Slope reliability analysis based on Monte Carlo simulation and sparse grid method

WU Guoxue, PENG Yijin, LIU Xuesong, HU Tao, WU Hao

世界地质(英文版) ›› 2019, Vol. 22 ›› Issue (3) : 152-158.

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PDF(434 KB)
世界地质(英文版) ›› 2019, Vol. 22 ›› Issue (3) : 152-158. DOI: 10.3969/j.issn.1673-9736.2019.03.02
论文

Slope reliability analysis based on Monte Carlo simulation and sparse grid method

  • WU Guoxue1, PENG Yijin1, LIU Xuesong1, HU Tao2, WU Hao2
作者信息 +

Slope reliability analysis based on Monte Carlo simulation and sparse grid method

  • WU Guoxue1, PENG Yijin1, LIU Xuesong1, HU Tao2, WU Hao2
Author information +
文章历史 +

摘要

In order to solve the problem of the reliability of slope engineering due to complex uncertainties, the Monte Carlo simulation method is adopted. Based on the characteristics of sparse grid, an interpolation algorithm, which can be applied to high dimensional problems, is introduced. A surrogate model of high dimensional implicit function is established, which makes Monte Carlo method more adaptable. Finally, a reliability analysis method is proposed to evaluate the reliability of the slope engineering, and is applied in the Sau Mau Ping slope project in Hong Kong. The reliability analysis method has great theoretical and practical significance for engineering quality evaluation and natural disaster assessment.

Abstract

In order to solve the problem of the reliability of slope engineering due to complex uncertainties, the Monte Carlo simulation method is adopted. Based on the characteristics of sparse grid, an interpolation algorithm, which can be applied to high dimensional problems, is introduced. A surrogate model of high dimensional implicit function is established, which makes Monte Carlo method more adaptable. Finally, a reliability analysis method is proposed to evaluate the reliability of the slope engineering, and is applied in the Sau Mau Ping slope project in Hong Kong. The reliability analysis method has great theoretical and practical significance for engineering quality evaluation and natural disaster assessment.

关键词

slope reliability analysis / high-dimension / sparse grid / Monte Carlo simulation

Key words

slope reliability analysis / high-dimension / sparse grid / Monte Carlo simulation

引用本文

导出引用
WU Guoxue, PENG Yijin, LIU Xuesong, HU Tao, WU Hao. Slope reliability analysis based on Monte Carlo simulation and sparse grid method[J]. 世界地质(英文版). 2019, 22(3): 152-158 https://doi.org/10.3969/j.issn.1673-9736.2019.03.02
WU Guoxue, PENG Yijin, LIU Xuesong, HU Tao, WU Hao. Slope reliability analysis based on Monte Carlo simulation and sparse grid method[J]. Global Geology. 2019, 22(3): 152-158 https://doi.org/10.3969/j.issn.1673-9736.2019.03.02

参考文献

Barthelmann V, Novak E, Ritter K, et al. 2000. High dimension polynomial interpolation on sparse grids.Advances in Computational Mathematics,12(4):273-288.
Dubourg V, Sudret B, Bourinet J M,et al. 2011. Reliability based design optimization using kriging surrogates and subset simulation.Structural and Multidisciplinary Optimization,44(5):673-690.
Gerstner T, Griebel M. 1998. Numerical integration using sparse grids.Numerical Algorithms,18:209-232.
Gerstner T, Griebel M. 2003. Dimension-adaptive tensor-product quadrature.Computing,71(1):65-87.
Hu C, Youn B D. An asymmetric dimension-adaptive tensor-product method for reliability analysis.Structural Safety,33(3):218-231.
Jia B, Xin M, Cheng Y,et al. 2012. Sparse-grid quadrature nonlinear filtering.Automatica,48(2):327-341.
Klimke A, Willner K, Wohlmuth B,et al. 2004. Uncertainty modeling using fuzzy arithmetic based on sparse grids. International Journal of Uncertainty, Fuzziness and Knowdge-Based Systems,12(6):745-759.
Klimke A, Wohlmuth B. 2005. Piecewise multilinear hierarchical sparse grid interpolation in MATLAB.ACM Transactions on Mathematical Software,31(4):561-579.
Li D Q, Chen Y F, Lu W B,et al. 2011. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables.Computers and Geotechnics,38(1):58-68.
Low B K. 2007. Reliability analysis of rock slopes involving correlated nonnormals.International Journal of Rock Mechanics and Mining Sciences,44(6):922-935.
Low B K. 2012. Roles of FORM, system-FORM, SORM, and RSM in geotechnical reliability analysis//Proceedings of the 5th Asian-Pacific Symposium on Structural Reliability and its Applications. Singapore:Research Publishing.
Ma X, Zabaras N. 2009. An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations,Journal of Computational Physics,228(8):3084-3113.
Sekhavatian A, Choobbasti A J. 2018. Reliability analysis of deep excavations by RS and MCS methods:case study. Innovative Infrastructure Solutions,3(1):https://doi.org/10.1007/s41062-018-0166-z
Vanem E. 2018.3-dimensional environmental contours based on a direct sampling method for structural reliability analysis of ships and offshore structures.Ships and Offshore Structures, 14:74-85.
Xiong F F, Greene S, Chen W,et al. 2010. A new sparse grid based method for uncertainty propagation.Structural and Multidisciplinary Optimization,41(3):335-349.
Yang X L, Zhou T, Li W T,et al. 2018. Reliability analysis of tunnel roof in layered Hoek-Brown rock masses.Computers and Geotechnics,104:302-309.
Zabaras N. 2007. Spare grid collocation schemes for stochastic natural convection problems.Journal of Computational Physics,225(1):652-685.
Zhang M. 2009. Structural reliability analysis-methods and procedures. Beijing:Science Press, 1-253. (in Chinese)

基金

Supported by projects of China Ocean Research Mineral Resources R & D Association (COMRA) Special Foundation (DY135-R2-1-01, DY135-46), and the Province/Jilin University Co-Construction Project-Funds for New Materials (SXGJSF2017-3).

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