基于突变理论的崩落法转充填法隔离矿柱安全厚度计算

Calculation of Safety Thickness of Isolated Pillars from Caving Method to Filling Method Based on Catastrophe Theory

崩落法转充填法开采过程中,合理确定隔离矿柱厚度对保证过渡采场安全回采具有重要意义。通过构建隔离矿柱力学模型,分析隔离矿柱破坏特征,建立了隔离矿柱的系统总势能关系式;基于突变理论,推导出隔离矿柱失稳的尖点突变模型;根据尖点突变模型失稳的充分条件和必要条件,建立了隔离矿柱安全厚度的计算模型。将此计算模型应用于研究鄂东某铁矿无底柱分段崩落法转充填法隔离矿柱厚度,理论计算的隔离矿柱厚度取值范围为15.49~19.36 m。在数值模拟验证和工程试验生产中,取隔离矿柱厚度为17.50 m时,隔离矿柱处于稳定状态。理论分析和验证结果表明,突变理论可解释隔离矿柱失稳的非线性动力学特征,隔离矿柱安全厚度计算模型可为工程设计提供一定的理论依据和工程指导。

In the process of transition from caving method to filling method, reasonable determination of the thickness of the isolated pillar is of great significance to ensure the mining safety of transition stope. The mechanical model was established and the failure characteristics of the isolated pillars were analyzed, and the system total potential energy relationship of the isolated pillars was established. Based on the catastrophe theory, the cusp catastrophe model of the instability of the isolated pillars was deduced. According to the cusp catastrophe model instability sufficient and necessary condition, the calculation model of the safety thickness of the isolated pillars was established. This calculation model was applied to study the thickness of the isolated pillars from caving method to filling method in an iron mine in the east of Hubei province, and the theoretically calculated thickness of the isolated pillars ranged from 15. 49 m to 19. 36 m. In the verification of numerical simulation and the production of engineering test, when the thickness of isolated pillars was 17. 50 m, the isolated pillars was in stable state. The theoretical analysis and verification results show that the catastrophe theory can explain the nonlinear dynamic characteristics of the isolated pillar instability. Besides,the calculation model of the safety thickness of the isolated pillars can provide a theoretical basis and engineering guidance for the engineering design.