基于Copula函数的堆石料非线性强度参数相关性及分布模型研究

Correlation and distribution model for nonlinear strength parameters of rockfill based on Copula function

堆石料非线性强度参数的不确定性及相关性是影响土石坝坝坡稳定可靠度分析结果的关键因素,但传统的正态分布模型无法准确地表征非线性强度参数的相关非正态分布特征。汇总了国内外124座土石坝工程的1257组筑坝堆石料非线性强度参数,基于Copula函数提出了堆石料非线性强度参数联合分布模型的构建方法。分别采用最小二乘法和BIC准则确定堆石料非线性强度参数的相关系数、最优边缘分布函数与最优Copula函数。结果表明:非线性强度参数间存在显著的正相关性;堆石料非线性强度参数的边缘分布和相关系数相同时,不同的Copula函数构造的联合分布函数差异显著;对于条件累积分布函数,当非线性强度参数取值减小时,基于不同Copula函数构造的非线性强度参数的条件累积分布函数差异越显著;与二维正态分布模型相比,基于Copula函数建立的非线性强度参数非线性强度参数联合分布模型灵活性强、适用范围广,能更准确地表征原始数据的分布情况,可为土石坝坝坡静、动力稳定可靠度分析提供简单、有效的分布模型。

The uncertainty and correlation of nonlinear strength parameters of rockfill are the key factors affecting the stability reliability analysis results of rockfill dam slopes. However, the conventional normal distribution model cannot accurately characterize the correlation and non-normal distribution characteristics of nonlinear strength parameters. In this study, the nonlinear strength parameters of rockfill for 1257 groups of 124 rockfill dam projects around the world are summarized. Based on the Copula function, the construction method of joint distribution model for nonlinear strength parameters of rockfill is proposed. The correlation coefficient, optimal marginal distribution function and optimal Copula function for nonlinear strength parameters of rockfill are determined by the least square method and BIC criterion respectively. The results show that there is a significant positive correlation between the nonlinear strength parameters. The joint distribution functions constructed by different Copula functions are significantly different despite the same marginal distribution and correlation coefficient of the nonlinear strength parameters. For the conditional cumulative distribution function, with the decrease of the nonlinear strength parameters, the greater difference is in the conditional cumulative distribution function of the nonlinear strength parameter constructed based on different Copula functions. Compared with the two-dimensional normal distribution model, the nonlinear strength parameter joint distribution model based on the Copula function is flexible and applicable in a wide range, which can more accurately represent the distribution of the original data and provide a simple and effective distribution model for the static and dynamic stability reliability analysis of rockfill dam slopes.