弹性地基条件下狭窄煤柱岩爆的突变理论分析  

Analysis of rockburst in narrow coal pillar by fold catastrophe theory on the condition of elastic foundation

作　　者：张勇[1] 潘岳[1] 

机构地区：[1]青岛理工大学土木工程学院,青岛266033

出　　处：《岩土力学》2007年第7期1469-1476,共8页Rock and Soil Mechanics

基　　金：山东省自然科学基金(No.Y2005-A03)资助项目;山东省教委重点资助项目(No.G04D15)

摘　　要：将未采煤层视为弹性地基条件下,运用maple9.5符号运算软件解得岩梁的挠曲线方程。根据能量守恒原理得到的功、能增量平衡关系式,求得岩梁–煤柱系统作准静态形变时的平衡方程——折迭突变模型平衡方程;用折迭突变总势能函数所作的稳定性判别表明,岩爆前兆阶段岩梁–煤柱系统处于不稳定平衡状态;煤柱岩爆的条件是Cook刚度准则,该准则可以动态地用煤柱形变增大时所需外界的能量输入率趋于0来表示;计算了煤柱岩爆地震能释放量,阐明煤柱岩爆机制是由于岩梁弹性能释放量超过峰后软化煤柱形变所耗的能量。通过岩梁弹性势能变化率曲线和煤柱耗能曲线,以几何形式描述了所得研究结果。计算表明,未开采煤层刚度变化对岩梁的等效刚度影响微弱。工作面开挖和采空区增大,将显著减小岩梁刚度Ke,对煤柱岩爆有重要影响。Under the condition of considering unexcavated coal seams as an elastic ground base, this paper deduces the equation of rock beam＇s deflection line using the symbolic operation software——Maple 9.5. Then it deduces the equilibrium equation for the rock beam-coal pillar system when the system deforms in a quasi-static way, which is the equilibrium equation of fold catastrophe model. The discrimination of stability by using total potential energy function of fold catastrophe shows that, the system of rock beam and coal pillar is in an unstable equilibrium state in premonitory phase of rockburst, and critical condition of rockburst in coal pillar is Cook＇s stiffness criterion. The criterion can be expressed dynamically that, the required energy input rate of the environment approaches to zero while the deformation of coal pillar increases. The releasing amount of earthquake energy is calculated; and it is clarified that the mechanism of rockburst in coal pillar is that the elastic energy released by rock beam exceeds the energy dissipated by the deformation of coal pillar with softening characteristics after peak value. The obtained findings is described by the geometric form in which the curves of energy input rate, rate of change of rock beam＇s elastic energy and dissipated energy of coal pillar are given. Calculations show that, the stiffness coefficient of unexcavated coal bed has faint influence on the rock beam＇s equivalent stiffness. The excavation of working surface and the increment of exhausted area lessen rock beam＇s equivalent stiffness remarkably.

关 键 词：煤柱岩爆 弹性地基 折迭突变模型 能量输入率 稳定性判别 等效刚度 

分 类 号：TD324.1[矿业工程—矿井建设]