Linear Energy Storage and Dissipation Laws of Rocks Under Preset Angle Shear Conditions

The processes of deformation and failure in rocks are unavoidably accompanied by the absorption, storage, dissipation, and release of energy. To explore energy allocation during rock shear fracturing, two series of single loading and unloading preset angle shear tests at inclined angles of 60° and 50° were performed on red sandstone and granite by varying the experimental unloading level. The area integral approach was employed to interpret the load–displacement responses of the rock specimens via calculation of the energy parameters (referring to the external input energy, internal elastic energy and internal dissipation energy). The interpretations of the results revealed that the increase in the experimental unloading level nonlinearly increases the internal elastic energy, internal dissipation energy and external input energy; these relationships can be described by quadratic functions. It was also realized that under different experimental unloading levels, not only the internal elastic energy but also the internal dissipation energy is closely proportional to the external input energy. The proportional energy relationship can be used to quantify the internal elastic energy and internal dissipation energy at any expected experimental unloading levels, and a real-time calculation model for the internal elastic energy and internal dissipation energy in the pre-peak duration (including the peak point) was introduced. Meanwhile, an invariable feature for the ultimate internal elastic index W_ed (the ratio of ultimate internal elastic energy to peak internal dissipation energy) was captured via quantitative analysis. Additionally, the energy allocation manner and transfer mechanisms of rocks bearing varied loading forms (including uniaxial compression, Brazilian splitting, point load, semicircular bending, and preset angle shear) were also comprehensively compared considering three basic rock fracture modes: the tensile, shear, and hybrid failure (mixed tensile-shear) modes. Thus, the proportional distribution patterns of internal elastic energy and internal dissipation energy or the linear correlations among the three energy parameters can be universally observed during the failure of homogeneous rocks, despite distinct loading forms under one-dimensional stress conditions.