A five-parameter constitutive model for hysteresis shearing and energy dissipation of rock joints

Rock joints exhibit hysteresis shearing behavior and produce energy dissipation under shear cyclic loads,which however cannot be accurately depicted by existing constitutive models. This paper establishes a constitutive model for hysteresis shearing and associated energy dissipation of rock joints. Analytical expressions of the model during cyclic shearing processes are derived. Derivation of the model indicates no energy dissipation in the elastic stage. When the shear load exceeds elastic boundary, nonlinear energy dissipation takes place. Validations with experiments show that the proposed model provides good conformities with direct shear curves and hysteresis loops, and can predict the energy dissipation characteristics of rock joints under different working conditions. Compared to the constitutive models using Weibull's distribution, the proposed one is smooth at the elastic boundary and can accurately capture the maximum shear stress. Unlike the existing incremental-type models, the proposed one provides clear and direct analytical expressions for both shear stress and energy dissipation during the whole displacement domain, which is more convenient in application.