Gas migrations; H2M couplings; Nuclear waste disposal; Numerical modelling; Second gradient model; Strain localisation; Claystones; Excavation damaged zones; Flow properties; Gas migration; Gradient modelling; H2M coupling; Numerical investigations; Strain localizations; Modeling and Simulation; Materials Science (all); Condensed Matter Physics; Mechanics of Materials; Mechanical Engineering; Applied Mathematics; General Materials Science
Abstract :
[en] Deep geological repository is the preferred solution in many countries to manage radioactive wastes, such as in France where the Callovo-Oxfordian (COx) claystone is the candidate host rock. In such clay rock formation, the drilling of storage gallery creates an Excavation Damaged Zone (EDZ) with altered flow properties in the short term, while corrosion processes release large amounts of gas in the long term. Assessing the evolution of gas pressures in the near-field and predicting the effect of the EDZ on gas transport remains a major issue. This paper presents a second gradient two-phase flow hydro-mechanical (H2M) model tackling the multi-physics couplings related to gas transfers and fractures development. The EDZ is reproduced by shear strain localisation bands using a microstructure enriched model with a second gradient approach. The gas migration is captured by a biphasic fluid transfer model. The impact of fracturing on the flow properties is addressed by relating the permeability and the water retention curve to mechanical strains. Using this tool, numerical modelling of a drift in the COx claystone is performed with the aim of emphasising the influence of the HM couplings on gas migrations at nuclear waste disposal scale.
Disciplines :
Civil engineering
Author, co-author :
Corman, Gilles ; Université de Liège - ULiège > Urban and Environmental Engineering
Vu, Minh-Ngoc; Andra, Châtenay-Malabry, France
Collin, Frédéric ; Université de Liège - ULiège > Département ArGEnCo
Language :
English
Title :
Numerical investigation of the couplings between strain localisation processes and gas migrations in clay materials
Alternative titles :
[fr] Etude numérique des couplages entre la localisation des déformations et les migrations de gas dans les matériaux argileux
H2020 - 847593 - EURAD - European Joint Programme on Radioactive Waste Management
Funders :
Union Européenne [BE]
Funding text :
The authors are grateful for financial supports from EURAD , the European Joint Programme on Radioactive Waste Management (under grant agreement No 847593 ), and from ANDRA, the French national radioactive waste management agency .
Aifantis, E.C., On the microstructural origin of certain inelastic models. J. Eng. Mater. Technol. 106:4 (1984), 326–330.
Amadei, B., Rock Anisotropy and the Theory of Stress Measurements Lecture Notes in Engineering Series, vol. 2, 1983, Springer-V edition, New-York, The United States.
Andra, B., Analyse de l'Interaction (Thermo-)Hydro-Mécanique des Alvéoles MAVL - Approche Milieu Continu: Technical report., 2016, Agence natioanle pour la gestion des déchets radioactifs, Châtenay-Malabry, France, 34.
Argilaga, A., Collin, F., Lacarrière, L., Charlier, R., Armand, G., Cerfontaine, B., Modelling of short-term interactions between concrete support and the excavated damage zone around galleries drilled in callovo–oxfordian claystone. Int. J. Civ. Eng., 17(1), 2019.
Armand, G., Leveau, F., Nussbaum, C., De La Vaissiere, R., Noiret, A., Jaeggi, D., Landrein, P., Righini, C., Geometry and properties of the excavation-induced fractures at the Meuse/Haute-Marne URL drifts. Rock Mech. Rock Eng. 47:1 (2014), 21–41.
Ausness, R.C., High-level radioactive waste management: The nuclear dilemma. Wis. Law Rev., 707, 1979.
Autio, J., Gribi, P., Johnson, L., Marschall, P., Effect of excavation damaged zone on gas migration in a KBS-3H type repository at Olkiluoto. Phys. Chem. Earth 31:10–14 (2006), 649–653.
Bažant, Z.P., Belytschko, T.B., Wave propagation in a strain-softening bar: Exact solution. J. Eng. Mech. 111:3 (1985), 381–389.
Bazant, Z.P., Belytschko, T.B., Chang, T.-P., Continuum theory for strain-softening. J. Eng. Mech. 110:12 (1984), 1666–1692.
Bernaud, D., Rousset, G., La « nouvelle méthode implicite » pour l’étude du dimensionnement des tunnels. Rev. Fr. Géotech.(60), 1992, 5–26.
