Finite difference approach for consolidation with variable compressibility and permeability

Abbasi, Nader; Rahimi, Hassan; Javadi, Akbar A.; Fakher, Ali

doi:10.1016/j.compgeo.2006.09.003

Cited by 67 publications

(35 citation statements)

References 16 publications

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“…In addition to the standard finite element method (FEM) [4,5] and the finite difference method (FDM) [6], newly developed numerical methods have been continuously used for the FCHM model of porous media, such as the mesh-free method [7], element-free Galerkin method [8], finite volume method [9] and numerical manifold method [10]. Additionally, new FEMs have been developed to overcome the pressure oscillations in lowpermeable and low-compressible porous media, such as the generalized conforming element [11], enhanced strain element [12], mixed finite element [13][14][15] and stabilized element [16].…”

Section: Previous Workmentioning

confidence: 99%

An unconditionally stable explicit and precise multiple timescale finite element modeling scheme for the fully coupled hydro-mechanical analysis of saturated poroelastic media

Tang

et al. 2016

Computers and Geotechnics

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Section: Previous Workmentioning

confidence: 99%

An unconditionally stable explicit and precise multiple timescale finite element modeling scheme for the fully coupled hydro-mechanical analysis of saturated poroelastic media

Tang

et al. 2016

Computers and Geotechnics

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“…Although a number of different numerical and analytical solutions for the non-linear consolidation equation where a variable c v is considered have been proposed (Gibson et al, 1967;Mesri & Choi, 1985;Morris, 2002;Lekha et al, 2003;Zhuang et al, 2005;Abbasi et al, 2007), these solutions are not popular in geotechnical engineering practice for the following reasons.…”

Section: Introductionmentioning

confidence: 99%

Modified Terzaghi consolidation curves with effective stress-dependent coefficient of consolidation

Abuel-Naga

Pender

2012

Géotechnique Letters

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One of the assumptions of the standard consolidation theory used in soil mechanics is that the coefficient of consolidation is a material property that remains constant during the consolidation process. This note demonstrates numerically the effect on the consolidation rate of a coefficient of consolidation that changes with increasing effective stress. The letter proposes a set of dimensionless consolidation curves when the coefficient of consolidation is changing linearly over the incremental effective stress generating the consolidation.

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“…In this way, the explicitness of the scheme is preserved while improving the stability of the scheme. Because of this merit, the ADE scheme has been popular for solving various engineering problems such as heat transfer and fluid diffusion problems, [3][4][5] advection-and convection-diffusion problems, [6][7][8][9] flow calculations in petroleum and natural gas reservoirs, 10,11 and even option pricing in engineering finance. 12 It should be noted that the implicit version of the ADE called the alternating direction implicit also exists and has been used to solve flow equation in reservoir engineering.…”

Section: Introductionmentioning

confidence: 99%

High‐order ADE scheme for solving the fluid diffusion equation in non‐uniform grids and its application in coupled hydro‐mechanical simulation

Prassetyo

Gutierrez

2018

Num Anal Meth Geomechanics

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Summary To improve the stability and efficiency of explicit technique, one proposed method is to use an unconditionally stable alternating direction explicit (ADE) scheme. However, the standard ADE scheme is only moderately accurate and restricted to uniform grids. This paper derives a novel high‐order ADE scheme capable of solving the fluid diffusion equation in non‐uniform grids. The new scheme is derived by performing a fourth‐order finite difference approximation to the spatial derivatives of the diffusion equation in non‐uniform grid. The implicit Crank‐Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new high‐order ADE scheme. Because the new scheme can be potentially applied in coupled hydro‐mechanical (H‐M) simulation, the pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer program Fast Lagrangian Analysis of Continua. This coupling procedure is called the sequentially explicit coupling technique based on the fourth‐order ADE scheme (SEA‐4). Verifications of well‐known consolidation problems showed that the new ADE scheme and SEA‐4 can reduce computer runtime by 46% to 75% to that of Fast Lagrangian Analysis of Continua's basic scheme. At the same time, the techniques still maintained average percentage error of 1.6% to 3.5% for pore pressure and 0.2% to 1.5% for displacement solutions and were still accurate under typical grid non‐uniformities. This result suggests that the new high‐order ADE scheme can provide an efficient explicit technique for solving the flow equation of a coupled H‐M problem, which will be beneficial for large‐scale and long‐term H‐M problems in geoengineering.

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Finite difference approach for consolidation with variable compressibility and permeability

Cited by 67 publications

References 16 publications

An unconditionally stable explicit and precise multiple timescale finite element modeling scheme for the fully coupled hydro-mechanical analysis of saturated poroelastic media

An unconditionally stable explicit and precise multiple timescale finite element modeling scheme for the fully coupled hydro-mechanical analysis of saturated poroelastic media

Modified Terzaghi consolidation curves with effective stress-dependent coefficient of consolidation

High‐order ADE scheme for solving the fluid diffusion equation in non‐uniform grids and its application in coupled hydro‐mechanical simulation

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