In reliability-based durability design of reinforced concrete (RC) structures, the depassivation of reinforcing steels is often taken as the durability limit state, and the target reliability index is a key parameter controlling the long-term durability performance of RC members. This study investigates the impact of target reliability of durability design in design phase on the life-cycle performance and the maintenance cost of RC structures. For this purpose, a chloride diffusion model for steel depassivation of RC members is firstly established; and then the cost models for maintenance of RC beam members are proposed. Based on the detailed section design and the durability limit state of steel depassivation, Monte-Carlo simulation is used to calculate the reliability index for the durability design of RC beam members; and then according to the defined maintenance inventions and associated costs, the maintenance costs for the whole service life are evaluated for different durability reliability indices. Finally, the impact of target reliability of durability design on the deterioration process and the maintenance cost is discussed

Li, L.

Li, Q.

Zhang, H.

Q. Li

H. Zhang

L. Li

Crossref

Impact of target reliability of durability design on maintenance cost of reinforced concrete members in chloride environment

University of Queensland eSpace

IM3ACT OF TARGET RELIABILIT< OF DURABILIT< DESIGN ON MAINTENANCE 
 COST OF REINFORCED CONCRETE MEMBERS IN CHLORIDE ENVIRONMENT  
 
 
Q. Li1, H. Zhang2, and L. Li3 
1Department of Civil Engineering, 
Tsinghua University, Beijing, 100084, China. Email: li_quanwang@tsinghua.edu.cn 
2School of Civil Engineering, 
University of Sydney, NSW 2006, Sydney, Australia 
3Department of Science and Technology Development, 
China Road & Bridge Corporation, Beijing, 100103, China 
 
 
ABSTRACT 
In reliability-based durability design of reinforced concrete (RC) structures, the depassivation of reinforcing 
steels is often taken as the durability limit state, and the target reliability index is a key parameter controlling the 
long-term durability performance of RC members. This study investigates the impact of target reliability of 
durability design in design phase on the life-cycle performance and the maintenance cost of RC structures. For 
this purpose, a chloride diffusion model for steel depassivation of RC members is firstly established; and then 
the cost models for maintenance of RC beam members are proposed. Based on the detailed section design and 
the durability limit state of steel depassivation, Monte-Carlo simulation is used to calculate the reliability index 
for the durability design of RC beam members; and then according to the defined maintenance inventions and 
associated costs, the maintenance costs for the whole service life are evaluated for different durability reliability 
indices. Finally, the impact of target reliability of durability design on the deterioration process and the 
maintenance cost is discussed.  
 
KEYWORDS 
 
Durability design; target reliability; maintenance cost; reinforced concrete members; chloride environment. 
 
INTRODUCTION 
Maintenance is essential to ensure the expected service life of reinforced concrete (RC) structures, especially for 
port structures which are subjected to the attack of chloride ions in marine environment. The maintenance cost of 
a port structure depends on the structural deterioration rate, allowable limit state intervention techniques, 
maintenance schemes and the generated user costs. Existing studies have investigated the impact of maintenance 
interval, discount rate, maintenance schemes and allowable limit states on maintenance cost (Val, 2005; Kendall 
et al., 2008; Chiu et al, 2010). And cost-based methods, e.g. life cycle cost analysis, have been extensively 
applied to optimize the maintenance works for RC structures (Singh and Tiong 2005; Bucher and Frangopol, 
2006; Li et al. 2009). In reliability-based durability design of RC structures, the depassivation of reinforcing 
steels is often taken as the durability limit state, and the target reliability level has important impact on the 
deterioration rate, thus also on the maintenance cost. In Chinese code for durability design of RC elements, the 
target reliability of embedded steel bars remaining passivated is stipulated as 1.3 (CCES, 2005), while in 
European code the target reliability is 1.5 (Duracrete, 1998). Theoretically, the determination of target reliability 
should distinguish the expected service life of the structure, which could be done in the context of life-cycle cost, 
however up to now, no research work has been performed on the life-based durability design of reinforce 
concrete structures.  
 
This paper investigates the impact of target reliability on the maintenance cost of RC structure of a marine port 
with a design service life of 30 years. The port of container wharf was built in 1998 and located in Guangzhou, 
China. The structure of wharf is a RC beam-slab system supported by high driven piles. The annual average 
temperature is between 22.3-23.1ºC with most elevated temperature as 28.4-28.8 ºC (July) and lowest 
temperature as 14.8-15.9 ºC (January). The annual average humidity is between 77-80% with important seasonal 
variation, and the seasonal humidity can reach 100% (spring and summer) and drop to 10% (winter). The main 
durability process for the RC structural members is identified as the chloride-induced corrosion of reinforcing 
steel bars. In this paper, the deterioration models and cost models are first established for the RC beams in the 
wharf. And then, the influence of target reliability of durability design for RC structures is investigated for its 
1537
impact on the deterioration process of RC elements as well as the resulted maintenance costs. As a result, the 
optimized target reliability is discussed for the durability design of RC elements. 
 
