基于突变和流变理论的采空区群系统稳定性

Stability of goaf group system based on catastrophe theory and rheological theory

为预防地下矿山采空区群系统高应变能的突然释放引发的灾害,通过构建顶板-矿柱三维空间力学模型,利用突变理论和流变力学理论对其稳定性及突变倾向性作定量与定性分析,推导出系统在不同时刻突变并释放能量的数学判据和力学条件,提出系统稳定性的分析算法并验证了其有效性和实用性,在此基础上探讨各影响因子对该系统稳定性的影响。结果表明:随着矿柱流变,系统突变倾向性减小,但顶板整体性逐渐破坏且边界条件依次进入固支、简支和自由边3个阶段,维持系统稳定的矿柱有效承载面积比率临界值ζ_(min)仅在各阶段内连续减小,在顶板简支和自由边的阶段起点处ζ_(min)值突跳增大,3个阶段ζ_(min)值的平均减小速率依次降低;顶板刚度D、上覆岩层荷载q_0、矿柱面积比率ζ和空区群尺寸之间的数值关系对系统稳定性起主导作用。该研究结果可为矿山安全开采规划和采空区群系统稳定性评判及调控提供新思路和新方法。

A three-dimensional（3D） roof-pillars model was established to prevent disasters caused by the sudden release of high strain energy of goaf group system in the underground mine. The stability and mutational tendency of this model were analysed qualitatively and quantitatively based on the catastrophe theory and rheological mechanics theory. The mathematical criterion and mechanical conditions of the mutation and energy release at different moments were also derived. Moreover, an analytical algorithm for the stability of goaf group system was proposed, and its validity and practicability were verified. The effect of each factor on the stability of this system was further discussed on this basis. The results showed that, with the rheological process of pillars, the tendency of system mutation decreased. However, the integrity of roof was destroyed gradually, and its boundary condition successively the following three stages： the fixed end, simple support and free end. The critical value （ζmin of the effective load bearing area ratio of pillars which maintained the system stability decreased at each stage, but ζminjumped at the starting point of the stage of simple support and free end. In addition, the average reduction rates of ζminat three stages decreased in turn. The system stability was dominated by the numerical relationship among the roof stiffness（D）, overlying strata load （q0）, the effective load bearing area ratio of pillars（ζ） and the size of goaf group. Therefore, the study results provide a new idea and method for the safe excavation of mine as well as the evaluation and control of goaf group system stability.