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Abstract:Local cubic law (LCL) is one of the most commonly applied physical laws for flow in single fractures (SF) and fractured media. The foundation of LCL is Darcian flow. This experimental study examines if LCL is valid for flow in a single rough fracture and how the fracture roughness and Reynolds number (Re) affect flow. Similar to the Moody diagram for flow in pipes, a diagram for flow in a single rough fracture has been generated to relate the friction coefficient with Re and the roughness. Under the experimental condition of this study, flow appears to be substantially different from Darcian flow. The flow law of q / e n J m appears to be valid for describing the flow scheme where q, e, and J are the unit width flux, the average aperture, and the hydraulic gradient. The value of the power index m is found to be around 0Ð83 ¾ 0Ð98, less than what has been used in Darcian flow (m D 1). The power index n is around 11Ð2 and 13Ð0, much greater than the n value used in the LCL (n D 3), and it increases with the average velocity. The Moody type of diagram shows that the friction factor for flow in SFs is influenced by Re and the roughness. It decreases with Re when Re is small, and becomes less sensitive to Re when Re is large enough. It also increases with the roughness.

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