MODELS 
Deterioration of RC members 
The control process for the deterioration of RC members is chloride-induced corrosion of the embedded steel 
bars. The durability limit state is defined as the steel de-passivation, i.e. the external chloride ions penetrate into 
the concrete and accumulate at the steel surface, to a critical concentration high enough to initiate the steel 
corrosion. The analytical solution of Fick’s second law is usually retained as engineering model (DuraCrete, 
1998; fib, 2006), and the design equation for corrosion process can be expressed as: 
   0 0 Cl
1 0
2
S Cr
xG C C C erf C
D t t
­ ½ª º§ ·° °« »¨ ¸     t® ¾¨ ¸« »° °© ¹¬ ¼¯ ¿
                 (1) 
in which C0 is the initial chloride content in the concrete; CS is a constant chloride concentration imposed on the 
surface; x is the thickness of concrete cover; DCl is the apparent chloride diffusion coefficient in concrete and erf 
is the mathematical error function. This apparent diffusion coefficient is found to be time-dependent (Bamforth, 
1999), and a power law is recommended for its ageing behavior (Mangat and Molloy, 1994), 
  0 0Cl Cl
atD t D t
§ · ¨ ¸© ¹
                                   
(2)
 
with DCl0 stands for the diffusion coefficient at concrete age t0, a for the exponential coefficient. In the 
calculation of DCl, t is taken as 30 years as t > 30 years 
 
Cost models 
The maintenance cost of a RC element during its service life can be is expressed as  
   
, ,
1 1 1i i
n
r i u i
m t t
i
C CC
r r 
§ ·
 ¨ ¸¨ ¸ © ¹
¦                               (3) 
in which Cm is the total maintenance cost; Cr,i is the cost of the ith maintenance intervention; Cu,i stands for the 
user cost of ith maintenance by possible disturbance and stoppage of berth service; n is the number of 
maintenances during service life and ti is the time (year) of the ith maintenance; r is the discount rate of currency.  
The discount rate r is determined by the social discount rate and the annual changing rate of producer price index 
(PPI). According to Cady (1983), the discount rate is assumed to adopt a step function:  
2.0% 0 ~ 30 years
2.7% 31 ~ 60 years
3.3% 61 ~ 90 years
4.0% 90 years
i
i
i
i
t
tr t
t
 ­
°  ° ®  °
° !¯
                             (4) 
 
DETERIORATION AND MAINTENANCE 
The exposure zones of RC elements in marine environment are classified as immerged zone, tidal zone, splash 
zone and atmospheric zone, as seen in Figure 1. In the paper, for purpose of simplicity, the maintenance plan 
concerns cross beams only. The design parameters of the cross sections are in Table 1. 
 
The function in Eq.1 is used to calculate the failure probability of RC elements under chloride action. The basic 
parameters are C0, CS, CCr, D and a. These parameters all depend on concrete material composition and have 
statistical properties. Their statistical properties are obtained by on-site survey of similar port structures in 
Guangzhou and referring to durability standards (CCES 2005; fib 2006), and listed in Table 1.  
 
 
 
 
1538
 
 
 
 
 
 
 
 
 
 
Figure1 Vertical view and exposure zone of RC elements in the wharf 
 
Table 1 Design values and statistics of durability parameters 
Design parameters 
Dimension (m) Concrete D0 (10-12m2/s) Concrete Cover (mm) 
8.5×1.4×2.0 C45 4.5 70 
Statistics of parameters in deterioration model 
Parameter Distribution Mean Value Coefficient of Variation 
C0 (%binder) Lognormal 0.06 0.1 
CS (%binder) Lognormal 4.5 0.15 
x (mm) Normal 65, 70, 75 0.1 
CCr (%binder) Lognormal 0.45 0.2 
D (10-12m2/s) Lognormal According to Eq.(2) 0.2 
a (-) Lognormal 0.4 0.1 
 
Monte-Carlo simulation is used to obtain the failure probability of Eq. 1. The total number of samples is 100,000. 
The failure probability of the cross beam is shown in Figure 2, which increases as the service age grows.  
 
 
Figure 2 Failure probability of cross beam as the increase of service age 
 
In practice, the maintenance intervention methods are decided based on the deterioration condition of RC 
members. The adopted intervention techniques depend strongly on the damage condition of members, which is 
dominantly affected by the corrosion extent of steel reinforcing bars, thus the corrosion extent of steel bars 
determines majorly the maintenance cost of RC members. Recognizing this, in this paper, three levels of 
intervention levels, named “preventive”, “necessary” and “mandatory” represented by failure probability of steel 
bar de-passivation, are defined in the maintenance planning of RC elements in the wharf, as seen in Table 2. The 
failure probabilities are 2%, 5% and 20% respectively corresponding to the “preventive”, “necessary” and 
“mandatory” maintenance levels, which are also shown in Figure 2. Table 2 lists the costs for the maintenance 
techniques considered in this study and the corresponding impact on port regular service of the three intervention 
levels. The maintenance cost is given as a “relative cost” which is calculated in terms of the price of new 
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
20 30 40 50 60 70 80 90 100
Fa
ilu
re
 p
ro
ba
bi
lit
y
Service age (year)
Preventive
Necessary
Mandatory
Platform 
Cross
beam 
Atmospheric 
Splashing 
Tidal 
Immerged 
Slab 
1539
member including the design cost, material cost and construction cost. The user daily cost is estimated on the 
basis of the income of berths in last 10 years in this port, which is roughly 0.009 of the price of the new 
structure.  
 
