Adaptive reliability analysis of spatially variable soil slopes using strength reduction sampling and Gaussian process regression

Spatial variability of soil parameters has significant impact on slope stability. The critical problem for the slope reliability analysis considering the spatial variability is the dramatic computational demand. Based on the strength reduction sampling (SRS) and Gaussian process regression (GPR), an adaptive reliability analysis method (SRS-GPR) for soil slopes considering the spatial variability is proposed. Firstly, the spatially variable soil strength parameters are discretized into high-dimensional random variables by the Karhunen-Loève expansion method. Then the critical sample points are generated according to the SRS. Next, the nonlinear relationship between the random fields of soil parameters and the safety factor of slopes is established by the GPR. With the active learning strategy, the best training sample points can be automatically identified, so the GPR model can be sequentially updated. Subsequently, the trained GPR model and Monte Carlo simulation are adopted to perform slope reliability analysis. Finally, the accuracy, efficiency, robustness and applicability of the proposed method are testified by two examples. The results show that the proposed method can effectively identify the best training sample points near the limit state surface, and the prediction accuracy of the updated GPR model in this region is gradually improved. Moreover, this method can be directly applied in the original high-dimensional parameter space with marginal impact of dimensionality of random variables, and a small number of evaluations of the slope stability model are required, which indicates a significant advantage in terms of the computational efficiency.