Abstract
In this work, an extended theory of plasticity with generalized hardening is proposed to describe the response of geomaterials under both mechanical and environmental processes, which include as special cases several elastoplastic constitutive equations proposed in the literature to model such processes as desaturation or suction hardening, thermal softening, chemo-mechanical coupling effects in fine-grained soils, as well as weathering of soft rocks. In the formulation of the theory, the coupling between mechanical and environmental processes takes place at two levels: first, as an additional direct contribution to the constitutive stress changes, taking place in both elastic and elastoplastic processes; and second, as a result of the evolution of the internal state variables induced by changes in the environmental process variables. This last effect is incorporated through a set of generalized hardening rules. As an example of application, the general formulation is specialized to the particular case of weak calcarenite rocks undergoing degradation processes due to plastic deformations, changes in degree of saturation (short-term debonding) and chemical dissolution of the bond material and the solid grains (long-term debonding). The resulting model is implemented in a FE code by means of an implicit generalized backward Euler algorithm, suitably modified to incorporate the full formalism of plasticity with generalized hardening. Results of numerical simulations carried out at the element level show the accuracy and efficiency properties of the proposed stress-point algorithm. The simulation of a representative initial-boundary value problem demonstrates the practical relevance of environmental degradation effects in practical applications, over periods of time comparable with the life cycle of most geotechnical structures.
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References
Alonso EE, Gens A, Josa A (1990) A constitutive model for partially saturated soils. Géotechnique 40(3):405–430
Bolzon G, Schrefler B, Zienkiewicz O (1996) Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique 46(2):279–289
Borja R, Sama K, Sanz P (2003) On the numerical integration of three-invariant elastoplastic constitutive models. Comput. Methods Appl Mech Eng 192(9):1227–1258
Borja RI (2006) On the mechanical energy and effective stress in saturated and unsaturated porous continua. Int J Solids Struct 43(6):1764–1786
Borja RI, Tamagnini C (1998) Cam-clay plasticity, part III: extension of the infinitesimal model to include finite strains. Comput Methods Appl Mech Eng 155:73–95
Castellanza R, Nova R (2004) Oedometric tests on artificially weathered carbonatic soft rocks. J Geotech Geoenviron Eng 130(7):728–739
Cekerevac C, Laloui L (2004) Experimental study of thermal effects on the mechanical behaviour of a clay. Int J Numer Anal Methods Geomech 28(3):209–228
Ciantia M, Castellanza R, Crosta G, Hueckel T (2015) Effects of mineral suspension and dissolution on strength and compressibility of soft carbonate rocks. ENGGEO 184:1–18
Ciantia M, Castellanza R, di Prisco C (2014) Experimental study on the water-induced weakening of calcarenites. Rock Mech Rock Eng 48(2):441–461
Ciantia M, Prisco C (2015) Extension of plasticity theory to debonding, grain dissolution, and chemical damage of calcarenites. Int J Numer Anal Methods Geomech 40(3):315–343
Ciantia MO (2013) Multiscale hydro-chemo-mechanical modelling of the weathering of calcareus rocks: an experimental, theoretical and numerical study. Ph.D. thesis, Politecnico di Milano
Ciantia MO, Hueckel T (2013) Weathering of stressed submerged calcarenites. Géotechnique 63:768–785
Ciantia MO, di Prisco C, Castellanza R (2013) Chemo-mechanical weathering of calcarenites: experiments and theory. In: Manassero M, Dominijanni A, Foti S, Musso G (eds) Coupled phenomena in environmental geotechnics. Balkema, Rotterdam, pp 541–548
Conti R, Tamagnini C, DeSimone A (2013) Critical softening in cam-clay plasticity: adaptive viscous regularization, dilated time and numerical integration across stress-strain jump discontinuities. Comput Methods Appl Mech Eng 258:118–133
Cui Y, Delage P (1996) Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46(2):291–311
Della Vecchia G, Jommi C, Romero E (2013) A fully coupled elastic-plastic hydromechanical model for compacted soils accounting for clay activity. Int J Numer Anal Methods Geomech 37(5):503–535
Fernandez-Merodo J, Castellanza R, Mabssout M, Pastor M, Nova R, Parma M (2007) Coupling transport of chemical species and damage of bonded geomaterials. Comput Geotech 34(4):200–215
