Dynamic reliability analysis of three-dimensional slopes considering the spatial variability in soil parameters

Slopes are commonly a significant aspect of geotechnical engineering projects. The incorrect evaluation and prediction of slope stability can cause serious disasters when it experiences seismic activity, and reliability is the key index a slope's dynamic state. Spatial variability is an inherent soil property and has an essential influence on the dynamic response of a slope body. However, in previous studies, soil was often described deterministically, and the interaction between the uncertainty and spatial dimensions was ignored. To fill this gap, in this paper, practical expressions for the cohesion and friction angle in each working condition are given to simulate spatial variability by a lognormal random field. Then, the finite element method and effective dynamic reliability calculation method are used to obtain the safety factor of a 3D slope. Finally, the generalized probability density evolution method is performed to obtained the probability density information of the dynamic slope response and judge the influence of the soil spatial variability probabilistically. Due to the spatial variability in soil, the probability density distribution under each condition is distributed in a large range and thus may not provide results that are much more dangerous than those of the deterministic simulation. Meanwhile, the friction angle is more sensitive than cohesion and shows stronger discreteness in the spatial variability. The change in the cross-correlation coefficient has a greater influence on reliability than the autocorrelation length. Consequently, the simplification of model slopes in dimension and variability could deviate the reliability results from actual dy-namic responses, either overestimating or underestimating, resulting in incorrect designs and evaluations.

Automated summary

Slopes are a critical factor in geotechnical engineering projects, and accurately evaluating and predicting their stability is crucial for disaster prevention during seismic activity. Previous studies often described soil deterministically, ignoring the interaction between uncertainty and spatial dimensions. This paper fills this gap by using a lognormal random field to simulate spatial variability, providing practical expressions for cohesion and friction angle under various conditions. The finite element method and effective dynamic reliability calculation method are employed to calculate the safety factor of a 3D slope. Additionally, the generalized probability density evolution method is used to analyze the probability density information of the dynamic slope response and assess the probabilistic influence of soil spatial variability.