Geotechnical system reliability of slopes

Abstract

In slope stability analysis it is customary to search for the critical slip surface considering the conventional factor of safety as an index of stability. With the development of reliability analysis approaches within a probabilistic framework, alternative definitions of the critical slip surface can be adopted. Thus one may define a critical slip surface as one with the lowest reliability index or one with the highest probability of failure. However, it is important to consider the slope stability problem in terms of a system of many potential slip surfaces. For such a system, the calculation of system reliability is appropriate and desirable. In this paper, system reliability bounds are calculated within a probabilistic framework. The ‘system reliability’ or the ‘system probability of failure’ must be estimated for comparison with the corresponding reliability or probability of failure with respect to a ‘critical’ slip surface. The general slope stability problem involving non-zero internal friction angle involves a non-linear performance function. Moreover, the expression for factor of safety is usually inexplicit except for the ordinary method of slices which is not accurate except when ‘ø = 0’. This paper addresses the system reliability for inexplicit and non-linear performance functions as well as for linear and explicit ones. Any version of the method of slices may be used although the proposed approach is presented on the basis of the Bishop simplified method. It is shown that the upper bound system failure probability is higher than the failure probability associated with a critical slip surface. The difference increases as the coefficient of variation of the shear strength parameters increases.