Theory of Consolidation

DOI: 10.1007/978-90-481-3441-0_4

ABSTRACT The next two chapters (Chaps.4 and5) deal with the important effect that soils are usually composed of two constituents:
solid particles and a fluid, usually water, but perhaps oil, or a mixture of a liquid and gas. Chapter4 presents the classical
theory, due to Terzaghi, of semi-static consolidation, and some elementary solutions. In Chap.5 the extension to the dynamical
case is presented, mainly for the one dimensional case, as first presented by De Josselin de Jong and Biot, in 1956. The solution
for the propagation of waves in a one dimensional column is presented, leading to the important conclusion that for most problems
a practically saturated soil can be considered as a medium in which the solid particles and the fluid move and deform together,
which in soil mechanics is usually denoted as a state of undrained deformations. For an elastic solid skeleton this means
that the soil behaves as an elastic material with Poisson’s ratio close to 0.5.

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    ABSTRACT: The focus of this work is efficient solution methods for mixed finite element models of variably saturated fluid flow through deformable porous media. In particular, we examine preconditioning techniques to accelerate the convergence of implicit Newton–Krylov solvers. We highlight an approach in which preconditioners are built from block-factorizations of the coupled system. The key result of the work is the identification of effective preconditioners for the various sub-problems that appear within the block decomposition. We use numerical examples drawn from both linear and nonlinear hydromechanical models to test the robustness and scalability of the proposed methods. Results demonstrate that an algebraic multigrid variant of the block preconditioner leads to mesh-independent convergence, good parallel efficiency, and insensitivity to the material parameters of the medium. KeywordsNewton–Krylov–Coupled geomechanics–Algebraic multigrid–Mixed finite elements
    Computational Geosciences 09/2011; 15(4):647-659. · 1.61 Impact Factor
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    ABSTRACT: An effective stress principle for saturated fractured porous media is proposed based on the double-porosity representation. Both the solid grains and the fractured porous medium are assumed to be linearly elastic materials. The derivation employs volume averaging technique to obtain macroscopic scale expressions. Two parameters, the bulk modulus of the fractured medium and bulk modulus of the porous matrix, are introduced in the formulation. The final expression reduces to the one obtained by Biot and Willis [1957], Skempton [1960], Nur and Byeerle [1971], and Verruijt [1984] when the volume fraction of the fractures vanishes, that is, for a nonfractured porous medium.
    Water Resources Research 12/1995; 31(12):3103-3106. · 3.71 Impact Factor
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    ABSTRACT: We experimentally validate a relatively recent electrokinetic formulation of the streaming potential (SP) coefficient as developed by Pride (1994). The start of our investigation focuses on the streaming potential coefficient, which gives rise to the coupling of mechanical and electromagnetic fields. It is found that the theoretical amplitude values of this dynamic SP coefficient are in good agreement with the normalized experimental results over a wide frequency range, assuming no frequency dependence of the bulk conductivity. By adopting the full set of electrokinetic equations, a full-waveform wave propagation model is formulated. We compare the model predictions, neglecting the interface response andmodeling only the coseismic fields, with laboratory measurements of a seismic wave of frequency 500 kHz that generates electromagnetic signals. Agreement is observed between measurement and electrokinetic theory regarding the coseismic electric field. The governing equations are subsequently adopted to study the applicability of seismoelectric interferometry. It is shown that seismic sources at a single boundary location are sufficient to retrieve the 1D seismoelectric responses, both for the coseismic and interface components, in a layered model.
    International Journal of Geophysics 01/2012; 2012.


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May 21, 2014