A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils

Héctor Ariel Di Rado; Pablo Alejandro Beneyto; Javier Luis Mroginski; Juan Emilio Manzolillo

doi:doi:10.11648/j.ajam.20150302.11

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A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils

Héctor Ariel Di Rado, Pablo Alejandro Beneyto, Javier Luis Mroginski, Juan Emilio Manzolillo

Published in American Journal of Applied Mathematics (Volume 3, Issue 2)

Received: 7 January 2015 Accepted: 28 January 2015 Published: 2 February 2015

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Abstract

The main scope of this paper is to present an alternative to tackle the problem of the non symmetries arising in the solution of the nonlinear couple consolidation problem based on a combination of different stress states. Being originally a non symmetric problem, it may be straightforward reduced to a symmetric one, and the conditions in which this reduction may be carried out, are addressed. Non linear saturation-suction and permeability-suction functions were regarded. The geometric model was developed considering an updated lagrangian description with a co-rotated Kirchhoff stress tensor. This description leads to a non-symmetric stiffness matrix and a simple alternative, using a symmetric constitutive matrix, is addressed to overcome this situation. The whole equation system was solved using an open finite element code FECCUND, developed by the authors. In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non linear and no symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and on the shear efforts level, as well. A numerical example show the predictive capability of this geometrically non linear fully coupled model for attaining the proposed goal.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.ajam.20150302.11
Page(s)	31-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Finite Element Analysis, Hypoelastic Formulations, Non Saturated Soil Model, Saturation-Suction Relationship Introduction

References

[1]	Z.Y. Ai, Y.C. Cheng, W.Z. Zeng, C. Wu, 3-D consolidation of multilayered porous medium with anisotropic permeability and compressible pore fluid, Meccanica 48 (2013), 491-499
[2]	M.A. Biot, General theory of three dimensional consolidation, J. Appl. Phys. 12 (1941),155-164
[3]	H.A. Di Rado, J.L. Mroginski, P.A. Beneyto, A.M. Awruch, A symmetric constitutive matrix for the nonlinear analysis of hypoelastic solids based on a formulation leading to a non-symmetric stiffness matrix, Communications in Numerical Methods in Engineering. 24 (2008), 1079–1092
[4]	H. Di Rado, P. Beneyto, J. Mroginski, A. Awruch, Influence of the saturation-suction relationship in the formulation of non-saturated soil consolidation models, Math. Comput. Model. 49 (2009) 1058-1070.
[5]	J. Ghaboussi, K. Kim, Quasistatic and Dynamic Analysis of Saturated and Partially Saturated Soils. Mechanics of Engineering Materials, 14 (1984) 277-296
[6]	S. Hassanizadeh, W. Gray, General conservation equation for multiphase systems: 1 Averaging procedure. Advances in water resources 2 (1979), 131-144
[7]	S. Hassanizadeh, W. Gray, General conservation equation for multiphase systems: 2 Mass, Momenta, Energy and Entropy equations, Advances in water resources, 2 (1979), 191-203
[8]	S. Hassanizadeh, W. Gray, General conservation equation for multiphase systems: 3 Constitutive theory for porous media flow, Advances in water resources, 3 (1980), 25-40
[9]	N. Khalili, M.H. Khabbaz, M.H., On the theory of three-dimensional consolidation in unsaturated soils, First International Conference on Unsaturated Soils - UNSAT'95, 1995, 745-750.
[10]	G. Klubertanz, F. Bouchelaghem, L. Laloui, L. Vulliet, Miscible and Immiscible Multiphase Flow in Deformable Porous Media, Mathematical and Computer Modeling. 37 pp. 571-582 (2003).
[11]	R.W. Lewis, B.A. Schrefler, The Finite Element Method in the Deformation and Consolidation of Porous Media, J. Wiley & Sons, New York. (1987).
[12]	R.W. Lewis, B.A. Schrefler, N.A. Rahman, A Finite Element Analysis of Multiphase Immiscible Flow in Deforming Porous Media for Subsurface Systems, Communications in Numerical Methods in Engineering, 14 (1998), 135-149.
[13]	L.E. Malvern, Introduction to the Mechanics of a Continuum Medium. Prentice Hall, USA.(1969).
[14]	I. Masters, W.K.S. Pao, and R. Lewis, Coupling temperature to a double porosity model of deformable porous media, Int. J. Numer. Anal. Meth. Geomech. 49 (2000), 421-438
[15]	R.J. Moitsheki, P. Broadbridge, M.P. Edwards, Symmetry solutions for transient solute transport in unsaturated soils with realistic water profile. Transport in Porous Media 61 (2005), 109-125
[16]	J.L. Mroginski, H.A. Di Rado, P.A. Beneyto, A.M. Awruch “A finite element approach for multiphase fluid flow in porous media, Mathematics and Computers in Simulation. 81 (2010), 76-91
[17]	J.L. Mroginski and G. Etse, A finite element formulation of gradient-based plasticity for porous media with C1 interpolation of state variables, Computers and Geotechnics, 49 (2013), 7-17
[18]	A.K.L. Ng, J.C. Small, Use of coupled finite element analysis in unsaturated soil problems, Int. J. Numer. Anal. Meth. Geomech. 24 (2000), 73-94
[19]	S. Pietraszezak, G.N. Pandle, On the mechanics of partially saturated soils, Computers and Geotechnics 12 (1991), 55-71 (1991)
[20]	P. Royer, C. Boutin, Time Analysis of the Three Characteristic Behaviours of Dual-Porosity Media. I: Fluid Flow and Solute Transport, Transport in porous media, 95 (2012), 603-626
[21]	B.A. Schrefler, Computer modeling in environmental geomechanics, Computers and structures, 79 (2001), 2209-2223
[22]	J.C. Simo, T.J.R. Hughes, Computational Inelasticity. Springer – Verlag. New York, Inc. (1998)
[23]	F. Su, F. Larsson, K. Runesson, Computational homogenization of coupled consolidation problems in micro heterogeneous porous media, Int. J. Num. M. Eng. 88 (2011), 1198–1218
[24]	P. Tritscher, W.W. Read, P. Broadbridge, J.H. Knight, Steady saturated-unsaturated flow in irregular porous domains. Mathematical and Computer Modelling 34 (2001), 177-194
[25]	H. A. Di Rado, “Numerical Simulation of physical and geometric nonlinearities. None saturated soil consolidation analysis” (Spanish). Doctoral Thesis, Northeast National University. Argentine, Ch. 5 (2006),121-133

