Energy evolution and damage constitutive model of anchored jointed rock masses under static and fatigue loads

Abstract

During propagation, cyclical impact loads transform into low-frequency fatigue loads, which induce the release of energy from far-field anchored jointed rock masses (AJRMs) under long-term disturbance loads. Shear tests of marble under static and fatigue loading rates were conducted using a servo-controlled compression shear test machine equipped with an improved specimen fixture system. The effects of static and fatigue loads on the mechanical behaviour of samples, for example, the stress–strain curve, peak stress, shear modulus, peak strain and failure strain, were explored. The energy evolution of different types of AJRMs was studied in detail. In addition, a damage constitutive model for AJRMs was developed based on the Weibull distribution under static loading and deformation characteristics under fatigue loading. The results showed that fatigue loading could reduce the strength and increase the deformation of specimens, while static loading had a cumulative effect on the deterioration of specimens, which could decrease the elasticity of AJRMs. In the energy transformation process, the total energy included elastic energy, which described the elastic deformation, and dissipated energy, which could be converted to describe the anchor deformation, fracture extension and plastic damage, depending on the application. The proposed damage constitutive model was established by considering the influence of static and fatigue loads, and a damage constitutive equation of AJRMs was derived. A comparison between the calculated and experimental data showed that the damage equation could accurately describe the effects of static and fatigue loading rates on the stress–strain responses of specimens, and its parameters had definite physical meanings. Thus, the proposed model is a very good tool for the analysis of load coupling problems involved in deep rock mass engineering.