Inverse geometric reliability analysis algorithm for geotechnical structures

WU Xingzheng; LIU He

doi:10.11835/j.issn.2096-6717.2021.176

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Inverse geometric reliability analysis algorithm for geotechnical structures

Civil Engineering | 更新时间：2023-09-19

- Inverse geometric reliability analysis algorithm for geotechnical structures
- Journal of Civil and Environmental Engineering Vol. 45, Issue 5, Pages: 106-115(2023)
- 作者机构：
  
  河北大学建筑工程学院，河北保定 071002
- 作者简介：
  
  WU Xingzheng (1971- ), PhD, associate professor, main research interests: uncertainty models in geotechnical, flood defence and coastal engineering, E-mail: xingzhengwu@163.com.
- 基金信息：
  
  Hebei Natural Science Foundation(E2019201296);Key Project of Science and Technology Research in Colleges and Universities of Hebei Province(ZD2018216);Advanced Talents Incubation Program of the Hebei University(801260201262)
- DOI：10.11835/j.issn.2096-6717.2021.176
  CLC： TU473.1
- Received：15 June 2021，
  
  Published：25 October 2023
- 稿件说明：
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WU Xingzheng, LIU He. Inverse geometric reliability analysis algorithm for geotechnical structures[J]. Journal of Civil and Environmental Engineering, 2023, 45(5): 106-115.
DOI：

WU Xingzheng, LIU He. Inverse geometric reliability analysis algorithm for geotechnical structures[J]. Journal of Civil and Environmental Engineering, 2023, 45(5): 106-115. DOI： 10.11835/j.issn.2096-6717.2021.176.

摘要

针对特定场地下土工构筑物的正常使用极限状态，考虑钻孔灌注桩、抗浮锚杆或CFG桩单桩荷载-位移测试曲线之间的离散性，将测试曲线拟合得到的回归参数集视作随机变量，基于几何可靠性算法框架，运用高斯Copula函数联合分布模型实施由标准正态空间到原始物理空间中随机变量的表征转换，构建基于概率密度等值线的逆几何可靠性算法。该算法假定描述随机变量服从正态分布的某一参数（均值或变异系数）未知，给定目标可靠指标，可推求随机变量的概率密度等值线。通过极限状态方程限定概率密度等值线的几何轮廓，可求解特定目标可靠指标下随机变量的未知均值或变异系数，并求出相应的安全系数。当随机变量服从其他非正态边缘分布时，等值线的几何轮廓仍由一系列离散点近似表征，逆可靠性分析同样适用。建议的算法主要用于解决随机变量部分统计参数缺失或不完备的难题，给定目标可靠指标时可根据构筑物重要性等级进行安全系数校准。

Abstract

For serviceability limit state of geotechnical structures at a specific site

the scatter among the load-displacement curves of bored piles

floating anchors or CFG piles is considered

and the set of regression parameters obtained by fitting these test curves is treated as a random variable. On the basis of theoretical framework of the geometric reliability method

a Gaussian Copula function is used to facilitate the transformation of random variables from the standard normal space to the original physical space

and then an inverse reliability algorithm based on probability density contours (PDCs) is constructed. In this algorithm

if one parameter of a normal probability density distribution is unknown

such as the mean or coefficient of variance

the PDC of the random variables can be derived when a target reliability index is specified. If the PDC is bounded by the limit state equation

the unknown mean value or coefficient of variance for the random variable under a given target reliability index is solved

and the corresponding safety factor is derived. While a non-normal marginal distribution is followed by random variables

the geometric configuration of the PDC can be still approximated by a set of discrete points

and the inverse reliability analysis is also applicable. The proposed algorithm is mainly used to solve problems with statistical parameters of random variables missing or incomplete. When the target reliability index is specified

the safety factor can be calibrated according to the importance hierarchy of the structure.

关键词

Keywords

references

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