Mechanical effect of rotating non-spherical particles on failure in compression

Abstract

When non-spherical particles (grains, blocks) in a rock or geomaterial under compression are sufficiently detached to enable rolling under shear stress the moment equilibrium dictates that further increase in displacement requires reduced shear stress. Thus the rolling non-spherical particle produces an effect of apparent negative stiffness whose value is proportional to the magnitude of the compressive stress. We model geomaterials with rolling particles at a macroscale as a matrix containing inclusions with negative shear modulus. We consider two extreme types of inclusions: spherical inclusions and shear cracks with negative stiffness shear springs inside. We show that there exists a critical concentration of inclusions at which the effective shear modulus abruptly becomes negative and the geomaterial loses stability. Furthermore, there exists a special value of negative shear modulus/stiffness of inclusions (and hence the magnitude of the compressive stress) at which the critical concentration is zero, such that the first rolling particle induces the global instability. This stress is of the order of the shear modulus the geomaterial exhibits at the advanced stage of fracturing when the particles are sufficiently detached to enable the rolling.