双重介质饱和-非饱和流随机分析

The Stochastic Analysis of Saturated-unsaturated Bimodal Porous Media

为描述天然介质的复杂构成,引入指示函数模型,推导了双重介质参数均值、方差和协方差函数的表达式,提出了拟单介质的概念,然后将基于Karhunnen-Loeve展开的谱方法应用于双重介质饱和-非饱和流随机分析中,分别模拟了双重介质和拟单介质的饱和-非饱和流运动,分析了饱和水力传导度(Ks)和土壤孔隙分布参数α的变异性对双重介质和拟单介质之间等效性的影响。结果表明:双重介质变异参数总体方差的增大并不会导致KL展开截断阶数的增加;如果仅考虑Ks或α的空间变异性,Ks或α的总体方差越大,拟单介质模型预测的水头方差准确性越差;当两种介质的Ks或α显著不同且各自具有小方差时,拟单介质可以代替双重介质;参数α比Ks更大程度影响等效性。如果同时考虑Ks和α的空间变异性,Ks或α均值差异越大,等效性越差,Ks或α的总体方差与等效性之间的相关关系不明显。

In order to depict the complex structure of the natural formations, the indicator function model was used and expressions for the mean, variance and covariance function of the medium parameters of the bimodal formations were derived. A quasi-unimodal porous medium was generated. The spectral method based on Kabunen-Loeve expansion was applied in the stochastic analysis of the bimodal media. The water flow in bimodal formations and qausi-unimdoal formation were simulated respectively, and the impact of the hydraulic conductivity and parameter α to equivalence between the bimodal and qausi-unimdoal formation was analyzed. It was shown that the increase of the total variance of the variable parameters doesn＇ t lead to a bigger truncation order. If considering the spatial variability of the parameter Ks or α only, the accuracy of the hydraulic head from quasi-unimodal formation becomes worse with the increase of the total variance ofK, or α ; When Ka or α of the two mediums distinguishes obviously and has small variance, the quasi-unimodal formation can substitute bimodal formations; The equivalence is affected more obviously by parameter cg than K, . If considering the spatial variability of the parameter K, and α at the same time, the larger gap of Kor α leads to a bad equivalence . The relation between the total variance ofK, or α and equivalence is obscure.