基于尖点突变模型的煤层底板突水预测研究

STUDY ON PREDICTION OF WATER-INRUSH FROM COAL FLOOR BASED ON CUSP CATASTROPHIC MODEL

当煤层开采后,底板岩层承受的水压超过自身强度时,而发生的不连续的发散突变,即底板岩层失稳破坏形成底板突水的现象,属于突变理论研究的范畴,故煤层底板突水可以引用突变理论来研究。通过建立煤层底板突水的一个尖点(cusp)突变模型,对煤层底板失稳破坏发生突水的机理进行了分析。基于平衡曲面方程,可求得煤层底板水压应力比I_(p)。当I_p>1时,发生突水:当I_p<1时,不会发生突水。实例分析表明:尖点突变模型用于描述煤层底板水压应力比的发展规律是恰当的,用其进行煤层底板突水预测也是较准确的。

When the water-pressure in floor stratum exceeds the floor strength after coal mining, the floor collapses and water-inrush from coal floor occurs. This phenomenon can be tackled by catastrophe theory. In the paper, a cusp catastrophic model of water-inrush from coal floor is established, and water-inrush mechanism of coal floor destruction is analyzed. The ratio of water pressure to stress Ip can be derived from the model. When Ip>1, water-inrush from coal floor may occur. When Ip <1, no water-inrush from coal floor occurs. The analysis of actual examples indicates that a cusp model is appropriate to describing the development of the ratio of water pressure to stress, and the prediction of water-inrush from coal floor is pertinent.