Slope hybrid reliability analysis considering the uncertainty of probability-interval using three-parameter Weibull dist
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Slope hybrid reliability analysis considering the uncertainty of probability‑interval using three‑parameter Weibull distribution Tonghui Wei1 · Wenjie Zuo1 · Hongwei Zheng1 · Feng Li1 Received: 13 November 2019 / Accepted: 11 September 2020 © Springer Nature B.V. 2020
Abstract A reliability model is proposed to solve the problem of hybrid uncertainty with both random and interval variables in slope engineering. A hybrid uncertainty model based on the dimension reduction method and Taylor expansion is constructed to approximate the limit state function. Using the polynomial theorem and variable transformation method, the origin and center moments’ interval of the limit state function are calculated. Moment information is applied to the expansion of a three-parameter Weibull distribution, and the cumulative distribution function and probability density function of limit state function are determined. As a result, the failure probability interval of the slope is calculated. The interval uncertainty problem is transformed into an interval certainty problem using Taylor expansion without solving for the statistical moment of limit state function using multiple integrals and iteratively searching for the most probable failure points. The numerical results from two slopes show that the proposed method is effective and feasible. Keywords Hybrid reliability analysis of slope · Strength reduction method · Probability of failure · Dimension reduction method · Three-parameter Weibull distribution
1 Introduction Slope stability in practical engineering design is defined by safety factor. However, slope stability assessment based on safety factor only obtains a certain value through deterministic analysis and fails to consider any inherent variability in design parameters. Deterministic analysis may lead to overly conservative slope design, and accurate uncertainty modeling and reliability analysis play a key role in slope reliability analysis. Slope reliability analysis methods can be generally divided into two categories: (1) approximation methods, including the first-order reliability method (FORM) and second-order reliability method (SORM) (Cho 2013; Ji 2014; Ji et al. 2018; Li et al. 2017; Suchomel and Masin 2010; Zeng et al. 2015); (2) simulation methods, including direct Monte Carlo simulation (MCS)
* Feng Li [email protected] 1
School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China
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Natural Hazards
and its various error reduction improvements (Jiang et al. 2015; Wang et al. 2011; Yang and Liu 2018). Suchomel and Masin (2010) combined the finite element method considering the spatial random field of cohesion and friction angle to estimate the slope failure possibility. Cho (2013) examined various slope failure modes and adopted a multi-point FORM to estimate failure probability for reliability problems using multiple design points. Ji (2014) studied the failure probability modes of long embankments and found that the 3-D safety factor consistently de
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