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APA Style

Héctor Ariel Di Rado, Pablo Alejandro Beneyto, Javier Luis Mroginski, Juan Emilio Manzolillo. (2015). A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils. American Journal of Applied Mathematics, 3(2), 31-35. https://doi.org/10.11648/j.ajam.20150302.11

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ACS Style

Héctor Ariel Di Rado; Pablo Alejandro Beneyto; Javier Luis Mroginski; Juan Emilio Manzolillo. A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils. Am. J. Appl. Math. 2015, 3(2), 31-35. doi: 10.11648/j.ajam.20150302.11

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AMA Style

Héctor Ariel Di Rado, Pablo Alejandro Beneyto, Javier Luis Mroginski, Juan Emilio Manzolillo. A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils. Am J Appl Math. 2015;3(2):31-35. doi: 10.11648/j.ajam.20150302.11

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@article{10.11648/j.ajam.20150302.11,
  author = {Héctor Ariel Di Rado and Pablo Alejandro Beneyto and Javier Luis Mroginski and Juan Emilio Manzolillo},
  title = {A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {31-35},
  doi = {10.11648/j.ajam.20150302.11},
  url = {https://doi.org/10.11648/j.ajam.20150302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150302.11},
  abstract = {The main scope of this paper is to present an alternative to tackle the problem of the non symmetries arising in the solution of the nonlinear couple consolidation problem based on a combination of different stress states. Being originally a non symmetric problem, it may be straightforward reduced to a symmetric one, and the conditions in which this reduction may be carried out, are addressed. Non linear saturation-suction and permeability-suction functions were regarded. The geometric model was developed considering an updated lagrangian description with a co-rotated Kirchhoff stress tensor. This description leads to a non-symmetric stiffness matrix and a simple alternative, using a symmetric constitutive matrix, is addressed to overcome this situation. The whole equation system was solved using an open finite element code FECCUND, developed by the authors. In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non linear and no symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and on the shear efforts level, as well. A numerical example show the predictive capability of this geometrically non linear fully coupled model for attaining the proposed goal.},
 year = {2015}
}

