Gravity retaining wall stability risk analysis based on reliability using fuzzy set theory

One-dimensional view of optimized design of engineering systems focusing on costs without considering other aspects such as risk and uncertainty in engineering design can increase risks during the operation of that engineering system. This paper indicates that if there are uncertainties in design parameters this cannot always cause poorly system operation, whereas may strengthen that system operation. For this purpose a gravity retaining wall is optimized and the optimal dimensions of that retaining wall are calculated. Then the effect of uncertainties, which are in the design parameters of that optimal gravity retaining wall, on the stability factors is calculated. Finally, using the concept of reliability, the risk in the safety factors of the retaining wall is obtained. In this paper, it is shown that if there is 10% uncertainty in design parameters the uncertainty propagation on safety factors is about (-80,+345)%, but this uncertainty propagation can increase the reliability(positive aspect of uncertainty) and risk(negative aspect of uncertainty) with a probability of 98.6039% and 1.3961% respectively. Then using the reliability block diagram, the total amount of reliability and risk for the gravity retaining wall is calculated which are equal to 79.3169 and 20.6830%, respectively. The innovations of this paper can be listed as below: 1) using Self-Adaptive Genetic Algorithm and Many Objective Genetic Algorithm, which have been used to optimize the retaining wall and calculate the uncertainty propagation on safety factors respectively. 2) calculating reliability and risk using fuzzy set theory.3) using reliability block diagram (RBD) to calculate the overall reliability and risk.