抗剪强度参数相关变量重构及Copula联合分布模型研究

在实际工程中,大样本的岩土体参数实测值往往不易获取,以抗剪强度参数为例,给出了一种相关变量样本重构方法。首先简要介绍了Ilich算法和Copula函数,基于实际的初始数据,生成了具有指定边缘分布的相关变量样本;并借助Copula函数研究了样本重构前后的联合分布模型,认为与初始样本具有相同最优联合分布的重构样本能更大程度地继承初始数据的信息。以一简单的算例将重构样本应用于可靠性分析中,通过对比分析基于重构样本的Monte Carlo法与设计验算点法,验证了计算结果的合理性。给出的重构方法所得到的样本将与初始样本具有相同的边缘分布信息、相关结构及联合分布模型。

Reconstruction of the shear strength parameters correlation variable and the study on the joint distribution model of Copula

The measured values of the rock and soil parameters are not easy to be gotten in practical engineering, so a new method for the reconstruction of correlated variables is presented in this paper and the shear strength parameters are taken as an example. First a brief introduction to the as Ilich algorithm and copula function is given, then a sample of related variables with the specified edge distribution is generated based on the actual initial data and the joint distribution model of samples before and after reconstruction is studied by the means of Copula, it is considered that the reconstructed samples with the same optimal joint distribution can inherit the information of the initial data to a greater extent. A simple numerical example is used in the reliability analysis, and the rationality of the calculation results is verified by comparing the Carlo Monte method and the design method based on the reconstructed samples. The samples obtained by the reconstruction method will have the same edge distribution information, the correlation structure and the joint distribution model with the original sample.