Evaluation of the Non-Darcy Effect of Water Inrush from Karst Collapse Columns by Means of a Nonlinear Flow Model

Abstract

Karst collapse columns (KCCs) are naturally formed geological structures that are widely observed in North China. Given their influence on normal mining operations and the progress of mining work, collapse columns pose a hidden danger in coal mining under the influence of manual mining. By communicating often with the aquifer, the water inrush from KCCs poses a serious threat to construction projects. This paper adopts three flow field models, namely, Darcy aquifer laminar flow, Forchheimer flow, and Navier–Stokes turbulent flow, based on the changes in the water inrush flow pattern in the aquifer and laneway, and uses COMSOL Multiphysics software to produce the numerical solutions of these models. As the water inrush flow velocity increases, the Forchheimer flow shows the effect of additional force (inertial resistance) on flow in KCCs, in addition to the effect of viscous resistance. After the joint action of viscous resistance and inertial resistance, the inertial resistance ultimately dominates and gradually changes the water inrush from the KCCs to fluid seepage. Forchheimer flow can comprehensively reflect the nonlinear flow process in the broken rock mass of KCCs, demonstrate the dynamic process from the Darcy aquifer to the final tunnel turbulence layer, and quantitatively show the changes in the flow patterns of the water inrush from KCCs.