Skip to main content
SpringerLink
Log in

A Regularised Anisotropic Elastoplastic Damage and Viscoplastic Model and Its Hydromechanical Application to a Meuse/Haute-Marne URL Drift

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

Clay formations are one of the options currently being considered for the storage of radioactive wastes worldwide. In France, the National Radioactive Waste Management Agency (Andra) operates the Meuse/Haute-Marne Underground Research Laboratory in the Callovo-Oxfordian (COx) clay formation to assess the feasibility and safety of an industrial radioactive waste repository. A good level of understanding of the thermo-hydromechanical behaviour of the host rock is paramount for the safety assessment. A new anisotropic elastoplastic damage and viscoplastic model is proposed to describe the hydromechanical behaviour of the COx claystone based on a large dataset of experimental evidence. The model is based on the Hoek and Brown criterion and considers recent findings of the COx hydromechanical behaviour. The key mechanisms considered are: plastic strain hardening prior to reaching the peak strength, a post-peak behaviour characterised by strain softening in the frame of continuum damage mechanics and a residual stage represented by a perfectly plastic behaviour. Time-dependent deformations are also included based on a creep model, which in this work is coupled with damage. The proposed model was implemented with a regularisation scheme based on the non-local implicit gradient in Comsol Multiphysics® with the purpose of performing THM modelling (1D, 2D and 3D) in the framework of the Cigéo project. The numerical implementation is first validated based on several simulations of creep tests at different deviatoric stress and triaxial compression tests at different confining pressures and angles between the loading direction and the bedding, α. Then, the GCS drift hydromechanical behaviour is simulated considering transverse isotropic conditions. It is shown that the model is capable of reproducing the measured peak of pore pressure in sensors near the GCS wall as well as the drift convergence. Importantly, the predicted extent of damaged zones around the drift is consistent with the in situ observations. The impact of damage on the time-dependent behaviour and the permeability was investigated numerically. It was found that the magnitude and anisotropy of drift convergence and the pore pressure drop are sensitive to this coupling and the best agreement was obtained when this effect was taken into account. Finally, the performance of the regularisation scheme is demonstrated with a set of simulations of the drift with different mesh refinements. It is concluded that the proposed model captures the key features of the hydromechanical behaviour of the COx claystone.

Highlights

  • An advanced constitutive model that takes into account the recent findings on the key mechanisms of deformation and failure of COx claystone is proposed.

  • Strain hardening/softening, anisotropic elasticity and plasticity, damage described in the framework of CDM and time-dependent behaviour of COx claystone are considered.

  • The effect of damage and shear fracturation on the transport and viscous properties are also addressed in the model.

  • The model with a regularisation scheme is implemented in Comsol Multiphysics®, which allows several physics to be considered, then to perform 1D, 2D and 3D THMC modellings.

  • The operational nature of the proposed model is successfully evidenced on the GCS drift of the MHM URL, for which the in situ observations are the most challenging to reproduce.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

Not applicable.

References

  • Aifantis EC (1984) On the microstructural origin of certain inelastic models. J Eng Mater Technol 106(4):326–330

    Article  Google Scholar 

  • Armand G, Noiret A, Zghondi J, Seyedi DM (2013) Short- and long term behaviors of drifts in the Callovo-Oxfordian claystone at the Meuse/Haute-Marne Underground Research Laboratory. J Rock Mech Geotech Eng 5(3):221–230

    Article  Google Scholar 

  • Armand G, Leveau F, Nussbaum C, de La Vaissiere R, Noiret A, Jaeggi D, Landrein P, Righini C (2014) Geometry and properties of the excavation induced fractures at the Meuse/Haute-Marne URL drifts. Rock Mech Rock Eng 47(1):21–41. https://doi.org/10.1007/s00603-012-0339-6

    Article  Google Scholar 

  • Armand G, Conil N, Talandier J, Seyedi DM (2017a) Fundamental aspects of the hydromechanical behaviour of Callovo-Oxfordian claystone: from experimental studies to model calibration and validation. Comput Geotech 85:277–286

    Article  Google Scholar 

  • Armand G, Bumbieler F, Conil N, de La Vaissière BJM, Vu MN (2017b) Main outcomes from in situ THM experiments programme to demonstrate feasibility of radioactive HL-ILW disposal in the Callovo-Oxfordian claystone. J Rock Mech Geotech Eng 9(3):415–427

