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Finite element analysis of non-isothermal multiphase geomaterials with application to strain localization simulation

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Abstract

Finite element analysis of non-isothermal elasto-plastic multiphase geomaterials is presented. The multiphase material is modelled as a deforming porous continuum where heat, water and gas flow are taken into account. The independent variables are the solid displacements, the capillary and the gas pressure and the temperature. The modified effective stress state is limited by the Drucker-Prager yield surface for simplicity. Small strains and quasi-static loading conditions are assumed. Numerical results of strain localization in globally undrained samples of dense, medium dense and loose sands and isochoric geomaterial are presented. A biaxial compression test is simulated assuming plane strain condition during the computations. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A case of strain localization induced by a thermal load where evaporation takes place is also analysed.

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References

  • Lewis RW, Schrefler BA (1998) The finite element method in the static and dynamic deformation and consolidation of porous media, 2nd edn. Wiley, Chichester

  • Gawin D, Baggio P, Schrefler BA (1995) Coupled heat, water and gas flow in deformable porous media. Int J Num Meth Fluids 20(7):967–987

    Google Scholar 

  • Schrefler BA (2002) Mechanics and thermodynamics of saturated-unsaturated porous materials and quantitative solutions. Appl Mech Review 55(4):351–388

    Article  Google Scholar 

  • Mokni M, Desrues J (1998) Strain localisation measurements in undrained plane-strain biaxial tests on hostun RF sand. Mech Cohesive-Frictional Materials 4:419–441

    Google Scholar 

  • Vardoulakis J, Sulem J (1995) Bifurcation analysis in geomechanics. Blakie Academic and Professional, London

  • Schrefler BA, Sanavia L, Majorana CE (1996) A multiphase medium model for localisation and postlocalisation simulation in geomaterials. Mech Cohesive-Frictional Mater 1:95–114

    Google Scholar 

  • Gawin D, Sanavia L, Schrefler BA (1998) Cavitation modelling in saturated geomaterials with application to dynamic strain localisation. Int J Num Meth Fluids 27:109–125

    Article  MATH  Google Scholar 

  • Schrefler BA, Sanavia L, Gawin D (1998) Modelling of strain localisation in fully saturated soils. In: Adachi T, Oka F, Yashima A (eds) Localization and Bifurcation Theory for Soils and Rocks, Balkema, Rotterdam

  • Borja RJ (2004) Cam-clay plasticity. Part V: A mathematical framework for three-phase deformation and strain localisation analyses of partially saturated porous media. Comp Meth Appl Mech Engrg 193:5301–5338

    Article  MATH  Google Scholar 

  • Ehlers W, Graf T, Ammann M (2004) Deformation and localization analysis of partially saturated soil. Comp Meth Appl Mech Engrg 193:2885–2910

    Article  MATH  Google Scholar 

  • Sanavia L, Gawin D, Pesavento F, Rossetto M, Schrefler BA (2003) Numerical analysis of non-isothermal multiphase geomaterials with application to strain localisation simulation of initially water saturated soils. In: Proceedings of the Complas VII, VII International Conference on Computational Plasticity, Barcelona, Spain April 7–10 (on CD)

  • Diebels S, Ehlers W, Ellsiepen P, Volk W (1998) On the regularization of shear band phenomena in liquid-saturated and empty soils. In: Brillard A, Ganghoffer JF (eds) Proceedings of the Euromech Colloquium 378 on Nonlocal Aspects in Solid Mechanics, University of Mulhouse, 58–63

  • Zhang HW, Sanavia L, Schrefler BA (1999) An internal length scale in strain localisation of multiphase porous media. Mech Cohesive-Frictional Mater 4:443–460

    Google Scholar 

  • Zhang HW, Schrefler BA (2000) Gradient dependent plasticity model and dynamic strain localisation analysis of saturated and partially saturated porous media: one-dimensional model. Eur J Mech A/Solids 19:503–524

    Google Scholar 

  • Schrefler BA, Zhang HW, Sanavia L. Interaction between different internal length scales in fully and partially saturated porous media-the 1-d case. Int J Numer Anal Meth geomech, accepted

  • Zhang HW, Schrefler BA (2004) Particular aspects of internal length scales in strain localisation analysis of multiphase porous materials. Comput Meth Appl Mech Eng 193:2867–2884

    Article  MATH  Google Scholar 

  • Goldstein RJ, Eckert ERG, Ibele WE, etal. (2003) Heat transfer – a review of 2001 literature. Int J Heat and Mass Transfer 11:1887–1992

    Article  MATH  Google Scholar 

  • Khalili N, Loret B (2001) An Elasto-Plastic Model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation. Int J Solids and Struct 38:8305–8330

    Article  MATH  Google Scholar 

  • Hassanizadeh M, Gray WG (1979) General conservation equations for multi-phase system: 1. Averaging technique. Adv Water Resources 2:131–144

