Analytical Solutions of Linear Finite-Strain One-Dimensional Consolidation

Morris, P. H.

doi:10.1061/(asce)1090-0241(2002)128:4(319)

Cited by 38 publications

(30 citation statements)

References 27 publications

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“…The numerical results are compared to the analytical solutions for one-dimensional consolidation at small deformation presented by Terzaghi [52]. The analytical solutions for one-dimensional consolidation at finite deformation have been obtained in [62][63][64][65]; the following solution by Morris [64] is compared here. The distribution of normalized void ratio E with surface drainage and surface step loading is obtained as…”

Section: Quasi-static Consolidation Of Saturated Poroelastic Materialsmentioning

confidence: 99%

Dynamics of unsaturated poroelastic solids at finite strain

Uzuoka

Borja

2011

Num Anal Meth Geomechanics

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SUMMARYWe derive the governing equations for the dynamic response of unsaturated poroelastic solids at finite strain. We obtain simplified governing equations from the complete coupled formulation by neglecting the material time derivative of the relative velocities and the advection terms of the pore fluids relative to the solid skeleton, leading to a so-called u s − p w − p a formulation. We impose the weak forms of the momentum and mass balance equations at the current configuration and implement the framework numerically using a mixed finite element formulation. We verify the proposed method through comparison with analytical solutions and experiments of quasi-static processes. We use a neo-Hookean hyperelastic constitutive model for the solid matrix and demonstrate, through numerical examples, the impact of large deformation on the dynamic response of unsaturated poroelastic solids under a variety of loading conditions.

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Section: Quasi-static Consolidation Of Saturated Poroelastic Materialsmentioning

confidence: 99%

Dynamics of unsaturated poroelastic solids at finite strain

Uzuoka

Borja

2011

Num Anal Meth Geomechanics

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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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“…where x is the natural vertical co-ordinate and e i ðxÞ the e at zero t: Equation (1) was introduced by Gibson et al [1] to overcome the shortcomings of the smallstrain Terzaghi [4] equation [5,6]. The latter, expressed in material co-ordinates, is [7] @ 2 e @z 2 ¼…”

Section: Introductionmentioning

confidence: 99%

“…where g is the finite-strain coefficient of consolidation. The parameter g is related to the classical Terzaghi [4] small-strain coefficient of consolidation c v by [7,8]…”

Section: Introductionmentioning

confidence: 99%

“…Solution charts for the finite-strain consolidation of saturated, thick, initially unconsolidated and initially normally consolidated soil layers with both one-way and two-way drainage based on a linear form of Equation (1) have been compiled previously by both numerical [8,9] and analytical [7] methods. Analytical solutions expressed in material co-ordinates for the smallstrain self-weight consolidation of initially unconsolidated soil and of initially normally consolidated soil under surcharge loading with both one-way and two-way drainage have also been presented previously [3].…”

Section: Introductionmentioning

confidence: 99%

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Analytical solutions of linear finite- and small-strain one-dimensional consolidation

Morris

2004

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

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SUMMARYAnalytical solutions are presented for linear finite-strain one-dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one-and two-way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small-strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small-strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non-linear finite-strain consolidation. They also clarify a formerly perplexing aspect of finite-strain solution charts first noted in numerical solutions.

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Analytical Solutions of Linear Finite-Strain One-Dimensional Consolidation

Cited by 38 publications

References 27 publications

Dynamics of unsaturated poroelastic solids at finite strain

Dynamics of unsaturated poroelastic solids at finite strain

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

Analytical solutions of linear finite- and small-strain one-dimensional consolidation

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