State‐Dependent Anisotropy: Comparisons of Quasi‐Analytical Solutions with Stochastic Results for Steady Gravity Drainage
State‐Dependent Anisotropy: Comparisons of Quasi‐Analytical Solutions with Stochastic Results for Steady Gravity Drainage
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状态相关各向异性：稳态重力排水的准解析解与随机结果的比较
DOI：
10.1029/95wr00790
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
D. Freyberg
中科院分区：
文献类型：
--
作者：
Timothy R. Green;D. Freyberg
层状土大尺度非饱和导水率的各向异性随含水量的变化而变化。在这里，状态依赖的各向异性计算条件下的大规模重力排水。用加德纳指数函数表示的土壤是完全成层的、周期性的和倾斜的。达西定律在每一层的分析整合的结果在一个系统的非线性方程，迭代求解层界面处的毛细吸力和垂直于分层的达西通量。计算的通量和吸力剖面被用来确定两个放大的水力传导率的主要方向和相应的“状态依赖”的各向异性比的函数的平均吸力。分析了三组分层土壤，并与Yeh等人（1985 b）随机结果的独立预测进行了比较。小扰动的方法预测适当的行为各向异性在非干旱条件下。然而，随机结果仅限于中等值的平均吸力，这种限制是联系在一起的一组统计和几何参数的泰勒级数近似。泰勒级数的两种替代形式提供了相对干燥土壤的状态相关各向异性的上限和下限。
Anisotropy in large-scale unsaturated hydraulic conductivity of layered soils changes with the moisture state. Here, state-dependent anisotropy is computed under conditions of large-scale gravity drainage. Soils represented by Gardner's exponential function are perfectly stratified, periodic, and inclined. Analytical integration of Darcy’s law across each layer results in a system of nonlinear equations that is solved iteratively for capillary suction at layer interfaces and for the Darcy flux normal to layering. Computed fluxes and suction profiles are used to determine both upscaled hydraulic conductivity in the principal directions and the corresponding “state-dependent” anisotropy ratio as functions of the mean suction. Three groups of layered soils are analyzed and compared with independent predictions from the stochastic results of Yeh et al. (1985b). The small-perturbation approach predicts appropriate behaviors for anisotropy under nonarid conditions. However, the stochastic results are limited to moderate values of mean suction; this limitation is linked to a Taylor series approximation in terms of a group of statistical and geometric parameters. Two alternative forms of the Taylor series provide upper and lower bounds for the state-dependent anisotropy of relatively dry soils.