A Micromechanical Approach for Anisotropic Rock Mass Thermo-Mechanical Properties Estimation

Abstract

In the present paper, an up-scaling thermo-mechanical approach is presented for rock masses considered as anisotropic composite materials. A mathematical framework is proposed to estimate overall thermo-mechanical properties based on local geometrical considerations using the Mori-Tanaka scheme. In addition, a homogenization-based effective thermal conductivity formulation is proposed for composite materials subjected to periodic micro-scale heat fluxes and governed by Fourier's heat law and the steady state balance equations. The particular case of isotropic material is also presented for completeness.The response of a Representative Elementary Volume (REV) to external mechanical loading is modeled using finite element numerical simulation in order to conclude the effective mechanical properties and compare them with the results of analytical calculations. The porosity of the REV is varied by changing the number or the radii of the embedded inclusions. As a first result, the two homogenization techniques are compared with reference to proximity to the numerical results. Moreover, it was noticed that the curves presenting the variation of effective bulk modulus with respect to the number of inclusions for different radii are convergent. Finally, the inclusions number and radius in the RVE which give close numerical and analytical results could then be determined.