A quantitative criterion to describe the deformation process of rock sample subjected to uniaxial compression: From criticality to final failure

It was found that the crack damage stress threshold, σ cd , is a phase transition point during the deformation process of rock and is equivalent to the unstable fixed point of renormalization group theory. Thus, a relationship exists between the renormalization group theory and the rock deformation process, through which we can investigate the critical behavior of rock deformation. Therefore, an improved renormalization group model, which takes into account the different stress transfer mechanisms that are closer to the actual mechanical processes, is introduced to reveal the critical behavior of the rock deformation process. Finally, a quantitative relationship between the crack damage stress threshold and peak strength, σ critical / σ peak , is theoretically established. To test the theoretical relationship we additionally present experimental results of an investigation of the ratio of the crack damage stress threshold to uniaxial compressive strength, σ cd / σ ucs , based on different rock types. The results show that the overall average and standard deviation of σ cd / σ ucs is 0.80 ( ± 0.10 ) for low-porosity igneous, metamorphic and sedimentary rocks, a figure that is closer to the theoretical solution of σ critical / σ peak from the improved renormalization group model with a stress transfer mechanism of S T M − 1 / r 3 . Our study implies that the σ critical / σ peak ratio may be intrinsic to low-porosity rocks, and therefore can be considered as a reliable predictor of the peak strength of rock samples in the laboratory.