Strong discontinuities in partially saturated poroplastic solids.

*(English)*Zbl 1231.74105Summary: This paper considers the analysis and numerical simulation of strong discontinuities in partially saturated solids. The goal is to study observed localized failures in such media like shear bands and similar. The developments consider a fully coupled partially saturated elastoplastic model for the (continuum) bulk response of the solid formulated in effective stresses, identifying the necessary mathematical conditions for the appearance of strong discontinuities (that is, discontinuities in the displacement field leading to singular strains) as well as the proper treatment for the fields characterizing the flow of the different fluid phases, namely, the fluid contents of these phases and their individual pore pressures. The geometrically linear range of infinitesimal strains is considered. These developments allow the formulation of multiphase cohesive laws along the strong discontinuity, capturing in this way the coupled localized dissipation observed in the aforementioned failures. Furthermore, the paper also presents the formulation of enhanced finite elements capturing all these discontinuous solutions in general unstructured meshes. In particular, the finite elements capture the strong discontinuity through the proper enhancements of the discrete element strains, allowing for a complete local resolution of these effects. This results in a particularly efficient computational approach, easily accommodated in an existing finite element code. Different representative numerical simulations are presented illustrating the performance of the proposed formulation, as well as its use in practical applications like the modeling of the excavation of tunnels in variably saturated media.

##### MSC:

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

74S05 | Finite element methods applied to problems in solid mechanics |

##### Keywords:

multiphase porous media; strain localization; strong discontinuities; enhanced finite element methods; partially saturated media##### Software:

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\textit{C. Callari} et al., Comput. Methods Appl. Mech. Eng. 199, No. 23--24, 1513--1535 (2010; Zbl 1231.74105)

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##### References:

[1] | A. Abati, C. Callari, Finite element formulation of unilateral boundary conditions for unsaturated flow in porous continua, in preparation (Report UniMol/ICAR-08 11/2009). |

[2] | Alonso, E.E.; Gens, A.; Josa, A., A constitutive model for partially saturated soils, Géotechnique, 40, 3, 403-430, (1990) |

[3] | Andrade, J.E.; Borja, R.I., Modeling deformation banding in dense and loose fluid-saturated sands, Finite elem. anal. des., 361-383, (2007) |

[4] | Armero, F., Large-scale modeling of localized dissipative mechanisms in a local continuum: applications to the numerical simulation of strain localization in rate-dependent inelastic solids, Mech. cohes. frict. mater., 4, 101-131, (1999) |

[5] | Armero, F., On the characterization of localized solutions in inelastic solids: an analysis of wave propagation in a softening bar, Comput. methods appl. mech. engrg., 191, 181-213, (2001) · Zbl 1037.74027 |

[6] | Armero, F.; Callari, C., An analysis of strong discontinuities in a saturated poro-plastic solid, Int. J. numer. methods engrg., 46, 10, 1673-1698, (1999) · Zbl 0971.74029 |

[7] | Armero, F.; Garikipati, K., Recent advances in the analysis and numerical simulation of strain localization in inelastic solids, () · Zbl 0924.73084 |

[8] | Armero, F.; Garikipati, K., Analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids, Int. J. solids struct., 33, 2863-2885, (1996) · Zbl 0924.73084 |

[9] | Armero, F.; Linder, C., New finite elements with embedded strong discontinuities in the finite deformation range, Comput. methods appl. mech. engrg., 197, 3138-3170, (2008) · Zbl 1194.74357 |

[10] | Belytschko, T.; Black, T., Elastic crack growth in finite elements with minimal remeshing, Int. J. numer. methods engrg., 45, 601-620, (1999) · Zbl 0943.74061 |

[11] | Biot, M.A., General theory of three-dimensional consolidation, J. appl. phys., 12, 155-164, (1941) · JFM 67.0837.01 |

[12] | Bolzon, G.; Schrefler, B.A.; Zienkiewicz, O.C., Elastoplastic soil constitutive laws generalized to partially saturated states, Géotechnique, 46, 2, 279-289, (1996) |

[13] | Borja, R., Cam-Clay plasticity. part V: A mathematical framework for three-phase deformation and strain localization analyses of partially saturated porous media, Comput. methods appl. mech. engrg., 193, 5301-5338, (2004) · Zbl 1112.74430 |

[14] | Borja, R., On the mechanical energy and effective stress in saturated and unsaturated porous continua, Int. J. sol. struct., 43, 1764-1786, (2006) · Zbl 1120.74446 |