    Article  Google Scholar 

  • Armand G, Dewonck S, J-M, Bosgiraud, Richard-Panot L (2015) Development and new research program in the Meuse Haute Marne Underground Research Laboratory (France). 13th ISRM International Congress of Rock Mechanics

  • Askes H, Sluys LJ (2002) Explicit and implicit gradient series in damage mechanics. Eur J Mech A Solids 21(3):379–390. https://doi.org/10.1016/S0997-7538(02)01214-7

    Article  Google Scholar 

  • Bazant ZP, Pijaudier-Cabot G (1989) Measurement of characteristic length of nonlocal continuum. J Eng Mech 115(4):755–767

    Article  Google Scholar 

  • Bazant ZP, Belytschko TB, Chang TP (1984) Continuum theory for strain softening. J Eng Mech 110(12):1666–1692

    Article  Google Scholar 

  • Bažant ZP, Jirásek M (2002) Nonlocal integral formulation for plasticity and damage: survey of progress. J Eng Mech ASCE 128:1119–1149

    Article  Google Scholar 

  • Belmokhtar M, Delage P, Ghabezloo S, Menaceur H, Tang AM, Conil N (2017) Poroelasticity of the Callovo-Oxfordian claystone. Rock Mech Rock Eng 50:871–889. https://doi.org/10.1007/s00603-016-1137-3

    Article  Google Scholar 

  • Belmokhtar M, Delage P, Ghabezloo S, Conil N (2018) Drained triaxial tests in low-permeability shales: application to the Callovo Oxfordian claystone. Rock Mech Rock Eng Spring Vienna 51(7):1979–1993

    Article  Google Scholar 

  • Bemer E, Longuemare P, Vincké O (2004) Poroelastic parameters of Meuse/Haute-Marne argillites: effect of loading and saturation states. Appl Clay Sci 26:359–366

    Article  Google Scholar 

  • Bésuelle P, Lanata P (2014) Characterization of the early strain localization in a sandstone and a clay rock. Cambridge, UK, 1–3 September 2014

  • Bian H, Zhang X, Shao JF (2017) A coupled elastoplastic and visco-plastic damage model for hard clay and its application for the underground gallery excavation. Underground Space 2:60–72

    Article  Google Scholar 

  • Braun P, Ghabezloo S, Delage P, Sulem J, Conil N (2021) Thermo-Poro-elastic behaviour of a transversely isotropic shale: thermal expansion and pressurization. Rock Mech Rock Eng 54:359–375. https://doi.org/10.1007/s00603-020-02269-y

    Article  Google Scholar 

  • Braun P (2019) Thermo-hydro-mechanical behavior of the Callovo-Oxfordian claystone: Effects of stress paths and temperature changes. PhD thesis, Paris-Est University

  • Chen L, Wang CP, Liu JF, Liu J, Wang J, Shao JF (2015) Damage and plastic deformation modeling of Beishan granite under compressive stress conditions. Rock Mech Rock Eng 48:1623–1633. https://doi.org/10.1007/s00603-014-0650-5

    Article  Google Scholar 

  • Chiarelli AS, Shao JF, Hoteit N (2003) Modeling of elastoplastic damage behavior of a claystone. Int J Plast 19:23–45

    Article  Google Scholar 

  • Coarita-Tintaya ED, Golfier F, Souley M, Vu MN (2020) Anisotropic hydro-viscoplastic modelling of a drift at the Meuse/Haute-Marne URL. Eur J Environ Civ Eng. https://doi.org/10.1080/19648189.2020.1797887

    Article  Google Scholar 

  • Conil N, Djeran-Maigre I, Cabrillac R, Su K (2004) Poroplastic damage model for claystones. Appl Clay Sci 26:473–487

    Article  Google Scholar 

  • Conil N, Talandier J, Djizanne H, de La Vaissière R, Righini-Waz C, Auvray C, Morlot C, Armand G (2018) How rock samples can be representative of in situ condition: a case study of Callovo-Oxfordian claystones. J Rock Mech Geotech Eng 10(4):613–623

