Cusp catastrophe model of water-inrush from collapse column

The water-inrush from collapse column is a typical nonlinear process of balance-deflection state. Mechanical model of collapse column top is established and the expression of total potential energy function is derived. Then the cusp catastrophe model for the water-inrush of collapse column is set up by catastrophe theory. The formula of necessary and sufficient condition for the water-inrush of collapse column is obtained. In the mean time, the mechanism water-inrush of collapse column and the main factors that affect the water-inrush are analyzed. The establishment of model is of great significance to judge and prevent the water-inrush from collapse column.