Biot, M.A., General theory for three-dimensional consolidation. J. Appl. Phys. 12:2 (1941), 155–164.
Bishop, A.W., The principle of effective stress. Tek. Ukebl. 39 (1959), 859–863.
Borja, R.I., Alarcón, E., A mathematical framework for finite strain elastoplastic consolidation Part 1: Balance laws, variational formulation, and linearization. Comput. Methods Appl. Mech. Engrg. 122:1–2 (1995), 145–171.
Bredehoeft, J.D., England, A.W., Steward, D.B., Trask, N.J., Winograd, I.J., Geologic disposal of high-level radioactive wastes, earth-science perspectives. U.S. Geological Survey Circular 779: Technical report, 1978, U.S. Geological Survey, 15.
Chambon, R., Caillerie, D., El Hassan, N., One-dimensional localisation studied with a second grade model. Eur. J. Mech. A/Solids 17:4 (1998), 637–656.
Chambon, R., Caillerie, D., Matsuchima, T., Plastic continuum with microstructure, local second gradient theories for geomaterials: Localization studies. Int. J. Solids Struct. 38:46–47 (2001), 8503–8527.
Chambon, R., Crochepeyre, S., Charlier, R., An algorithm and a method to search bifurcation points in non-linear problems. Internat. J. Numer. Methods Engrg. 51:3 (2001), 315–332.
Chambon, R., Moullet, J.C., Uniqueness studies in boundary value problems involving some second gradient models. Comput. Methods Appl. Mech. Engrg. 193:27–29 (2004), 2771–2796.
Charlier, R., Approche Unifiée de Quelques Problèmes Non Linéaires de Mécanique des Milieux Continus par la Méthode des Éléments Finis (Grandes Déformations des Métaux et des Sols, Contact Unilatéral de Solides, Conduction Thermique et Écoulements en Milieux Poreux). (Ph.D. thesis), 1987, Faculty of Applied Sciences, University of Liège, Belgium, 301.
Charlier, R., Collin, F., Pardoen, B., Talandier, J., Radu, J.-P., Gerard, P., An unsaturated hydro-mechanical modelling of two in-situ experiments in Callovo-Oxfordian argillite. Eng. Geol. 165 (2013), 46–63.
Cheng, A.H.-D., Material coefficients of anisotropic poroelasticity. Int. J. Rock Mech. Min. Sci. 34:2 (1997), 199–205.
Clapeyron, E., Mémoire sur la Puissance Motrice de la Chaleur. J. Éc. Polytech. 23 (1834), 153–191.
Collin, F., Couplages Thermo-Hydro-Mécaniques dans les Sols et les Roches Tendres Partiellement Saturés. (thésis / mémoire), 2003, Faculty of Applied Sciences, University of Liège, Belgium, 332.
Collin, F., Caillerie, D., Chambon, R., Analytical solutions for the thick-walled cylinder problem modeled with an isotropic elastic second gradient constitutive equation. Int. J. Solids Struct. 46:22–23 (2009), 3927–3937.
Collin, F., Chambon, R., Charlier, R., A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models. Internat. J. Numer. Methods Engrg. 65:11 (2006), 1749–1772.
Cosserat, E., Cosserat, F., Théorie des Corps Déformables. 1909, A Hermann edition, Paris, France, 250.
Coussy, O., 1995. Mechanics of Porous Continua. Chichester., p. 472.
Coussy, O., 2004. Poromechanics. London, England, p. 315.
Dalton, J., Essay IV. On the expansion of elastic fluids by heat. Mem. Lit. Philos. Soc. Manch. 5:2 (1802), 595–602.
Darcy, H., Dalmont, V., (eds.) Les Fontaines Publiques de la Ville de Dijon, 1856, Librairie des Corps Impériaux des Ponts et Chaussées et des Mines, Paris, France, 647.
De Borst, R., Mühlhaus, H.-B., Gradient-dependent plasticity: Formulation and algorithmic aspects. Internat. J. Numer. Methods Engrg. 35:3 (1992), 521–539.
De Borst, R., Sluys, L.J., Mühlhaus, H.-B., Pamin, J., Fundamental issues in finite element analyses of localization of deformation. Eng. Comput. 10:2 (1993), 99–121.
