基于多元联系数－三角模糊数随机模拟的围岩稳定性风险评价

围岩稳定性评价受具有随机性、模糊性和未确知性特点的诸多因素影响与控制，应用传统的围岩稳定性评价方法已很难满足当今复杂地下工程的围岩稳定性评价需求。基于集对分析理论和三角模糊数随机模拟理论，探讨基于联系数和三角模糊数随机模拟的围岩稳定性风险评价模型，即基于待评样本的评价指标体集和围岩稳定性等级标准集构成的集对，构造多元联系数表达式来定量描述评价指标样本与评价标准等级之间隶属关系的层次性和模糊性；采用三角模糊数表达多元联系数的差异度分量系数的连续变化过程和不确定性，以及围岩稳定性等级标准的模糊性，并通过随机模拟技术把三角模糊数及其函数之间的运算转化为普通实数之间的运算，实现克服现有三角模糊数的乘法、除法和函数运算尚不够严谨、操作较为复杂等问题；结合指标权重计算综合联系数以风险评估样本的围岩稳定性等级。实例应用及与其他方法评价结果对比分析表明，本文方法应用于围岩稳定性的风险评价是有效可行的，且取得较好成果，此也为工程设计和施工风险评价提供了重要依据。

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.