    Article  Google Scholar 

  • Coussy O (2004) Poromechanics. John Wiley & Sons, Ltd, 2004. — XVI + 298 p. — ISBN: 0–470–84920–7

  • Cuvilliez S, Djouadi I, Raude S, Fernandes R (2017) An elastoviscoplastic constitutive model for geomaterials: Application to hydromechanical modelling of claystone response to drift excavation. Comput Geotech 85:321–340

    Article  Google Scholar 

  • David C, Robion P, Menendez B (2005) Anisotropy of elastic, magnetic and microstructural properties of the Callovo-Oxfordian shales (Meuse). In: 2nd Int Meeting Clays in Natural & Engineered Barriers for Radioactive Waste Confinement

  • de Borst R, Mühlhaus HB (1992) Gradient-dependent plasticity: formulation and algorithm aspects. Int J Numer Meth Eng 35(3):521–539

    Article  Google Scholar 

  • de Borst R, Sluys LJ, Mühlhaus H-B, Pamin J (1993) Fundamental issues in finite element analyses of localization of deformation. Engng Comput 10:99–121

    Article  Google Scholar 

  • de la Vaissière R, Armand G, Talandier J (2015) Gas and water flow in an excavation-induced fracture network around an underground drift: a case study for a radioactive waste repository in clay rock. J Hydrol 521:141–156

    Article  Google Scholar 

  • Desbois G, Höhne N, Urai JL, Bésuelle B, Viggiani G (2017) Deformation in cemented mudrock (Callovo–Oxfordian Clay) by microcracking, granular flow and phyllosilicate plasticity: insights from triaxial deformation, broad ion beam polishing and scanning electron microscopy. Solid Earth 8:291–305

    Article  Google Scholar 

  • Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Meth Geomech 28:279–321. https://doi.org/10.1002/nag.338

    Article  Google Scholar 

  • Detournay E, Cheng AHD (1993) Fundamentals of poroelasticity. In Fairhurst C (Ed) Comprehensive rock engineering: Principles, practice and projects. Vol. II. Analysis and design method (pp. 113–171). Pergamon Press

  • Dinç Göğüş Ö, Scholtès L (2018) Discrete analysis of damage and shear banding in argillaceous rocks. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-017-1397-6

    Article  Google Scholar 

  • Djouadi I, Giot R, Raude S, Cuvilliez S, Laigle F, Fernandes R (2020) Integration of transverse isotropy in the instantaneous behaviour of geomaterials with application to numerical modelling of underground structures. Geotech Geol Eng 38:4917–4938. https://doi.org/10.1007/s10706-020-01336-z

    Article  Google Scholar 

  • Escofer S (2002) Caractérisation expérimentale du comportement hydroméchanique des argilites de Meuse/Haute-Marne. PhD thesis, Institut National Polytechnique de Lorraine

  • Fabre G, Pellet F (2006) Creep and time-dependent damage in argillaceous rocks. Int J Rock Mech Min Sci 43:950–960

    Article  Google Scholar 

  • Gasc-Barbier M, Chanchole S, Bérest P (2004) Creep behavior of Bure clayey rock. Appl Clay Sci 26(1–4):449–458. https://www.sciencedirect.com/science/article/abs/pii/S016913170300293X

  • Geers MGD, de Borst R, Brekelmans WAM, Peerlings RHJ (1998) Strain-based transient-gradient damage model for failure analyses. Comput Methods Appl Mech Eng 160:133–153. https://doi.org/10.1016/S0045-7825(98)80011-X

    Article  Google Scholar 

  • Geers MGD, Peerlings RHJ, Brekelmans WAM (2000) Phenomenological nonlocal approaches based on implicit gradient-enhanced damage. Acta Mech 144:1–15. https://doi.org/10.1007/BF01181824

    Article  Google Scholar 

  • Giry C, Dufour F, Mazars J (2011) Stress-based nonlocal damage model. Int J Solids Struct 48:3431–3443

    Article  Google Scholar 

  • Hoek E (1990) Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion. Int J Rock Mech Min Sci Geomech Abst 27:227–229

    Article  Google Scholar 

  • Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Eng Div ASCE 106(GT9):1013–1035