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TY  - JOUR
T1  - A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils
AU  - Héctor Ariel Di Rado
AU  - Pablo Alejandro Beneyto
AU  - Javier Luis Mroginski
AU  - Juan Emilio Manzolillo
Y1  - 2015/02/02
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150302.11
DO  - 10.11648/j.ajam.20150302.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 31
EP  - 35
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150302.11
AB  - The main scope of this paper is to present an alternative to tackle the problem of the non symmetries arising in the solution of the nonlinear couple consolidation problem based on a combination of different stress states. Being originally a non symmetric problem, it may be straightforward reduced to a symmetric one, and the conditions in which this reduction may be carried out, are addressed. Non linear saturation-suction and permeability-suction functions were regarded. The geometric model was developed considering an updated lagrangian description with a co-rotated Kirchhoff stress tensor. This description leads to a non-symmetric stiffness matrix and a simple alternative, using a symmetric constitutive matrix, is addressed to overcome this situation. The whole equation system was solved using an open finite element code FECCUND, developed by the authors. In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non linear and no symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and on the shear efforts level, as well. A numerical example show the predictive capability of this geometrically non linear fully coupled model for attaining the proposed goal.
VL  - 3
IS  - 2
ER  -

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Author Information

Héctor Ariel Di Rado

Applied Mechanical Dept., Northeast National University (UNNE), Las Heras, Resistencia, Chaco, Argentina
Pablo Alejandro Beneyto

Applied Mechanical Dept., Northeast National University (UNNE), Las Heras, Resistencia, Chaco, Argentina
Javier Luis Mroginski

Applied Mechanical Dept., Northeast National University (UNNE), Las Heras, Resistencia, Chaco, Argentina
Juan Emilio Manzolillo

Applied Mechanical Dept., Northeast National University (UNNE), Las Heras, Resistencia, Chaco, Argentina

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APA Style

Héctor Ariel Di Rado, Pablo Alejandro Beneyto, Javier Luis Mroginski, Juan Emilio Manzolillo. (2015). A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils. American Journal of Applied Mathematics, 3(2), 31-35. https://doi.org/10.11648/j.ajam.20150302.11

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ACS Style

Héctor Ariel Di Rado; Pablo Alejandro Beneyto; Javier Luis Mroginski; Juan Emilio Manzolillo. A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils. Am. J. Appl. Math. 2015, 3(2), 31-35. doi: 10.11648/j.ajam.20150302.11

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AMA Style

Héctor Ariel Di Rado, Pablo Alejandro Beneyto, Javier Luis Mroginski, Juan Emilio Manzolillo. A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils. Am J Appl Math. 2015;3(2):31-35. doi: 10.11648/j.ajam.20150302.11

Copy | Download

@article{10.11648/j.ajam.20150302.11,
  author = {Héctor Ariel Di Rado and Pablo Alejandro Beneyto and Javier Luis Mroginski and Juan Emilio Manzolillo},
  title = {A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {31-35},
  doi = {10.11648/j.ajam.20150302.11},
  url = {https://doi.org/10.11648/j.ajam.20150302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150302.11},
  abstract = {The main scope of this paper is to present an alternative to tackle the problem of the non symmetries arising in the solution of the nonlinear couple consolidation problem based on a combination of different stress states. Being originally a non symmetric problem, it may be straightforward reduced to a symmetric one, and the conditions in which this reduction may be carried out, are addressed. Non linear saturation-suction and permeability-suction functions were regarded. The geometric model was developed considering an updated lagrangian description with a co-rotated Kirchhoff stress tensor. This description leads to a non-symmetric stiffness matrix and a simple alternative, using a symmetric constitutive matrix, is addressed to overcome this situation. The whole equation system was solved using an open finite element code FECCUND, developed by the authors. In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non linear and no symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and on the shear efforts level, as well. A numerical example show the predictive capability of this geometrically non linear fully coupled model for attaining the proposed goal.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils
AU  - Héctor Ariel Di Rado
AU  - Pablo Alejandro Beneyto
AU  - Javier Luis Mroginski
AU  - Juan Emilio Manzolillo
Y1  - 2015/02/02
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150302.11
DO  - 10.11648/j.ajam.20150302.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 31
EP  - 35
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150302.11
AB  - The main scope of this paper is to present an alternative to tackle the problem of the non symmetries arising in the solution of the nonlinear couple consolidation problem based on a combination of different stress states. Being originally a non symmetric problem, it may be straightforward reduced to a symmetric one, and the conditions in which this reduction may be carried out, are addressed. Non linear saturation-suction and permeability-suction functions were regarded. The geometric model was developed considering an updated lagrangian description with a co-rotated Kirchhoff stress tensor. This description leads to a non-symmetric stiffness matrix and a simple alternative, using a symmetric constitutive matrix, is addressed to overcome this situation. The whole equation system was solved using an open finite element code FECCUND, developed by the authors. In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non linear and no symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and on the shear efforts level, as well. A numerical example show the predictive capability of this geometrically non linear fully coupled model for attaining the proposed goal.
VL  - 3
IS  - 2
ER  -

Copy | Download