PSI - Issue 22

Mahdi Shadab Fara et al. / Procedia Structural Integrity 22 (2019) 345–352

347

Shadab Far and Huang / Structural Integrity Procedia 00 (2018) 000–000

3

25

20

1

2

15

10

Marine clay

Elevation (m)

5

0

0

5 10 15 20 25 30 35 40 45 50 55 60 65 70

Distance (m)

Fig. 1. Schematic view and geometric characteristics of the Lodalen slope.

V 2 and V n + 1 with line x = x 3 . Additionally, the point H is obtained from the intersection of the line connecting V 1 and V 2 with line x = x 3 . Then, the coordinates of y 3 min and y 3 max are calculated as follows: y 3 min = max { y H , bedrock at x = x 3 } , y 3 max = min { y G , upper boundary of slope at x = x 3 } . (1) In continuation, the coordinates of ( y 4 min , y 4 max ) , ..., ( y nmin , y nmax ) are calculated in the same way. The schematic view of the boundary condition is shown in Fig. 2a. Next, the slip surface generated in the form of the vector X = [ x 1 , y 1 , x 2 , y 2 , ..., x n + 1 , y n + 1 ] is given to the SA optimization algorithm as a potential sample. Next, the optimization algorithm should identify the slip surface that gives the lowest SF value. In this paper, to study the critical slip surface, both conventional circular surface and SA algorithms were used. The parameters used in the SA algorithm are as listed in Table 1. The result of the analysis for two di ff erent types of safety factor, i.e., Bishop and Janbo methods, is shown in Fig. 2b. As can be seen, the slip surface found by the SA algorithm in both cases presents a lower SF than conventional circular slip surface. This di ff erence can be attributed to the intelligent algorithm implemented to look for the most critical condition. In addition, in contrast with the circular method, no limitation is applied to the shape of the slip surface in the SA algorithm. Therefore, almost any form of slip surface that may produce smaller SF could be evaluated by the searching process of the SA algorithm.

3. Probabilistic analysis

3.1. Monte Carlo simulation

To determine the probability of slope failure, it is necessary to model the parameters involved in the problem as random variables. For this purpose, three parameters of C , φ , and γ were taken as normal random variables with probabilistic characteristics shown in Table 2. Their minimum and maximum limits were considered to be three times their coe ffi cient of variation. It was also assumed that C and φ correlate with a correlation coe ffi cient of 0.5. In the following, for each random variable involved, 10,000 random samples were generated according to their characteristics listed in Table 2. For each set of random samples, a SA algorithm was utilized and the critical slip

Table 1. Parameters used in the SA algorithm. Parameter

Value

The initial number of surface vertices Number of annealing generation steps

8

1000

Tolerance for stopping criteria

0.0001

The coe ffi cient in temperature reduction

8