Abstract: The failure hydraulic gradient is a crucial parameter for slope stability analysis and seepage control. Based on the experiment of seepage-induced deformation, the correlations among the critical hydraulic gradients of a coarse-grained soils, void ratios e, nonuniformity coefficients , and curvature coefficient of granular gradation are analyzed. By taking the advantage of Copula theory in constructing the joint distribution function of multiple non-independent variables, an optimal fitting Copula function of , e, and is proposed and used to estimate the critical hydraulic gradient. It is shown that the Nelsen No.6 function of the four-dimensional symmetric Archimedean Copula functions with single parameter is the optimal Copula function. By calculating the conditional probability for the optimal Copula function, the guarantee rates of estimated values can be obtained, or the critical hydraulic gradients with a certain guarantee rate can be calculated. Comparisons of the measured critical hydraulic gradient and the estimations of Copula theory, Terzaghi formulation, and Liu Jie’s formulation, the reliability of Copula theory is shown. These results lay a new foundation for developing the relationship among multiple factors including critical hydraulic gradient, void ratio and gradation characteristics and estimating the critical hydraulic gradient for coarse materials.

Key words: Copula theory, coarse-grained soil, critical hydraulic gradient, void ratio, grain gradation