Study On Numerical Simulation And Parameters Of Characterization Equation For Nonlinear Flow Within Single Fractures

Under the influence of geotectonic movement and external disturbance,there are many criss-crossing fractures forming within the underground rock masses.Serving as the primary flow channel of rock masses,the investigation of the hydraulic characteristics within fractures has attracted wide concern in many fields including hydraulic engineering.On the one hand,researchers focus on flow characteristics within fractures,and on the other hand,they focus on the effect of fracture flow on the stability of rock masses.For a long time,the fluid flow in fractures is characterized using the cubic law.However,owing to the geometric characteristics of the fracture and the effect of underground environment,the linear cubic law may no longer hold,where a nonlinear relationship between the flow rate and hydraulic gradient generally exists.Using the cubic law to characterize the fluid flow may lead to serious deviations,thereby increasing the risk of engineering accidents.Therefore,it is necessary to investigate the nonlinear flow characteristics in fractures.In this paper,the nonlinear flow characteristics are systematically studied by conducting numerical simulations and theoretical analysis.The primary research contents and conclusions are as follows:(1)The main surface and internal geometric features that can affect fracture flow are reviewed and analyzed.It is found that the selection of roughness parameters should consider the influence of sampling intervals and different roughness values.Many parameters are found to be suitable for the study of mechanical behaviors,but their applications in hydraulic properties may be limited.Roughness at different scales exhibits different contributions to flow behaviors,and using a single roughness parameter simplifies the multi-scale roughness effects,especially for investigating nonlinear flow.(2)With the Weierstrass-Mandelbrot(W-M)fractal function,fractures with different geometric characteristics are constructed,and the effects of shearing,aperture,roughness,and hydraulic gradient on nonlinear flow are comprehensively studied.The enhancement of nonlinear flow within rough fractures is accompanied by the development and evolution of eddies,and it is also reflected by the increases in the parameters of Forchheimer’s and Izbash’s laws.Under a higher Reynolds number,both eddies and fracture geometries can affect the nonlinear flow.For rough fractures with joint roughness coefficient JRC<18,the aperture ratio E/e versus the Reynolds number Re relationship follows a unified power function under different shear displacements and hydraulic gradients.However,this relationship becomes invalid as roughness further increases,with a strong variability on flow field.(3)The relationship between Forchheimer’s and Izbash’s laws is established,and the detailed expression of Izbash’s exponent m is obtained based on mathematical derivations.It is found that m is a dimensionless parameter related to flow rate,depending on the hydraulic conditions and geometric characteristics of a fracture.The improved Izbash’s law can describe the local nonlinear flow characteristics in contrast to Izbash’s law.At the maximum values of the flow rate and pressure gradient for a given curve,the corrected coefficient mI in the improved Izbash’s law is approximately equal to that of m.The final results successfully revealed the relationship between cubic law,Forchheimer’s law,Izbash’s law,and the improved Izbash’s law.(4)With the Forchheimer number F0,the critical value for characterizing the onset of nonlinear flow is determined for the improved Izbash’s law or Izbash’s law at F0=0.11,that is,mcri=1.1.This relationship indicates that when the magnitude of m or mi exceeds 1.1,the effect of nonlinear flow cannot be ignored.(5)The field data of the high-pressure packer tests is analyzed using the improved Izbash’s law,and a new equation with a simple form and a clear meaning is established to predict the hydraulic conductivity for nonlinear flow with this law.The results indicate that the nonlinear hydraulic conductivity is smaller than the linear hydraulic conductivity,where their difference is positively related to the corrected coefficient mI.The accuracy and feasibility of the improved Izbash’s law is validated using the field data.Compared with the previous predictions,this method is featured with more convenience and comparable accuracy.