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Modeling Saturated Porous Media Using Extended Finite Element Method

Haghighat, Ehsan | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40539 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. Soil structures have important roles in civil engineering applications. The most important types of these structures are soil dams and foundations which their damages may cause huge loss. Thus, appropriate analysis of these structures under possible loading conditions is unavoidable. The real behavior of this media can be achieved from the solution of its coupled governing differential equations. In order to solve this set of equations in practical applications, appropriate numerical solutions should be used. The finite element method can be called as one of the most important numerical solutions of differential equations which have been used in analyzing different types of engineering problems. Its essential drawback is modeling discontinuities. In solid mechanic problems, discontinuity may occur in displacement field, such as crack or contact problems, or in their derivatives, such as multi-material problems. Major soil structures include some internal regions that there are some meshing problems during their FEM solutions. In order to solve this problem, some methods have been proposed which XFEM is one of the most new ones. In this method, by choosing appropriate shape functions in regions that include discontinuities, the discontinuity can be included in numerical analysis independently from the domain mesh. In this research, XFEM formulation of two phase media is presented, and it is used in dynamic analysis of this media. Firstly, saturated and unsaturated two phase media governing equations is presented, and then, their FEM solution is shown. Afterwards, XFEM applications in solid mechanics are announced. Finally, with some modification in FEM solution of two phase media, XFEM formulation is extended to this media and its applications in multi-material modeling of two-phase media is presented with different examples. Discontinuity interfaces are modeled by appropriate using of degrees of freedom and shape functions.

  9. Keywords:
  10. Saturated Porous Medium ; Finite Element Method ; Extended Finite Element Method ; Dynamic Analysis ; Unsaturated Porous Media ; Coupled Governing Equations

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