Efficient numerical implementation of limit equilibrium method for stability analysis of unsaturated soil slopes using Gaussian integral

Abstract

Unsaturated soil is widely distributed around the world but less considered in design due to the absence of a convenient analysis method in practice. The Morgenstern–Price (MP) method incorporating the extended Mohr–Coulomb shear strength equation provides a reliable approach to evaluate slope stability in such conditions. However, this method is time-consuming due to the need for a tedious trial-and-error process in determining the scaling factor, which involves complex iterations during each trial. Furthermore, since the relatively complicated nature of unsaturated soil, a dense slice division is necessary to obtain reliable results, making the analysis even more cumbersome. In this paper, an improved MP method for unsaturated soil slope stability analysis is presented, which eliminates the need for a dense slice mesh by employing only a few strategically placed Gauss points along the slip surface. Moreover, the trial-and-error process for determining the scaling factor with the corresponding complex iterations is replaced by an efficient search algorithm with a more concise iteration process, resulting in a more convenient implementation of the proposed method. Extensive examples are provided to validate the effectiveness of the proposed improved MP method, indicating its potential as an accurate and efficient analysis method for unsaturated soil slopes in practical application and relative study involving repetitive analyses.