Abstract:The study subject of the renormalization group theory is supposed to have a scaleless property in theory. In other words, the primitive cell level tends to be infinite. However, the level cannot be set at a very high value in actual engineering projects. In order to solve this problem, comparative studies of damage probability of limited primitive cell levels were carried out using the percolation model, the fault rupture model, the rock breaking model, and the structural damage probability model of a triangular prism unit for a gravity dam based on the renormalization group theory. The results of iterative computations show that level 3 of a primitive cell or three iterations can be applicable to actual engineering projects. A safety evaluation classification method for an overall structure is proposed based on the damage probability of a primitive cell of level 3. The steps of determing the overall safety of a gravity dam using the triangular prism model are presented. According to the key points and fixed points of the damage probability, three safety states of the overall structure were classified as follows: (a)a safe state; (b)an intermediate state, between safey and overall collapse; and(c)an overall collapse state.