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Numerical Homogenization of a Fractured Rock Mass: A Geometrical Approach to Determine the Mechanical
Michel Chalhoub Université Saint Esprit de Kaslik, Jounieh, Lebanon; Ecole des Mines de Paris, Centre de Géosciences, Université de Marne la Vallée, Cité Descartes, Bâtiment IFI, 5 boulevard Descartes 77454 Marne-la-Vallée Cedex 2, France Ahmad Pouya Laboratoire Central des Ponts et Chaussées, 58 boulevard Lefebvre, 75732 Paris Cedex 15, France | |
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ABSTRACT |
Numerical Homogenization (NH) using finite element method is an indirect and rigorous method allowing the determination of large scale mechanical properties (tensor of elasticity, strength) of a fractured rock mass (Pouya and Ghoreychi 2001, Min and Jing 2003, Chalhoub 2006, Pouya and Chalhoub 2008). However, and in order to obtain a representative equivalent homogenized medium, it is necessary to determine the Representative Elementary Volume (REV). Using NH, this parameter is identified by preliminary iterative calculations of some mechanical properties on a set of increasing domains’ size. Moreover, heavy mesh generation and cost computing time are required for each fractured domain especially in the case of finite fractures’ length. In this paper we examine if it is possible to determine the mechanical REV from analyses carried out on geometrical parameters, which don’t require mesh making. As a case study, a 2D fractured rock mass is analyzed where the mechanical properties of randomly distributed fractures are homogenous. It is shown that the mechanical REV can be deduced from the geometrical REV obtained for the fractures spacing.
Keywords: Representative Elementary Volume (REV), Rock Mass, Numerical Homogenization, Cost computing time, Anisotropic elasticity.
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