Stabilized mixed finite element formulations for materially nonlinear partially saturated two-phase media

Truty, Andrzej; Zimmermann, Thomas

doi:10.1016/j.cma.2005.05.044

Cited by 64 publications

(55 citation statements)

References 24 publications

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“…In the discrete setting, the presence of this constraint introduces an inf-sup stability restriction on the choice of finite element spaces that can be used without spurious pressure oscillations-in exactly the same manner as for mixed finite element implementations of Stokes flow or incompressible elasticity [28][29][30][31]. As a result, the mixed finite element implementation must either adopt a Ladyzhenskaya-Babuska-Brezzi (LBB)-stable finite element pair or employ a stabilized formulation that allows for a broader range of stable combinations [6,[32][33][34]. In this work, we adopt the stabilized formulation proposed in [32], which allows for equal-order linear interpolation of the displacement and pressure fields while maintaining optimal convergence.…”

Section: Simplified Modelsmentioning

confidence: 98%

Block-preconditioned Newton–Krylov solvers for fully coupled flow and geomechanics

2011

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The focus of this work is efficient solution methods for mixed finite element models of variably saturated fluid flow through deformable porous media. In particular, we examine preconditioning techniques to accelerate the convergence of implicit NewtonKrylov solvers. We highlight an approach in which preconditioners are built from block-factorizations of the coupled system. The key result of the work is the identification of effective preconditioners for the various sub-problems that appear within the block decomposition. We use numerical examples drawn from both linear and nonlinear hydromechanical models to test the robustness and scalability of the proposed methods. Results demonstrate that an algebraic multigrid variant of the block preconditioner leads to mesh-independent convergence, good parallel efficiency, and insensitivity to the material parameters of the medium.

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Section: Simplified Modelsmentioning

confidence: 98%

Block-preconditioned Newton–Krylov solvers for fully coupled flow and geomechanics

2011

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“…Reference [34] analyses a similar problem, in which the medium has an elasto-plastic behaviour, but it does not give information about the state of the variables at time steps preceding 4 days; differently, we have collected the results at various time instances: 10 h, 1 day and 4 days, obtaining pore overpressures and displacement amplitudes according to Figures 15 and 16, respectively.…”

Section: Assessment Of the Stabilizing Propertymentioning

confidence: 99%

A CBS-type stabilizing algorithm for the consolidation of saturated porous media

Salomoni

Schrefler

2005

Int. J. Numer. Meth. Engng

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The presented method stems from the works by Zienkiewicz and co-workers for coupled fluid/thermal problems starting from the early 1990s. They propose algorithms to overcome the difficulties connected to the application of the FEM to the area of fluid mechanics, which include the problems of singular behaviour in incompressibility and the problems connected to convective terms. The major step forward was to introduce the concept of characteristic lines (the particle paths in a simple convection situation): for a class of problems with a single scalar variable, the equations in the characteristic co-ordinates regain self-adjointness. The procedure is called characteristic based split algorithm (CBS). We use here a CBS-type procedure for a saturated deformable elastic porous medium, in which the fluid velocity is governed by Darcy's equation (which comes directly from Navier-Stokes ones). The physical-mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains. The power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual 'u-p' problem into a 4u-v-p one, where it generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid, respectively. Attention is focused on the expression of Darcy's velocity which is considered as the starting point of the algorithm. The accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u-p Solutions. A good fitting arnong different results has been obtained. It is further shown that the procedure eliminates the oscillations at the onset of consolidation, typical for many schemes. The FEM code Ed-Multifield has been used for implementing and testing the procedure

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“…Further details concerning this issue and a comprehensive explanation of advanced stabilization techniques that are needed to handle quasi-undrained cases can be found in Truty [15], Truty and Zimmermann [16].…”

Section: Two-phase Formulation For Partially Saturated Mediamentioning

confidence: 99%

Selected aspects of designing deep excavations

Obrzud¹,

Hartmann

Podleś

2016

Studia Geotechnica Et Mechanica

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This paper analyzes two approaches to serviceability limit state (SLS) verification for the deep excavation boundary value problem. The verification is carried out by means of the finite element (FE) method with the aid of the commercial program ZSoil v2014. In numerical simulations, deep excavation in non-cohesive soil is supported with a diaphragm wall. In the first approach, the diaphragm wall is modeled with the Hookean material assuming reduced average stiffness and possible concrete cracking. The second approach is divided into two stages. In the first stage, the wall is modeled by defining its stiffness with the highest nominal Young's modulus. The modulus makes it possible to find design bending moments which are used to compute the minimal design cross-section reinforcement for the retaining structure. The computed reinforcement is then used in a non-linear structural analysis which is viewed as the "actual" SLS verification.In the second part, the paper examines the same boundary value problem assuming that the excavation takes place in quasiimpermeable cohesive soils, which are modeled with the Hardening Soil model. This example demonstrates the consequences of applying the steady-state type analysis for an intrinsically time-dependent problem. The results of this analysis are compared to the results from the consolidation-type analysis, which are considered as a reference. For both analysis types, the two-phase formulation for partially-saturated medium, after Aubry and Ozanam, is used to describe the interaction between the soil skeleton and pore water pressure.

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Stabilized mixed finite element formulations for materially nonlinear partially saturated two-phase media

Cited by 64 publications

References 24 publications

Block-preconditioned Newton–Krylov solvers for fully coupled flow and geomechanics

Block-preconditioned Newton–Krylov solvers for fully coupled flow and geomechanics

A CBS-type stabilizing algorithm for the consolidation of saturated porous media

Selected aspects of designing deep excavations

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