Analytical solution to 1D coupled water infiltration and deformation in two‐layer unsaturated soils

Abstract

SUMMARYAn analytical solution to 1D coupled water infiltration and deformation in layered soils is derived using a Laplace transformation. Coupling between seepage and deformation, and initial conditions defined by arbitrary continuous pore‐water pressure distributions are considered. The analytical solutions describe the transient pore‐water pressure distributions during 1D, vertical infiltration toward the water table through two‐layer unsaturated soils. The nonlinear coupled formulations are first linearized and transformed into a form that is solvable using a Laplace transformation. The solutions provide a reliable means of comparing the accuracy of various numerical methods. Parameters considered in the coupled analysis include the saturated permeability (ks), desaturation coefficient (α), and saturated volumetric water content (θs) of each soil layer, and antecedent and subsequent rainfall infiltration rates. The analytical solution demonstrates that the coupling of seepage and deformation plays an important role in water infiltration in layered unsaturated soils. A smaller value of α or a smaller absolute value of the elastic modulus of the soil with respect to a change in soil suction (H) for layered unsaturated soils means more marked coupling effect. A smaller absolute value of H of the upper layer soil also tends to cause more marked coupling effect. A large difference between the saturated coefficients of permeability for the top and bottom soil layers leads to reduced rainfall infiltration into the deep soil layer. The initial conditions also play a significant role in the pore‐water pressure redistribution and coupling effect. Copyright © 2011 John Wiley & Sons, Ltd.