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摘要
The time-dependent hydromechanical behavior of a finite two-dimensional (2D) fluid-saturated poroelastic medium induced by sine /constant-rate point sink is investigated analytically in detail. In the case of sine point sink, the displacements and pore pressure exhibit approximate cyclicity with time, which is in tune with the periodicity of sine point sink. In the case of a constant-rate point sink, the analytical solution is compared with an uncoupled exact solution available in the literature. Their similarity in form validates the accuracy of the presented analytical solution in some sense. Then the time-dependent behavior in this case is analyzed, and the effects of concerned parameters on the poroelastic behavior are studied. The results reveal that pore pressure tends to be linear with respect to time rather than presenting a typical dissipation effect. This phenomenon is mainly determined by impervious boundary conditions. Unlike the behavior of a pore pressure field, the displacements increase rapidly with time at the early stage and eventually reach a steady state as time is large enough. This remarkable feature is the consequence of combined actions of the pore pressure dissipation effect and the dragging effect. Parametric studies show that the location change of the point sink has a significant influence on the distributions of displacement field and pore pressure field, while the magnitude of pumping rate or scaled sink strength only affects the size of pore pressure or the displacements. Additionally, the geometrical size of the studied region plays a dominant role in determining the consolidation time. The results in this paper are of great help to provide in-depth insights into the time-dependent behavior of fluid-solid interaction due to fluid withdrawal within finite 2D porous materials.
