A probabilistic approach for the evaluation of the stabilizing forces of fully grouted bolts

The essential task of the ground reinforcement techniques is to keep the rock as stable as possible. In particular passive rock bolt should resist the rock movements along its entire length and through the resulting reaction forces, to improve the load-bearing capacity of the rock. Among different calculation techniques, the calculations based on Block Reinforcement Procedure (BRP) was used in this paper, also adopting some simplified equations available in the scientific literature. However, parameters influencing the interaction are difficult to evaluate. Therefore, the problem of the reliable definition of the parameters that most influence the behavior of the bolts and the evaluation of the stabilizing forces of the potentially unstable block of rock remains. A new probabilistic approach is presented in this article, able to appropriately manage the uncertainties present on the fundamental parameters of the bolt-rock interaction and on the mechanical characteristics of the sliding surface of the block. Through the use of a Monte Carlo procedure, in fact, it was possible to obtain different samples of the safety factors of the rock block, one for each diameter of the steel bars used for its stabilization. Finally, the probabilistic management of the safety factor samples allowed the correct design of the steel bars, by evaluating the probability that the safety factor of the block with regard to potential slipping has a value lower than a pre-established limit. The probabilistic approach developed was applied to a real problem of stabilization of a potentially unstable rock block due to planar sliding, present on a municipal road in North Italy.