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

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.