论文导读 | 基于Copula的空间变土壤边坡条件可靠性分析

摘要：Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring (Central South University),

01 / 文章信息

文章标题：

Copula-based conditional reliability analysis of slopes in spatially variable soils

文章作者(*为通讯)：

1. Yue-Bing Xu 1.2.3

2. Lei-Lei Liu 1.2.3.*

作者单位：

1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring (Central South University), Ministry of Education, Changsha 410083, PR China

2. Key Laboratory of Non-ferrous and Geological Hazard Detection, Changsha 410083, PR China

3. School of Geosciences and Info-Physics, Central South University, Changsha 410083, PR China

Conditional random field; Copula dependence structure; Slope reliability; Spatial variability.

互相关条件随机场（CRFs）能够通过融合多元场地勘察数据更好地表征土壤空间变异性。然而现有研究常假定强度参数在CRFs中遵循高斯copula依赖结构，这一假设在实践中可能并不成立。本研究深入探讨了互相关CRFs间非高斯copula依赖结构对边坡可靠性分析的影响。采用多重响应面法与子集模拟相结合的计算策略，有效求解了边坡稳定失效概率（ P ）。以典型粘聚力-内摩擦角土坡为例，通过参数化研究系统分析了非高斯copula依赖结构对安全系数（FS）、临界滑裂面（CSS）及的影响。研究结果表明：基于高斯copula的CRFs可能低估 P ，当实际依赖结构遵循No.16 copula时这种低估现象最为显著；与基于copula的无条件随机场相比，基于copula的CRFs能更有效降低FS的不确定性和CSS的空间分布变异性。本研究为利用多元场地数据进行条件边坡可靠性分析时的copula选择提供了实用指导，填补了岩土可靠性分析与风险评估领域的重要空白。

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的对比

c 和 φ 的三种分布

04 / 原文信息

Abstract

Cross-correlated conditional random fields (CRFs) can better characterize soil spatial variability by incorporating multivariate site investigation data. However, existing studies often assume a Gaussian copula dependence structure for strength parameters in CRFs, which may not hold in practice. This study advances the understanding of how non-Gaussian copula dependence structures between cross-correlated CRFs influence slope reliability analysis. A combined approach of the multiple response surface method and subset simulation is employed to efficiently compute the probability of failure ( P f ) of slope stability. Using a typical cohesive-frictional soil slope as an illustrative example, parametric studies are conducted to investigate the effects of non-Gaussian copula dependence structures on the factor of safety (FS), critical slip surface (CSS) and P f . The results show that the commonly used Gaussian copula-based CRFs may underestimate the P f , and such situation becomes the most severe when the underlying dependence structure follows the No.16 copula. Compared with copula-based unconditional random fields, the copula-based CRFs can more efficiently reduce the uncertainty of the FS and spatial distribution of CSS. This study provides practical guidance for copula selection in conditional slope reliability analysis leveraging multivariate site data, addressing a critical gap in geotechnical reliability analysis and risk assessment.