1. Department of Civil Engineering, Technocrats Institute of Technology, Anand Nagar Bhopal, Madhya Pradesh, India 2. Department of Civil Engineering, Institute of Technology, Rajiv Gandhi Technological University, Airport Road Bhopal, Madhya Pradesh, India
Performance of concrete structures is significantly influenced and governed by its durability and resistance to environmental or exposure conditions, apart from its physical strength. It can be monitored, evaluated and predicted through modeling of physical deterioration mechanisms, performance characteristics and parameters and condition monitoring of in situ concrete structures. One such study has been conducted using Non-destructive testing equipment in the city of Bhopal and around located in India. Some selected parameters influencing durability of reinforced concrete (RC) structures such as concrete cover, carbonation depth, chloride concentration, half cell potential and compressive strength have been measured, for establishing correlation among various parameters and age of structures. Effects of concrete cover and compressive strength over the variation of chloride content with time are also investigated.
tLt=t1(Xcrδt1D1)2/1−βwhere δ=Xcr/DLttLt and β=ln(D2/D1)/ln(t1/t2)tLt = duration of service life in years, t1 and t2 are exposure ages in years for first and second inspection, Xcr = concrete cover depth (mm), D1 and D2 are chloride diffusion coefficient at t1 and t2, DLt = chloride diffusion coefficient at tLt, and b = age parameter and d= reduction parameter.
A service life model has been proposed for RC structures exposed to chloride environment. Presented time and depth dependent chloride diffusion coefficient. This model is comparable with well known LightCon model. However, predicted service life is longer than the life calculated by LightCon model.
Proposed model is based on Fick’s second law of diffusion, considering diffusion coefficient as function of the content of chloride and dependent on time and depth. This is a good approach, as now several researchers realized that diffusion coefficient is not a constant, it depends on the quality of concrete and exposure conditions. Increasing inspection period and considering environmental factors produces more realistic and accurate results.
Masada et al. (2007) [29]
concrete condition rating
Y=a0+a1·x1+a2·x2+?+an·xnY=a0(x1)a1(x2)a2...(xn)anWhere Y= concrete condition rating; x1, x2, …, xn = age of structure in years, wall thickness, sulfate concentration etc.; a1, a2, …, an = parameters determined during analysis.
Applied this new inspection procedure for concrete culverts at 25 sites in Ohio, and inspection data has been examined to detect common problem in existing concrete culverts. A risk assessment method has been also presented to compute overall structural health rating and to recommend a course of action.
Most of the significant parameters influencing the service life have been considered in this model to evaluate the condition of concrete. Both linear and non linear models had been proposed as rate of deterioration may be constant or variable.
Huang et al. (2004) [30]
performance curve and estimated service life of a treatment or maintenance
ESL={[(t*−to)2+K(tm−to)2]0.5−(t*−to)}/K*(−5.37*K+6.88)forK≠0ESL=0.5(tm−to)2/(t*−to)*6.88forK=0ESL= estimated service life (years), t* = time when treatment performed, tm = time to reach maximum tolerable condition index, to = time at the first sign of corrosion, and K (mm / √year) is a factor depends on the rate of corrosion. t*, tm and to are in years
Developed a project level decision support tool for making maintenance scenarios for concrete bridge decks deteriorated as a result of chloride induced corrosion.
A performance curve i.e., relation between condition and age of structure has been proposed based on spalled percentage, delaminated areas, and chloride content at rebar depth. Delamination and spalling are obtained by visual inspection based on experience; these types of evaluation may vary depending upon the surveyor and predictions made by the surveyor. Only chloride attack among several chemical attacks has been considered. If other attacks such as carbonation, sulfate, alkali silica reaction etc. were considered then accuracy will increase significantly.
Marques and Costa (2010) [31]
corrosion initiation period
Rc65=(a/D)t1=[(Rc65.c2)/1.4×10−3k0k1k2(t0)2n]1/(1−2n) t1= initiation period (year), c = concrete cover (mm), D = diffusion coefficient of carbon-dioxide (mm / √year), a= amount of carbon- dioxide that origins the carbonation of the concrete, Rc65= carbonation resistance, t0 = reference period 1 year, n = accounts for wet and dry cycle influence, K0 = accounts for testing methods and condition, K1 = accounts for the presence of relative humidity, K2 = accounts for cure.
