Abstract
For the performance assessment of a high radioactive waste underground repository, the excavation induced damage zone surrounding an underground drift as well as its evolution, particularly has been researched. After emplacing nuclear waste in underground cells, the disposal will be closed by the sealing system, in which the main element is the bentonite core. Bentonite core will offer a swelling pressure against the walls of underground drifts during the resaturation process. This study concentrates on the numerical analysis of the self-sealing of excavation induced damage zone under mechanical compression and hydration on the basis of a particular CDZ in-situ experiment, which has been made within the Meuse/Haute-Marne Underground Research Laboratory. This is the first time that the numerical modelling has been adopted for simulating the large scale self-sealing of the Callovo-Oxfordian claystone. In this study, a plastic damage model is applied to represent the mechanical behaviour of Callovo-Oxfordian claystone (COx). Meanwhile, a supplemented deformation model combined with the standard Biot model to represent the significant deformation of COx during water content changing. Computation of crack parameters (opening, orientation) and permeability of unsaturated fractured COx are performed using post-processing from damage variable in accordance with the fracture energy regularization and the cubic law, respectively. The validation of the proposed model is carried out by numerical simulation of: (1) COx sample deformation during a resaturation process under constant vertical stresses, (2) global water permeability tests of the self-sealing of a fractured COx sample during water injection, (3) CDZ in-situ experiment to describe the self-sealing of EDZ under mechanical compression and hydration. According to comparisons between the numerical and experimental findings, the capability of the proposed model to depict the self-sealing of the fractured COx claystone correctly, and the global water permeability of EDZ decrease in the resaturation process explains the accomplishment of the self-sealing of excavation induced damage zone. The present model is shown as a useful tool to evaluate the performance of nuclear waste disposal when taking into account the self-sealing process.
Highlights
-
COx swelling.
-
Self-sealing of fractured COx claystone in nuclear waste disposal scheme.
-
CDZ experiment and the corresponding numerical simulation.
Similar content being viewed by others
Abbreviations
- \(P_{c}\) :
-
Capillary pressure
- \(u_{a}\) :
-
Pore air pressure
- \(u_{w}\) :
-
Pore water pressure
- C :
-
Water mass capacity
- t :
-
Time
- k :
-
Hydraulic conductivity
- ρ :
-
Water density
- g :
-
Acceleration of gravity
- z :
-
Water level
- θ :
-
Volumetric water content
- \(S_{e}\) :
-
Effective saturation degree
- \(P_{{c\left( {{\text{aev}}} \right)}}\) :
-
Air-entry value of capillary pressure
- \(\theta_{s}\) :
-
Saturated water content
- \(\theta_{r}\) :
-
Residual water content
- \(\theta_{m}\) :
-
Maximum water content
- \({\varvec{\varepsilon}}_{{{\text{added}}\left( {{\text{desaturation}}} \right)}}\) :
-
Added strain from desaturation
- \({\varvec{\varepsilon}}_{{\text{added(resaturation)}}}\) :
-
Added strain from resaturation
- \({\varvec{\varepsilon}}_{{{\text{COX}}\left( {{\text{desaturation}}} \right)}}\) :
-
COx strain from desaturation
- \({\varvec{\varepsilon}}_{{{\text{COX}}\left( {{\text{resaturation}}} \right)}}\) :
-
COx strain from resaturation
- \({\varvec{\varepsilon}}_{{{\text{added}}\left( {\text{i}} \right)}}\) :
-
Added strain
- \({\varvec{\varepsilon}}_{{{\text{Biot}}}}\) :
-
Biot strain
- \(a_{i} ,b_{i}\) :
-
Parameters
- \({\varvec{\sigma}}\) :
-
Total stress
- \({\varvec{\sigma}}^{{{\varvec{e}}ff}}\) :
-
Skeleton effective stress
- \(S_{r}\) :
-
Saturation degree
- \(\kappa\) :
-
Intrinsic permeability
- \(\kappa_{R}\) :
-
Relative permeability
