PSI - Issue 5

K Bouzelha et al. / Procedia Structural Integrity 5 (2017) 77–84 K Bouzelha et al./ StructuralIntegrity Procedia 00 (2017) 000 – 000

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Thus, the reliability analysis consists to calculate the failure probability of the structure defined by (7): P f = P(G{X}) ≤ 0 (7) Which is given by the integral of the joint function of the probability density f x (x) of the random vector {X} as follows: P f = ∫ f x (x)dx Df (8) D f is the ruin domain defined by:     D = x R / G 0   f x . The analytical evaluation of the probability failure of earthen dam by using (8) is very difficult or impossible. Several approaches based on numerical integrations and approximations are suggested in the literature. In this steady, we use classical simulation method of Monte Carlo. This old and intuitive technique assesses the failure probability Pf by succession independent random draws. It consists to reach a significant number Nt of random variables according to their joint distribution law. Thus, a ruin indicator IG is used to define the failure state of the system for the given state function G (Lemairet al., 2005). This ruin indicator IG is given by (9): I G ≤0 = { 1 si G ≤ 0 0 si G > 0 (9) For each mode of ruin, the probability of failure P f is given by (10) (Lemaire et al., 2005): P f = ∑ I N1 t G N t (10) 4. Practical application To illustrate the reliability analysis of a small dam, we consider a homogeneous embankment, implanted on loose soil designated as site S 3 by the RPA. Geometrical characteristics of this small dam are summarized in Table 2 (AGC, 2008), and calculation parameters are given in fig. 2.

Table2: Geometrical characteristics of the small dam. Symbol Designation

Value 18,00

Unit

H

Height of the embankment

m m

b

Thickness of slices Material density

0,3

γ s γ h

1800,00 2000,25 3000,80

Kg/m Kg/m Kg/m

3

Humid density

3

γ sat

Dry density

3

- -

Upstream slope Downstream slope

1 : 3

1 : 2.5

level of the crest : 637.69

Highest level of the reservoir : 636.49

Normal level of the reservoir : 634.25

1 ,00

Minimum operating level : 631.48

2,5

3

1

1

3

2,5

1

1

Natural land : 619.69

1,5

1

5

2

1

0 ,50

0 ,30

1

1

1

1

1

1

Fig. 2. Cross section of the analyzed embankment.