Desrues, J., Viggiani, G., Strain localization in sand: An overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Methods Geomech. 28:4 (2004), 279–321.
Detournay, E., Cheng, A., Fundamentals of poroelasticity. Comprehensive Rock Engineering: Principles, Practice and Projects. Vol. 2, 1993, Pergamon Press, Oxford, 113–171 chapter 5.
Ehlers, W., Volk, W., On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials. Int. J. Solids Struct. 35:34–35 (1998), 4597–4617.
EuropeanCommission, W., Ventilation Experiment in Opalinus Clay for the Disposal of Radioactive Waste in Underground Repositories (Project Funded By the European Community under the ‘EURATOM’ Programme 1998–2002 under Contract No. FIKWCT-2001-00126). Technical Report. 2005, Nuclear Sc edition, Luxembourg, 54.
Ewing, R.C., Whittleston, R.A., Yardley, B.W.D., Geological disposal of nuclear waste: A primer. Elements 12:4 (2016), 233–237.
Fick, A., Über diffusion [Translated: On liquid diffusion]. Poggendorff's Ann. Phys. Chem. 170:1 (1855), 59–86.
Finno, R.J., Wendell, W.H., Mooney, M.A., Viggiani, G., Strain localization and undrained steady state of sand. J. Geotech. Geoenviron. Eng. 122:6 (1996), 462–473.
Gallé, C., Gas breakthrough pressure in compacted Fo-Ca clay and interfacial gas overpressure in waste disposal context. Appl. Clay Sci. 17:1–2 (2000), 85–97.
Gerard, P., Impact des Transferts de Gaz sur le Comportement Poro-Mécanique des Matériaux Argileux Thèse Présentée Par. (Thésis présentée par), 2011, University of Liège, 301.
Gerard, P., Charlier, R., Su, K., Duveau, G., Giot, R., Chavant, C., Collin, F., Numerical modelling of coupled mechanics and gas tansfer around radioactive waste in long-term storage. J. Theoret. Appl. Mech. 38 (2008), 25–44.
Gerard, P., Harrington, J., Charlier, R., Collin, F., Hydro-mechanical modelling of the development of preferential gas pathways in claystone. Unsaturated Soils: Research and Applications, 2012, 175–180.
Gerard, P., Harrington, J., Charlier, R., Collin, F., Modelling of localised gas preferential pathways in claystone. Int. J. Rock Mech. Min. Sci. 67 (2014), 104–114.
Germain, P., The method of virtual power in continuum mechanics. Part 2 microstructure. Soc. Ind. Appl. Math. 25:3 (1973), 556–575.
Hill, R.H., General stability theory of uniqueness and stability in elasto-plastic solids. J. Mech. Phys. Solids 6 (1958), 239–249.
Hill, R., Hutchinson, J.W., Bifurcation phenomena in the plane tension test. J. Mech. Phys. Solids 23:4–5 (1975), 239–264.
IAEA, R., Scientific and technical basis for the geological disposal of radioactive wastes., 2003, International Atomic Energy Agency, New-York, 90.
Jia, Y., Bian, H.B., Duveau, G., Su, K., Shao, J.F., Hydromechanical modelling of shaft excavation in Meuse/Haute-Marne laboratory. Phys. Chem. Earth 33:SUPPL. 1 (2008), 422–435.
Jouan, G., Kotronis, P., Caillerie, D., Collin, F., A second gradient cohesive element for mode I crack propagation. Finite Elem. Anal. Des., 204(30), 2022, 103732.
Lekhnitskii, S.G., Theory of Elasticity of an Anisotropic Elastic Body. 1963, Holden-Day edition, San Fransisco, The USA, 793.
Levasseur, S., Collin, F., Charlier, R., Kondo, D., A micro-macro approach of permeability evolution in rocks excavation damaged zones. Comput. Geotech. 49 (2013), 245–252.
Lewis, R.W., Schrefler, B.A., The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. 2000, John Wiley & Sons, New-York, The United States, 477.
Li, X., et al. TIMODAZ: Thermal Impact on the Damaged Zone Around a Radioactive Waste Disposal in Clay Host Rocks. Deliverable 2. State of the Art on THMC: Technical report., 2007, Euratom European Project, 203.
Lisjak, A., Garitte, B., Grasselli, G., Müller, H.R., Vietor, T., The excavation of a circular tunnel in a bedded argillaceous rock (Opalinus Clay): Short-term rock mass response and FDEM numerical analysis. Tunn. Undergr. Space Technol. 45:February 2019 (2015), 227–248.
