Three-Dimensional Asymmetrical Slope Stability Analysis Extension of Bishop’s, Janbu’s, and Morgenstern–Price’s Techniques

TLDR

Existing 3D slope stability methods largely extend 2D techniques assuming a plane of symmetry or slide direction. This study develops 3D asymmetric slope stability models extending Bishop’s, Janbu’s, and Morgenstern–Price’s simplified methods. The new formulations determine a unique slide direction from 3D force/moment equilibrium. The models produce results comparable to classical methods in typical cases, remain numerically stable under transverse loading, are equivalent to Jiang and Yamagami’s axes‑rotation approach yet more convenient, and reveal inherent limitations absent in 2D analyses.

Abstract

Most existing three-dimensional (3D) slope stability analysis methods are based on simple extensions of corresponding two-dimensional (2D) methods of analysis and a plane of symmetry or direction of slide is implicitly assumed. In this paper, 3D asymmetric slope stability models based on extensions of Bishop's simplified, Janbu's simplified, and Morgenstern–Price's methods are developed. Under these new formulations, the direction of slide is unique and is determined from 3D force/moment equilibrium. Results from the new formulations are similar to the classical methods in normal cases but are numerically stable under transverse load. Further, the writers demonstrate that the present formulation is actually equivalent to the axes rotation formulation by Jiang and Yamagami but is much more convenient to be used for general problems. The writers have also discovered some inherent limitations of 3D limit equilibrium analysis which are absent in the corresponding 2D analysis.