- B :
-
Biot coefficient
- \(\Delta {\varvec{\varepsilon}}_{{{\text{added}}}}\) :
-
Added deformation
- K :
-
Bulk modulus
- I :
-
Unit matrix
- E :
-
COx Young modulus
- \({\text{RH }}\) :
-
Relative humidity
- \(F\left( {\overline{\sigma }} \right)\) :
-
Plastic flow
- \(\overline{\sigma }_{v}\) :
-
Von Mises equivalent stress
- \({\varvec{\varepsilon}}^{p}\) :
-
Plastic strain
- \({\varvec{\sigma}}_{ij}^{eff}\) :
-
Effective stress in damage model
- \(\overline{\varvec{\sigma }}_{ij}^{ + }\) :
-
The tensile part of \({\overline{\sigma }}_{{{\text{ij}}}}\)
- \(\overline{\varvec{\sigma }}_{ij}^{ - }\) :
-
The compressive part of \({\overline{\sigma }}_{{{\text{ij}}}}\)
- \(\sigma_{t }\) :
-
Tensile stress
- \(G_{f}\) :
-
Fracture energy
- E :
-
Young modulus
- d :
-
Damage
- β :
-
Hardening/softening variable
- \(\varepsilon_{d0}\) :
-
Tensile strain threshold
- \({\varvec{\varepsilon}}_{{{\text{kl}}}}\) :
-
Total strain of the skeleton phase
- h :
-
The size of numerical mesh element
- \(\tilde{\varvec{\varepsilon }}\) :
-
Equivalent strain
- \({\varvec{\varepsilon}}_{{\text{I}}}^{ + } ,{\varvec{\varepsilon}}_{{{\text{II}}}}^{ + } ,{ }{\varvec{\varepsilon}}_{{{\text{III}}}}^{ + }\) :
-
Postive principal elastic strains
- \({\varvec{\varepsilon}}_{ij}^{{{\text{uco}}}}\) :
-
Unitary Crack Opening strain tensor
- \({\varvec{\delta}}_{n}\) :
-
The value of the normal crack opening displacement
- \({\varvec{\sigma}}_{\theta }\) :
-
Tangential stress
References
Andra (2005) Dossier 2005: Argile. Référentiel du site de Meuse/Haute-Marne. Le site de Meuse/Haute-Marne: histoire géologique et état actuel. Agence nationale pour la gestion des déchets radioactifs (France)
Armand G, Leveau F, Nussbaum C et al (2014) Geometry and properties of the excavation-induced fractures at the Meuse/Haute-Marne URL drifts. Rock Mech Rock Eng 47(1):21–41
Armand G, Bumbieler F, Conil N et al (2017a) Main outcomes from in situ thermo-hydro-mechanical experiments programme to demonstrate feasibility of radioactive high-level waste disposal in the Callovo-Oxfordian claystone. J Rock Mech Geotech Eng 9(3):415–427
Armand G, Conil N, Talandier J et al (2017b) Fundamental aspects of the hydromechanical behaviour of Callovo-Oxfordian claystone: from experimental studies to model calibration and validation. Comput Geotech 85:277–286
Baechler S, Lavanchy JM, Armand G et al (2011) Characterisation of the hydraulic properties within the EDZ around drifts at level− 490 m of the Meuse/Haute-Marne URL: a methodology for consistent interpretation of hydraulic tests. Phys Chem Earth Parts a/b/c 36(17–18):1922–1931
Benkemoun N, Al Khazraji H, Poullain P et al (2018) 3-D mesoscale simulation of crack-permeability coupling in the Brazilian splitting test[J]. Int J Numer Anal Meth Geomech 42(3):449–468
Biot MA (1941) General theory of three dimensional consolidation. J Appl Phys 12(2):155–164
Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26(2):182–185
Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J Acoust Soc Am 28(2):179–191
Biot MA (1962) Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33(4):1482–1498
Bishop AW (1955) Lecture delivered in Oslo, Norway, entitled “The principle of effective stress. Teknisk Ukeblad 39(1959):859–863
Bishop AW, Blight GE (1963) Some aspects of effective stress in saturated and partly saturated soils. Geotechnique 13(3):177–197
Butscher C, Scheidler S, Farhadian H et al (2017) Swelling potential of clay-sulfate rocks in tunneling in complex geological settings and impact of hydraulic measures assessed by 3D groundwater modeling. Eng Geol 221:143–153
Coussy O (1991) Mécanique des milieux poreux. Editions Technip
Coussy O (2011) Mechanics and physics of porous solids. John Wiley & Sons
Choinska M, Dufour F, Pijaudier-Cabot G (2007) Matching permeability law from diffuse damage to discontinuous crack opening. In: 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures.
