Prediction of height effect, plastic deformation and fracture energy for high-strength concrete by linear shear softening constitutive relation based on energy conservation method

Based on the energy conservation method, the slopes of post-peak stress-deformation curves undergoing class I behaviour and class II behaviour are presented for a high-strength concrete specimen subjected to shear failure in the form of shear band exhibiting linear strain softening beyond peak shear stress. The predicted height effect coincides well with the previous experiments. The transition occurs from class I behaviour to class II behaviour as specimen height increases. The slope of the relative stress-plastic deformation curve is derived. The horsetail- like profile of the measured curves for different heights cannot be explained if shear band inclination is only related to friction or/and dilation angles. The deduction that shear band inclination depends on specimen height is verified by previous experiments and numerical prediction using fast Lagrangian analysis of continua. If the dependence of strength and shear band inclination on geometrical size is neglected, then post-peak shear fracture energy is a material parameter. The linear regression on scattered experimental data shows that post-peak fracture energy is independent of specimen height, as is consistent with the present analysis regardless of the size effects of strength and shear band inclination. The size-dependent strength and shear band inclination as well as the sensitivity of shear band inclination and pattern to boundary condition and position of material imperfections are responsible for the scattered post-peak shear fracture energy.