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Transversely Isotropic Poroelastic Behaviour of the Callovo-Oxfordian Claystone: A Set of Stress-Dependent Parameters

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Abstract

In the framework of a deep geological radioactive waste disposal in France, the hydromechanical properties of the designated host rock, the Callovo-Oxfordian claystone (COx), are investigated in laboratory tests. Experiments presented in this study are carried out to determine several coefficients required within a transversely isotropic material model. They include isotropic compression tests, pore pressure tests, and deviatoric loading tests parallel and perpendicular to the bedding plane. We emphasize the adapted experimental devices and testing procedures, necessary to detect small strains under high pressures, on a material, which is sensitive to water and has a very low permeability. In particular, we discovered a significant decrease of elastic stiffness with decreasing effective stress, which was observed to be reversible. In both isotropic and deviatoric tests, a notable anisotropic strain response was found. The Young modulus parallel to bedding was about 1.8 times higher than the one perpendicular to the bedding plane. A notably low Poisson ratio perpendicular to the bedding plane with values between 0.1 and 0.2 was evidenced. While the anisotropy of the back-calculated Biot coefficient was found to be low, a significant anisotropy of the Skempton’s coefficient was computed. The performed experiments provide an overdetermined set of material parameters at different stress levels. Using all determined parameters in a least square error regression scheme, seven independent elastic coefficients and their effective stress dependency are characterized. Parameters measured under isotropic loading are well represented by this set of coefficients, while the poroelastic framework with isotropic stress dependency is not sufficient to describe laboratory findings from triaxial loading.

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Abbreviations

\(\varepsilon _i\) :

Strain vector containing the six independent components of the second rank strain tensor

\(M_{ij}\) :

Drained stiffness tensor in matrix format

\(C_{ij}\) :

Drained compliance tensor in matrix format

\(\sigma _i\) :

Stress vector containing the six independent components of the second rank stress tensor

\(b_i\) :

Biot’s coefficient for i-th direction

\(p_f\) :

Pore fluid pressure

\(E_{i}\) :

Drained Young’s modulus in the i-th direction

\(\nu _{zh}\) :

Drained Poisson’s ratio perpendicular to bedding

\(\nu '_{zh}\) :

Apparent drained Poisson’s ratio under loading parallel to bedding

\(\nu _{hh}\) :

Drained Poisson’s ratio parallel to bedding

G :

Shear modulus perpendicular to bedding

\(G'\) :

Shear modulus parallel to bedding

\({\phi _0}\) :

Porosity

M :

Biot’s undrained modulus M

N :

Biot’s skeleton modulus N

\(K_{f}\) :

Bulk modulus of the pore fluid

\(K_{\phi }\) :

Unjacketed pore modulus

\(B_i\) :

Skempton’s coefficient for i-th direction

\(K_{s}\) :

Unjacketed bulk modulus

\(M_{ij}^{u}\) :

Undrained stiffness tensor in matrix format

\(C_{ij}^{u}\) :

Undrained compliance tensor in matrix format

\(E_{u,i}\) :

Undrained Young’s modulus in the i-th direction

\(\nu _{u,zh}\) :

Undrained Poisson’s ratio perpendicular to bedding

\(\nu _{u,hh}\) :

Undrained Poisson’s ratio parallel to bedding

\(\sigma '\) :

Terzaghi isotropic effective stress

\(\sigma \) :

Isotropic total stress

\(\varepsilon _v\) :

Volumetric strain

\(K_{d}\) :

Isotropic drained bulk modulus

H :

Biot’s pore pressure loading modulus

b :

Isotropic Biot’s coefficient

V :

Specimen volume

\(m_f\) :

Pore fluid mass

\(K_{u}\) :

Isotropic undrained bulk modulus

B :

Isotropic Skempton’s coefficient

\(D_{i}\) :

Drained isotropic compression modulus in the i-th direction

\(U_{i}\) :

Undrained isotropic compression modulus in the i-th direction

\(H_{i}\) :

Biot’s pore pressure loading modulus in the i-th direction

\(R_{D}\) :

Anisotropy ratio in drained isotropic compression

\(R_{U}\) :

Anisotropy ratio in undrained isotropic compression

\(R_{H}\) :

Anisotropy ratio in pore pressure loading

\(R_{E}\) :

Anisotropy ratio of drained Young’s moduli

q :

Deviatoric stress

\(E_z^{\infty }\), \(E_z^{0}\), \(\beta \) :

Model parameters for regression analysis

\(\rho \) :

Wet density

\(\rho _d\) :

Dry density

w :

Water content

\(S_r\) :

Saturation degree

s :

Suction

S :

Standard deviation of the estimate

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Authors and Affiliations

  1. Laboratoire Navier, 6-8 Avenue Blaise-Pascal, Cité Descartes 77455 Champs-sur-Marne, Paris, France

    Philipp Braun, Siavash Ghabezloo, Pierre Delage & Jean Sulem

  2. Andra, Meuse/Haute-Marne Underground Research Laboratory, Bure, France

    Nathalie Conil

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  1. Philipp Braun
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  2. Siavash Ghabezloo
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  3. Pierre Delage
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Correspondence to Philipp Braun.

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Braun, P., Ghabezloo, S., Delage, P. et al. Transversely Isotropic Poroelastic Behaviour of the Callovo-Oxfordian Claystone: A Set of Stress-Dependent Parameters. Rock Mech Rock Eng 54, 377–396 (2021). https://doi.org/10.1007/s00603-020-02268-z

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