An Introduction to Soil Dynamics
This book presents the basic principles of soil dynamics, and a variety of solutions of practical interest for geotechnical engineering, geophysics and earthquake engineering. Emphasis is on analytical solutions, often including the full derivation of the
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Theory of Consolidation
4.1 Consolidation Soft soils such as sand and clay consist of small particles, and often the pore space between the particles is filled with water. In soil mechanics this is denoted as a saturated or a partially saturated porous medium. The deformation of such porous media depends upon the stiffness of the porous material, but also upon the behaviour of the fluid in the pores. If the permeability of the material is small, the deformations may be considerably hindered, or at least retarded, by the pore fluid. The simultaneous deformation of the porous material and flow of pore fluid is the subject of the theory of consolidation, often denoted as poroelasticity. The theory was developed originally by Terzaghi (1925) for the one-dimensional case, and extended to three dimensions by Biot (1941), and it has been studied extensively since. In Terzaghi’s original theory the pore fluid and the solid particles were assumed to be completely incompressible. This means that deformations of the porous medium are possible only by a rearrangement of the particles, and that volume changes must be accompanied by the expulsion of pore water. This is a good approximation of the real behaviour of soft soils, especially clay, and also soft sands. Such soils are highly compressible (deformations may be as large as several percents), whereas the constituents, particles and fluid are very stiff. In later presentations of the theory, starting with those of Biot, compression of the pore fluid and compression of the particles has been taken into account. This generalization made it possible to also consider the deformations of materials such as sandstone and other porous rocks, which are very important in the engineering of deep reservoirs of oil or gas. The linear theory of poroelasticity (or consolidation) has now reached a stage where there is practically general consensus on the basic equations, see e.g. De Boer (2000), Wang (2000), Coussy (2004), Verruijt (2008b). In this chapter the basic equations of the general theory of linear consolidation are derived, for the case of a linear material, and for pseudo-static deformations (in which inertial forces are disregarded). A simplified version of the theory, in which the soil deformation is assumed to be strictly vertical, is also presented in A. Verruijt, An Introduction to Soil Dynamics, Theory and Applications of Transport in Porous Media 24, © Springer Science+Business Media B.V. 2010
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4 Theory of Consolidation
this chapter. The analytical solutions for two simple examples are given. In the next chapter the generalization to dynamics is presented. Before deriving the basic equations of consolidation it is convenient to consider some of the basic principles underlying the theory, especially the influence of the compressibilities of the two constituents (solid particles and pore fluid) on the behaviour of a porous medium in the absence of drainage.
4.1.1 Undrained Compression of a Porous Medium Consider an element of porous soil or rock, of porosity n,
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