Abstract
Present study investigates applicability, superiorities and impediments of point estimate methods (PEM) in probabilistic stability analysis of rock slopes. A rock slope which involves correlated non-normally distributed variables, is considered and probabilistic analyses are carried out incorporating four different PEMs with numerical method. It is illustrated that correlation and asymmetry in random variables can be treated in different ways by using different PEMs. Some methods like Rosenblueth’s or Zhou & Nowak’s PEMs are originally applicable for correlated skewed random parameters while deficiencies of Harr’s and Hong’s PEMs arise when random variables are non-normally distributed and correlated, respectively. It is shown that how can manipulate these two methods in order to make them usable for correlated non-normal variables.
1. Introduction
Having considered the recent works which have been done by [1-9] in recent two decades, it can be said that probabilistic analyses are increasingly becoming popular in geotechnical engineering in order to take uncertainties into account where stability of geotechnical structures are investigated. When these analyses are performed using numerical methods, it is vital to select an appropriate probabilistic tool that not only can readily be incorporated with numerical method, but also makes the analyses efficient. Monte Carlo Simulation (MCS) [10], reliability methods and point estimate method (PEM) [11] are some probabilistic tools which are widely used in geotechnical engineering. In case that model evaluation is time consuming, MCS is infeasible because small number of simulations leads to inaccurate results and on the other hand, large number of simulations leads to inefficiency. FORM [12] and SORM [13] need to calculate derivatives of performance function with respect to random parameters; as a result, these methods may not easily be combined with numerical methods. Under such circumstances, PEMs often constitute more practical alternatives as they require smaller amount of computations along with statistical moments for inputs only. In this research, the applicability of PEMs in analyzing the stability of a rock slope probabilistically, is investigated.
