Abstract:
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.
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