Risk evaluation of surrounding rock stability based on stochastic simulation of multi-element connection number and triangular fuzzy numbers

The evaluation of surrounding rock stability is a complicate uncertainty system problem since it is influenced by many random, fuzzy and uncertainty factors. The traditional evaluation methods do not meet the need of the super-long, super-overlay and super-pressure underground projects. Consequently, a novel risk method to assess the surrounding rock stability is investigated to ensure the safety and economy of underground projects. Based on the theory of set pair analysis, triangular fuzzy numbers and stochastic simulation, an integrated risk evaluation model based on the set pair consisting of evaluation index sets and classification standard sets of the surrounding rock stability is discussed. A concept of multi-element connection number is introduced to express the hierarchy and fuzziness of membership between evaluation samples and classification standards, and the fuzziness among the grades is depicted by the interval censoring of triangular fuzzy numbers. Moreover, the stochastic simulation of Monte-Carlo method is presented to simulate the triangular fuzzy numbers for transforming the operations of the triangular fuzzy numbers and their functions into the conventional operations of real numbers. It can resolve the difficulties of operations of triangular fuzzy numbers and their functions. Combined with the weight of evaluation indexes, the integrated connection number is calculated to assess the credible degree of the grade of surrounding rock stability of the samples. Finally, a practical example is described to confirm and compare with the other methods of fuzzy mathematics, extenics and variable fuzzy sets. The results show that the proposed risk assessment model is more feasible and easier to operate, and the results are good and provide an important basis for the risk design and construction of projects.