    Article  Google Scholar 

  • Hoxha D, Giraud A, Homand F, Auvray C (2007) Saturated and unsaturated behavior modelling of Meuse/Haute-Marne argillite. Int J Plast 23:733–766

    Article  Google Scholar 

  • Hu DW, Zhang F, Shao JF (2014) Experimental study of poromechanical behavior of saturated claystone under triaxial compression. Acta Geotech 9(2):207–214

    Article  Google Scholar 

  • Jia Y, Bian HB, Su K, Kondo D, Shao JF (2009) Elastoplastic damage modeling of desaturation and resaturation in argillites. Int J Numer Anal Meth Geomech 34:187–220

    Article  Google Scholar 

  • Jirásek M (2007) Nonlocal damage mechanics. Revue Européenne De Génie Civil 11(7–8):993–1021. https://doi.org/10.1080/17747120.2007.9692974

    Article  Google Scholar 

  • Jung S, Vu MN, Pouya A, Ghabezloo S (2022) Effect of anisotropic creep on the convergence of deep drifts in Callovo-Oxfordian claystone. Comput Geotech 152:105010

    Article  Google Scholar 

  • Le Bellego C, Dube JF, Pijaudier-Cabot G, Gerard B (2003) Calibration of non local damage model from size effect tests. Eur J Mech A/Solids 22:33–46

    Article  Google Scholar 

  • Lee Y, Bobet A (2014) Instantaneous friction angle and cohesion of 2-D and 3-D Hoek-Brown rock failure criteria in terms of stress invariants. Rock Mech Rock Eng 47:371–385

    Article  Google Scholar 

  • Lekhnitskii SG (1981) Theory of elasticity of an anisotropic body. Mir Publishers, Moscow

    Google Scholar 

  • Lemaitre J (1985) A course on damage mechanics, 2nd edn. Springer

    Google Scholar 

  • Liu ZB, Xie SY, Shao JF, Conil N (2018) Multi-step triaxial compressive creep behaviour and induced gas permeability change of clay-rich rock. Géotechnique 68:281–289. https://doi.org/10.1680/jgeot.16.P.117

    Article  Google Scholar 

  • Liu Z, Shao J, Xie S, Conil N, Talandier J (2019) Mechanical behavior of claystone in lateral decompression test and thermal effect. Rock Mech Rock Eng 52(2):321–334 (Springer Vienna)

    Article  Google Scholar 

  • Lu X, Bardet J-P, Huang M (2009) Numerical solutions of strain localization with nonlocal softening plasticity. Comput Methods Appl Mech Eng 198(47–48):3702–3711

    Article  Google Scholar 

  • Mánica MA, Gens A, Vaunat J, Ruiz D-F (2017) A time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone. Comput Geotech 85:341–350

    Article  Google Scholar 

  • Mánica MA, Gens A, Vaunat J, Ruiz D-F (2018) Nonlocal plasticity modelling of strain localisation in stiff clays. Comput Geotech 103:138–150

    Article  Google Scholar 

  • Mánica MA, Gens A, Vaunat J, Armand G, Vu MN (2022) Numerical simulation of underground excavations in an indurated clay using non-local regularisation. Part 1: formulation and base case. Geotechnique 72(12):1092–1112

    Article  Google Scholar 

  • Mazars J (1986) A description of micro- and macro-scale damage of concrete structures. Eng Fract Mech 25(5–6):729–737

    Article  Google Scholar 

  • Menaceur H, Delage P, Tang AM, Conil N (2015) The thermomechanical behaviour of the Callovo-Oxfordian claystone. Int J Rock Mech Min Sci 78:290–303

    Article  Google Scholar 

  • Miehe C, Aldakheel F, Mauthe S (2013) Mixed variational principles and robust finite element implementations of gradient plasticity at small strains. Int J Numer Methods Engrg 94(11):1037–1074

    Article  Google Scholar 

  • Mohajerani M, Delage P, Sulem J, Monfared M, Tang AM, Gatmiri B (2012) A laboratory investigation of thermally induced pore pressures in the Callovo-Oxfordian claystone. Int J Rock Mech Min Sci 52:112–121

    Article  Google Scholar 

  • Mohamad-Hussein A, Shao JF (2007) An elastoplastic damage model for semi-brittle rocks. Geomech Geoeng 2(4):253–267. https://doi.org/10.1080/17486020701618329

