Seepage consolidation under space deformation of elastic half-space

The process of seepage consolidation of elastic saturated half-space under the action of an arbitrary normal load on its surface was investigated in the case of space deformation. The fluid and skeleton grains were assumed to be incompressible. The purpose of the study was to obtain analytical formulas for the main characteristics of consolidation. To fulfill this purpose, a mathematical model of consolidation with the use of the compatibility equation was proposed. The sum of the effective normal stresses was found as a solution to the first boundary value problem for the heat equation in a half-space. Then the first boundary value problem for an auxiliary function satisfying the Laplace equation was solved. This made it possible to obtain explicit expressions for the fluid pressure and the sum of the total normal stresses. Finally, the surface settlement of the half-space was determined. To illustrate the proposed approach, examples of determining the characteristics of consolidation with load on the surface of a half-space, load over the areas of a circle and a square were given. The maximum settlement of the square centre was determined. The obtained results can be used as tests when applying numerical methods for solving the problems of seepage consolidation.