Theoretical model and experimental verification on non-linear flow at low velocity through rough-walled rock fracture

Non-linear flow in rough-walled rock fracture is one of significant issues of rock mass seepage properties. Based on viscous pressure drop and local pressure drop, a novel non-linear flow model (MT model) at the low velocity though rough-walled rock fracture is proposed for the assumption of velocity proportional to an aperture in sub-fracture which takes place assumption of equal velocity in Javadi's T model. Saturated seepage experiments of five rock fracture replicas at the low flow rate are carried out. The results show that MT model is preferable to fit experimental data compared with preceding others, so the MT model is more exact in describing non-linear flow. Furthermore, the MT model is applicable to the case: the fractures with JRC less than or equal to 10 and Reynolds number lower than 1 000. After a thorough study of MT model, it is discovered that there are two flow regimes in rough-walled rock fractures: Darcy flow in small Reynolds number and Forchheimer flow in large Reynolds number, and a critical Reynolds number is defined to differentiate between them. The effects of fracture roughness and aperture on non-linear flow are discussed. The rougher and smaller aperture of fracture is, the smaller critical Reynolds number is, and the stronger non-linear effect is. A formulation of the critical Reynolds number, hydraulic aperture and absolute roughness is developed. In addition, the formulation is reasonable in rough-walled fracture with JRC less than or equal to 10.