HR: 0800h
AN: H21B-1342    [Abstracts]
TI: Decoupling of the Coupled Poroelastic Equations for Quasistatic Flow in Deformable Unsaturated Porous Media
AU: * Lo, W
EM: lowc@mail.ncku.edu.tw
AF: National Cheng Kung University, Department of Hydraulic and Ocean Engineering, Tainan, 701 Taiwan
AB: The study of the poroelastic behavior of sedimentary materials containing two immiscible fluids in response to either applied stress or pore pressure change in a quasistatic limit, i.e. negligible second time-derivatives, is of great importance to many hydrogelogical problems, e.g. land subsidence caused by withdrawal of subsurface fluids. The poroelasticity models developed for analyzing these problems feature partial differential equations that are coupled in the terms describing viscous damping and strain field. To determine closed-form analytical solutions for induced volumetric strain (dilatation) of the solid framework and its interaction with fluid flows, the choice of normal coordinates whose transformation can be performed to decouple these poroelastic equations is highly desirable. In this paper, we show that normal coordinates exact for decoupling these equations are real-valued and equal to three different linear combinations of the dilatations of the solid and the fluids (or equivalently, three different linear combinations of two individual fluid pressures and solid dilatation). In contrast to fully-saturated porous media, it is found that the viscous damping effect must be represented in normal coordinates in the presence of the second fluid. The resulting decoupled equations representing independent motional modes are a Laplace equation and two diffusion equations, which can be solved analytically under a variety of initial and boundary conditions. Thus, after inverse transformation of normal coordinates is performed, the closed-form analytical solutions for induced solid volumetric strains and excess pore pressures can be obtained simultaneously from our decoupled partial differential equations.
DE: 1835 Hydrogeophysics
DE: 1875 Vadose zone
DE: 3200 MATHEMATICAL GEOPHYSICS (0500, 4400, 7833)
SC: Hydrology [H]
MN: Fall Meeting 2005