Quantitative Evaluation of the Onset and Evolution for the Non‐Darcy Behavior of the Partially Filled Rough Fracture

The non‐Darcy flow behavior in unfilled and fully filled rough fractures has been investigated thoroughly for decades. Natural fractures usually be partially filled with porous media due to long‐term internal and external dynamic disturbances and water flow erosion. However, how to evaluate the nonlinear seepage characteristics of the partially filled rough fracture (PFRF) is never scrutinized. In the present study, 2D direct numerical simulations are conducted to investigate the non‐Darcy behavior for flow through 6 PFRF models under different filling conditions (i.e., filling degree, roughness, and hydraulic conductivity capability of the filling medium), which included coupling between the free and seepage flow in the unfilled and filled region, respectively. The results show that the critical non‐Darcy factor E = 0.02 can be used to judge the onset of the non‐Darcy regime in PFRF, which is also the critical point of eddy region (ER) volume mutation. The higher the filling degree and the weaker the hydraulic conductivity of the filled medium, the more significant the non‐Darcy behavior. Furthermore, the variation of ER volume can be divided into three stages with the increasing inertia effect, that is, stable stage (E 0.1). In addition, a new model for quantitatively evaluating the non‐Darcy behavior of PFRF is developed via gene expression programming based on 735 simulation data set, which is further employed to establish the relationship between the friction factor. Plain Language Summary The nonlinear flow behavior in partially filled rough fractures (PFRF) was investigated by using 2D simulations. The simulation results revealed a critical non‐Darcy factor of 0.02 to determine the onset of non‐Darcy behavior in PFRF. Higher filling degrees and weaker hydraulic conductivity of filling region intensified the non‐Darcy effect. The volume of eddy regions exhibited three stages of variation with increasing inertia effect (i.e., stable stage, slow nonlinear growth stage, and rapid linear growth stage). We developed a new model based on gene expression programming to quantitatively evaluate PFRF's non‐Darcy behavior. This study enhances the understanding of fluid flow in partially filled rough fractures, benefiting for advancing the understanding of nonlinear seepage and solute transport in partially filled rough fractures. Key Points Critical non‐Darcy factor E = 0.