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A mathematical model for predicting moisture flow in an unsaturated soil under hydraulic and temperature gradients

, : A mathematical model for predicting moisture flow in an unsaturated soil under hydraulic and temperature gradients. Water Resources Research 17(3): 714-722

A theoretical model is presented to predict the moisture flow in an unsaturated soil as the result of hydraulic and temperature gradients. A partial differential heat flow equation (for above-freezing conditions) and the 2 partial differential transient flow equations (one for the water phase and the other for the air phase), are derived in this paper and solved using a finite difference technique. Darcy's law is used to describe the flow in the water phase, while Fick's law is used for the air phase. The constitutive equations proposed by Fredlund and Morgenstern are used to define the volume change of an unsaturated soil. The simultaneous solution of the partial differential equations gives the temperature, the pore water pressure, and the pore air pressure distribution with space and time in an unsaturated soil. The pressure changes can, in turn, be used to compute the quantity of moisture flow.


DOI: 10.1029/wr017i003p00714

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