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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 4

Reliability algorithms applied to reinforced concrete durability assessment

must be the covers adopted to

reach the condition of reliability

index stabilization. Thus, this

type of analyses gives an in-

teresting parameter which can

be used to establish periods of

structural maintenance accor-

ding the type of concrete used

and the environment where the

structure is located.

5.3 Example 3

The proposed probabilistic mo-

del can be used to determine

intervals of time in order to plan

inspection and maintenance

procedures in reinforced concrete structures as function of w/c ra-

tio adopted. For each w/c value adopted for concrete conception,

an abacus can be constructed using the probabilistic model. These

abacuses allow the choice of an optimum value of concrete cover

in order to perform maintenance procedures in fixed time intervals.

It is important to stress that these intervals are based on safety

criterion. Then, the costs involved in maintenance and repair costs

are not considered.

For this proposal, a reference value, named target, of reliability

index was chosen, which was assumed as minimum requirement

of safety. Then, when the structure has a reliability index lower

than the target one, maintenance is required. According [29], the

target reliability index expresses the requirements of structural sa-

fety, which guarantees acceptable values of structural failure risk

considering a given scenario. In this regard, [29] defines a set of

values of target reliability index considering failure limit state and

serviceability limit state scenarios. The corrosion time initiation is

considered as a serviceability limit state scenario. In this study, the

loss of reinforcements cross sections have not been considered,

which is a failure limit state. Therefore, the target reliability index

adopted is 1.30 leading a probability of failure close to 10%. Other

values of target reliability index can, evidently, be adopted as func-

tion of the structural risk desired.

The analyses in this application were carried out considering the

random variables presented in table 2, as well its statistical proper-

ties. It was considered two clas-

ses of aggressiveness, C.A.

II and C.A. III. The abacuses

involving reliability index, time

and cover depth for C.A.II are

presented in figures 13 and 14.

It is worth to mention that only

w/c ratio 0.40 and 0.50 were

analyzed, since higher w/c ratio

led to reliability indexes lower

than the target. Consequently,

it indicates that these w/c ratios

should not be used in reinforced

concrete applications.

Figure 13 presents the beha-

viour of the reliability index in

function of time for concretes

with w/c ratio equal to 0.40 and C.A.II. According these results,

cover depth value of 10mm is not recommended, because it indi-

cates failure (reliability index lower than the target) even for short

time after construction. For cover depth of 20mm, the maintenance

procedures should be performed 10 years after construction. At

this time, the structural reliability index is equal to the target. After

this time, the structural reliability becomes lower than the target,

indicating failure. It is worth to mention that cover depths values

bigger than 30mm lead maintenance time interval bigger than 25

years. In these cases, the analysts should study the possibility of

change of w/c ratio in order to allow, at least, one inspection in the

first 25 years of structural life-time.

Similar behaviour can be observed in figure 14, where concretes

with w/c 0.50 and C.A. II were considered. In this case, the mini-

mum cover required is 30mm, which lead to maintenance procedu-

res 8 years after construction. Otherwise, considering cover depth

equal to 50mm, the maintenance procedure should be performed

21 years after construction in order to keep the structural safety

at a desired level. Therefore, by changing the cover depth from

30mm to 50mm, or increasing the cover in 20mm, the maintenance

can be performed 13 years later.

On the other hand, considering cover depth of 30mm, the main-

tenance time for concretes with w/c ratio 0.40 and 0.50 are 23

and 8 years, respectively, in C.A.II. Then, it can be verified an in-

crement of 187.5% on the maintenance time interval by slightly

Figure 12 – Evolution for probability of corrosion

initiation – C.A.III structural life-time = 25 years

0,0

0,2

0,4

0,6

0,8

1,0

10,0

20,0

30,0

40,0

50,0

60,0

Concrete cover (mm)

Probability of corrosion

initiation

w/c=0,4

w/c=0,5

w/c=0,6

w/c=0,7

Figure 13 – Required reliability index

abacus for C.A.II and w/c = 0.40

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

5

7

9 11 13 15 17 19 21 23 25

Time (years)

Reliability index

p=10

p=20

p=30

p=40

p=50

p=60

target

Figure 14 – Required reliability index

abacus for C.A.II and w/c = 0.50

-0.50

-0.25