Conducted an experimental study to evaluate performance properties of different concrete compositions. These test results have been considered in the mathematical models of the performance-based specifications. Service life has been evaluated using factor of safety and probabilistic approaches, of each composition. Evaluated service life has been compared to the target periods defined in the prescriptive specification. It has been observed from results that the convergence between the two methodologies still needs to be improved.
This model considered several factors such as carbonation, diffusion rate, wet and dry cycle, testing conditions, humidity and effect of cure. But, it is better to evaluate initiation period considering both carbonation and chloride attack.
corrosion propagation period
tp=k·φo·(1/1.15αIcorr)where k=(74.5+7.3(c/Øo)−17.4fcd)(0.2/Øo)Icorr = corrosion current density, x = steel reduction radius in mm, Øo = initial diameter of the reinforcing steel in mm, a = 2, and fcd = concrete splitting tensile strength.
Model is based on the faradays law and Portuguese performance based specification, also considered corrosion current density dependent on different corrosion level and exposure conditions. Reduction in steel area reduces the load carrying capacity and indicates the deterioration level of RC.
Parameswaran et al. (2008) [20]
corrosion initiation period
ti=(c/Kc)2c = concrete cover in mm, Kc = carbonation in mm / √year rate factor depends on exposure condition and air entrained coefficient.
This study has been conducted to observe the deterioration of concrete bridges due to carbonation. Remaining life assessed has been found to be essential for Bridge Management System.
These models have been developed to evaluate initiation and propagation periods by considering exposure conditions, concrete quality, cover, w/c ratio and other factors. Also considered effects of the factors, affecting service life of structures such as addition of admixtures, grade of concrete, concrete cover, air entrainment, and diameter of steel bars.
corrosion propagation period
tp=80(c/dr)where c = concrete cover in mm, dr = rate of corrosion
Li et al. (2011) [18]
chloride diffusion coefficient (D)
D=Do·Ks·θ(x)·t−m=x2×10−6/{4t[erf−1(1−C(x,t)/Cs)]2}where Do = diffusion coefficient in unstressed concrete m2/s, Ks = influence coefficient of state of stress, q(x) = depth modification factor, m= an empirical coefficient, x = depth in mm, t = time in years, C(x,t) = chloride content at depth x and time t, Cs = surface chloride content in % wt. of concrete
Observed that steel corrosion due to chloride penetration has been one of the most common problem related to durability of concrete structures. Usually studies were performed on unstressed concrete structure. However, in this study tests have been performed on specimens stressed and exposed to salt solution to study the effect of stress on the resistance to chloride ion penetration and diffusion of chlorides in concrete.
Evaluated diffusion coefficient is of mortar in concrete, and diffusion coefficient of concrete can be evaluated using this. Also presented effect of w/c ratio and concrete stress on penetration of chloride ion. For the concrete in tension penetration of chloride is rapid when compared with unstressed or compressed concrete, and smaller the w/c ratio smaller the ‘D’ and chloride content. Temperature has been considered as constant; however, if the variation of temperature and its effects on penetration of chloride ion is evaluated then proposed relation is more realistic.
Bastidas-Arteaga et al. (2008) [32]
effective diameter of bar
dbar(t)=do[1−W(t)/Wo] where dbar(t) = diameter of the bar at time t, do = initial diameter of the bar in mm, W(t) = amount of corrosion products at time t, and Wo = is the initial weight of bar.
Developed a probability based model based on effects of bio-deterioration in degradation of RC structures, to assess the life time of RC structures. This Model includes corrosive environment and cyclic loading. The developed model is applied for the analysis of bridge girders located in chloride contaminated environments, and it has been explained with a numerical example by computing the probability of failure of a reinforced concrete pile. This analysis indicated that the failure probability of RC structures depends on the corrosion rates, surface chloride concentration and the frequency of traffic.
