Non-intrusive stochastic finite element method for slope reliability analysis based on Latin hypercube sampling

A non-intrusive stochastic finite element method based on the Latin hypercube sampling for slope reliability analysis is proposed. The finite element method for stress analysis of sliding surface is used to calculate the safety factor of slopes. The safety factor of slopes is explicitly expressed as the input random variables using the Hermite polynomial chaos expansion. The Latin hypercube sampling points are selected as the collocation points to calculate the coefficients of polynomial chaos expansion. An example of reliability analysis of natural slope at the left abutment of Jinping I Hydropower Station is presented to demonstrate the validity and capability of the proposed method. The results indicate the proposed non-intrusive stochastic finite element method based on the Latin hypercube sampling can effectively evaluate the reliability of high-steep rock slopes, which decouples the reliability analysis with finite element analysis of slope stability and produces sufficiently accurate reliability results. The coefficients of polynomial chaos expansion determined by the Latin hypercube sampling are more effective than those by the frequently-used probabilistic collocation method, since the number of sampling points required by the former are only approximately equal to that of unknown coefficients. The internal fiction angle of fault f_42-9 at Jinping left abutment slope has a significant effect on the slope stability due to its largest sensitivity, followed by the internal fiction angle of III₂ class rock mass, whereas the other variables affect the slope stability slightly. The Sobol’s indices used for representing the sensitivities of input uncertain parameters can provide a referential basis for working out the reinforcement schemes.