Fernandez Merodo, JA, Mira, P, Pastor M, Li T (1999) GeHoMadrid User Manual. Internal report, CEDEX, Madrid
Gens A (2010) Soil-environment interactions in geotechnical engineering. Géotechnique 60(1):3–74
Gens A, Guimaraes LdN, Olivella S (2002) Coupled chemomechanical analysis for saturated and unsaturated soils. In: Environmental Geomechanics, pp. 109–123
Gens A, Guimarães LDN, Olivella S (2005) THMC coupling in partially saturated geomaterials. Revue européenne de génie civil 9(5–6):747–765
Hueckel T (1997) Chemo-plasticity of clays subjected to stress and flow of a single contaminant. Int J Numer Anal Methods Geomech 21:43–72
Jommi C (2000) Remarks on the constitutive modelling of unsaturated soils. In: Tarantino A, Mancuso C (eds) Experimental evidence and theoretical approaches in unsaturated soils, vol 153. Balkema, Rotterdam
Jommi C, Di Prisco C (1994) A simple theoretical approach for modelling the mechanical behaviour of unsaturated soils. Proceedings of the Conference Il ruolo dei fluidi nei problemi di Ingegneria geotecnica 1:167–188 (in Italian)
Lagioia R, Puzrin AM, Potts DM (1996) A new versatile expression for yield and plastic potential surfaces. Comput Geotech 19:171–191
Loret B, Hueckel T, Gajo A (2002) Chemo-mechanical coupling in saturated porous media: elastic-plastic behaviour of homoionic expansive clays. Int J Solids Struct 39(10):2773–2806
Maier G (1966) On associative incremental elastic-plastic constitutive models. Rend Ist Lombardo di Scienze e Lettere 100:809–838 (in Italian)
Nova R (1986) Soil models as a basis for modelling the behaviour of geophysical materials. Acta Mech 64:31–44
Nova R (2000) Modelling the weathering effects on the mechanical behaviour of granite. In: Kolymbas D (ed) Constitutive modelling of granular materials. Springer, Berlin
Nova R, Castellanza R, Tamagnini C (2003) A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation. Int J Numer Anal Methods Geomech 27(9):705–732
Nova R, Castellanza R, Tamagnini C (2004) A constitutive model for mechanical and thermal loading of bonded geomaterials based on the concept of plasticity with extended hardening. Proc NUMOG 9 (2004)
Ogden RW (1997) Non-linear elastic deformations. Dover, New York
Parise M, Lollino P (2011) A preliminary analysis of failure mechanisms in karst and man-made underground caves in southern italy. Geomorphology 134(1):132–143
Saetta A, Scotta R, Vitaliani R (1998) Mechanical behavior of concrete under physical-chemical attacks. J Eng Mech 124(10):1100–1109
Saetta A, Scotta R, Vitaliani R (1999) Coupled environmental-mechanical damage model of rc structures. J Eng Mech 125(8):930–940
Schrefler B (1984) The finite element method in soil consolidation (with applications to surface subsidence). Ph.D. thesis, University College of Swansea
Sheng D, Sloan S, Gens A (2004) A constitutive model for unsaturated soils: thermomechanical and computational aspects. Comput Mech 33(6):453–465
Simo J (1998) Numerical analysis and simulation of plasticity. In: Handbook of numerical analysis, vol 6, pp 183–499
Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New York
Simo JC, Taylor RL (1985) Consistent tangent operators for rate independent elasto-plasticity. Comput Methods Appl Mech Eng 48:101–118
Tamagnini C, Castellanza R, Nova R (2002) A generalized backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials. Int J Numer Anal Methods Geomech 26:963–1004
Tamagnini R (2004) An extended cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique 54(3):223–228
Uchaipichat A, Khalili N (2009) Experimental investigation of thermo-hydro-mechanical behaviour of an unsaturated silt. Geotechnique 59(4):339–353
van Eekelen HAM (1980) Isotropic yield surfaces in three dimensions for use in soil mechanics. Int J Numer Anal Methods Geomech 4:89–101
Wheeler S, Sivakumar V (1995) An elasto-plastic critical state framework for unsaturated soil. Géotechnique 45(1):35–53
Acknowledgments
The authors would like to warmly acknowledge the fundamental role played by their mentor and friend Roberto Nova in inspiring this work. The authors would like to thank Claudio di Prisco and Riccardo Castellanza for many fruitful discussions and José Antonio Fernandez–Merodo for the support provided with the FE code GeHoMadrid. The financial support of the Project “PRIN 2010–2011” is also gratefully acknowledged.
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Tamagnini, C., Ciantia, M.O. Plasticity with generalized hardening: constitutive modeling and computational aspects. Acta Geotech. 11, 595–623 (2016). https://doi.org/10.1007/s11440-016-0438-8
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DOI: https://doi.org/10.1007/s11440-016-0438-8