Conil N, Vitel M, Plua C et al (2020) In situ investigation of the THM behavior of the Callovo-Oxfordian claystone. Rock Mech Rock Eng 53(6):2747–2769
Crisci E, Ferrari A, Giger SB et al (2019) Hydro-mechanical behaviour of shallow Opalinus Clay shale. Eng Geol 251:214–227
Dangla P, Coussy O, Olchitzky E et al (1999) A micromechanical approach to the behaviour of unsaturated porous media. Symposium on theoretical and numerical methods in continuum mechanics of porous materials. IUTAM, Stuttgart
Darde B, Dangla P, Roux JN et al (2020) Modelling the behaviour of bentonite pellet-powder mixtures upon hydration from dry granular state to saturated homogeneous state. Eng Geol 278:105847
Davy CA, Skoczylas F, Barnichon JD et al (2007) Permeability of macro-cracked argillite under confinement: gas and water testing. Phys Chem Earth Parts a/b/c 32(8–14):667–680
De La Vaissière R, Morel J, Noiret A et al (2014) Excavation-induced fractures network surrounding tunnel: properties and evolution under loading. Geol Soc Lond Spec Publ 400(1):279–291
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
Descostes M, Blin V, Bazer-Bachi F et al (2008) Diffusion of anionic species in Callovo-Oxfordian argillites and Oxfordian limestones (Meuse/Haute–Marne, France). Appl Geochem 23(4):655–677
Di Donna A, Charrier P, Salager S et al (2019) Self-sealing capacity of argillite samples. In: 7th International Symposium on Deformation Characteristics of Geomaterials
Diederichs MS (2003) Manuel rocha medal recipient rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381
Fahy C, Gallipoli D, Grassl P (2013) A lattice model for liquid transport in unsaturated porous materials. Advances in unsaturated soils. CRC Press, London, pp 525–530
Favero V, Ferrari A, Laloui L (2016) On the hydro-mechanical behaviour of remoulded and natural Opalinus Clay shale. Eng Geol 208:128–135
Fichant S, La Borderie C, Pijaudier-Cabot G (1999) Isotropic and anisotropic descriptions of damage in concrete structures. Mech Cohes-Frict 4(4):339–359
Fouché O, Wright H, Le Cléac’h JM et al (2004) Fabric control on strain and rupture of heterogeneous shale samples by using a non-conventional mechanical test. Appl Clay Sci 26(1–4):367–387
Gens A, Alonso EE (1992) A framework for the behaviour of unsaturated expansive clays. Can Geotech J 29(6):1013–1032
Giot R, Auvray C, Conil N et al (2018) Multi-stage water permeability measurements on claystone by steady and transient flow methods. Eng Geol 247:27–37
Grasberger S, Meschke G (2004) Thermo-hygro-mechanical degradation of concrete: From coupled 3D material modelling to durability-oriented multifield structural analyses. Mater Struct 37(4):244–256
Hammood MN, Benkemoun N, Amiri O (2016) A study of the effect of crack-induced diffusivity on the service life prediction. Acad J Civil Eng 34(1):106–116
He Y, Ye W, Chen Y et al (2020) Effects of NaCl solution on the swelling and shrinkage behavior of compacted bentonite under one-dimensional conditions. Bull Eng Geol Env 79(1):399–410
Huang Z, Jiang Z, Zhu S et al (2016) Influence of structure and water pressure on the hydraulic conductivity of the rock mass around underground excavations. Eng Geol 202:74–84
Jia LY, Chen YG, Ye WM et al (2019) Effects of a simulated gap on anisotropic swelling pressure of compacted GMZ bentonite. Eng Geol 248:155–163
La Borderie C, Matallah M (2017) Simulation at the meso-scale of the crack induced permeability in concrete, estimate of the non linear evolution of the flow coefficient. In: CFRAC 2017
Matallah M, La Borderie C. 3D numerical modeling of the crack-permeability interaction in fractured concrete. In: Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures (Framcos 9), Berkeley, CA, USA, pp 22–25
