The effect of single rough element on fracture nonlinear seepage behavior by lattice Boltzmann method

Fracture seepage is a critical issue in both engineering and scientific research, yet the role of rough fracture surfaces in driving nonlinear behavior remains poorly understood. This study uses the lattice Boltzmann method to numerically simulate the effects of semicircular rough elements of varying sizes on the flow field, starting from a simplified scenario to explore the nonlinear evolution of rough fractures. The results reveal that rough elements alter both velocity and pressure profiles, with increased velocity above the rough elements and a corresponding pressure drop. Recirculation zones are also formed, growing larger as the rough element radius increases. A relationship was established to describe the interaction between rough elements and fluid, linking the drag coefficient to relative roughness and Reynolds number. Pressure distribution analysis around the rough elements shows that they experience forces primarily in the direction of fluid flow within the channel. By examining non-Darcy flow behavior, a nonlinear seepage model based on the Forchheimer equation was developed for individual rough elements. The findings demonstrate that rough elements are the key factor driving nonlinear seepage changes [Re∈100,160]. The complex morphology of the fracture surface leads to variations in velocity and pressure, formation of recirculation zones, and the emergence of nonlinear behavior.