[15] | C. Callari, The application of a strong-discontinuity FEM to the analysis of strain localization induced by underground openings, in: G.N. Pande, S. Pietruszczak, (Eds.), Eighth Int. Symp. Numerical Models in Geomechanics (NUMOG VIII), Balkema, Rotterdam, 2002, pp. 163-170. |

[16] | Callari, C., Coupled numerical analysis of strain localization induced by shallow tunnels in saturated soils, Comput. geotechn., 31, 193-207, (2004) |

[17] | C. Callari, A. Abati, Hyperelastic multiphase porous media with strain-dependent retention laws, submitted for publication. |

[18] | Callari, C.; Abati, A., Finite element methods for unsaturated porous solids and their application to dam engineering problems, Comput. struct., 87, 485-501, (2009) |

[19] | Callari, C.; Armero, F., Finite element methods for the analysis of strong discontinuities in coupled poro-plastic media, Comput. methods appl. mech. engrg., 191, 4371-4400, (2002) · Zbl 1124.74324 |

[20] | Callari, C.; Armero, F., Analysis and numerical simulation of strong discontinuities in finite strain poroplasticity, Comput. methods appl. mech. engrg., 193, 2941-2986, (2004) · Zbl 1067.74519 |

[21] | Callari, C.; Casini, S., Tunnels in saturated elasto-plastic soils: three-dimensional validation of a plane simulation procedure, (), 143-164 · Zbl 1181.74084 |

[22] | Callari, C.; Lupoi, A., Localization analysis in dilatant elasto-plastic solids by a strong-discontinuity method, (), 121-132 · Zbl 1130.74350 |

[23] | Coussy, O., Mechanics of porous continua, (1995), Wiley Chichester |

[24] | Ehlers, W.; Graf, T.; Ammann, M., Deformation and localization analysis of partially saturated soil, Comput. methods appl. mech. engrg., 193, 2885-2910, (2004) · Zbl 1067.74543 |

[25] | Gray, W.G.; Schrefler, B.A., Analysis of the solid phase stress tensor in multiphase porous media, Int. J. numer. anal. methods geomech., 31, 541-581, (2007) · Zbl 1196.74040 |

[26] | Hansbo, A.; Hansbo, P., A finite element method for the simulation of strong and weak discontinuities in solid mechanics, Comput. methods appl. mech. engrg., 193, 3523-3540, (2004) · Zbl 1068.74076 |

[27] | Hansmire, W.H.; Cording, E.J., Soil tunnel test section: case history summary, J. geotech. engrg. div. ASCE, 111, 1301-1320, (1985) |

[28] | Houlsby, G.T., The work input to an unsaturated granular material, Géotechnique, 47, 193-196, (1997) |

[29] | Hughes, T.J.R., The finite element method, (1987), Prentice Hall |

[30] | C. Jommi, Remarks on the constitutive modelling of unsaturated soils, in: Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Balkema, Rotterdam, 2000. |

[31] | Kimoto, S.; Oka, F.; Higo, Y., Strain localization analysis of elasto-viscoplastic soil considering structural degradation, Comput. methods appl. mech. engrg., 193, 2845-2866, (2004) · Zbl 1067.74566 |

[32] | Larsson, R.; Steinmann, P.; Runesson, K., Finite element embedded localization band for finite strain plasticity based on a regularized strong discontinuity, Mech. cohes. frict. mater., 4, 171-194, (1998) |

[33] | Lewis, R.W.; Schrefler, B.A., A finite element simulation of the subsidence of gas reservoirs undergoing a water drive, Finite elem. fluids, 4, 179-199, (1982) |

[34] | Linder, C.; Armero, F., Finite elements with embedded strong discontinuities for the modeling of failure in solids, Int. J. numer. methods engrg., 72, 191-1433, (2007) · Zbl 1194.74431 |

[35] | Londe, P., The malpasset dam failure, Eng. geol., 24, 295-329, (1987) |

[36] | Loret, B.; Prevost, J.H., Dynamic strain localization in fluid-saturated porous media, J. eng. mech., 117, 907-922, (1993) |

[37] | Maier, G.; Hueckel, T., Nonassociated and coupled flow rules of elastoplasticity for rock-like materials, Int. J. rock mech. MIN. sci. geomech. abstr., 16, 77-92, (1979) |

[38] | Meguid, M.A.; Saada, O.; Nunes, M.A.; Mattar, J., Physical modeling of tunnels in soft ground: A review, Tunn. undergr. sp. tech., 23, 185-198, (2008) |

