Dynamic Analysis of 3D Saturated Poroelastic Media with Boundary Element Method

Morteza Jiryaei Sharahi , Mohsen Kamalian
Department of Geotechnical Engineering, International Institute of Earthquake Engineering and Seismology
(IIEES)
Keywords: boundary element, dynamic poroelasticity, time domain
ABSTRACT: This paper presents the direct boundary element formulation for solving three-dimensional problems
of dynamic poroelasticity in the time domain. At first, the boundary integral equations (BIE) are obtained for the
three-dimensional well known u-p formulation of saturated porous media with incompressible fluid and solid
particles. Subsequently, the analytical form of the time domain dynamic kernels that appear in the discretized
governing BIE are derived. Finally, numerical results are presented to investigate accuracies and stability of this
approach for wave propagation analysis.
1 Introduction
The dynamic analysis of saturated porous media, is of interest in various fields, such as geophysics, acoustics,
soil dynamics and many earthquake engineering problems. From a macroscopical point of view, saturated soil is
a two-phase medium constituted of solid skeleton and fluid. Dynamic behaviours of each phase as well as that of
the whole mixture are governed by the basic principles of continuum mechanics. In dynamic phenomena with
medium speeds, such as earthquake problems, it is reasonable to neglect the fluid inertial effects, and to reduce
the complete dynamic governing differential equations to the simple commonly called u-p formulation. The
governing differential equations could be further simplified by neglecting the compressibility of the solid particles
and fluid, which could be reasonably assumed incompressible compared to the soil skeleton.
The BEM is one of the most efficient numerical mehods for solving wave propagation problems in elastic media,
because of its efficiency in dealing with semi-infinite or infinite domain problems that has long been recognized.
Predeleanu (1984), Manolis & Beskos (1989) and Wiebe & Antes (1991) were among the firsts who developed
boundary integral equations and fundamental solutions governing the dynamics of poroelastic media, in terms of
solid skeleton displacement and fluid displacements components. Later, Cheng et al. (1991), Dominguez (1992),
Chen & Dargush (1994) and recently Schanz (2001) developed another forms of boundary integral equations and
fundamental solutions of dynamic poroelasticity in terms of less independent variables. But their algorithms were
based on transformed domain fundamental solutions.
Obviously, time domain BEM for modeling the transient behaviour of media is preferred than the transformed
domain BEM, because formulating the numerical procedure entirely in time domain and combining it with the
FEM, provides the basis for solving nonlinear wave propagation problems.
Proper fundamental solutions are one of the key ingredients required for solving wave propagation problems in
saturated porous media by the BEM. Considering the independent practical variables of solid skeleton
displacement and fluid pressure, Kaynia (1992) was the first who presented approximate transient 3D
displacement fundamental solutions for the special case of short-time. Chen (1994) proposed another
approximate transient 2D and 3D displacement solutions for the special case of short time as well as the general
case, which were too complicated to be applied in BE algorithms. Gatmiri & Kamalian (2002) showed that Chen's
approximation could not be used in the simplified case of u-p formulation. They derived another approximate
transient 2D displacement fundamental solutions for the u-p formulation which were still too complicated to be
used in BE algorithms. Later Gatmiri & Nguyen (2004) proposed much less complicated transient 2D fundamental
solutions for the u-p formulation of saturated porous media consisted of incompressible constituents. Recently
Kamalian and Jiryaei (2006, 2007) derived the transient displacement and traction fundamental solutions for the
simplified u-p formulation of 3D poroelastic media with incompressible constituents.

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Dynamic Analysis of 3D Saturated Poroelastic Media with Boundary Element Method 2011-04-12T01:42:00-07:00 Rating: 4.5 Diposkan Oleh: Andre S