    Article  Google Scholar 

  • Pardoen B, Collin F (2017) Modelling the influence of strain localisation and viscosity on the behaviour of underground drifts drilled in claystone. Comput Geotech 85(2017):351–367

    Article  Google Scholar 

  • Patzák B, Jirásek M (2004) Adaptive resolution of localized damage in Quasi-brittle materials. J Eng Mech 130:720–732

    Article  Google Scholar 

  • Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996a) Gradient-enhanced damage for quasi-brittle materials. Int J Numer Meth Eng 39:3391–3403

    Article  Google Scholar 

  • Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP, Spee I (1996b) Some observations on localisation in non-local and gradient damage models. Eur J Mech A/Solids 15(6):937–953

    Google Scholar 

  • Perzyna P (1966) Fundamental problems in viscoplasticity. Adv Appl Mech 1966:9

    Google Scholar 

  • Pietruszczak S, Mroz Z (1981) Finite element analysis of deformation of strain-softening materials. Int J Mum Meth Engng 17:327–334

    Article  Google Scholar 

  • Pietruszczak S, Mroz Z (2000) Formulation of anisotropic failure criteria incorporating a microstructure tensor. Comput Geotech 26:105–112

    Article  Google Scholar 

  • Pietruszczak S, Lydzba D, Shao JF (2002) Modelling of inherent anisotropy in sedimentary rocks. Int J Solids Struct 39:637–648

    Article  Google Scholar 

  • Pijaudier-Cabot G, Bazant ZP (1987) Nonlocal damage theory. J Eng Mech 113(10):1512–1533

    Article  Google Scholar 

  • Read HE, Hegemier GA (1984) Strain softening of rock, soil and concrete—a review article. Mech Mater 3:271–294

    Article  Google Scholar 

  • Rezania M, Bonnier P, Brinkgreve R, Karstunen M (2012) Non-local regularisation of Drucker-Prager softening model. In: Proceedings of the 20th UK Conference of the Association for Computational Mechanics in Engineering 27 – 28th March 2012, the University of Manchester, Manchester

  • Sabet SA, de Borst R (2019) Structural softening, mesh dependence, and regularisation in non-associated plastic flow. Int J Numer Anal Methods Geomech 43:2170–2183

    Article  Google Scholar 

  • de Saint-Venant B. (1863) Sur la distribution des élasticités autour de chaque point d’un solide ou d’un milieu de contexture quelconque, particulièrement lorsqu’il est amorphe sans être isotrope. J de Mathématiques Pures et Appliquées, Série 2, Vol. 8, pp. 353–430 ; 257–295

  • Sarout J, Guéguen Y (2008) Anisotropy of elastic wave velocities in deformed shales. Part I: experimental results. Geophysics 73(5):D75–D89

    Article  Google Scholar 

  • Schreter M, Neuner M, Hofstetter (2018) Evaluation of the implicit gradient-enhanced regularization of a damage-plasticity rock model. Appl Sci-Basel 8(6):1004

    Article  Google Scholar 

  • Seyedi DM, Armand G, Noiret A (2017) Transverse Action—a model benchmark exercise for numerical analysis of the Callovo-Oxfordian claystone hydromechanical response to excavation operations. Comput Geotech 85:287–305

    Article  Google Scholar 

  • Simone A (2007) Explicit and implicit gradient-enhanced damage models. Revue Européenne De Génie Civil 11(7–8):1023–1044. https://doi.org/10.1080/17747120.2007.9692975

    Article  Google Scholar 

  • Souley M, Armand G, Su K, Ghoreychi M (2011) (2011) Modelling of the viscoplastic behaviour including damage for deep argillaceous rocks. Phys Chem Earth 36:1949–1959

    Article  Google Scholar 

  • Souley M, Armand G, Kazmierczak J-B (2017) Hydro-elasto-viscoplastic modeling of a drift at the Meuse/Haute-Marne underground research laboratoratory (URL). Comput Geotech 85(2017):306–320

