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Slope hybrid reliability analysis considering the uncertainty of probability-interval using three-parameter Weibull distribution
Authors:Wei  Tonghui  Zuo  Wenjie  Zheng  Hongwei  Li  Feng
Institution:1.School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China
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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.

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