[39] | Moës, N.; Dolbow, J.; Belytschko, T., A finite element method for crack growth without remeshing, Int. J. numer. methods engrg., 46, 131-150, (1999) · Zbl 0955.74066 |

[40] | Mokni, M.; Desrues, J., Strain localization measurements in undrained plane strain biaxial tests on hostun RF sand, Mech. cohes. frict. mater., 4, 4, 419-441, (1999) |

[41] | Needleman, A., A continuum model for void nucleation by inclusion debonding, J. appl. mech., 54, 525-531, (1987) · Zbl 0626.73010 |

[42] | Oliver, J., Modelling string discontinuities in solid mechanics via strain softening constitutive equations. part 1: fundamentals. part 2: numerical simulation, Int. J. numer. methods engrg., 39, 3575-3623, (1996) · Zbl 0888.73018 |

[43] | Ortiz, M.; Pandolfi, A., Finite deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, Int. J. numer. methods engrg., 44, 1267-1282, (1999) · Zbl 0932.74067 |

[44] | M. Panet, P. Guellec, Contribution á l’étude du soutenement d’un tunnel derriére le front de taille, in: Proc. Third ISRM Congress, 2, Part B, Denver, 1974, pp. 1130-1134. |

[45] | Piccolroaz, A.; Bigoni, D.; Gajo, A., An elastoplastic framework for granular materials becoming cohesive through mechanical densification. part I - small strain formulation, part II - the formulation of elastoplastic coupling at large strain, Eur. J. mech. A/solids, 25, 334-369, (2006) · Zbl 1087.74021 |

[46] | Pietruszczak, S., Undrained response of granular soil involving localized deformation, J. eng. mech., 121, 1292-1297, (1995) |

[47] | Rice, J.R., On the stability of dilatant hardening for saturated rock masses, J. geophys. res., 80, 1531-1536, (1975) |

[48] | Rudnicki, K.; Rice, J.R., Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. mech. phys. solids, 23, 371-394, (1975) |

[49] | Rutqvist, J.; Stephansson, O., The role of hydro-mechanical coupling in fractured rock engineering, Hydrogeol. J., 11, 7-40, (2003) |

[50] | 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) · Zbl 1138.74407 |

[51] | Santagiuliana, R.; Schrefler, B.A., Enhancing the bolzon – schrefler – zienkiewicz constitutive model for partially saturated soil, Transp. porous media, 65, 1-30, (2006) |

[52] | Schrefler, B.A.; Majorana, C.E.; Sanavia, L., Shear band localization in saturated porous media, Arch. mech., 47, 577-599, (1995) · Zbl 0834.73004 |

[53] | Schrefler, B.A.; Sanavia, L.; Majorana, C.E., A multiphase medium model for localisation and postlocalisation simulation in geomaterials, Mech. cohes. frict. mater., 1, 95-114, (1996) |

[54] | Sheng, D.; Sloan, S.W.; Gens, A., A constitutive model for unsaturated soils: thermomechanical and computational aspects, Comput. mech., 33, 453-465, (2004) · Zbl 1115.74347 |

[55] | Simo, J.C.; Oliver, J.; Armero, F., An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Comput. mech., 12, 277-296, (1993) · Zbl 0783.73024 |

[56] | Stackgold, I., Green’s functions and boundary value problems, (1979), Wiley New York |

[57] | R.L. Taylor, FEAP - A Finite Element Analysis Program: Version 7.5 Theory Manual, University of California at Berkeley, 2003. |

[58] | Truesdell, C.; Noll, W., The nonlinear field theories, handbuch der physik, band III/3, (1965), Springer Berlin |

[59] | van Genuchten, M.T., A closed form equation predicting the hydraulic conductivity of unsaturated soils, Soil sci. soc. am. J., 44, 892-898, (1980) |

[60] | Vardoulakis, I., Deformation of water-saturated sand: I. uniform undrained deformation and shear banding; II. effect of pore water flow and shear banding, Géotechnique, 46, 441-472, (1996) |

[61] | Wells, G.N.; Sluys, L.J., A new method for modelling cohesive cracks using finite elements, Int. J. numer. methods engrg., 50, 2667-2682, (2001) · Zbl 1013.74074 |

[62] | Xu, X.P.; Needleman, A., Numerical simulations of fast crack growth in brittle solids, J. mech. phys. solids, 42, 1397-1434, (1994) · Zbl 0825.73579 |

[63] | Zhang, H.W.; Sanavia L, L.; Schrefler, B.A., A modified generalised plasticity model for strain localisation analysis of partially saturated sand, Comput. struct., 79, 441-459, (2001) |

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