概率统计法测算非饱和土渗透系数的理论研究

Theoretical study of the statistical method for estimating hydraulic conductivity function of unsaturated soil

基于概率统计理论,从非饱和土的孔径分布函数(PSDF)及土水特征曲线(SWCC)出发,对非饱和土截面上各组孔隙进行归组分析,讨论不同孔隙连接情况下允许水流通过的有效面积,最终推导得到了非饱和土渗透系数的数学表达式.推导过程中,采用等分基质吸力区间的方法,基于毛细定律确定非饱和土截面上各组孔隙的特征半径.利用PSDF,讨论各种情况下不同孔隙连接的概率,从理论上得到任一吸力条件下非饱和土截面的有效渗流面积.最后基于阀门模型,计算得到非饱和土相对渗透系数.此外,将所推导公式与已有的非饱和土相对渗透系数计算式进行对比,通过理论分析,证明两者在本质上是一致的,且所推导公式可采用EXCEL直接计算,易于推广使用.

Based on the statistical method,an equation of the hydraulic conductivity of unsaturated soil is derived from the pore size distribution function(PSDF)and soil-water characteristic curve(SWCC).The pores of unsaturated soil are divided into groups in the suction domain,and then the effective area allowing water passing through is calculated.During the process of derivation,the characteristic radius of each group of pores is determined based on the capillary law.Using the PSDF,the probability of different pore connections is discussed.As a result,the equation for calculating the relative hydraulic conductivity of unsaturated soil is proposed using the valve model.In addition,the proposed equation is also theoretically compared with the existing equation.It is proved that both equations are essentially the same.An electronic spreadsheet can be created from the proposed equation,which is easy to be promoted and used in engineering.