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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 49352 (09)
- University: Sharif University of Technology
- Department: Civil Engineering
- Advisor(s): Ataie Ashtiani, Behzad
- Abstract:
- In this study a locally mass conservative finite volume method (FVM) is employed to simulate the coupled model of flow and geomechanics for the land subsidence problem. At the first step, a FV numerical method is implemented to solve a Biot consolidation model with discontinuous coefficients one dimensionally. The studies show that the FV scheme leads to a locally mass conservative approach which removes pressure oscillations especially along the interface between materials with different properties and yields higher accuracy for the flow and mechanics parameters. Then this numerical discretization is utilized to investigate different sequential strategies with various degrees of coupling including: iteratively, explicitly and loosely coupled methods. A comprehensive study is performed on the stability, accuracy and rate of convergence of all of these sequential methods. In the iterative and explicit solutions four splits of drained, undrained, fixed-stress and fixed-strain are studied. In loosely coupled methods three techniques of the local error method, the pore pressure method, and constant step size are considered and results are compared with other types of coupling methods. It is shown that the fixed-stress method is the best operator split in comparison with other sequential methods because of its unconditional stability, accuracy and the rate of convergence. At the second step, FVM is employed to model the one- dimensional, two-phase immiscible flow in a poroelastic media. Since, an appropriate choice of primary variables is critical in simulating multiphase subsurface flow, depending on such a choice, the governing equations can be expressed in different forms. By implementing Picard iteration to a highly nonlinear system of equations, three numerical models including pressure form, mixed form and mixed form with a modified Picard linearization are developed in this study. These models have been evaluated in terms of stability, convergence and mass conservation in various one-dimensional test cases. Selecting water saturation in the mixed form as a primary variable could produce convergence problems in transition from saturated to unsaturated regimes, but in other conditions show good convergence and also mass balance properties. The pressure form and the mixed form with a modified Picard linearization converge in all test cases even near the fully saturated conditions. The pressure form suffers from poor mass balance and the mixed form with a modified Picard linearization poses superior mass balance property than the pressure form. At the third stage, the second order accurate cell-centered FVM is coupled with the finite element geomechanical simulator to solve the coupled model two dimensionally. The proposed discretization technique is applied to the fully unstructured triangular grids to simulate actual geological formations. A number of numerical techniques are applied to ensure stability and local mass conservation in complex geometries. The proposed discretization model ensures stability, yields local mass conservation and accommodates complex geometries based on unstructured grids. Finally the real case of subsidence in plain of Tehran is simulated. For this purpose, a new conceptualization is proposed by incorporating one-dimensional two-phase hydro-mechanical solver into a two-dimensional fully saturated subsidence model presented in this study. The present solution is capable of considering the subsidence induced from saturated-unsaturated flow in an aquifer and also the deformation of the saturated zones. The rate and cumulative subsidence of each zone are calculated according to the different values of mechanical properties
- Keywords:
- Finite Volume Method ; Land Subsidence ; Fully Coupled Analysis ; Numerical Modeling ; Iteratively Coupled Method
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