The Effects of Seismic Coefficient Uncertainty on Pseudo-Static Slope Stability: A Probabilistic Sensitivity Analysis

Dongli Li,Tao Yang,Echuan Yan,Miaojun Sun

doi:10.3390/su13158647

Abstract

The method of pseudo-static analysis has been widely used to perform seismic slope stability, in which a seismic coefficient is used to represent the earthquake shaking effect. However, it is important but difficult to select the magnitude of seismic coefficients, which are inevitably subjected to different levels of uncertainties. This paper aimed to study the influences of seismic coefficient uncertainties on pseudo-static slope stability from the perspective of probabilistic sensitivity analysis. The deterministic critical slope height was estimated by the method of upper-bound limit analysis with the method of pseudo-static analysis. The soil shear strength parameters, the slope geometrical parameters (including slope inclinations, slope heights, and the slope widths), the horizontal seismic acceleration coefficient, and the unit weight of soil masses were considered as random variables. The influences of their uncertainty degrees, the correlation relations, and the distribution types of random variables on probabilistic density functions, failure probabilities, and sensitivity analysis were discussed. It was shown that the uncertainty degrees greatly impact the probability density distributions of critical slope heights, the computed failure probabilities, and Sobol’ index, and the horizontal seismic coefficient was the second most important variable compared to the soil shear strength parameters.

Highlights

The pseudo-static analysis is a classical approach to perform seismic stability of slopes in the geotechnical community [1,2], by combining it with other analytical deterministic computational models, for example, the limit equilibrium methods [3,4], as well as the method of upper-bound limit analysis [5,6]
The influence of the uncertainty degree, correlation structures, and distribution types of the six input random variables on the assessed probabilistic density functions, failure probability, and sensitivity analysis using the method of sparse polynomial chaos expansions (SPCE)-MCS were investigated and discussed
A higher uncertainty level leads to a shorter and wider shape of probability density functions (PDFs). This was expected, since lower COVs of input parameters should result in higher accuracy, which shows a higher peak in the PDFs

Summary

Introduction

The pseudo-static analysis is a classical approach to perform seismic stability of slopes in the geotechnical community [1,2], by combining it with other analytical deterministic computational models, for example, the limit equilibrium methods [3,4], as well as the method of upper-bound limit analysis [5,6]. Compared to LEM, the method of upper-bound limit analysis is an efficient method for geotechnical stability analysis that can provide a rigorous upper estimation to the critical height of slopes, or a lower bound to the necessary face pressures against failure [5]. Both the limit equilibrium method and the upper-bound limit analysis mentioned above can make reliable evaluations on slope stability; the predictive accuracy highly depends on whether the associated input parameters are exactly given [3,5]. It is necessary to study the influence of model

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Results

Conclusion