Proceedings of the International rilem conference Materials, Systems and Structures in Civil Engineering 2016

31

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures

 

 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

                                                             (2) 

 

 

 

3.

 

Reliability concepts to model the corrosion initiation due to carbonation 

 

The safety margin (M) or limit state function for corrosion initiation can be defined as Eq. (3), 

where ‘t’ is the exposure period, ‘X’ is random variables.  

 

     M = G(X, t)= T

i

 – t                                                                                                               (3) 

 

Assuming that a system fails when corrosion initiation takes place, the probability of 

corrosion initiation (P

f

) is evaluated by integrating G(X,  t)   0 over the failure domain, 

considering the statistical distribution of each random variable. Eq. (4) shows how to estimate 

’P

f

’ using the joint density function fx(x

i

) with random variables [5].  

 

                                                       (4) 

 

In addition, Monte Carlo simulation can be used to calculate ‘P

f

’ by simulating the limit state 

function for a range of sampling. In this approach, the mean value of I (x

i

) can be an estimator 

for the probability of corrosion initiation as given in Eq. (5).  

 

 

                                                                                                          (5) 

 

where 

 

 

In estimating ‘P

f

’, it is vital to identify the basic set of random variables, of which 

uncertainties have to be considered. Then, the randomness of all the variables is modelled, 

recognizing the probability distributions of the variables. These probability distributions can 

be defined by physical observations, statistical studies, laboratory analysis, and expert opinion 

[5, 6, 7]. 

 

 

4.

 

Case study: condition assessment of reinforced concrete consoles 

 

4.1 Statistical quantification of random variables and prediction of corrosion initiation 

Three consoles, with almost no visible corrosion damage, were chosen to be tested 53 years 

into their service life. They are located on the fourth floor in a residential building in Bergen, 

Norway (about 2-3 km away from  sea and 50 m above sea level); one of the consoles is 

shown in Figure 1. While assessing the present condition of the consoles, it is necessary to 

collect existing data. The existing data includes general information about the structure, 

material properties and exposure condition, documentation of former inspections/monitoring 

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32

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures

 

 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

and documentation of former maintenance and repair. In the absence of information about the 

actual cement type and water/cement ratio, cement type CEM I R and w/c 0.5 are chosen for 

this analysis. The probability distributions for the random variables (R

-1ACC

,, 

t

, RH

real

, C

s,atm

, 

b

c

, b

w

, X

cover

) for Eq. (2) were chosen, taking into consideration the actual exposure condition, 

as given in Tab. 1. Based on the exposure condition to rain, the probability of corrosion 

initiation has been found for two cases: sheltered from rain and partially exposed to rain, as 

shown in Figure 1.  

 

Sheltered from rain

Partially exposed to rain

 

Figure 1: Reinforced concrete Console 1 in the building 

 

Table 1: Statistical characteristics of variables  

Parameter  

Distribution 

Mean 

Standard 

deviation 

Reference 

R

-1

ACC,

(10

-11

*mm

2

/s/kg/m

3

) 

 Normal 

6.8(w/c=0.50 

and CEM I R) 

2.5 

fib Bulletin 34[1] 

t

 (mm

2

/s/kg/m

3

) 

 Normal 

315.5 48 

fib Bulletin 34[1] 

k

t

 

 Normal 

1.25  0.35 

fib Bulletin 34[1] 

ke =

 

 

RH

real 

RH

ref 

f

e 

g

e 

WBmax(w=1) 

Constant 

Constant 

Constant 

0.825 

0.65 

2.5 

5.0 

0.032 

- 

- 

- 

From weather 

station 

fib Bulletin 34[1] 

 

C

s

=C

s,atm

 +C

s,em

(kg/m

3

) 

C

s,atm 

C

s,em 

Normal 

- 

0.0008 

0 

0.0001 

fib Bulletin 34[1] 

 

k

c 

 

b

c 

t

c   

(days)  

 

Normal 

Constant 

-0.567 

1 

0.02 

- 

fib Bulletin 34[1] 

 

W(t)        Exposed to rain 

t

0

(years)

 

ToW 

b

w 

Constant 

Constant 

Normal  

0.0767 

0.010 

0.446 

- 

- 

0.163         

fib Bulletin 34[1] 

 

fib Bulletin 34[1] 

               Sheltered from rain 

W(t) Constant  1 

 

 

X

cover

(mm) 

 Normal 

25 

8  

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