New models to predict rock failure by linking the volume dilatant point with the peak stress point

The rock mass failure process can be divided into several distinct deformation stages: the compaction stage, elastic stage, stable failure stage, accelerated failure stage, and post-peak stage. Although each stage has been well studied, the relationship among the stages has not been established. Here, we establish two models which are the Strain model Q and Energy density model S by using the renormalization group theory and investigate the mechanical relationship between the volume dilatant point and peak stress point on the rock stress-strain curve. Our models show that the strain ratio ( epsilon(f)/epsilon(c)) and energy ratio ( E-f/E-c) at the volume dilatant point and peak stress point are solely functions of the shape parameter m. To verify our models, we further studied the failure process of rock specimens through several uniaxial compression experiments and found that the relationship between epsilon(f)/epsilon(c) or E-f/E-c and m shares a notably similar pattern to that from our theoretical model. However, the epsilon(f)/epsilon(c) and E-f/E-c values in our experiments are slightly smaller than those predicted by the models. In brief, we demonstrate that our models can be used to predict the failure process of the laboratory-scale hard brittle rock samples.