    Article  Google Scholar 

  • Souley M, Vu MN, Armand G (2022) 3D modelling of excavation-induced anisotropic responses of deep drifts at the Meuse/Haute-Marne URL. Rock Mech Rock Eng 55:4183–4207. https://doi.org/10.1007/s00603-022-02841-8

    Article  Google Scholar 

  • Sulem J (2010) Bifurcation theory and localization phenomena. Eur J Environ Civ Eng 14:989–1009 (Taylor & Francis)

    Article  Google Scholar 

  • Summersgill FC, Kontoe S, Potts DM (2017) Critical assessment of nonlocal strain-softening methods in biaxial compression. Int J Geomech 17:04017006

    Article  Google Scholar 

  • Tourchi S, Vaunat J, Gens A, Bumbieler F, Vu MN, Armand G (2021) A full-scale in situ heating test in Callovo-Oxfordian claystone: observations, analysis and interpretation. Comput Geotech 133:104045. https://doi.org/10.1016/j.compgeo.2021.104045

    Article  Google Scholar 

  • Trivellato E, Pouya A, Vu MN, Seyedi D (2019) A softening damage-based model for the failure zone around deep tunnels in quasi-brittle claystone. In Proceedings “Tunnels and Underground Cities: Engineering and Innovation meet Archaeology”, WTC 2019 ITA-AITES World Tunnel Congress, Naples, Italy, pp 4242–4251. https://doi.org/10.1201/9780429424441-449

  • Tsang CF, Bernier F, Davies C (2005) Geohydromechanical processes in the excavation damaged zone in crystalline rock, rock salt, and indurated and plastic clays—in the context of radioactive waste disposal. Int J Rock Mech Min Sci 42(1):109–125

    Article  Google Scholar 

  • Valanis KC, Peters JF (1996) Ill-posedness of the initial and boundary value problems in non-associative plasticity. Acta Mech 114:1–25

    Article  Google Scholar 

  • Vu MN, Guayacán-Carrillo L-M, Armand G (2020) Excavation induced over pore pressure around drifts in the Callovo-Oxfordian claystone. Eur J Environ Civ Eng. https://doi.org/10.1080/19648189.2020.1784800

    Article  Google Scholar 

  • Wileveau Y, Cornet FH, Desroches J, Blumling P (2007) Complete in situ stress determination in an argillite sedimentary formation. Phys Chem Earth 32(8–14):866–878

    Article  Google Scholar 

  • Wu S, Wang X (2010) Mesh dependence and nonlocal regularization of one-dimensional strain softening plasticity. J Eng Mech 136(11):1354–1365

    Article  Google Scholar 

  • Yanqiu H, Shao JF (2013) A micromechanical analysis of time-dependent behavior based on subcritical damage in claystones. Int J Damage Mech 22:773–790

    Article  Google Scholar 

  • Yao C, Shao JF, Jiang QH, Zhou CB (2017) Numerical study of excavation induced fractures using an extended rigid block spring method. Comput Geotech 85:368–383

    Article  Google Scholar 

  • Yu Z, Shao JF, Duveau G, Vu MN, Armand G (2021) Numerical modeling of deformation and damage around underground excavation by phase-field method with hydromechanical coupling. Comput Geotech 138:104369. https://doi.org/10.1016/j.compgeo.2021.10436

    Article  Google Scholar 

  • Zhang C-L (2016) The stress-strain-permeability behaviour of clay rock during damage and recompaction. J Rock Mech Geotech Engng 8(2016):16–26

    Article  Google Scholar 

  • Zhang C-L (2018) Thermo-hydro-mechanical behavior of clay rock for deep geological disposal of high-level radioactive waste. J Rock Mech Geotech Eng 10(5):992–1008 (Elsevier Ltd)

    Article  Google Scholar 

  • Zhang C, Rothfuchs T (2004) Experimental study of the hydromechanical behaviour of the Callovo-Oxfordian argillite. Appl Clay Sci 26(1–4):325–336 (Elsevier)

    Article  Google Scholar 

  • Zhang CL, Czaikowski O, Rothfuchs T (2010) Thermo-hydro-mechanical behavior of the Callovo-Oxfordian clay rock, GRS-266. GRS, Germany

    Google Scholar 

  • Zhang F, Xie SY, Hu DW, Shao JF, Gatmiri B (2012) Effect of water content and structural anisotropy on mechanical property of claystone. Appl Clay Sci 69:79–86

