基于Copula理论的粗粒土渗透破坏临界水力比降估值

Estimation of critical hydraulic gradient of coarse-grained soils based on Copula theory

破坏水力比降是土体渗透稳定性分析和渗流控制的基础。以渗透变形试验为基础,分析了粗粒土临界水力比降与孔隙比、级配不均匀系数和曲率系数间的相关性。利用Copula理论适合建立多个非独立变量间联合分布函数的优点,构造了拟合粗粒土临界水力比降crJ、孔隙比e、级配不均匀系数uC和曲率系数cC间相关关系的最优Copula函数,并将其应用于粗粒土临界水力比降估值。结果表明:具有单参数的四维对称Archimedean Copula函数的Nelsen No 6为最优Copula函数。利用构造的最优Copula函数求条件概率,便可得到粗粒土临界水力比降估值的保证率,或者计算在一定保证率条件下临界水力比降估值。通过比较临界水力比降试验值与Copula理论方法、Terzaghi公式及刘杰公式估值,阐述了Copula理论的可靠性,为建立粗粒土临界水力比降与孔隙比及级配特征的多变量统计概率关系及临界水力比降估值提供了一种新途径。

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 Jcr of a coarse-grained soils, void ratios e, nonuniformity coefficients Cu , and curvature coefficient Ce 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 Jcr, e, Cu and Cc 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.