Land Subsidence — A. A State-of-the-Art Review

Abstract

Following a description of the phenomena of land subsidence, its main features and its occurrence in many parts of the world, the review starts with the simplest depth-porosity model and models that are based on field data and empirical relations. It then continues through models that are based on the theories and physical concepts. The first studies of these kind are the semi- infinite elastic solid models which assume the earth to behave like a homogeneous, isotropic half space with a uniform elasticity modulus. A more rigorous approach to model land subsidence includes transient flow and equilibrium equations for isothermal reservoirs. A solution of this set of coupled equations can be obtained either by full-coupling which could be quite lengthy or by partial coupling which can be separated into two subgroups: “leap frog” and “two step” techniques. In the “two-step” method, the aquifer flow equation is solved in a three or two-dimensional space and then it is assumed that the solid deformation is one dimensional and one-dimensional consolidation equations are solved for aquitards in the reservoir. The results of the flow equation are the time dependent boundary conditions of the consolidation equations. An alternative approach to explain the behaviour of aquitards is given by viscoelastic models which assume a Theological constitutive equation instead of an elastic one as employed by the “two-step” technique. Later, models using a plastic stress- strain relation, and models for horizontal displacements are also reviewed. Finally, geothermal reservoir models that require an additional energy equation are discussed.