Thermo-Poro-Elastic Behaviour of a Transversely Isotropic Shale: Thermal Expansion and Pressurization
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ORIGINAL PAPER
Thermo‑Poro‑Elastic Behaviour of a Transversely Isotropic Shale: Thermal Expansion and Pressurization Philipp Braun1 · Siavash Ghabezloo1 · Pierre Delage1 · Jean Sulem1 · Nathalie Conil2 Received: 5 May 2019 / Accepted: 5 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The Callovo-Oxfordian (COx) claystone is considered as a candidate host rock for a deep geological radioactive waste repository in France. Due to the exothermic waste packages, the rock is expected to be submitted to temperatures up to 90 °C. The temperature rise induces deformations of the host rock, together with an increase in pore pressures, involving complex thermo-hydro-mechanical (THM) couplings. This study aims to better characterize the THM response of the COx claystone to temperature changes in the laboratory. To this end, claystone specimens were tested in a temperature controlled, high pressure isotropic compression cell, under stress conditions close to the in-situ ones. Thermal loads were applied on the specimens along different heating and cooling paths. A temperature corrected strain gage system provided precise measurements of the anisotropic strain response of the specimens. Drained and undrained thermal expansion coefficients in both transversely isotropic directions were determined. The measurement of pore pressure changes in undrained condition yielded the thermal pressurization coefficient. All parameters were analysed for their compatibility within the thermo-poro-elastic framework, and their stress and temperature dependency was identified. Keywords Thermo-poro-elasticity · Transverse isotropy · Thermal pressurization · Claystone List of Symbols 𝜀i Strain vector containing the 6 independent components of the second rank strain tensor 𝜀v Volumetric strain Cij Drained compliance tensor in matrix format 𝜎i Stress vector containing the 6 independent components of the second rank stress tensor 𝜎 Isotropic confining stress 𝜎 ′ Terzaghi isotropic effective stress bi Biot’s coefficient for i-th direction pf Pore fluid pressure T Temperature 𝛼d,i Linear drained thermal expansion coefficient in the i-th direction 𝛼d Volumetric drained thermal expansion coefficient Hi Biot’s linear pore pressure loading modulus in the i-th direction * Philipp Braun [email protected] 1
Laboratoire Navier, 6‑8 avenue Blaise‑Pascal, Cité Descartes, 77455 Champs‑sur‑Marne, Paris, France
Andra, Meuse/Haute-Marne Underground Research Laboratory, Bure, France
2
H Biot’s volumetric pore pressure loading modulus Kd Drained bulk modulus Ks Unjacketed bulk modulus 𝛼u,i Linear undrained thermal expansion coefficient in the i-th direction 𝛼u Volumetric undrained thermal expansion coefficient 𝛬 Thermal pressurization coefficient 𝛼f Volumetric thermal expansion coefficient of the pore fluid 𝛼𝜙 Volumetric thermal expansion coefficient of the pore space 𝜙 Porosity K𝜙 Unjacketed pore modulus Kf Bulk modulus of the pore fluid 𝛬mes Measured thermal pressurization coefficient 𝛬cor C
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