岩溶陷落柱顶端突水的尖点突变模型

he water-inrush of collapse column is a typical nonlinear process. A mechanical model of collapse column top is established，based on which，the expression of total potential energy function is derived. Then the cusp catastrophic model for the water-inrush of collapse column is set up by catastrophic theory. The formula of necessary and sufficient condition for the water-inrush of collapse column is obtained according to the cusp catastrophic model. In the mean time，the mechanism water-inrush of collapse column is analyzed according to the model. The cusp catastrophic model indicates that the main factors that effect the water-inrush include the size of collapse column, the nature of top strata, the depth of collapse column, the pressure of confined water, the mine pressure and so on. The establishment of model is of great significance to judge and prevent the water-inrush of collapse column.