Degradation of RC structures can be evaluated by measuring loss in diameter of steel bars. Loss in effective diameter of rebars due to corrosion reduces the load carrying capacity of structures resulting in failure of RC. In this research author has coupled bio-deterioration, chloride ingress and cracking for determining the condition of RC structures, through the loss in effective diameter of rebars.
Cheung et al. (2009) [33]
corrosion initiation time (t)
t=(1/k)·(hmean)a·(Cs)b·dcwhere hmean = annual mean relative humidity, Cs = source chloride concentration, d = effective cover depth, k, a, b and c = adjustment factor for the w/c ratio and weighing factors.
Developed a 2-D finite element based coupled model to evaluate the chloride penetration process in changing environmental conditions to predict the initiation time of corrosion. Observed that corrosion initiation period is governed by environmental conditions to which concrete is exposed and physical properties of the structure which includes heat transfer, moisture transfer, chloride diffusion etc.
Changes in environmental conditions significantly influence the corrosion initiation process. Proposed model calculate initiation period considering only chloride attack, but carbonation depth and other chemical attacks also have significant influence on the performance of structures.
Cao and Sirivivatnanon (2001) [34]
time (t) required by chloride (Cx) to reach at depth (x)
t=(x2/2k1k2k3Da).[erf−1(1−Cx/ζθCs)] where Da = apparent diffusion coefficient, k1,k2 and k3 are the exposure time, temperature, and stress correction factor respectively; Cs = surface chloride content, z = microclimatic load factor, and q = crack width factor.
Presented a simple model to predict the service life of RC structures based on the solution derived from Fick’s 2nd law of diffusion with modifications. Acceptable steel corrosion rate is suggested for use in the prediction of service life.
Usually chloride ingress models are valid for uniform materials, absolute concrete cover and unified environment. The proposed model accounts for most of the factors affecting the service life such as exposure time, temperature and stress variations, microclimatic conditions etc.
Liang et al. (2009) [35]
degree of deterioration
Dd=1−(x/10)where x is the integrity of RC structure its value ranges from zero to ten.
Proposed a mathematical model based on Fick’s 2nd law of diffusion to evaluate the service life of RC bridges. Also considered three stages of corrosion initiation time (tc), depassivation time (tp) and propagation time (tcorr). Hence, total service life of existing RC bridge is t = tc + tp + tcorr.
Most of the researchers divided service life in three phases such as initiation, depassivation and propagation. And proposed a model to calculate depassivation time. Model has been proposed for chloride environment, so it may not be valid for other conditions. More research is required to develop a model for all the environmental conditions.
depassivation time (tp)
tp=(1/4Dc)·[L/(1−C*/Co)]2 where L= concrete cove, Dc = chloride ion diffusion coefficient, C* = threshold value of chloride content, Co = surface chloride content.
Klinesmith et al. (2007) [36]
corrosion loss (y)
Y=AtB(TOW/C)D(1+SO2/E)F(1+Cl/G)HeJ(T+To)Where Y = corrosion loss; t = exposure time; TOW= time of wetness; SO2 = sulfur dioxide; Cl= chloride deposition rate; t = air temperature; and A, B, C, D, E, F, G, H, and To = empirical coefficients.
Evaluated the effect of environmental conditions over the corrosion. Formulated a model considering different environmental variables such as wetness time, sulfur dioxide, Salinity and temperature. Observed that developed models are reliable for use in several conditions.
To evaluate corrosion loss accurately effect of environmental factors such as sulfur dioxide and wetness time, chloride deposition rate and air temperature has been considered.
Stewart and Val (2003) [37]
crack propagation (Tser)
Tser=[A×(WC/C)−B]/icorrwhere WC = water cement ratio; C = concrete cover in mm; icorr = corrosion rate; A and B are empirical constants
Presented models for reliability and life-cycle cost analyses of reinforced concrete bridges damaged by corrosion. A stochastic deterioration process for corrosion initiation and propagation and then crack initiation and propagation has been used to examine the effect of cracking, spalling and loss of reinforcement area on structural strength and reliability. Expected costs of failure for serviceability and ultimate strength limit states have been calculated and compared for different repair strategies and inspection intervals.