    Article  Google Scholar 

  • Hassanizadeh M, Gray WG (1979) General conservation equations for multi-phase system: 2. Mass, momenta, energy and entropy equations. Adv Water Resources 2:191–201

    Article  Google Scholar 

  • Hassanizadeh M, Gray WG (1980) General conservation equations for multi-phase system: 3. Constitutive theory for porous media flow. Adv Water Resources 3:25–40

    Article  Google Scholar 

  • Gray WG, Hassanizadeh M (1991) Unsaturated Flow Theory including Interfacial Phenomena. Water Resources Res 27(8):1855–1863

    Article  Google Scholar 

  • Schrefler BA (1984) The finite element method in soil consolidation (with applications to surface subsidence) (Ph.D. Thesis). University College of Swansea, C/Ph/76/84, Swansea (UK)

  • Lewis RW, Schrefler BA (1987) The finite element method in the deformation and consolidation of porous media, 1st edn. Wiley, Chichester

  • Schrefler BA, Simoni L, Li X, Zienkiewicz OC (1990) Mechanics of partially saturated porous media. In: Desai CS, Gioda G (eds) Numerical Methods and Constitutive Modelling in Geomechanics, CISM Courses and Lectures, No 311, Springer-Verlag

  • Hofstetter G, Taylor RL (1991) Treatment of the corner region for Drucker-Prager type plasticity. ZAMM Z angew Math Mech 71:589–591

    Google Scholar 

  • Sanavia L, Schrefler BA, Steinmann P (2002) A formulation for an unsaturated porous medium undergoing large inelastic strains. Comput Mech 28:137–151

    Article  MATH  Google Scholar 

  • Simo JC (1998) Numerical Analysis and Simulation of Plasticity. In: Ciarlet PG, Lions JL (eds) Numerical Methods for Solids. Handbook of Numerical Analysis (Part 3) vol. 6, North-Holland

  • Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Quart Appl Math 10(2):157–165

    MATH  MathSciNet  Google Scholar 

  • Alonso EE, Gens A, Josa A (1990) A constitutive model for partially saturated soils. Géotechnique 40:403–430

    Google Scholar 

  • Bolzon G, Schrefler BA, Zienkiewicz OC (1996) Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique 46:279–289

    Google Scholar 

  • Zhang HW, Sanavia L, Schrefler BA (2000) Numerical analysis of dynamic strain localisation in initially water saturated dense sand with a modified generalised plasticity model. Comput Struct 79:441–459

    Article  Google Scholar 

  • Simo JC, Hughes TJR (1998) Computational inelasticity. Springer

  • Bear J, Bachmat Y (1990) Introduction to modeling of transport phenomena in porous media. Kluwer, Dordrecht

  • Nochetto RH, Paolini M, Verdi C (1991) An adaptive finite element method for two-phase Stefan problems in two space variables. Math Comput 78–108

  • Gawin D, Pesavento F, Schrefler BA (2002) Modelling of hygro-thermal behaviour and damage of concrete at temperature above the critical point of water. Int J Numer Anal Meth Geomech 26:537–562

    Article  MATH  Google Scholar 

  • Gawin D, Baggio P, Schrefler BA (1996) Modelling heat and moisture transfer in deformable porous building materials. Arch of Civil Engng 42:325–349

    Google Scholar 

  • Gawin D, Pesavento F, Schrefler BA (2002) Simulation of damage-permeability coupling in hygro-thermo-mechanical analysis of concrete at high temperature. Commun Numer Meth Eng 18:113–119

    Article  MATH  Google Scholar 

  • Schrefler BA, Gawin D (1996) The effective stress principle: incremental or finite form? Int J Numer Anal Meth Geomech 20:785–815

    Article  Google Scholar 

  • Gray WG, Schrefler BA (2001) Thermodynamic approach to effective stress in partially saturated porous media. Eur J Mech A/Solids 20:521–538

    Google Scholar 

  • Gawin D, Schrefler BA (1996) Thermo-hydro-mechanical analysis of partially saturated porous materials. Eng Comput 13(7):113–143

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Structural and Transportation Engineering, University of Padua, via F. Marzolo 9, 35131, Padova, Italy

    L. Sanavia, F. Pesavento & B. A. Schrefler

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  1. L. Sanavia
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  2. F. Pesavento
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  3. B. A. Schrefler
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Dedicated to Professor S. Valliappan in occasion of his retirement

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Sanavia, L., Pesavento, F. & Schrefler, B.A. Finite element analysis of non-isothermal multiphase geomaterials with application to strain localization simulation. Comput Mech 37, 331–348 (2006). https://doi.org/10.1007/s00466-005-0673-6

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  • DOI: https://doi.org/10.1007/s00466-005-0673-6

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