Analysis of plastic deformation and fracture energy of rock specimen in uniaxial compression

Firstly, axial plastic deformation of rock specimen in uniaxial compression subjected to shear failure is investigated. Assumption is made that shear localization in the form of a single shear band is initiated at peak shear stress in shear plane and that axial plastic deformation stems from the plastic shear slip of shear band. Relative shear displacement along shear band depends on shear stress level and shear band thickness described by gradient-dependent plasticity. The relative displacement can be decomposed into axial and lateral parts. The former is equal to axial plastic compressive deformation at rock specimen end. Then, relation between the axial plastic deformation and the flow compressive stress is proposed. It is found that shear band inclination angle influences the slope of the relation curve. If the angle is not dependent on specimen length, then the relation curve is not a strict straight line; but a narrow zone like a horsetail. In fact, the influence of shear band inclination angle can be neglected so that the slope can be approximately regarded as a constant, as is in agreement with some experimental results. Secondly, the effect of specimen length on total fracture energy in uniaxial compression subjected to shear failure is analyzed. Total fracture energy is the sum of pre-peak fracture energy and post-peak fracture energy. In pre-peak stage, Scott model is used to describe the nonlinear elastic stress-strain relation and analytical solution of pre-peak fracture energy is derived. The solution shows that the pre-peak fracture energy is related to specimen length. In strain-softening stage, linear strain-softening constitutive relation between shear stress and plastic shear strain is adopted. Analytical solution of post-peak fracture energy dissipated by localized plastic shear deformation is derived based on gradient-dependent plasticity. The reasonability of present analytical solution of total fracture energy for quasi-brittle materials is verified by linear regression on earlier experimental result. Longer length of specimen leads to higher total fracture energy, and bigger elastic modulus to lower the total fracture energy. If the size effects of compressive strength and inclination angle of shear band are neglected, the reason for size effect of total fracture energy is the uniform plastic compressive deformation in pre-peak stage.