Table 2 Definition of 3 interventions 
Maintenance level Operations Intervention cost Service disturbance 
Preventive, Pf = 2% Chloride extraction 0.88 Almost no disturbance 
Necessary, Pf = 5% Chloride extraction & 
Surface treatment 
1.14 Limited disturbance 
Mandatory, Pf = 20% Cover reconstruction 
& Steel supplement 
2.10 Close for 90 days. 
 
According to the deterioration process shown in Figure 2, suppose that the port structure is expected to work for 
100 years, the intervention times for the “preventive” level are 21year, 42year, 63year and 84year, respectively; 
for “necessary” level they are 29 year, 58year and 87year; for “mandatory” level they are 44year and 88year. 
With the intervention costs in Table 2, the maintenance costs for difference intervention levels are obtained. They 
are 1.04, 0.95 and 1.12 for the 3 intervention levels respectively. From the cost analysis, it can be seen that 
“necessary” maintenance achieves the lowest cost; “preventive” maintenance generates higher costs because of 
the very frequent operations; “mandatory” maintenance generates higher costs due to the associated high user 
costs caused by closed service during the heavy maintenance operations.  
 
IMPACT OF TARGET RELIABILITY  
The cross beams in the considered port structure has a reliability level of E= 1.6 (failure probability of 5.5%) for 
durability for design life of 30 years. If the target reliability increases to 1.9 (failure probability of 3%) or 
decreases to 1.3 (failure probability of 10%), with concrete diffusion coefficient remaining unchanged, the 
concrete cover thickness needs to increase to 75mm, or decreases to 65mm, respectively. For these two cases, the 
failure probabilities of the cross beam are obtained through Monte-Carlo simulation and shown in Figure 3. 
 
              
(a) E = 1.9                                     (b) E = 1.3 
Figure 3 Failure probability of cross beam with changed target reliability level 
  
With the deterioration process in Figure 3 and the maintenance costs in Table 2, the maintenance intervals and 
costs for the three intervention levels are determined and given in Table 3. It can be seen that the “necessary” 
maintenance always achieves the lowest cost, which indicates that the optimum maintenance plan should be 
made referring to the “necessary” maintenance level. To investigate the impact of target reliability on the 
maintenance cost, more reliability indices are considered, and the associated maintenance costs are plot in 
Figure4. It is clearly seen that the maintenance cost decreases with the increase of durability reliability; in the 
range of durability reliability index being smaller than 1.6, the decrease of maintenance cost is relatively rapid, 
while in the range of durability reliability index being larger than 2.0, the decrease of maintenance cost is 
relatively slow. Therefore, it can be concluded that the optimum target reliability index should lie between 1.6 
and 2.0, and the determination of it should refer to the increase in the construction cost as the target reliability 
index becomes larger.  
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
20 30 40 50 60 70 80 90 100
Fa
ilu
re
 p
ro
ba
bi
lit
y
Service age (year)
Preventive
Necessary
Mandatory
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
20 30 40 50 60 70 80 90 100
Fa
ilu
re
 p
ro
ba
bi
lit
y
Service age (year)
Preventive
Necessary
Mandatory
1540
 
Table 3 Maintenance levels and costs 
Target 
reliability 
Maintenance 
Level 
Maintenance 
Interval 
Intervention 
cost 
User cost Maintenance 
 
1.3 
Preventive 17 1.36 0 1.36 
Necessary 23 1.21 0 1.21 
Mandatory 37 0.97 0.38 1.35 
 
1.6 
Preventive 21 1.04 0 1.04 
Necessary 29 0.95 0 0.95 
Mandatory 44 0.81 0.31 1.12 
 
1.9 
Preventive 26 0.82 0 0.82 
Necessary 33 0.63 0 0.63 
Mandatory 49 0.50 0.18 0.68 
 
 
Figure 4 Dependence of maintenance cost on target reliability index 
 
CONCLUSIONS  
This paper establishes the deterioration model and maintenance cost model for the life-cycle cost analysis of RC 
elements in marine environments. Through Monte-Carlo simulations, taking the de-passivation of embedded 
reinforcing steel bars as durability limit state, the cost analyses for different durability reliabilities and 
maintenance levels are performed. The results show that the “necessary” maintenance, with failure probability of 
5% for design life of 30 years as intervention threshold, always achieves the optimized maintenance cost; the 
maintenance cost decreases as the durability reliability becomes larger, but the optimum target reliability index 
lie between 1.6 and 2.0, and the determination of it needs to consider the change in the construction cost. 
 
ACKNOWLEDGEMENTS  
The research is partly supported by the China Road & Bridge Corporation. The support from Major 
Projects Foundation of Chinese Ministry of Transport under grants 201332849A090 is also acknowledged. 
 
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1541
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Impact of target reliability of durability design on maintenance cost of reinforced concrete members in chloride environment

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