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Probing the Hydro-mechanical Response of a Clayey Rock for Radioactive Waste Disposal Using a Transversely Isotropic Damage Constitutive Model

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Abstract

To develop a geological nuclear waste disposal facility from scratch, the hydro-mechanical properties of the host rock are fundamental for its initial construction, long-term system evolution, closure, and post-closure phases. In this paper, a transversely isotropic damage constitutive model was developed to describe the nonlinear behavior of clayey rock, based on the modified Drucker–Prager Cap model. Considering the self-sealing effect, a hydraulic conductivity evolution law of typical clayey rock was established based on in situ measurements. These theoretical models were further implemented in the finite element method software ABAQUS FEA (Finite Element Analysis) utilizing the subroutine USDFLD, which is a user subroutine to redefine field variables at a material point in ABAQUS. The hydro-mechanical response of an underground research laboratory during excavation and operation was reproduced by three-dimensional numerical simulation to validate the proposed models. The results highlighted that the developed theoretical model could efficiently reproduce the evolution of pore water pressure and deformation, compared to the in situ measurements in the excavation damaged/disturbed zone (EDZ) and hydraulic disturbed zone (HDZ) driven by tunnel excavation.

Highlights

  • A damage constitutive model and a permeability evolution law are developed.

  • Theoretical models are implemented in the software ABAQUS FEA.

  • Hydro-mechanical responses of an underground research laboratory during excavation and operation are simulated.

  • Comparison with the in-situ measurements highlights the theories’ efficiency.

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Data availability

The data that support the findings of this study are available from the authors upon reasonable request.

Abbreviations

\({\mathbf{C}}\) :

Elastic tensor

\({\mathbf{C}}_{0}\) :

Initial elastic tensor

\(c\) :

Cohesion

\(c_{0}\) :

Initial cohesion

\(D_{e}\) :

Elastic damage

\(D_{p}\) :

Plastic damage

\(E_{h0}\) :

Initial horizontal elastic moduli

\(E_{v0}\) :

Initial vertical elastic moduli

\(\overline{e}\) :

Energy factor

\(\overline{e}_{oe}\) :

Energy factor threshold for the onset of elastic damage

\({\varvec{e}}_{{\text{p}}}^{{}}\) :

Deviatoric plastic strain tensor

\(F_{s}^{{}}\) :

Shearing yield surface

\(F_{c}^{{}}\) :

Drucker–Prager Cap yield surface

\(f_{0}\) :

Parameter for non-dimensionalization

\(G_{s}^{{}}\) :

Plastic potential in the shearing failure region

\(G_{c}^{{}}\) :

Plastic potential in the shearing cap region

\(G_{vh0}\) :

Initial shear modulus in the vertical plane

\(k_{0h}\) :

Initial horizontal hydraulic conductivity

\(k_{0v}\) :

Initial vertical hydraulic conductivity

\(k_{h}\) :

Horizontal hydraulic conductivity

\(k_{hd}\) :

Horizontal hydraulic conductivity considering damage

\(k_{v}\) :

Vertical hydraulic conductivity

\(k_{vd}\) :

Vertical hydraulic conductivity considering damage

\(p^{\prime}\) :

Mean effective stress

\(p_{c}\) :

Preconsolidation pressure

\(q\) :

Deviatoric stress

\(R_{0}\) :

Connecting gallery radius

\(r\) :

Distance from the gallery center

s :

Deviatoric stress tensor

sij :

Deviatoric stress components

\(t\) :

Time

\(\alpha\) :

Slope of the shearing surface

\({{\varvec{\updelta}}}\) :

Kronecker delta

\({{\varvec{\upvarepsilon}}}_{p}\) :

Plastic strain tensor

\(\kappa\) :

Slope and intercept of the shearing surface

\(v_{hh0}\) :

Initial Poisson ratios in the horizontal planes

\(v_{vh0}\) :

Initial Poisson ratios in the vertical planes

\(\xi_{p}\) :

Equivalent deviatoric plastic strain

σ :

Stress tensor

\(\sigma_{ij}\) :

Stress components

\(\varphi\) :

Friction angle

\(\varphi_{0}\) :

Initial friction angle

b, c p, c p1, \(\overline{e}_{oe}\) , h p0, p c0, R, R c0, \(\beta_{M}\) :

Parameters for the transversely isotropic damage constitutive model

A', a h, a v, a 3, m, β' :

Parameters for the hydraulic conductivity evolution law

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Acknowledgements

The authors thank the European Underground Research Infrastructure for Disposal of Nuclear Waste in Clay Environment (EURIDICE) for collaborating on the long-term HM behavior of Boom Clay. Owing to this international cooperation, we could perform the research in this paper. The financial support of the National Natural Science Foundation of China (No. 42377179, 51979266, and 42293355) is greatly acknowledged. Appreciations are extended to Sweetland K, who has given valuable suggestions and worked hard on improving the English of this article.

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, China

    Hongdan Yu, Weizhong Chen, Xianjun Tan & Jianping Yang

  2. Anhui Transportation Consulting & Design Institute Co., LTD., Engineering Technology Research Institute, Hefei, 230088, Anhui, China

    Fanfan Li

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  1. Hongdan Yu
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Yu, H., Chen, W., Li, F. et al. Probing the Hydro-mechanical Response of a Clayey Rock for Radioactive Waste Disposal Using a Transversely Isotropic Damage Constitutive Model. Rock Mech Rock Eng 57, 131–143 (2024). https://doi.org/10.1007/s00603-023-03557-z

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