Numerical performance of some finite element schemes for analysis of seepage in porous elastic media

Sandhu, Ranbir S.; Liu, Honho; Singh, Kamar J.

doi:10.1002/nag.1610010205

Cited by 69 publications

(36 citation statements)

References 5 publications

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“…Note that if h is kept constant, then the matrix [C # hK] needs to be factorised only once to obtain the solution for all time steps. Because may assume a range of values, equation (21) can be used to generate a number of single-stage single-step schemes that all march the solution X forward in time without the need for information from previous steps.…”

Section: The Methodsmentioning

confidence: 99%

Biot consolidation analysis with automatic time stepping and error control Part 1: theory and implementation

Sloan

Abbo

1999

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYA new "nite element algorithm for solving elastic and elastoplastic coupled consolidation problems is described. The procedure treats the governing consolidation relations as a system of "rst-order di!erential equations and is based on the backward Euler and Thomas and Gladwell schemes with automatic subincrementation of a prescribed series of time increments. The prescribed time increments, which are called coarse time steps, serve to start the procedure and are chosen by the user. The automatic consolidation algorithm attempts to select the time subincrements such that, for a given mesh, the time-stepping (or temporal discretisation) error in the displacements lies close to a speci"ed tolerance.Unlike existing solution techniques, the new algorithm computes not only the displacements and pore pressures, but also their derivatives with respect to time. These extra variables permit a family of unconditionally stable integration algorithms to be constructed which automatically provide an estimate of the local truncation error for each time step. This error estimate is inexpensive to compute and may be used to develop a simple and e$cient automatic time stepping mechanism. For the elastic case, the displacements and pore pressures at the end of each subincrement may be solved directly without the need for iteration. For elastoplastic behaviour, however, the governing relationships are non-linear and a system of non-linear equations must be solved to compute the updates.

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Section: The Methodsmentioning

confidence: 99%

Biot consolidation analysis with automatic time stepping and error control Part 1: theory and implementation

Sloan

Abbo

1999

Int. J. Numer. Anal. Meth. Geomech.

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“…This condition is often satisfied when the approximation order of the displacement field is chosen one degree higher than the approximation order of the pressure field [33]. In standard finite element analysis, it is relatively straightforward to generate meshes that have interpolations of different orders within an element, for example, using the Taylor-Hood elements.…”

Section: Meshes Of Different Ordermentioning

confidence: 99%

Isogeometric analysis of fluid‐saturated porous media including flow in the cracks

Vignollet

May

Borst

2016

Numerical Meth Engineering

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SUMMARYAn isogeometric model is developed for the analysis of fluid transport in pre-existing faults or cracks that are embedded in a fluid-saturated deformable porous medium. Flow of the interstitial fluid in the porous medium and fluid transport in the discontinuities are accounted for and are coupled. The modelling of a fluid-saturated porous medium in general requires the interpolation of the displacements of the solid to be one order higher than that of the pressure of the interstitial fluid. Using order elevation and Bézier projection, a consistent procedure has been developed to accomplish this in an isogeometric framework. Particular attention has also been given to the spatial integration along the isogeometric interface element in order to suppress traction oscillations that can arise for certain integration rules when a relatively high dummy stiffness is used in a poromechanical model.

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“…The load is applied to the footing as a uniform prescribed pressure and is imposed over the initial period of (¹ J ) "0)01, where ¹ J is the time factor de"ned by equation (7). The subsequent consolidation is modelled up to total time factor of ¹ J "1000.…”

Section: Consolidation Of Yexible Strip Footing With Associated Yow Rulementioning

confidence: 99%

Biot consolidation analysis with automatic time stepping and error control Part 2: applications

Sloan

Abbo²

1999

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYThe automatic time-stepping algorithms developed in a companion paper are used to study the behaviour of several problems involving the consolidation of porous media. The aim of these analyses is to demonstrate that the new procedures are robust, e$cient, and can control the global temporal discretization (or time-stepping) error in the displacements to lie near a prescribed error tolerance.

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Numerical performance of some finite element schemes for analysis of seepage in porous elastic media

Cited by 69 publications

References 5 publications

Biot consolidation analysis with automatic time stepping and error control Part 1: theory and implementation

Biot consolidation analysis with automatic time stepping and error control Part 1: theory and implementation

Isogeometric analysis of fluid‐saturated porous media including flow in the cracks

Biot consolidation analysis with automatic time stepping and error control Part 2: applications

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