Matallah M, La Borderie C (2009) Inelasticity–damage-based model for numerical modeling of concrete cracking. Eng Fract Mech 76(8):1087–1108
Nadai A (1950) Theory of fracture and flow of solids. Book Co., New York
Pardoen B, Talandier J, Collin F (2016) Permeability evolution and water transfer in the excavation damaged zone of a ventilated gallery. Int J Rock Mech Min Sci 85:192–208
Pham QT, Vales F, Malinsky L et al (2007) Effects of desaturation–resaturation on mudstone. Phys Chem Earth Parts a/b/c 32(8–14):646–655
Rastiello G, Boulay C, Dal Pont S et al (2014) Real-time water permeability evolution of a localized crack in concrete under loading. Cem Concr Res 56:20–28
Secchi S, Schrefler BA (2012) A method for 3-D hydraulic fracturing simulation. Int J Fract 178(1–2):245–258
Seyedi DM, Plúa C, Vitel M et al (2021) Upscaling THM modeling from small-scale to full-scale in-situ experiments in the Callovo-Oxfordian claystone. Int J Rock Mech Min Sci 144:104582
Souley M, Vu MN, Armand G (2020) 3D anisotropic modelling of deep drifts at the Meuse/Haute-Marne URL. In: 5th International Itasca Symposium, Vienna, Austria
Souza RFC, Pejon OJ (2020) Pore size distribution and swelling behavior of compacted bentonite/claystone and bentonite/sand mixtures. Eng Geol 275:105738
Sun H, Liu X, Ye Z, Wang E (2021a) Experimental investigation of the nonlinear evolution from pipe flow to fissure flow during carbonate rock failures. Bull Eng Geol Environ 80:4459–4470
Sun H, Du WS, Liu C (2021b) Uniaxial compressive strength determination of rocks using X-ray computed tomography and convolutional neural networks. Rock Mech Rock Eng 54:4225–4237
Sun H, Liu X, Ye Z et al (2022) A new proposed method for observing fluid in rock fractures using enhanced x-ray images from digital radiography. Geomech Geophys Geo-Energy Geo-Resour 8:10
Trivellato E, Pouya A, Vu MN et al (2019) A softening damage-based model for the failure zone around deep tunnels in quasi-brittle claystone. Tunnels and underground cities: engineering and innovation meet archaeology architecture and art. CRC Press, London, pp 4242–4251
Van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892–898
Vinsot A, Leveau F, Bouchet A et al (2014) Oxidation front and oxygen transfer in the fractured zone surrounding the Meuse/Haute-Marne URL drifts in the Callovian-Oxfordian argillaceous rock. Geol Soc Lond Spec Publ 400(1):207–220
Vogel T, Gerke HH, Zhang R et al (2000) Modeling flow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties. J Hydrol 238(1–2):78–89
Volckaert G, Bernier F, Sillen X et al (2004) Similarities and differences in the behaviour of plastic and indurated clays. In: 6th European Commission Conference on the Management and Disposal of Radioactive Waste (Euradwaste’04), Community Policy and Research & Training Activities.
Vu MN, Guayacán Carrillo LM, Armand G (2020) Excavation induced over pore pressure around drifts in the Callovo-Oxfordian claystone. Eur J Environ Civil Eng. https://doi.org/10.1080/19648189.2020.1784800
Wang Q, Tang AM, Cui YJ et al (2012) Experimental study on the swelling behaviour of bentonite/claystone mixture. Eng Geol 124:59–66
Wang H, La Borderie C, Gallipoli D et al (2020) Numerical modelling of the hydro-mechanical behaviour of unsaturated COx. Geotechnical Research 8(1):3–15
Wang H, de La Vaissière R, Vu MN et al (2022) Numerical modelling and in-situ experiment for self-sealing of the induced fracture network of drift into the Callovo-Oxfordian claystone during a hydration process. Comput Geotech 141:104487
Wileveau Y, Cornet FH, Desroches J et al (2007) Complete in situ stress determination in an argillite sedimentary formation. Phys Chem Earth Parts a/b/c 32(8–14):866–878
