Anisotropic characteristics of the energy index during the shale failure process under triaxial compression

Abstract

Energy conversion is an essential driving force of shale anisotropic deformation, damage initiation and evolution. In this study, theoretical calculations of five energy indexes (total input energy Ut, releasable energy Ue, dissipated energy Ud, dilatational energy UV and distortional energy UD) during the shale failure process considering the inherent anisotropy of shale are presented in detail for the first time. The anisotropic features of the five energy indexes are systematically discussed. The results indicate that bedding structure considerably influences these energy indexes. Ue, UV and UD all decrease to a minimum as the bedding orientation reaches 60° and then increase with the bedding degree. The relationships between Ue, UV and UD and the confining pressure can be described by linear functions, similar to the variation in the compressive strength with either bedding inclination angle or confining pressure. As the axial strain increases, the rates of increase in Ue, UV and UD first increase, then remain constant, and then decrease before failure; however, the rates of increase in Ut and Ud continue to increase until failure. Ue, UD and UV have strong relationships with the peak compressive strength but weak relationships with the peak axial strain, whereas Ut and Ud exhibit the opposite relationships with the peak strength and strain. The anisotropic characteristics of the energy indexes can help to further elucidate the failure mechanisms of shale and are of great significance to hydraulic fracturing design.