Abstract Multivariate information of soil parameters is quite important for the design and risk assessment of geotechnical engineering problems. It is necessary to have an accurate and realistic statistical multivariate model for representing the soil properties and thus evaluating the soil conditions. Thus, advanced multivariate modeling of soil parameters could help to improve the geotechnical engineering practice. In this paper, the asymmetric copulas are introduced to model the geotechnical soil data. Compared to extensive previous research on the use of symmetric copulas on the modeling of engineering data, this study is focusing on capturing asymmetric dependencies among the natural soil parameters, which are critical for engineering design. A copula-based multivariate probabilistic model is built based on a set of collected samples from a granite residual soil from Portugal. Several asymmetric copula functions, capable of capturing nonlinear asymmetric dependence structures, are tested and analyzed. The fundamental information on tail dependencies and measures of asymmetric dependencies are also exploited. To demonstrate the advantages of asymmetric copulas, its concept is compared with the traditional copula approaches for modeling site soil data. The performance of these asymmetric copulas is discussed and compared based on data fitting and extreme value characterizations.

中文翻译：

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用于岩土工程分析的多元土壤数据之间的非对称依赖建模——非对称 copula 方法

摘要 土参数的多变量信息对于岩土工程问题的设计和风险评估具有重要意义。有必要有一个准确和现实的统计多元模型来表示土壤特性，从而评估土壤条件。因此，先进的土壤参数多变量建模有助于改进岩土工程实践。在本文中，非对称 copula 被引入到岩土数据建模中。与之前在工程数据建模中使用对称 copula 的广泛研究相比，本研究侧重于捕获对工程设计至关重要的天然土壤参数之间的不对称依赖关系。基于 copula 的多元概率模型是基于从葡萄牙花岗岩残余土壤中收集的一组样本构建的。测试和分析了几个能够捕捉非线性非对称依赖结构的非对称 copula 函数。还利用了关于尾依赖和非对称依赖度量的基本信息。为了展示非对称 copula 的优势，将其概念与用于模拟场地土壤数据的传统 copula 方法进行了比较。基于数据拟合和极值特征讨论和比较这些非对称 copula 的性能。还利用了关于尾依赖和非对称依赖度量的基本信息。为了展示非对称 copula 的优势，将其概念与用于模拟场地土壤数据的传统 copula 方法进行了比较。基于数据拟合和极值特征讨论和比较这些非对称 copula 的性能。还利用了关于尾依赖和非对称依赖度量的基本信息。为了展示非对称 copula 的优势，将其概念与用于模拟场地土壤数据的传统 copula 方法进行了比较。基于数据拟合和极值特征讨论和比较这些非对称 copula 的性能。