Quantile-based reliability analysis and design in slope stability

Abstract

The study and analysis of slopes are essential for understanding their performance and, in particular, their stability, reliability, and deformations. Traditional slope stability analysis involves predicting the location of the critical slip surface for a given slope and computing a safety factor at that location, which belongs to the deterministic frame. It is found that multiple sources of uncertainties often exist in the evaluation of slope stability. When assessing the stability of slopes in the face of risks, it is desirable, and sometimes necessary, to adopt reliability-based approaches that consider these uncertainties explicitly. The thesis develops an efficient methodology of soil modeling using maximum entropy based quantile distribution constrained by probability weighted moments, conducts field vane shear soil testing in the Nipigon river area and establishes the soil strength models. The research proposes a new reliability-based method to study the stability of the Nipigon river slope and carries out a reliability-based design of slopes by combining quantile-based reliability and multi-objective optimization. In general, the probability distribution describes the randomness of soil parameters collected empirically or tested by the few numbers of collected soil samples. However, the substantial effect of sample size on the estimation of random properties of the soil strength requires an extensive data to explore uncertainties, which is uneconomical and sometimes impossible to obtain. This study aims to consolidate recent advancement in probabilistic characterization and develops an inverse cumulative distribution function (ICDF) or quantile distribution, for direct quantification of the actual variability of various soil samples. Based on the analysis, a framework is developed that streamlines the formulation of probability weighted moments (PWM), and maximum entropy (MaxEnt) based distribution function for various soil properties when estimated using different field or laboratory tests, leading to a reliable procedure for applications of the proposed framework to different site characterization problems. Examples are provided to illustrate the implementation and step-by-step procedures of the proposed framework. This research further extends the reliability approach for slope stability problems and utilizes the first-order reliability method (FORM) with quantiles for improving the efficiency of the FORM with relatively small samples. Reliability analysis is combined with deterministic slope stability analysis and implemented using an efficient algorithm. The analysis is validated through comparison with other reliability methods and used to explore the effect of variability of the soil properties on slope system. It is found that, when variability of soil properties is defined by assuming a conventional distribution, the variance of factor of safety is overestimated or underestimated. The approach not only provides sufficiently accurate reliability estimates of slope stability but also significantly improves the computational efficiency of soil slope design in comparison with conventional design methods.