Research on flow field characteristics in the karst tunnel face drilling hole (conduit) under the coupling between turbulence and seepage

•A model explores water gushing in karst tunnel face drilling hole is established.•Model confirmed via comparisons with 4 classic models and COMSOL simulations.•Model successfully applied to water inrush in the Zhongliangshan karst tunnel.•The thickness of the transition layer decreases with increasing conduit radius. Tunnel water inrush is one of the most common engineering problems during tunnel construction and operation, especially in karst aquifers. Among them, tunnel face drilling holes and karst conduits are strong water conductivity channels (called the “conduit” here), while the porous rock matrix is a weak water conductivity area. A second-order accuracy tunnel face water inrush model is established to investigate the coupling between the turbulent flow in the conduit and the seepage in the porous rock matrix. In the model, the incompressible Reynolds average Navier–Stokes (RANS) equation and the Brinkman-extended Darcy equation are used to govern the turbulence in the conduit and seepage in the porous rock matrix, respectively. The expressions of velocity distribution and water inflow discharge are derived requiring the velocities and their gradients of the turbulent and seepage flow to be equaled at the flow-solid interface. The validity of the present model is verified by the existing analytical solutions and COMSOL numerical solutions. Furthermore, parameter sensitivity results show that the velocity has a positive relation with the Laplace parameter, Reynolds number, Darcy number, and conduit radius. Finally, the tunnel face water inrush in the new Zhongliangshan expansion tunnel is selected as a real field engineering case. The error of the water inflow discharge in the tunnel face drilling hole between the present predicted results and the field measured results is within 10%. After introducing cosine fluctuation with amplitude 0.15 and period 500 s to optimize the model, the error for the stable water gushing stage can be reduced to within 5%. This model can provide a reference for predicting the water inflow discharge in the drilling holes or karst conduits on tunnel faces.