In a groundwater outburst through a fault, the velocity is generally so high that the relationship between the velocity and the hydraulic gradient deviates from the linear Darcy regime. This study uses the Forchheimer equation to model the flow in both the aquifer and the fault zone. The model is used to investigate the effects of non-Darcy flow on a specific inrush episode at the Zhongguan iron mine by varying the fault permeability. It shows that the flow behavior in the aquifer was not always Darcy flow or non-Darcy flow, but changed depending on the fault permeability. The region in the aquifer near the fault is most likely affected by non-Darcy flow, and the non-Darcy-effect region expands away from the fault with the increase of the fault permeability. Considering a 10% non-Darcy effect for engineering, the Forchheimer equation can be approximately used to describe the flow mechanism from Darcy to non-Darcy. Furthermore, the Forchheimer equation is also acceptable for predicting the groundwater inflow during groundwater outburst through fault.

A non-linear flow model that couples three flow types is built based on flow transition to investigate the flow behavior of water inrush induced by KCC.

A karst collapse column (KCC), a type of vertical structure that is common in the Carboniferous-Permian coal fields of North China, contains many graded broken rocks and often functions as a channel for groundwater inrush. This study used a custom-built apparatus to investigate the effects of the particle-size distribution on the seepage behavior of a sand particle mixture subjected to a high hydraulic gradient. Three different flow regimes were identified: (1) the Darcy regime, (2) the Forchheimer regime, and (3) the turbulent regime. When flow transition begins, the critical flow velocity, critical Reynolds number, and Forchheimer number increase as the nonuniformity coefficient $C_u$ (or the coefficient of curvature $C_c$ ) increases when the porosity remains constant, and the critical hydraulic gradient decreases. The permeability increases linearly, and the inertia factor decreases exponentially as $C_u\times C_c$ increases. Using new experimental data, the validity of five widely used empirical formulas for permeability and the inertia factor were evaluated. The results indicated that the empirically corrected formulas for permeability and the inertia factor yielded high prediction accuracy and can be used to predict the permeability and inertia factor of KCCs in practical engineering.

Statistics indicate that granular rock mass frequently acts as the flow channel and cause water inrush disasters under high water pressure in underground mining and tunnel engineering. The flow velocity of water inrush is so high that the flow behavior shows nonlinearity and cannot be described by Darcy’s law. During the water inrush, the non-Darcy flow behavior associated with the porosity of granular rock mass is constantly changing due to seepage erosion. Therefore, this paper aims at the non-Darcy flow behavior of the granular limestone with a wide range of porosity (from 0.242 to 0.449). The non-Darcy flow properties were experimental investigated under steady-state condition by a self-designed apparatus. Based on the experimental data, an empirical hydraulic conductivity-porosity relation together with the expression of inertial coefficient was proposed. Then the non-Darcy flow regime was quantitative studied by the hydraulic conductivity-based Reynolds number. And the Forchheimer number associated with porosity was used to determine the critical flow velocity of the non-Darcy flow. From the point of view of seepage, two reasons for water inrush frequently occurred through granular rock mass with high porosity were finally discussed.