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Investigation of Hydro-mechanical Behaviour of Excavation Induced Damage Zone of Callovo-Oxfordian Claystone: Numerical Modeling and In-situ Experiment

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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.

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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

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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.

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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

Armand et al. (2014), Seyedi et al. (2021)

\({b}_{k}\)

\(2.5\times {10}^{6} \mathrm{Pa}\)

 

\({b}_{w}\)

\(2.748\times {10}^{7 }\mathrm{Pa}\)

 

\({E}_{saturated}\)

\(4.32\times {10}^{9}\mathrm{ Pa}\)

Armand et al. (2017a, b)

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)

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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

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