The nonlinear energy model and stress–strain model of sandstone

The relationship between strain and elastic energy is simplified by introducing a stress state parameter based on the generalised Hooke’s law. It is assumed that the micro-element strengths satisfy the Weibull distribution and a new model for the non-linear evolution of energy is developed by introducing the concept of rock micro-element strengths. A sensitivity analysis of the model parameters is carried out on this basis. The results show that the model agrees well with the experimental data. The model is close to the deformation and damage laws of the rock and is able to reflect the relationship between the elastic energy and strain of the rock. By comparing with other model curves, the model of this paper is more suitable for the experimental curve. They show that the improved model could better describe the stress–strain relationship of rock. Finally, according to the analysis of the influence of the distribution parameter on the variation pattern of the elastic energy of the rock, the magnitude of the distribution parameter can directly reflect the peak energy of the rock.