Predicting Erosion-Induced Water Inrush of Karst Collapse Pillars Using Inverse Velocity Theory

Although the impact of Karst Collapse Pillars (KCPs) on water inrush has been widely recognized and studied, few have investigated the fluid-solid interaction, the particles migration inside KCPs, and the evolution feature of water inrush channels. Moreover, an effective approach to reliably predict the water inrush time has yet to be developed. In this work, a suite of fully coupled governing equations considering the processes of water flow, fracture erosion, and the change of rock permeability due to erosion were presented. The inverse velocity theory was then introduced to predict the water inrush time under different geological and flow conditions. The impact of four different controlling factors on the fracture geometry change, water flow, and inrush time was discussed in detail. The results showed that the inverse velocity theory was capable of predicting the occurrences of water inrush under different conditions, and the time of water inrush had a power relationship with the rock heterogeneity, water pressure, and initial particle concentration and an exponential relationship with the initial fracture apertures. The general approach developed in this work can be extended to other engineering applications such as the tunneling and tailing dam erosion.