基于Copula理论的岩土体参数不确定性表征与边坡可靠度分析

Characterization of uncertainty in properties of rock and soil materials is the basis for reliability analysis and risk mitigation in geotechnical engineering. However, there exists a strong correlation among these geotechnical parameters, which requires a joint probability distribution function to characterize the statistical properties. Furthermore, there is large statistical uncertainty in the joint probability distribution function of correlated geotechnical parameters derived from a small sample. This project aims to propose a copula-based approach for the modeling and simulation of the multivariate distribution of correlated geotechnical parameters. By this approach, the multivariate distribution of correlated non-normal geotechnical parameters is constructed and used as input to conduct reliability analysis of geotechnical structures. Then, the technique for modeling the statistical uncertainty in the joint probability distribution function of correlated geotechnical parameters derived from a small sample is developed. The statistical uncertainty in the joint probability distribution function of correlated geotechnical parameters is further incorporated into the reliability evaluation of geotechnical structures. Finally, the copula-based approach is employed to model the joint probability distribution of shear strength parameters. The impact of copula selection on slope reliability is investigated. The left abutment slope of Jinping I Hydropower Station is used to demonstrate the application of the proposed approach. The project will improve the statistical characterization of uncertainty in correlated geotechnical parameters and evaluation of stability of geotechnical structures.

岩土体物理力学参数不确定性的定量表征是岩土工程可靠度分析与风险控制的前提，且岩土体参数存在相关性和具有小样本特性是岩土工程中一个客观存在的事实。本项目将提出基于Copula理论的岩土体参数多维分布模型构建方法，建立有限数据条件下岩土体参数多维非正态分布模型。提出有限数据条件下岩土体参数联合分布模型的统计不确定性模拟方法，研究考虑岩土体参数联合分布模型统计不确定性的岩土结构物可靠度评估方法。阐明基于Copula函数的岩土体抗剪强度参数多维分布模型对边坡可靠度的影响规律，揭示抗剪强度参数多维正态分布模型可靠度结果的失真机制。最后以锦屏一级水电站左岸高边坡工程为例研究Copula理论在岩体抗剪强度参数不确定性表征及边坡稳定可靠度评估中的应用。本项目对丰富岩土体参数不确定性分析理论、提高我国水利水电工程高边坡风险控制水平具有重要的理论意义和显著的工程应用价值。

在岩土工程可靠度分析与风险控制中，岩土体物理力学参数通常被视为随机变量。众所周知，不同岩土体参数之间存在一定的相关性，且实际工程中岩土体参数的试验数据非常有限。因此，有限数据条件下如何表征岩土体参数的相关性是岩土工程可靠度分析与风险控制亟待解决的关键问题。本项目主要围绕以下3个方面开展研究：（1）多维岩土体参数联合分布模型建立方法；（2）有限数据条件下岩土体参数统计不确定性表征方法；（3）考虑岩土体抗剪强度参数相关性的边坡可靠度分析方法。通过本项目研究，提出了基于Copula理论的多维岩土体参数联合分布模型构建方法，有效地解决了多维非正态岩土体参数联合分布模型建模的难题；提出了有限数据条件下岩土体参数联合分布模型的统计不确定性表征方法，建立了考虑岩土体参数统计不确定性的岩土结构物可靠度分析方法；研究了表征抗剪强度参数相关性的Copula函数对边坡可靠度的影响，阐明了不同相关结构对边坡单一失效模式可靠度和多失效模式系统可靠度的影响规律；最后以锦屏一级水电站左岸高边坡工程为例探究了所提方法在实际工程中的应用。研究成果丰富了相关非正态岩土体参数联合分布建模理论，对提高我国水利水电工程高边坡防灾减灾水平具有重要的理论意义和显著的工程应用价值。