Application of fuzzy set theory to evaluate the probability of failure in rock slopes

Because uncertainty pervades the field of rock slope stability analysis, the importance of uncertainty has been recognized. Subsequently, probability theory has been used to quantify the uncertainty. However, some uncertainties, due to incomplete information, cannot be managed satisfactorily by probability theory, so fuzzy set theory is more appropriate in the case. In this study, the uncertain parameters in rock slope stability analysis were expressed as fuzzy numbers and fuzzy set theory was employed. The Monte Carlo simulation technique and reliability index approach were implemented with fuzzy set theory in order to take into account the fuzzy uncertainties in the evaluation of the probability of failure. In order to check the feasibility of the proposed approaches, the presented methods were applied to a practical example. Based on the results of the practical application, it was concluded that the application of fuzzy set theory shows consistent analysis results and can obtain reasonable results.

► The random variables in rock slope analysis were considered as fuzzy numbers and the fuzzy set theory was employed.
► Fuzzy based Monte Carlo simulation technique and fuzzy based reliability approach were implemented.
► Deterministic and probabilistic analyses were also carried out to compare with the results of the proposed approaches.
► The fuzzy based Monte Carlo simulation and fuzzy based reliability index showed consistent results.
► These approaches could be effective alternatives in cases where only limited information is provided for random parameters.