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Biot’s Theory of Consolidation

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Land Subsidence Analysis in Urban Areas

Part of the book series: Springer Environmental Science and Engineering ((SPRINGERENVIRON))

Abstract

In this chapter, we present the constitutive equations of the Biot model. The main difficulties of this model are the coupling of the equations and the application of the superposition principle. We present the general solution of the coupled problem resulting from the Biot model. This solution is based on a new method for decoupling the equations. This decoupling approach permits to derive a superposition principle of the loadings. Several types of loadings and boundary conditions for the water pressure and the displacement field are discussed. Analytical solutions are also derived and discussed.

Also, the problem of the computation of the different causes and their relative contribution to the total subsidence and/or settlement is analyzed in terms of two main principles of the partial differential equations, as follows:

  • the coupling/decoupling of the system of equations; and

  • the principle of superposition of loadings.

For soft clays and/or loose sand, the ratio between the maximum vertical displacements using the coupled model may be 170 times larger than the maximum vertical displacement computed with the decoupled model.

Also, for large values of the shear modulus and a standard value of the Young modulus (gravel sand), the consolidation ratio of the coupled solution and the decoupled solution are similar. This ratio deceases rapidly with the radial distance to the pumping well. However, for small values of the shear modulus, the consolidation ratio is decreasing slowly with the radial distance to the pumping well.

Eliyahu Wakshal (Deceased)

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Authors and Affiliations

  1. Jerusalem College of Technology, Jerusalem, Israel

    David G. Zeitoun

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  1. David G. Zeitoun
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  2. Eliyahu Wakshal
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Zeitoun, D.G., Wakshal, E. (2013). Biot’s Theory of Consolidation. In: Land Subsidence Analysis in Urban Areas. Springer Environmental Science and Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5506-2_5

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