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Slope hybrid reliability analysis considering the uncertainty of probability-interval using three-parameter Weibull distribution

Author

Listed:
  • Tonghui Wei

    (Jilin University)

  • Wenjie Zuo

    (Jilin University)

  • Hongwei Zheng

    (Jilin University)

  • Feng Li

    (Jilin University)

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.

Suggested Citation

  • Tonghui Wei & Wenjie Zuo & Hongwei Zheng & Feng Li, 2021. "Slope hybrid reliability analysis considering the uncertainty of probability-interval using three-parameter Weibull distribution," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 105(1), pages 565-586, January.
    • Handle: RePEc:spr:nathaz:v:105:y:2021:i:1:d:10.1007_s11069-020-04323-y
    DOI: 10.1007/s11069-020-04323-y
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    References listed on IDEAS

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    1. Andriy Andreev & Antti Kanto & Pekka Malo, 2007. "Computational Examples of a New Method for Distribution Selection in the Pearson System," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(4), pages 487-506.
    2. Li, Dian-Qing & Tang, Xiao-Song & Phoon, Kok-Kwang, 2015. "Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 99-106.
    3. Omer F. Usluogullari & Ahmet Temugan & Esra S. Duman, 2016. "Comparison of slope stabilization methods by three-dimensional finite element analysis," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 1027-1050, March.
    4. Omer Usluogullari & Ahmet Temugan & Esra Duman, 2016. "Comparison of slope stabilization methods by three-dimensional finite element analysis," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 1027-1050, March.
    5. Shaojun Li & Hong-Bo Zhao & Zhongliang Ru, 2013. "Slope reliability analysis by updated support vector machine and Monte Carlo simulation," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 65(1), pages 707-722, January.
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