A study of the characteristics of the accumulative rock failure and its evolution byapplication of the group renormalization method were presented. In addition, the interactionand long-range correlated effects between the immediate neighboring units was studied.The concept of mechanical transference for model OFC, employed in the study ofself-organized criticality, and the coefficient a were introduced into the calculation model forgroup renormalization. With the introduction, mechanisms for the drastic increase and decrease of failure intensity of rocks were investigated under similar macro-conditions. A study of the characteristics of the accumulative rock failure and its evolution by application of the group renormalization method were presented. In addition, the interaction and long-range correlated effects between the immediate neighboring units was studied. The concept of mechanical transference for model OFC, employed in the study of self-organized criticality, and the coefficient a were introduced into the calculation model for group renormalization. With the introduction, mechanisms for the drastic increase and decrease of failure intensity of rocks were investigated under similar macro-conditions.