Witherspoon PA, Wang JSY, Iwai K et al (1980) Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16(6):1016–1024
Ye Z, Liu X, Dong Q, Wang E, Sun H (2022) Hydro-damage properties of red-bed mudstone failures induced by nonlinear seepage and diffusion effect. Water 14:351
Yin ZY, Jin YF, Shen JS et al (2018) Optimization techniques for identifying soil parameters in geotechnical engineering: comparative study and enhancement. Int J Numer Anal Meth Geomech 42(1):70–94
Zhang CL (2013) Sealing of fractures in claystone. J Rock Mech Geotech Eng 5(3):214–220
Zhang CL, Wieczorek K, Xie ML (2010) Swelling experiments on mudstones. J Rock Mech Geotech Eng 2(1):44–51
Zhang F, Jia Y, Bian HB et al (2013) Modeling the influence of water content on the mechanical behavior of Callovo-Oxfordian argillite. Phys Chem Earth Parts a/b/c 65:79–89
Zhang CL, Armand G, Conil N et al (2019) Investigation on anisotropy of mechanical properties of Callovo-Oxfordian claystone. Eng Geol 251:128–145
Zhang F, Cui YJ, Conil N et al (2020) Assessment of swelling pressure determination methods with intact Callovo-Oxfordian claystone. Rock Mech Rock Eng 53(4):1879–1888
Zhang F, Cui YJ, Conil N et al (2021) Effect of fracture voids on the swelling behaviour of Callovo-Oxfordian claystone. Eng Geol 280:105935
Acknowledgements
The authors gratefully acknowledge the funding by the French National Radioactive Waste Management Agency (Andra), China Scholarship Committee (CSC), The Research Fund for Innovation Platform of Hainan Academician (Approval No. YSPTZX202106), Scientific Research Fund of Hainan University (Approval No. KYQD(ZR)-21067 and KYQD(ZR)-22122), Major Science and Technology Projects of Hainan Province, China (No. ZDKJ2021023). The author wants to express appreciation as well to his PhD supervisors Christian La Borderie and Domenico Gallipoli for their patient supervision.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix
Parameters Appendix
Sign | Value | |
---|---|---|
a | \(1.86237\times {10}^{7}Pa\) | Wang et al. (2020) |
\({a}_{k}\) | \(-1.54\mathrm{\%}\) | |
\({a}_{w}\) | \({a}_{w}=-1.534\mathrm{\%}\) | |
B | 0.85 | |
\({b}_{k}\) | \(2.5\times {10}^{6} \mathrm{Pa}\) | |
\({b}_{w}\) | \(2.748\times {10}^{7 }\mathrm{Pa}\) | |
\({E}_{saturated}\) | \(4.32\times {10}^{9}\mathrm{ Pa}\) | |
g | 9.8 m/s2 | |
\({G}_{f0}\) | 6.4 N/m | Wang et al. (2020) |
\({\kappa }_{0}\) | \(2\times {10}^{-20}{\mathrm{ m}}^{2}\) | Andra (2005) |
m | 0.45 | |
\({P}_{gf}\) | \(-4.8{\times 10}^{7} \mathrm{Pa}\) | Wang et al. (2020) |
\({P}_{t}\) | \(-5.9\times {10}^{7}\mathrm{ Pa}\) | Wang et al. (2020) |
R | \(8.314J/(\mathrm{mol}\times \mathrm{K})\) | |
\({R}_{0}\) | 2.5 m | Armand et al. (2014) |
T | \(298\mathrm{ K}\) | |
\(\upmu\) | \(1\times {10}^{-3}\mathrm{t}/\mathrm{m}\times \mathrm{s}\) | |
\(\upupsilon\) | 0.295 | |
\({W}_{W}\) | \(18\mathrm{g}/\mathrm{mol}\) | |
\({W}_{f}\) | 278 μm | |
\(\upgamma\) | \(1.45\) | |
\(\mathrm{\alpha }1\) | 15 | |
\({\sigma }_{t0}\) | \(5.\times {10}^{5} \mathrm{Pa}\) | Wang et al. (2020) |
\({\sigma }_{h}\) | 12.5 MPa | Armand et al. (2014) |
\({\sigma }_{H}\) | 16 MPa | Armand et al. (2014) |
\({\sigma }_{v}\) | 12.5 MPa | Armand et al. (2014) |
Rights and permissions
About this article
Cite this article
Wang, H., Dong, Q., de La Vaissière, R. et al. Investigation of Hydro-mechanical Behaviour of Excavation Induced Damage Zone of Callovo-Oxfordian Claystone: Numerical Modeling and In-situ Experiment. Rock Mech Rock Eng 55, 6079–6102 (2022). https://doi.org/10.1007/s00603-022-02938-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-022-02938-0