Upscaling Theory for Coupled Hydro-Mechanics in 3D Fractured Porous Rock
Résumé
A methodology for upscaling 3D coupled Hydro-Mechanical (HM) properties of fractured porous rocks is developed theoretically, then tested on synthetic fractured rock samples, and finally, applied to a damaged and fractured claystone around a drift (the GMR gallery located in the 400 m to 600 m deep layer of Callovo-Oxfordian claystone at the Meuse/Haute-Marne Underground Research Laboratory operated by ANDRA). We focus on the Mechanical and coupled Hydro-Mechanical (HM) properties of fractured porous rock (Darcy permeability was upscaled separately in Ababou, Cañamón Valera et al. 2011, JPCE). In the application, the geometric structure of the EDZ (Excavation Damaged Zone) around the GMR gallery is described by a hybrid model comprising (i) a set of 10 000 statistical fissures with radially inhomogeneous statistics (size, thickness and density increase near the wall), and (ii) a deterministic set of large curves fractures (“chevrons”), periodically spaced along the axis of the gallery according to a 3D chevron pattern. The upscaled HM coefficients are obtained theoretically and calculated for different cases (synthetic samples, and application to the GMR drift). They include scalars, 2nd rank, and 4th rank tensors. The “3D” and “2D transverse” distributions of the upscaled coefficients are analyzed (displayed using spheres or ellipsoïds). Global values are obtained by upscaling over the entire damaged/fractured annular zone around the drift. Equivalent isotropic coefficients are also extracted from these tensors: Young modulus E, bulk modulus K, Lamé shear modulus , Poisson ratio , and HM coupling coefficients: Biot coefficient B (stress/pressure) and Biot modulus M (pressure / fluid production). Theoretical expressions are provided in the tensorial case, and in the simplified case of statistically isotropic cracks. The isotropic expressions are tested by running 3D “upscaling experiments” on synthetic Poissonian crack systems with isotropic orientations. The impact of fissuring/fracturing on equivalent stiffnesses and HM couplings is analyzed. References: Cañamón, Ababou et al. 2019 (to appear in IJRMMS); Ababou, Cañamón et al. 2014 (Geol. Soc. London, Spec. Publi., v.400).
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