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Accurately evaluating the flow characteristics in fracture intersections is important to advance the understanding of groundwater flow and solute transport in crossed rock fractures. However, mainly two-dimensional (2D) intersection models have been adopted in previous studies, and the influence of intersection angles and related three-dimensional (3D) effects (channel flow and transverse flow) on the fracture seepage and the solute transport is still neglected. In this study, the 3D crossed fracture models, coupled with various intersection angles, were established through the intersection of two rough-walled fractures. The characteristic parameters of the fluid flow and the solute transport under different inlet velocity conditions were calculated by the Navier–Stokes equation and the advective–diffusion equation, respectively. The results indicated that the intricate geometry of the intersection in 3D rough-walled models led to channeling flows, which subsequently impacted mixing behavior depending on velocity. Due to the presence of channeling flows, the velocity ratio at the outlet was different from that of a 2D fracture as the inlet hydraulic conditions evolved. The coefficient matrices describing nonlinear flow behavior in different fracture intersection angles were quantified simultaneously. The reallocation of fluid pathways induced by intersecting angles affects mixing behavior by influencing the geometrical structure of fracture intersections. Moreover, the breakthrough curves and solute mixing process were significantly dependent on the intersection angle and the inlet velocity. In the linear region, the mixing ratio is random due to the intersection of heterogeneous, while in the nonlinear region, the mixing ratio decreases with the increase in water flow. Above all, the correlation established in this study between hydraulic parameters and the intersection angle parameter can enhance their efficacy in predicting solute transport in fractured rocks. [ABSTRACT FROM AUTHOR]

The Izbash equation has been widely used in the subsurface applications. However, the Izbash equation is still empirical, and its coefficients (scaling factor λ and power exponent M) have not been systematically characterized and quantified. In this study, laboratory experiments and numerical simulations of fluid flow across a wide range of hydraulic gradients (J = 0–4) in horizontal rough fractures were conducted to comprehensively characterize and quantify the influence of fracture geometric attributes and fluid inertial effects on λ and M. The results showed that λ increased with fracture relative roughness (RSD). The fluid inertial effect (quantified by the non-Darcy effect factor E and Re) had a two-stage influence on λ. When the fluid flow was laminar, λ increased with E. However, when the fluid flow regime starts to transition from laminar flow to turbulent flow, λ decreased with increasing E. M is positively correlated with RSD and the fluid inertia effect E. We found that the transition of flow regime from laminar to turbulent flow depended on whether the recirculation zones are fully developed. The fully developed recirculation zones determine the distortions of the velocity field and flow field, which induced the turbulent flow. The quantitative models of λ and M were obtained based on numerical simulations, which quantified the coupling influence of the fracture geometric property and fluid inertial effect. The validity of quantitative models was verified by laboratory experiments. Our work provided a new understanding of the Izbash coefficients and laid a foundation for theoretical background exploration of the Izbash equation. [ABSTRACT FROM AUTHOR]

The cross section of a fracture along the streamwise direction determines the water-passing capacity of the fracture. The seepage fields in four fracture models with different contact conditions are analyzed and investigated via computational fluid dynamics simulations. The main results are as follows: (1) a kind of low-velocity region is formed under small local aperture conditions; (2) the blocking degree of the contact area to the fracture seepage depends on the local flow channels compressed by it (flow angle and local aperture); (3) on a cross section, the interference of the contact area and roughness on the fluid flow make the average flow velocity (Uavg) greater than its streamwise component (uavg) except for seepage inlet, which increases with the decrease in the average mechanical aperture and the expansion of the contact area [C = 17.90%, compared to lower C, the whole average flow velocity (1.88 m/s) is the maximum]; (4) there may be an upward trend of pressure along the streamwise direction: where the cross-sectional area increases, the additional kinetic energy generated by the reduced flow velocity will be converted into pressure potential energy if it is not fully consumed by the viscous force; (5) along the streamwise direction, there is a linear correlation between the change rate in uavg (∂uavg/∂x) and that of average pressure on a cross section (∂P/∂x), which is affected by the interference of the contact area and roughness (R2 = 0.25 at C = 17.90%), a conceptual model derived from this linear correlation can describe the relation between the hydraulic characteristics of a fracture and streamwise cross section. [ABSTRACT FROM AUTHOR]