    Article  Google Scholar 

  • Zhang F, Jia Y, Bian HB, Duveau G (2013) Modeling the influence of water content on the mechanical behavior of Callovo-Oxfordian argillite. Phys Chem Earth 65(2013):79–89

    Article  Google Scholar 

  • Zhang C-L, Armand G, Conil N, Laurich B (2019) Investigation on anisotropy of mechanical properties of Callovo-Oxfordian claystone. Eng Geol 251(2019):128–145

    Article  Google Scholar 

  • Zhou S, Rabczuk T, Zhuang X (2018) Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies. Adv Eng Softw 122:31–49

    Article  Google Scholar 

  • Zhou S, Zhuang X, Rabczuk T (2019) Phase field modeling of brittle compressive-shear fractures in rock-like materials: a new driving force and a hybrid formulation. Comput Methods Appl Mech Eng 355:729–752

    Article  Google Scholar 

  • Zreid I, Kaliske M (2018) A gradient enhanced plasticity–damage microplane model for concrete. Comput Mech 62:1239–1257. https://doi.org/10.1007/s00466-018-1561-1

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute for Industrial Environment and Risks (Ineris), Nancy, France

    M. Souley & E.-D. Coarita-Tintaya

  2. GeoRessources Laboratory, University of Lorraine (UL), CNRS, Nancy, France

    E.-D. Coarita-Tintaya & F. Golfier

  3. French National Radioactive Waste Management Agency (Andra), Châtenay-Malabry, France

    M.-N. Vu & G. Armand

  4. Amphos 21 Consulting, Barcelona, Spain

    M. Laviña & A. Idiart

Authors
  1. M. Souley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E.-D. Coarita-Tintaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M.-N. Vu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Golfier
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. Armand
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Laviña
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. Idiart
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Souley.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Illustration of Mesh Independency on the Results of GCS Drift Simulation

This section is dedicated to the evaluation of the effect of the mesh size on the numerical results presented in this paper in terms of extensions of damaged and plastic zones, drift convergences, pore pressure distribution and deformation of the rock mass in the near and far fields. For this, we started from the last configuration discussed above (Case 3). The reference mesh is the one used in all the simulations previously discussed, i.e. M40 × 60Q consisting of 40 × 60 quadrilateral elements in an annulus of one GCS diameter from the wall (i.e. 40 radial elements with a geometric progression, 60 orthoradial elements with an arithmetic distribution). Coarser and finer meshes were used, especially around the GCS drift wall. They are summarised in Table

Table 3 Sensitivity analysis on mesh size
Full size table

3.

For these different meshes, the extension of the damaged and plastic zones, the pressure along the horizontal profile for different times, the evolution of the GCS convergences and the displacement in the massif are shown in Figs. 

Fig. 20
figure 20

Extent of damaged and plastic zones around GCS drift at 4 years. Effect of mesh size

Full size image

20,

Fig. 21
figure 21

Pore pressure evolution along the horizon profile. Effect of mesh size

Full size image

21,

Fig. 22
figure 22

Horizontal and vertical convergences around the GCS. Effect of mesh size

Full size image

22 and

Fig. 23
figure 23

Relative radial displacement (from the GCS wall) in the rock mass along the borehole OHZ1501. Effect of mesh size

Full size image

23. They indicate a quasi-absence of mesh dependence, which was not the case when no regularisation scheme was used (Coarita-Tintaya et al. 2020). However, moderate differences are obtained in terms of 2D distribution of the damaged zone. For the cases in which the selected characteristic length (0.08 m) is close to the distance between evaluation nodes, an almost continuous pattern is found. In turn, for the most spatially refined case, the large ratio between characteristic length and mesh size results in a more localised discrete band pattern in which its width is defined by the characteristic length selected.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Souley, M., Coarita-Tintaya, ED., Vu, MN. et al. A Regularised Anisotropic Elastoplastic Damage and Viscoplastic Model and Its Hydromechanical Application to a Meuse/Haute-Marne URL Drift. Rock Mech Rock Eng (2023). https://doi.org/10.1007/s00603-023-03563-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00603-023-03563-1

Keywords

Search

Navigation