This model assumed constant corrosion rate, but it is better to consider time variant corrosion rate.
Sobhani and Ramezanianpour (2008) [38]
corrosion Initiation period (Ti)
Ti=(c2/4Dc).[erf−1(Cs−Ccr/Cs)] where c is cover depth in mm, Dc is diffusion coefficient m2/s, Cs is surface chloride content and Ccr is critical chloride concentration (% wt. of concrete)
Developed an algorithm to evaluate the fuzzy membership functions from available information. Proposed an integrated system to convert the probablistic information into the corresponding fuzzy sets. Also detected that under harmful enviromental conditions, concrete prepared and placed properly can also get corroded.
Considered environmental conditions such as relative humidity, degree of drying and wetting, and average temperature. This model provides good results in estimating service life and predicting life cycle of structures.
corrosion induced cracking period (Tcr)
Tcr=(Wcrit)2/2kpwhere Wcrit is amount of corrosion products and kp is the rate of rust production.
Caner et al. (2008) [39]
remaining life of bridges
B1=(Gc−3)/Mswhere Bl = remaining bridge life in years; Gc = current condition rating based on inspection; and Ms = slope for deterioration of element
28 bridges of different age and conditions are inspected to develop a methodology for evaluating the remaining service life of a bridge and also, proposed a relationship between the current condition rating and age of the brides.
Proposed a methodology to evaluate the remaining service life of a bridge based on current condition. This model is based on the results of a short-term field tests, but it has been recognized that models developed using results of long-term regular inspections are better in accuracy.
Li et al. (2005) [40]
serviceability failure probability of corrosion affected concrete structures
Limit state function ‘G’ can be defined as G(L,S,t)=L(t)−S(t)where S(t) denotes the response of structure at time t, such as stresses and deformation; and L(t) denotes a critical limit for structural response, which may change with time but in most practical use it is a constant prescribed in the design codes. With the limit state function, the probability of serviceability failure ps, can be determined by: Ps(t)=P[G(L,S,T)⟨=0]=Ps(t)⟩L(t)
A performance based methodology for assessing the serviceability of corrosion affected concrete structures has been presented. Time-dependent reliability methods have been applied to evaluate the probability of serviceability failure.
Major advantage of this model is that the structural response has been directly related to the design criteria used by structural engineers and asset managers.
Tab.1
S. No. of surveyed structure
concrete cover (mm)
carbonation depth (mm)
chloride content (% wt. of concrete)
half cell potential (mV)
compressive strength (MPa)
age (years)
1
32
3
0.0050
-10.33
25
1
2
45
5
0.0060
-34.10
22
3
3
48
7
0.0062
-45.10
18
4
4
37
12
0.0065
-121.10
16
8
5
57
9
0.0068
-64.40
21
8
6
56
11
0.0080
-64.88
18
9
7
57
10
0.0080
-74.40
21
10
8
54
14
0.0080
-64.27
18
10
9
51
10
0.0100
-121.20
19
10
10
53
10
0.0100
-58.15
17
10
11
