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Quasi-static Response of an Isotropic Half-space Saturated with Viscous Fluid based on the Theory of Porous Media

Behboodi, Mohammad Ali | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54406 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Eskandari, Morteza
  7. Abstract:
  8. The purpose of this study is to apply the governing equations of the theory of porous media with the concept of volume fractions to calculate the isotropic half-space responses subjected to a surface and asymmetric loading and to compare the responses with Biot’s theory. For this purpose, each of the components is first considered continuous and the equilibrium equations of mass and momentum for the solid and fluid phases based on the mixture theory are expressed. The concept of volume fractions and the effect of interaction between the two phases, distinguish these equations from the equations of the continuum theory. Thus, the governing coupled partial differential equations of the theory of porous media are obtained and rewritten for quasi-static analysis. To solve these equations analytically, the potential functions method is used to decouple the equations, and Laplace and Hankel transformations, as well as the Fourier series, are used to derive ordinary differential equations. Quasi-static analysis of isotropic saturated half-space with viscous fluid subjected to a general static loading on the surface presents the functions of displacement, stress, and water pressure in the transformed domain. In the following, the results of Biot’s theory are presented with the same method. Finally, using the numerical inverse transformation of Laplace and Hankel, the saturated half-space responses to a vertical circular loading on the surface are obtained for a soil sample. Furthermore, the effect of some soil parameters on the answers of the theory of porous media is investigated and the results of the theory of porous media and Biot’s theory are compared for two states of compressible and incompressible components
  9. Keywords:
  10. Volume Fraction ; Quasi Static Analysis ; Half Spaces ; Porous Media ; Biot Strain ; Mixture Model ; Potential Theory

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