VARIATIONAL PRINCIPLES FOR CONSOLIDATION

Abstract

The purpose of this paper is to derive, as a basis of the finite element method, a generalized variational principle for consolidation under the following assumptions : Soil is inhomogeneous, anisotropically elastic with respect to effective stress, and saturated by incompressible water; deformation of soil does not depend on pore water pressure but on effective stress; water flows through soil according to Darcy's law. The paper is of theoretical nature.The derived variational principle which is equivalent to the governing equations in consolidation problems comprises six independent and piecewise continuous fields of displacement of soil skeleton, strain of soil skeleton, effective stress, water head, hydraulic gradient, and velocity of water relative to soil. The principle is so general that the already published variational principles for consolidation can be derived by setting some of the governing equations as side conditions. Furthermore, by making arbitrary sets of the governing equations subsidiary and boundary conditions, various variational principles can be developed, some of which may be useful for deriving effective finite element methods by application of the direct method.