The evaluation of the probability of rock wedge failure using the point estimate method

Abstract

In a probabilistic analysis of rock slope stability, the Monte Carlo simulation technique has been widely used to evaluate the probability of slope failure. While the Monte Carlo simulation technique has many advantages, the technique requires complete information of the random variables in stability analysis; however, in practice, it is difficult to obtain complete information from a field investigation. The information on random variables is usually limited due to the restraints of sampling numbers. This is why approximation methods have been proposed for reliability analyses. Approximation methods, such as the first-order second-moment method and the point estimate method, require only the mean and standard deviation of the random variable; therefore, it is easy to utilize when the information is limited. Usually, a single closed form of the formula for the evaluation of the factor of safety is needed for an approximation method. However, the commonly used stability analysis method of wedge failure is complicated and cumbersome and does not provide a simple equation for the evaluation of the factor of safety. Consequently, the approximation method is not appropriate for wedge failure. In order to overcome this limitation, a simple equation, which is obtained from the maximum likelihood estimation method for wedge failure, is utilized to calculate the probability of failure. A simple equation for the direct estimation of the safety factors for wedge failure has been empirically derived from failed and stable cases of slope, using the maximum likelihood estimation method. The developed technique has been applied to a practical example, and the results from the developed technique were compared to the results from the Monte Carlo simulation technique.