On the constraints and relations of elastic constants of transversely isotropic geomaterials

Summarization: In the present work two basic aspects of the theory of anisotropic elasticity are studied, namely the estimation of the lower and upper bounds in the variation of elastic moduli of transversely isotropic rocks and the possibility of the existence of phenomenological (empirical) relations among the elastic moduli of orthotropic or transversely isotropic rocks that may be derived experimentally. If such relationships exist then the inversion of laboratory and field measurements pertaining to the characterization of the deformability of orthotropic or transversely isotropic rocks in engineering applications is greatly simplified. These two aspects are investigated here for the plane stress and plane strain configurations by recourse to a special formulation of anisotropic elasticity theory and experimental evidence. Finally, several examples of application of the proposed formulation are given and it is illustrated as to how the hydrostatic and deviatoric concepts of the isotropic elasticity and plasticity theories are effectively generalized for the study of failure of anisotropic geomaterials.Presented on: International Journal of Rock Mechanics and Mining Science