Theory of Consolidation

DOI: 10.1007/978-90-481-3441-0_4 In book: An Introduction to Soil Dynamics, pp.65-90


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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    • "Fluid pressure is related to fluid displacement by p f l = −K f ∇· u f l . Pore-fluid pressure and intergranular stresses are obtained following the basic equations described in [60] [61] [62] [63] [64]. "
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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.
    Full-text · Article · Jul 2012 · International Journal of Geophysics
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    ABSTRACT: The field and constitutive equations expressing the dynamic behavior of a partially saturated porous medium considered as a solid-fluid-gas system are developed. The corresponding governing equations are then constructed and subsequently linearized to form a system of 11 partial differential equations with 11 unknowns. This system is reduced to 7 equations with 7 unknowns for the special case of the nearly saturated porous medium. The various phenomenological coefficients of the theory are identified and expressed in terms of measurable quantities. The case of a fully saturated porous medium is obtained from the present formulation as a special case, which is then compared with Biot's theory as well as with other known theories. An investigation of the harmonic response of an unbounded nearly saturated medium reveals the existence of three kinds of body waves, one rotational and two dilatational which are significantly affected by the degree of saturation of the medium. Finally, the transient, one-dimensional ‘Blot's column problem’ for a saturated and a nearly saturated porous medium is solved with the aid of numerical Laplace transform and the effect of the degree of saturation on the response is demonstrated.
    No preview · Article · Mar 1986 · Mechanics of Materials
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    ABSTRACT: In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain. These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities in a porous medium domain. It is shown that the methodology of averaging leads to a better understanding of the effective stress concept employed in dealing with transport phenomena in deformable porous media.
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