Probabilistic Slope Stability Analysis with Spatial Soil Variability Using Improved Multiple Kriging Metamodels

Recently, a multiple Kriging metamodel method has been proposed to simultaneously evaluate slope reliability and assess risk of slope failure within the framework of limit equilibrium method. However, the inherent spatial variability (ISV) of soil properties was not considered because of the "curse of dimensionality". This study develops an improved multiple Kriging (IMK) method for efficient slope reliability analysis and risk assessment considering ISV of properties by a four-stage dimension reduction method. The proposed method proceeds with the simulation of random fields of soil properties with a small number of independent variables by using Karhunen-Loève expansion method. Then, representative slip surfaces (RSSs) of a slope are identified to reduce the number of Kriging models to be built, which is followed by using sliced inverse regression (SIR) to further reduce the number of variables. Thereafter, a Kriging metamodel is established for each RSS with the reduced random variables, while using a new sequential sampling strategy to actively learn and update the MK models to further improve the efficiency. A slope example is studied to illustrate the accuracy and efficiency of the IMK method for slope reliability analysis and risk assessment. The influence of the size of the training samples on the accuracy of the proposed model is discussed. The results show that the proposed IMK method performs accurately and effectively on slope reliability analysis and risk assessment considering ISV of soil properties.

Keywords: Slope reliability analysis, risk assessment, spatial variability, Kriging, active learning, representative slip surface, sliced inverse regression, Karhunen-Loève expansion.