTS The 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 the Department of Civil Engineering at KFUPM is also ac knowledged.
NOTATION As′ As C C c C f C v D′ D d F f c′ f y I app I corr I corr T J r M ex,c M ex,uc M res M th,c M th,uc m, n, A P Pr R T T s W α β γst ρ
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
cross-sectional area of corroded reinforcement cross-sectional area of uncorroded reinforcement compressive force in concrete M ex,uc / M th,uc ratio M ex,c / M th,c ratio concrete cover thickness diameter of corroded reinforcing bar diameter of uncorroded reinforcing bar neutral axis depth Faraday’s constant (96487 A-sec) 28-day compressive strength of concrete yield strength of reinforcing bar applied corrosion current density corrosion current density corrosion activity index instantaneous corrosion rate (mass of metal lost/surface area/time) experimental ultimate moment capacity of corroded beam experimental ultimate moment capacity of uncorroded beam residual ultimate moment capacity of corroded beam theoretical ultimate moment capacity of corroded beam theoretical ultimate moment capacity of uncorroded beam empirical constants load applied on beam penetration rate (penetration depth/time) M ex,uc) percentage residual strength ( M ex,c × 100/ corrosion duration in days total tensile force in steel equivalent weight of steel (27.9 g) D metal loss factor = 2Pr T / correction factor density of steel (7.85 g/cm3) percentage weight loss of metal due to induced corrosion
ACI Materials Journal/January-February 2007
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