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Wave propagation in saturated porous media

Citation

van der Kogel, Hans (1977) Wave propagation in saturated porous media. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:03052010-152258919

Abstract

Wave propagation in saturated porous media is investigated in the framework of two models, a theoretical and an experimental one. The theoretical model has two phases, a fluid phase and a solid phase, both modeled as a continuum. The solid phase consists of incompressible grains forming a compressible skeleton. The fluid phase represents a compressible fluid located between the grains. Interactive forces, due to relative motion between the skeleton and the fluid are taken into account. Non-linear balance laws and equations of state are formulated for plane waves. Linearization of the non-linear balance laws yields a set of equations which in limiting cases reduce to well-known results (e.g. consolidation equation, condition for fluidization). The harmonic solution of the linearized field equations contains two modes: one in which the phases move almost together (which is slightly damped) and one in which the phases move in opposite directions (which is highly damped). Solutions are presented in system form. Applying a step loading in the variables at the boundary generates, in general, two propagating discontinuities in the variables and these discontinuities decay as they propagate. If we assume that the parameters take "practical" values of wet sand then the jump in pore-pressure is always large with respect to the jump in effective pressure along the faster discontinuity propagating into a medium at rest, while velocity differences between the phases are generated if the densities of the phases are different. Non-linear effects due to a non-linear constitutive equation for the fluid oppose the decay of gradients in the variables along the faster propagating discontinuity. The influence of non-linear convective terms can be neglected if the phase velocities are small with respect to the velocities of the discontinuities. The solution to the problem of reflection and refraction of a discontinuity propagating in a fluid and impinging on a two-phase medium is presented. The theory is extended in multi-dimensions, in order to allow shear waves to propagate. The existence of non- propagating discontinuities in dilatant shear is demonstrated. The experimental model consists of a disc configuration, dry and saturated. The interparticle stresses due to impact are visualized by a photo-elastic technique and recorded by a high-speed camera. Changing stress patterns in the discs behind the wavefront are observed. In the dry case a wavefront emerges, behind which the particles are relatively well stressed, while no such definite stress front can be identified in the saturated case. Phase velocity differences occur and separation of particles was observed to take place due to indirect loading of the discs via the fluid.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Civil Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Civil Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Scott, Ronald F.
Thesis Committee:
  • Unknown, Unknown
Defense Date:16 May 1977
Record Number:CaltechTHESIS:03052010-152258919
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:03052010-152258919
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5580
Collection:CaltechTHESIS
Deposited By: Tony Diaz
Deposited On:05 Mar 2010 23:40
Last Modified:26 Dec 2012 03:22

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