Finite Element Schemes for Porous Elastic Media

In soil mechanics, consolidation theories are capable of describing the physical process under certain assumptions. Unfortunately, they fail to calculate analytically, e.g., the initial pore pressure field in function of applied loads with arbitrary boundary conditions. This is an opportunity for numerical treatment of this problem. First, the theory of mixtures is used to describe the behavior of a porous elastic medium saturated with a fluid. On this basis principles of virtual work are derived that replace equilibrium and continuity statements within the field as well as on the boundary. Second, with the aid of these principles, three finite element schemes are proposed. A following examination reveals the advantages and disadvantages of these schemes. It is possible to state numerically a unique initial pore pressure field. The number of unknowns can be reduced to a minimum. Computer costs are also discussed.