Abstract: Based on 1 174 sets of testing data of shear strength parameters from 103 hydropower projects in China, a Copula-based function is adopted to investigate the joint distribution model of shear strength parameters for rock foundation. The construction method of the joint distribution model is explored. Firstly, the statistics of shear strength parameters have been achieved using the least square method. Then, based on the Akaike Information Criterion (AIC), the best-fit marginal distributions of shear strength parameters is identified. Finally, four Copula functions are chosen to build the bivariate distribution of shear strength parameters. The advantages of using Copulas to model the bivariate distribution of shear strength parameters are discussed. The results indicate that there exists a strong negative correlation among the shear strength parameters of rocks in hydropower projects. The proposed Copula-based approach can incorporate various marginal distributions and Copulas into a multivariate distribution, which provides a flexible way of modeling the bivariate distribution of shear strength parameters. With the known marginal distributions and correlation coefficient of shear strength parameters, the bivariate distribution of shear strength parameters cannot be determined uniquely. The bivariate distributions using various Copulas differ considerably under the premise that the edge distribution function and the correlation coefficient are exactly the same. Compared with the commonly used bivariate normal distribution of shear strength parameters, the proposed Copula-based approach provides a more general way of modeling the bivariate distribution and thus its modeled results are more accurate. Design values of shear strength parameters in hydropower projects are commonly determined by using the small value average method in China. The conditional cumulative distribution functions of cohesion associated with various Copulas differ considerably when friction coefficient takes a smaller value. Such differences directly lead to a significant effect on the determination of design values of shear strength parameters and the associated design schemes of hydraulic structures.

Key words: shear strength parameters, correlation, bivariate distribution, joint probability distribution function, Copula