粗粒土孔隙比及级配参数与渗透系数概率的相关性研究

Study on probabilistic relation between permeability coefficient and void ratio and grain composition of coarse grained soils using Copula theory

孔隙比和颗粒级配是粗粒土渗流力学特性的重要影响因素。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,以渗透试验成果为数据基础,构造了反映粗粒土渗透系数k、孔隙比e、级配不均匀系数Cu和曲率系数Cc间相关关系的四维最优Archimedean Copula函数(即Nelsen No 13,四维单参数对称Archimedean Copula函数)。利用构造的最优四维Copula函数求条件概率,便可得到粗粒土渗透系数估值的保证率,或者计算在一定保证率条件下的渗透系数。通过比较渗透系数试验值与Copula函数法、Terzaghi法及Hazen法计算值,阐述了Copula理论用于粗粒土渗透参数估值的可靠性。

The void ratio and grain composition are the important factors to determine the seepage mechanical properties of cohesionless coarse grained soils. Based on the laboratory permeability test data, a four di- mensions optimal fitting Copula function,i.e., Nelsen No 13 function with single parameter in four-dimen- sional symmetric Archimedean Copula functions, is established to represent the relation between the permeability coefficients （k） and void ratios （e）, non-uniform coefficients （Cu） and coefficients of curvature （Cu） of granular composition. Utilizing the optimal Copula function to calculate the conditional probability, the guarantee rates of estimated permeability coefficients can be obtained, whereas the permeability coefficients with a certain guarantee rate can be calculated too. Compared the test values with the calculating values of the Copula function, the K. Terzaghi and the A. Hazen methods, it has been demonstrated that the pro- posed Copula-based method is an effective tool in estimating the permeability coefficients of cohesionless coarse grained soils.