PSI - Issue 22

Mahdi Shadab Fara et al. / Procedia Structural Integrity 22 (2019) 345–352 Shadab Far and Huang / Structural Integrity Procedia 00 (2018) 000–000

351

7

0 10 20 30 40 50 60 70 80 90 100

1.5

1

Factor of safety

Failure probability (%)

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.5

0.75

1

1.25

1.5

Normalized water table location

Factor of safety

(a) Cumulative failure probability

(b) The factor of safety versus water table position

Fig. 7. The results of analyses presenting (a) cumulative failure probability and (b) factor of safety per di ff erent water table positions.

Table 3. Di ff erent distribution functions assumed for water table level. Distribution function

Failure probability

Uniform

15.33 11.42

Triangular

Normal

9.81 7.76

Exponential

10 20 30 40 50 60 70 80 90 100

Unform distribution Triangular distribution Normal distribution Exponential distribution Withough considering Y wn as a variable

Failure probability (%)

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 0

Factor of safety, SF

Fig. 8. Cumulative failure probability curve for di ff erent water table distribution functions.

large failure probability might be obtained. Furthermore, the exponential distribution function estimates a relatively low probability of failure and provides a more optimistic estimate of the slope stability.

5. Conclusion

In this paper, the slope stability problem was formulated as an optimization problem. For this purpose, introducing the Lodalen slope as a benchmark example, Simulated Annealing method was utilized to look for the most critical