https://enpc.hal.science/hal-00688316Stefanou, IoannisIoannisStefanouDepartment of Mechanics - NTUA - National Technical University of Athens [Athens]msa - Matériaux et Structures Architecturés - navier umr 8205 - Laboratoire Navier - IFSTTAR - Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche ScientifiqueSulem, JeanJeanSulemcermes - Géotechnique - navier umr 8205 - Laboratoire Navier - IFSTTAR - Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche ScientifiqueThree-dimensional Cosserat continuum modeling of fractured rock massesHAL CCSD2010homogenization3D Cosseratrock masses[SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph][SDE] Environmental SciencesStefanou, Ioannis2012-04-17 13:09:202023-08-07 15:22:082012-04-17 13:09:20enJournal articles10.1142/S17569737100004241The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum. © 2010 Imperial College Press.