Reliability-based design of the rock slope support considering the planar failure of multiple blocks

Summary

Abstract

The assessment of rock slope stability is inherently complex due to the discontinuous nature of rock masses, where failure mechanisms are primarily governed by the geometric and mechanical properties of discontinuities. Traditionally, engineers have relied on deterministic methods based on the concept of factor of safety. However, these approaches often fail to explicitly quantify the uncertainties associated with rock mass properties and geometry. This paper investigates the stability of a multiple-block planar sliding using an analytical system-component formulation. By reducing the potential failure modes of an N-block system to N primary failure modes, the study compares the traditional deterministic design with a reliability-based design approach aligned with the Eurocodes. The research specifically addresses the influence of geometric uncertainties, considering the dip angle of the sliding surface as a random variable. A comparative analysis was conducted for a slope with six blocks, evaluating the support force required to achieve target reliability indices versus the typical values of the factor of safety. Results indicate that traditional deterministic approaches often overestimate the required support force, serving as an upper bound. Conversely, the equivalent factors of safety derived from the reliability-based design approach vary with the mean dip angle but on average align with the partial factors for the shear strength suggested in Eurocode 7. Furthermore, the study demonstrates that while multi-block interactions significantly impact stability at lower dip angles, the system tends to behave as a single monolithic volume as the dip angle increases. These findings suggest the adequacy of semi-probabilistic partial factors for idealized rock slope problems while highlighting the benefits of reliability-based methods for design optimization.