Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation
نویسندگان
چکیده
In this study, we derive analytical solutions of the first two moments (mean and variance) of pressure head for one-dimensional steady state unsaturated flow in a randomly heterogeneous layered soil column under random boundary conditions. We first linearize the steady state unsaturated flow equations by Kirchhoff transformation and solve the moments of the transformed variable up to second order in terms of rY and rb, the standard deviations of log hydraulic conductivity Y 1⁄4 lnðKsÞ and of the log pore size distribution parameter b 1⁄4 lnðaÞ. In addition, we also give solutions for the mean and variance of the unsaturated hydraulic conductivity. The analytical solutions of moment equations are validated via Monte Carlo simulations. 2004 Elsevier Ltd. All rights reserved.
منابع مشابه
Explicit analytical solutions for one-dimensional steady state flow in layered, heterogeneous unsaturated soils under random boundary conditions
[1] In this study, we directly derive first-order analytical solutions to the pressure head moments (mean and variance) for one-dimensional steady state unsaturated flow in randomly heterogeneous layered soil columns under various random boundary conditions. We assume that the constitutive relation between the unsaturated hydraulic conductivity and the pressure head follows an exponential model...
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