Stability of Non-Uniform Soils Slope with Tension Cracks Under Unsaturated Flow Conditions

The soil slopes in nature are normally unsaturated, heterogeneous, and even carry cracks. In order to assess the stability of slope with crack under steady unsaturated flow and non-uniform conditions, this work proposes a novel discretization-based method to generate the rotational failure mechanism in the context of the kinematic limit analysis. A point-to-point strategy is used to generate the potential failure surface of the failure mechanism. The failure surface consists of a series of log-spiral segments instead of linear segments employed in previous studies. Two kinds of cracks—open cracks and formation cracks—are considered in the stability analysis. The maximum depth of the vertical crack is modified by considering the effect of the unsaturated properties of soils. According to the work–energy balance equation, the explicit expression about the slope factor safety for different crack types is obtained, which is formulated as a multivariate nonlinear optimization problem optimized by an intelligent optimization algorithm. Numerical results for different unsaturated parameters and non-uniform distribution of soil strength are calculated and presented in the form of graphs for potential use in practical engineering. Then, a sensitivity analysis is conducted to find more insights into the effect of unsaturation and heterogeneity on the crack slopes.