Closed-form solution for planar failure in rock slopes with an inclined upper surface using Barton-Bandis and Mohr–Coulomb models

Abstract

Rock slope stability, having a plane mode of failure, can be assessed by different methods. The traditional analytical approaches used in the analysis are limited to those in which the upper slope surface is horizontal and the tension crack is inclined, and generally imply the resolution of nonlinear equations which require an exhaustive calculation. The aim of this study is to develop a systematic analytical solution for estimating the safety factor of a rock slope with an inclined upper surface. By employing the basic assumptions of the limit equilibrium method, simplified expressions considering the nonlinear Barton-Bandis and linear Mohr–Coulomb failure criteria were proposed to analyze the stability of a slope with no tension cracks and sliding on a planar failure surface. Furthermore, some other expressions for the normal stress, length of the planar failure line, and self-weight of the block masses are presented. Finally, the relationships between the derived closed-form solutions and some main parameters, such as the height, cohesion, total unit weight, internal friction angle, slope face angle, failure plane angle, basic friction angle, joint roughness coefficient, and joint compressive strength and upper surface angle, are illustrated with typical examples. These results are in good agreement with practical case studies in literature and numerical simulation results. This method can be effectively utilized in rock and soil slope engineering to provide a reference for preventing and controlling planar slope failure.