Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

Infiltration processes in fractured-porous media remain a crucial, yet not very well understood component of recharge and vulnerability assessment. Under partially saturated condition flows in fractures, percolating fracture networks and fault zones contribute to the fastest spectrum of infiltration velocities via preferential pathways. Specifically, the partitioning dynamics at fracture intersections determine the magnitude of flow fragmentation into vertical and horizontal components, hence the bulk flow velocity and dispersion of fracture networks. Here we derive an approximate analytical solution for the partitioning process and validate it using smoothed particle hydrodynamics simulations. The transfer function is conceptually based on simulation results and laboratory experiments carried out in previous works. It allows efficient flow simulation through fracture networks with simple cubic structures and an arbitrary number of fractures and aperture sizes via linear response theory and convolution of a given input signal. We derive a nondimensional bulk flow velocity ((Formula presented.)) and dispersion coefficient ((Formula presented.)) to characterize fracture networks in terms of dimensionless horizontal and vertical time scales τ_m and τ₀. The dispersion coefficient strongly depends on the horizontal time scale and converges toward a constant value of 0.08 within reasonable fluid and geometrical parameter ranges, while the nondimensional velocity exhibits a characteristic (Formula presented.) scaling. Given that hydraulic information is often only available at limited places within (fractured-porous) aquifer systems (boreholes or springs), our study intends to provide an analytical concept to potentially reconstruct internal fracture network geometries from external boundary information, such as the dispersive properties of discharge (groundwater level fluctuations).