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