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Stabilized finite element methods fo...

Stanford University.

Stabilized finite element methods for coupled flow and geomechanics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stabilized finite element methods for coupled flow and geomechanics.
Author:	White, Joshua A.
Description:	96 p.
Notes:	Source: Dissertation Abstracts International, Volume: 70-10, Section: B, page: .
Notes:	Adviser: Ronaldo I. Borja.
Contained By:	Dissertation Abstracts International70-10B.
Subject:	Geotechnology.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3382958
ISBN:	9781109450446

Stabilized finite element methods for coupled flow and geomechanics.
White, Joshua A.

Stabilized finite element methods for coupled flow and geomechanics. - 96 p.

Source: Dissertation Abstracts International, Volume: 70-10, Section: B, page: .

Thesis (Ph.D.)--Stanford University, 2009.

In this work, we present a finite element formulation for variably-saturated porous geomaterials undergoing elastoplastic deformations. The deforming body is treated as a multiphase continuum, and the governing mass and momentum balance equations are solved in a fully- coupled manner. It is well-known, however, that mixed formulations of the type examined here may lead to unstable approximations unless the spaces chosen for the pressure and displacement interpolation satisfy stringent stability restrictions. Failure to choose a stable pair typically leads to spurious pressure oscillations and poor convergence behavior. Unfortunately, many seemingly natural combinations---including equal-order interpolation for all field variables---do not satisfy the necessary requirements. In this work, we propose a stabilized formulation, based on a minor modification of the variational equations, which allows one to circumvent these restrictions and employ equal-order mixed elements. Several numerical examples are used to demonstrate the computationally appealing features of this alternative formulation.

ISBN: 9781109450446Subjects--Topical Terms:

227307
Geotechnology.

Stabilized finite element methods for coupled flow and geomechanics.
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100 1 $a White, Joshua A. $3 384354
245 1 0 $a Stabilized finite element methods for coupled flow and geomechanics.
300 $a 96 p.
500 $a Source: Dissertation Abstracts International, Volume: 70-10, Section: B, page: .
500 $a Adviser: Ronaldo I. Borja.
502 $a Thesis (Ph.D.)--Stanford University, 2009.
520 $a In this work, we present a finite element formulation for variably-saturated porous geomaterials undergoing elastoplastic deformations. The deforming body is treated as a multiphase continuum, and the governing mass and momentum balance equations are solved in a fully- coupled manner. It is well-known, however, that mixed formulations of the type examined here may lead to unstable approximations unless the spaces chosen for the pressure and displacement interpolation satisfy stringent stability restrictions. Failure to choose a stable pair typically leads to spurious pressure oscillations and poor convergence behavior. Unfortunately, many seemingly natural combinations---including equal-order interpolation for all field variables---do not satisfy the necessary requirements. In this work, we propose a stabilized formulation, based on a minor modification of the variational equations, which allows one to circumvent these restrictions and employ equal-order mixed elements. Several numerical examples are used to demonstrate the computationally appealing features of this alternative formulation.
520 $a The resulting implicit, nonlinear algebraic systems are then solved using an inexact Newton algorithm. We discuss methods for solving the linearized systems using memory-efficient iterative solvers, both on serial and parallel computing platforms. In order to deal with inherent ill-conditioning, we propose a block-structured, multilevel preconditioner that both accelerates the convergence of the Krylov solver and exhibits excellent scaling properties as the number of unknowns and number of processors increase.
520 $a To demonstrate the effectiveness of these approaches, the analysis framework is applied to modeling hydrologically-driven slope failure. This analysis is motivated by a recent landslide that occurred at a steep experimental catchment (CB1) near Coos Bay, Oregon. Simulations are used to quantify the rainfall-induced slope deformation and assess the failure potential. Results of parametric studies suggest that for a steep hillside slope underlain by shallow bedrock similar to the CB1 site, failure would occur by a multiple slide block mechanism, with progressive failure surfaces forming at the bedrock interface and then propagating to the slope surface. A key observation is that significant computational resources are required to capture these complex solid/fluid interaction mechanisms at sufficient resolution, further justifying the use of the proposed approaches over conventional methods.
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650 4 $a Engineering, Civil. $3 212394
650 4 $a Engineering, Petroleum. $3 227008
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773 0 $t Dissertation Abstracts International $g 70-10B.
790 1 0 $a Borja, Ronaldo I., $e advisor
790 $a 0212
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3382958