Development of anisotropy in the incremental shear moduli for rock undergoing inelastic deformation

Abstract

Abstract New experimental data on the evolution of two incremental shear moduli have been obtained for rock undergoing inelastic deformation. Changes in the incremental shear moduli during increasing axial straining probably reflect the development of a deformation-induced, anisotropic fabric resulting from accumulation of oriented damage. These incremental moduli occupy a prominent position in a constitutive equation for the plane deformation of inelastic solids that has evolved over nearly 30 years to include pressure-sensitivity, compressibility and plastic non-normality. This equation is often used in analyses of strain localization. One of the moduli, G, governs shearing parallel to the coordinate axes, and the other one, G ∗ , governs shearing at 45° to the coordinate axes. They both were measured on the loading branch of the constitutive equation. The modulus for shearing at 45° was also measured on the unloading branch, where it is called G ∗ . Though the predicted onset of strain localization for this type of constitutive model is a strong function of G ∗ /G , there appears to have been no such data collected for rock. Experiments to obtain estimates of these incremental moduli were conducted on solid cylinders and thin-walled tubes of Tennessee marble during axisymmetric compression under fluid confining pressures of 60 MPa. All three moduli were equal to the isotropic elastic value of E/2(1 + ν) ≃ 30 GPa in the elastic range of axisymmetric compression, but then the moduli decreased with increasing axial strain up to 0.01, always with G ∗ ≤ G ∗ ≤ G , and the ratio G ∗ /G decreased markedly. The decreased ratio, G ∗ /G , allows strain localization to occur earlier in a program of axial straining than would be predicted for a similar material that did not exhibit such a change in moduli.