基于Copula函数的土体抗剪强度参数二维分布模型

Bivariate Distribution Model of Soil Shear Strength Parameter Using Copula

传统的土体抗剪强度参数二维正态分布模型不足以表征抗剪强度参数的非正态分布特性。为此,提出了基于Copula函数的土体抗剪强度参数二维非正态分布模型建模方法。收集整理了小浪底水利枢纽工程中土体抗剪强度参数的三组试验数据,采用A-D检验法识别出抗剪强度参数的最优边缘分布模型。基于Copula函数建立了土体抗剪强度参数的二维分布模型,并采用最小平方欧氏距离法识别出表征抗剪强度参数间相关性的最优Copula函数。在此基础上,系统地比较了基于Copula函数的二维非正态分布模型与二维正态分布模型的优缺点。结果表明:提出的基于Copula函数的土体抗剪强度参数二维分布模型能够有效地表征抗剪强度参数的统计特性;与抗剪强度参数二维正态分布模型相比,基于最优Copula函数和最优边缘分布函数建立的抗剪强度参数二维非正态分布模型在适用性和拟合能力方面均具有一定的优势;此外,常用的Gaussian copula并不一定是表征抗剪强度参数间相关性的最优Copula函数。

This paper aims to propose a new method for modeling the bivariate non-normal distribution of soil shear strength parameter using Copula, due to the limitation of bivariate normal distribution to show the non-normal statistical characteristic. First, three datasets of soil triaxial shear strength from Xiaolangdi Hydraulic Project are collected, and the A-D method is used to identify the best-fit marginal distributions model. Then, the method for dependence modeling of soil shear strength parameter using Copula is briefly introduced, with the Least Square Euclidean Distances method used to identify the best-fit Copula underlying the collected shear strength parameter. Finally, the advantage and disadvantage to reproduce the bivariate model of soil shear strength parameter using the proposed method and the traditional bivariate normal distribution is compared systematically. The results indicate that it is an effective way to show the non-normal statistical characteristic of soil shear strength parameter using Copula. Compared with the traditional bivariate normal distribution, the proposed Copula-based method can provide a more general way of modeling the bivariate non-normal distribution of shear strength parameter in isolation from their marginal distributions, which results in more accurate results. Furthermore, the Ganssian copula, often adopted out of experience, is not always the best-fit Copula for modeling the dependence structure underlying the shear strength parameter.