LEM for Stability Analysis of 3D Slopes with General-Shaped Slip Surfaces

Abstract

Three-dimensional (3D) slope stability analysis is a present research interest for geotechnical engineering. This work established a new 3D limit equilibrium method (LEM) to solve 3D slope stability with general-shaped slip surfaces. In the proposed method, a simple initial normal stress on a slip surface is used by analyzing the stresses on a vertical microcolumn. To ensure the accuracy of the results, a dimensionless variable is adopted to amend the initial normal stress. Then, by using the Mohr-Coulomb (M-C) criterion, the shear stress on the slip surface is also assumed. Different from the traditional LEM, global limit equilibrium (LE) conditions are used to avoid the effect of intercolumn forces on slope stability. Moreover, the Cartesian coordinate system is constructed on the basis of the main direction of a 3D sliding body; thus, strict solutions of 3D slope stability can be achieved with only three equations of static equilibrium on the sliding body. After contrasting the results in several classic slope examples, the proposed method’s feasibility is verified with the following advantages: (1) it has a simple derivation process to obtain rigorous results, and compared with the same simple 3D nonrigorous method, the improvement of more than 10% on the slope factor of safety (FOS) is achieved; (2) it is easy to program with a fast solution speed, and compared with the conventional 3D Morgenstern-Price (M-P) method, the calculation speed is increased more than 1.5 times; and (3) it can directly obtain the distribution of normal and shear stress on the slip surface and can also visually draw the global and local sliding trends of a 3D sliding body.