Anisotropy of rocks and rock masses application of closed quartics to the study of deformability and rupture

Abstract

This work analyses the problem of the anisotropy of rocks and rock masses in general terms, and deals more particularly with the application of closed quartics to the study of the spatial anisotropy of the moduli of elasticity and of ultimate strengths under uniaxial compression. The four hypotheses on which the method is based are indicated, which resulted from experimental values obtained through 13 years and lead to the definition of a spatial law, of the closed quartics type, to reproduce the anisotropy of the moduli of elasticity and of the ultimate strengths. Four anisotropy cofficients are defined, namely, those concerning mass, surface, total or maximum anisotropies, which characterize the different types of anisotropy dependent on the intrinsic properties of rock masses. The method proposed is described in detail for the three following cases:  rocks and rock masses, with one preferencial orientation, with two, and with none. For each case both the statistical processing required for obtaining the most probable quartics that define anisotropies, and a specific example are presented.