Global Sensitivity Analysis of Slope Stability Considering Effective Rainfall with Analytical Solutions

Abstract

Rainfall-induced landslides are widely distributed in many countries. Rainfall impacts the hydraulic dynamics of groundwater and, therefore, slope stability. We derive an analytical solution of slope stability considering effective rainfall based on the Richards equation. We define effective rainfall as the total volume of rainfall stored within a given range of the unsaturated zone during rainfall events. The slope stability at the depth of interest is provided as a function of effective rainfall. The validity of analytical solutions of system states related to effective rainfall, for infinite slopes of a granite residual soil, is verified by comparing them with the corresponding numerical solutions. Additionally, three approaches to global sensitivity analysis are used to compute the sensitivity of the slope stability to a variety of factors of interest. These factors are the reciprocal of the air-entry value of the soil α, the thickness of the unsaturated zone L, the cohesion of soil c, the internal friction angle ϕ related to the effective normal stress, the slope angle β, the unit weights of soil particles γs, and the saturated hydraulic conductivity Ks. The results show the following: (1) The analytical solutions are accurate in terms of the relative differences between the analytical and the numerical solutions, which are within 5.00% when considering the latter as references. (2) The temporal evolutions of the shear strength of soil can be sequentially characterized as four periods: (i) strength improvement due to the increasing weight of soil caused by rainfall infiltration, (ii) strength reduction controlled by the increasing pore water pressure, (iii) strength reduction due to the effect of hydrostatic pressure in the transient saturation zone, and (iv) stable strength when all the soil is saturated. (3) The large α corresponds to high effective rainfall. (4) The factors ranked in descending order of sensitivity are as follows: α > L > c > β > γs > Ks > ϕ.