Lyapunov, A.M., The General Problem of the Stability of Motion. 1892, Taylor & Francis (1992) translated edition.
Marschall, P., Horseman, S., Gimmi, T., Characterisation of gas transport properties of the opalinus clay, a potential host rock formation for radioactive waste disposal. Oil Gas Sci. Technol. – Rev. IFP 60:1 (2005), 121–139.
Matsushima, T., Chambon, R., Caillerie, D., Large strain finite element analysis of a local second gradient model: Application to localization. Internat. J. Numer. Methods Engrg. 54:4 (2002), 499–521.
Mindlin, R.D., Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16:1 (1964), 51–78.
Mindlin, R.D., Second gradient of strain and surface-tension in linear elasticity. Int. J. Solids Struct. 1:4 (1965), 417–438.
Mualem, J., A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12:3 (1976), 513–522.
NEA Expert Group, J., Shallow Land Disposal of Radioactive Waste: Refrence Levels for the Acceptance of Long-lived Radionuclides: Technical report., 1986, Nuclear Energy Agency and Economic Cooperation and development, Paris, 76.
Olivella, S., Alonso, E.E., Gas flow through clay barriers. Géotechnique 58:3 (2008), 157–176.
Ortiz, L., Volckaert, G., Mallants, D., Gas generation and migration in Boom Clay, a potential host rock formation for nuclear waste storage. Eng. Geol. 64:2–3 (2002), 287–296.
Pardoen, B., Collin, F., Modelling the influence of strain localisation and viscosity on the behaviour of underground drifts drilled in claystone. Comput. Geotech. 85 (2017), 351–367.
Pardoen, B., Levasseur, S., Collin, F., Excavation damaged zone modelling including hydraulic permeability evolution in unsaturated argilaceous rock. Unsaturated Soils: Research and Applications - Proceedings of the 6th International Conference on Unsaturated Soils, UNSAT 2014, 2(Desrues), 2014, 1387–1393.
Pardoen, B., Levasseur, S., Collin, F., Using local second gradient model and shear strain localisation to model the excavation damaged zone in unsaturated claystone. Rock Mech. Rock Eng. 48:2 (2015), 691–714.
Pardoen, B., Seyedi, D.M., Collin, F., Shear banding modelling in cross-anisotropic rocks. Int. J. Solids Struct. 72 (2015), 63–87.
Pardoen, B., Talandier, J., Collin, F., Permeability evolution and water transfer in the excavation damaged zone of a ventilated gallery. Int. J. Rock Mech. Min. Sci. 85 (2016), 192–208.
Peerlings, R.H.J., De Borst, R., Brekelmans, W.A.M., De Vree, J.H.P., Gradient enhanced damage for quasi-brittle materials. Internat. J. Numer. Methods Engrg. 39:19 (1996), 3391–3403.
Pellet, F., Roosefid, M., Deleruyelle, F., On the 3D numerical modelling of the time-dependent development of the damage zone around underground galleries during and after excavation. Tunn. Undergr. Space Technol. 24:6 (2009), 665–674.
Pietruszczak, S.T., Mróz, Z., Finite element analysis of deformation of strain-softening materials. Internat. J. Numer. Methods Engrg. 17:3 (1981), 327–334.
Plassart, R., Fernandes, R., Giraud, A., Hoxha, D., Laigle, F., Hydromechanical modelling of an excavation in an underground research laboratory with an elastoviscoplastic behaviour law and regularization by second gradient of dilation. Int. J. Rock Mech. Min. Sci. 58 (2013), 23–33.
Rattez, H., Stefanou, I., Sulem, J., Veveakis, M., Poulet, T., Numerical analysis of strain localization in rocks with thermo-hydro-mechanical couplings using cosserat continuum. Rock Mech. Rock Eng. 51:10 (2018), 3295–3311.
Rice, J.R., Localization of plastic deformation. Koiter, W.T., (eds.) Theoretical and Applied Mechanics, Vol. 1, 1976, North-Holland Publishing Company, 207–220.
Rodwell, W.R., Harris, A.W., Horseman, S.T., Lalieux, P., Müller, W., Ortiz Amaya, L., Pruess, K., Gas Migration and Two-Phase Flow through Engineered and Geological Barriers for a Deep Repository for Radioctive Waste. A Joint EC/NEA Status Report: Technical report., 1999, European Commission, Brussels, Belgium, 429.