42
10
0.0950
-91.20
19
10
12
55
12
0.0100
-88.15
19
10
13
56
14
0.0130
-100.70
19
12
14
38
16
0.0150
-115.08
20
12
15
52
16
0.0180
-135.35
18
13
16
42
15
0.1100
-143.20
30
14
17
45
19
0.0800
-155.96
18
14
18
58
12
0.0150
-50.70
19
15
19
52
20
0.0200
-145.08
20
15
20
44
20
0.0500
-165.35
18
15
21
42
12
0.1100
-173.20
30
15
22
40
20
0.1200
-154.72
29
15
23
39
20
0.1100
-166.20
16
16
24
41
22
0.1300
-182.10
15
16
25
42
23
0.1300
-207.60
14
17
26
37
25
0.2200
-329.70
16
17
27
43
24
0.1600
-219.90
18
19
28
45
20
0.0800
-185.96
18
20
29
47
20
0.1200
-154.72
29
20
30
38
25
0.1500
-254.20
30
20
31
44
28
0.1700
-270.72
31
22
32
46
21
0.0900
-195.92
18
22
33
45
22
0.1300
-154.72
29
23
34
43
28
0.1900
-331.52
28
24
35
39
28
0.1900
-354.20
30
24
36
45
24
0.0900
-246.20
16
25
37
47
25
0.0800
-232.10
15
25
38
47
35
0.0900
-507.60
14
25
39
32
30
0.3000
-629.70
16
25
40
39
30
0.1900
-277.05
14
25
41
38
30
0.2100
-296.20
14
25
42
37
30
0.2200
-381.52
28
25
43
45
27
0.1200
-296.20
16
26
44
37
31
0.2500
-468.10
14
28
45
42
32
0.2300
-303.80
13
28
46
48
30
0.1100
-329.90
18
28
47
41
29
0.1800
-302.10
15
28
48
37
31
0.2500
-468.10
14
28
49
39
25
0.1500
-227.60
18
30
50
47
30
0.1200
-274.20
30
30
51
53
40
0.1300
-170.72
31
30
52
37
40
0.3500
-331.52
28
30
53
42
34
0.2500
-351.76
16
30
54
40
35
0.2800
-471.88
12
30
55
48
25
0.1500
-227.60
18
30
56
43
34
0.2400
-457.90
14
31
57
41
33
0.2800
-559.70
16
31
58
49
41
0.1400
-190.72
31
31
59
42
35
0.2700
-390.72
31
32
60
37
33
0.2900
-397.05
14
32
61
42
30
0.2000
-275.05
14
35
62
46
30
0.2200
-286.20
14
35
63
48
35
0.1900
-374.20
30
35
64
44
33
0.2600
-341.52
28
35
65
44
33
0.2600
-407.60
14
37
66
46
36
0.2800
-383.80
13
38
67
44
34
0.2800
-391.76
16
38
68
43
35
0.3100
-439.70
16
39
69
41
40
0.3100
-406.20
14
39
70
42
30
0.2300
-268.10
14
40
71
45
30
0.2900
-411.88
12
40
72
44
32
0.2800
-368.10
14
42
73
42
40
0.2900
-382.10
15
44
74
46
30
0.2600
-375.05
14
44
75
45
35
0.2500
-503.80
13
45
76
46
31
0.2700
-296.20
14
45
77
43
34
0.2900
-403.80
13
45
78
45
37
0.3000
-356.20
16
46
79
43
36
0.3000
-381.33
13
48
80
44
38
0.3200
-392.39
13
48
81
45
38
0.3000
-371.76
16
50
82
43
38
0.3000
-371.76
16
50
83
41
35
0.3400
-371.88
12
50
84
46
40
0.3500
-447.60
12
52
85
49
40
0.3400
-437.60
12
52
86
49
39
0.3100
-381.33
13
55
87
45
38
0.3200
-390.19
13
55
88
45
42
0.3700
-481.33
13
55
89
47
38
0.3500
-390.19
13
56
90
47
40
0.3000
-271.88
12
58
91
48
40
0.3000
-281.33
13
58
92
48
35
0.3000
-290.19
13
58
93
46
25
0.3200
-347.60
12
58
94
45
42
0.3400
-447.60
12
58
95
44
30
0.3800
-433.44
14
60
96
48
32
0.3600
-443.44
14
60
97
45
40
0.3600
-483.44
14
62
98
55
40
0.3600
-434.56
15
62
Tab.2
S. No.
half cell potential (mV)
% chance of corrosion
1
>−119
10
2
−119 to −269
50
3
<−269
90
Tab.3
Fig.1
Fig.2
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
Fig.9
Fig.10
Fig.11
Fig.12
group
concrete cover (mm)
No. of structures
Cc1
≤40
16
Cc2
>40 and≤45
35
Cc3
>45 and≤50
34
Cc4
>50
13
Tab.4
group
compressive strength (MPa)
No. of structures
Cs1
0 to 15
44
Cs2
16 to 25
38
Cs3
more than 25
16
Tab.5
Fig.13
Fig.14
Fig.15
Fig.16
Fig.17
Fig.18
Fig.19
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