Issue 61

M.E. Kerkar et alii, Frattura ed Integrità Strutturale, 61 (2022) 530-544; DOI: 10.3221/IGF-ESIS.61.36

of failure of the system under study [28, 30]. Thus this method is the process that is used to estimate the sampling of the probability of failure of a structure, if N f is the number of simulation cycles in which the structure fails and N is the total number of simulation cycles, the probability of failure P f is expressed by [28, 30]:

N

f

(10)



P

f

N

Latin Hyper cube Sampling method If we are talking about an array of symbols or numbers and each appears only once, the array is called a "Latin square", extending this concept to higher dimensions for many design variables represents the term "hyper cube". Hence, this method is the sampling method in a Monte Carlo approach, it is also known as “stratified sampling technique” [28]. Each random variable can be subdivided into n intervals of equal probability, there are n points of analysis, randomly mixed, so each of the n compartments has 1/ n of the probability of distribution. The general steps of this method are: 1- Decompose the distribution of each variable into n non-overlapping intervals with equal probability. 2- Select a value at random in each interval in relation to its probability density. 3- Repeat steps 1 and 2 until you have selected values for variables, such as x 1 , x 2 , ..., x k . 4- Combine the n values obtained for each x k with the n values obtained for the other at random x j ≠ i see Fig. 10.

Figure10: Basic concept of LHS with two variables and five realizations [28]

A PPLICATION OF THE MODELS he application of the three reliability methods on the Beni Harroun dam gave failure probabilities during certain scenarios, each scenario having its own specific load combinations, e.g. P f estimated in scenario 47 ( C 47 ) is the probability of failure at the landslide in relation to the dam-foundation interface when the dam is subjected to seismic loading and when the functional probability for the drainage system to operate at 90% is equal to 1. The calculation code retains the most unfavourable probability of failure ( P f = 3.51x10 -3 ) among the results of the three reliability calculation methods. The results are shown in Tab. 3. T

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