Transient seepage model for saturated–unsaturated soil systems: a geotechnical engineering approach

Abstract

A two-dimensional finite element model is proposed to simulate transient seepage for complex groundwater flow systems. The complete soil system is treated as a continuum encompassing flow in both saturated and unsaturated zones. In the unsaturated zone, the air phase is assumed to be continuous and open to atmospheric pressure. The coefficient of permeability of the unsaturated soil is assumed to be a function of pore-water pressure.The governing differential equation is derived within a framework familiar to geotechnical engineers. The stress state variables and the constitutive relationships for an unsaturated soil are used in the derivation. The finite element solution to the governing differential equation is based on the Galerkin weighted-residual method. The nonlinearity of the equation is solved by iterative procedures.The finite element formulation is implemented into a computer model named TRASEE. The model can be applied to a wide variety of problems involving complex boundary conditions and geometries with arbitrary degrees of heterogeneity and anisotropy. Example problems are presented to demonstrate the capabilities of the model. The results indicate that the quantity of water flow in the unsaturated zone may be substantial, and that the phreatic line is not a flow line. It has been found that the traditional "saturated-only" flow-net technique can be approximated as a special case to the proposed saturated–unsaturated model. Key words: unsaturated flow, finite element model, phreatic line, permeability function, transient seepage.