Rutqvist, J., Bäckström, A., Chijimatsu, M., Feng, X.T., Pan, P.Z., Hudson, J., Jing, L., Kobayashi, A., Koyama, T., Lee, H.S., Huang, X.H., Rinne, M., Shen, B., A multiple-code simulation study of the long-term EDZ evolution of geological nuclear waste repositories. Environ. Geol. 57:6 (2009), 1313–1324.
Sentís, M.L., Two-phase flow modeling with TOUGH2-MP of a deep geological repository within the first benchmark of the FORGE project. Nucl. Technol. 187:2 (2014), 117–130.
Shao, J.F., Zhu, Q.Z., Su, K., Modeling of creep in rock materials in terms of material degradation. Comput. Geotech. 30:7 (2003), 549–555.
Sieffert, Y., Buzzi, O., Collin, F., Numerical study of shear band instability and effect of cavitation on the response of a specimen under undrained biaxial loading. Int. J. Solids Struct. 51:9 (2014), 1686–1696.
Sieffert, Y., Marinelli, F., Chambon, R., Local second gradient models for thermo-hydro-mechanical coupling in rock like materials. Bonelli, S., Dascalu, C., Nicot, F., (eds.) Advances in Bifurcation and Degradation in Geomaterials. Proceedings of the 9th International Workshop on Bifurcation and Degradation in Geomaterials., 2011, 219–226.
Talandier, J., La Production et le Transfert de Gaz Dans un Stockage et Dans la Couche du Callovo-Oxfordien - Lien Avec le Transitoire Hydraulique - Site de Meuse / Haute-Marne. Rapport Andra n°C.NT.ASCM.03.0042: Technical report., 2005, Andra.
Triantafyllidis, N., Bifurcation phenomena in pure bending. J. Mech. Phys. Solids 28:3–4 (1980), 221–245.
Tsang, C.F., Bernier, F., Davies, C., 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 (2005), 109–125.
Van Eekelen, H.A.M., Isotropic yield surfaces in three dimensions for use in soil mechanics. Int. J. Numer. Anal. Methods Geomech. 4:1 (1980), 89–101.
Van Genuchten, M.T., Predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:5 (1980), 892–898.
Vardoulakis, I., Goldscheider, M., Gudehus, G., Formation of shear bands in sand bodies as a bifurcation problem. Int. J. Numer. Anal. Methods Geomech. 2:2 (1978), 99–128.
Volckaert, G., Ortiz, L., Canniere, P.D., Put, M., Horseman, S.T., Harrington, J.F., Fioravante, V., Impey, M., MEGAS: Modelling and Experiments on GAS Migration in Repository Host Rocks. Final Report Phase 1: Technical report., 1995, Eur. Comm., [Rep.] EUR 16235 EN, 464.
Webber, J.B.W., A bi-symmetric log transformation for wide-range data. Meas. Sci. Technol., 24(2), 2013.
Xue, Y., Dang, F., Shi, F., Li, R., Cao, Z., Evaluation of gas migration and rock damage characteristics for underground nuclear waste storage based on a coupled model. Sci. Technol. Nucl. Install. 2018 (2018), 1–11.
Yu, L., Weetjens, E., Perko, J., Mallants, D., Comparison of numerical tools through thermo-hydro-gas transport modeling for a geological repository in boom clay. Nucl. Technol. 174:3 (2011), 411–423.
Zbib, H.M., Aifantis, E.C., On the localization and postlocalization behavior of plastic deformation. Part I. On the initiation of shear bands. Part II. On the evolution and thickness of shear bands. Aifantis, S., et al. (eds.) Res Mechanica, Vol. 23, 1988, Special Issue on Material Instabilities, 261–277; 279–292.
Zervos, A., Papanastasiou, P., Vardoulakis, I., Modelling of localisation and scale effect in thick-walled cylinders with gradient elastoplasticity. Int. J. Solids Struct. 38 (2001), 5081–5095.
Zhou, H., Jia, Y., Shao, J.F., A unified elastic–plastic and viscoplastic damage model for quasi-brittle rocks. Int. J. Rock Mech. Min. Sci. 45:8 (2008), 1237–1251.
