Critical slip surface and landslide volume of a soil slope under random earthquake ground motions

Finding the critical slip surface and estimating the landslide volume are of primary importance for slope seismic design. However, this may be difficult due to the uncertainty of ground motions. To address this problem, a new method for calculating uncertainties is recommended in this paper, especially for the critical slip surface and landslide volume under random earthquake ground motions. Firstly, a series of intensity-frequency nonstationary random earthquake ground motions were generated based on an improved orthogonal expansion method. A given number of potential slip surfaces were set in a soil slope. Subsequently, the factor of safety (FOS) of each slip surface for all ground motions was calculated and the minimum FOS curves were obtained. It was found that the critical slip surfaces and failure times are uncertain under different earthquakes. The Monte Carlo method was used to verify the accuracy of probability density evolution method (PDEM), and the results of the PDEM and the Monte Carlo method are consistent, meaning that the PEDM has higher computational efficiency. Moreover, the distributions of earthquake-triggered landslide volume and landslide depth were analyzed by considering equivalent extreme events. Both landslide volume and depth exhibit a normal distribution for a homogeneous soil slope. The framework of this study is meaningful for slope seismic design in engineering, for example, the location of critical slip surface can be used for slope reinforcement, and the distribution of sliding volume can be used for disaster assessment.