Application of the tortuous surface method to stochastic analysis of bimslope stability

Abstract

This article presents a summary of the research on the novel tortuous surface method to stochastically analyze the stability of two-dimensional bimslopes, which are slopes composed of bimrocks or bimsoils. Tortuous failure surfaces (TFSs) are slip surfaces that develop around blocks when bimslopes fail. The method was automated through an algorithm that locates a slip surface passing around the blocks as if it were the solution of a “maze puzzle.” Slope stability analyses were performed using the limit equilibrium method (LEM). To compare many different models, the normalized factor of safety of a TFS ( $f_{\mathrm {n}}^{\ast }$ ) was computed. $f_{\mathrm {n}}^{\ast }$ is obtained by dividing the fs from the TFS by the fs from the surface potentially produced when there are no blocks (the critical circular surface or the matrix-only surface (MOS)). Two groups of analyses were performed. First, two tortuosity parameters, the tortuous length ratio (TLR) and the average tortuous width (ATW), were analyzed through the evaluation of a hypothetical slope of 10 m height and 35∘ inclination with varying block proportions. Second, similar hypothetical models were developed with three different values of the slope height, slope inclination, and ratio of the unit weight of the blocks to the unit weight of the matrix; then, the behavior of $f_{\mathrm {n}}^{\ast }$ for different values of both the cohesion and friction angle of the matrix was presented in a sensitivity analysis. A prime conclusion of the research is that for prudent geotechnical design, stochastically based stability analyses of bimslopes are far preferable to deterministic analyses.