Non-linear flow behavior in rough fractures with shear dislocations is numerically investigated in this study with the validated multi-relaxation time lattice Boltzmann method. Fracture flow tests with different degrees of fractal roughness are simulated and the results show that the surface roughness has an inhibiting effect on fracture flow. With increasing roughness parameter, the effective transmissivity decreases accordingly. Deviation of fracture flow from the linear regime appears earlier for fractures with rougher surfaces and the non-linearity of fracture flow is enhanced with the tortuous flow-path and corner eddies during the closure process. The non-linearity of fracture flow was found to be anisotropic when applying the pressure gradient parallel and perpendicular to the shear direction. Though the anisotropic feature shows a non-monotonic trend during the closure process, it is enhanced with the increasing roughness parameter. Evaluation of the Forchheimer law in quantifying the non-linear fracture flow is also conducted. The relative difference between the Forchheimer linear transmissivity and intrinsic linear transmissivity is about 1–3%. Assuming that the Forchheimer linear transmissivity is equal to intrinsic linear transmissivity, the linear pressure drop can be underestimated. Relating the non-linear parameters with the dimensionless effective hydraulic aperture, a new model is proposed to predict the critical hydraulic behavior of rough fractures.

在这项研究中，采用经过验证的多重弛豫时间格子Boltzmann方法，对具有剪切错位的粗糙裂缝中的非线性流动行为进行了数值研究。对不同程度的分形粗糙度进行了裂隙流动试验，结果表明表面粗糙度对裂隙流动具有抑制作用。随着粗糙度参数的增加，有效透射率相应地降低。对于具有较粗糙表面的裂缝，裂缝流动与线性状态的偏差较早出现，并且在闭合过程中，弯曲流动的路径和拐角涡流会增强裂缝流动的非线性。当施加平行于和垂直于剪切方向的压力梯度时，裂缝流动的非线性是各向异性的。尽管各向异性特征在闭合过程中显示出非单调趋势，但随着粗糙度参数的增加，各向异性特征得以增强。还进行了Forchheimer定律的定量非线性裂缝流评估。Forchheimer线性透射率与固有线性透射率之间的相对差约为1-3％。假设Forchheimer线性透射率等于本征线性透射率，则线性压降可能会被低估。将非线性参数与无因次有效水力孔径联系起来，提出了一个新模型来预测粗糙裂缝的临界水力行为。还评估了Forchheimer定律以量化非线性裂缝流动。Forchheimer线性透射率与固有线性透射率之间的相对差约为1-3％。假设Forchheimer线性透射率等于本征线性透射率，则线性压降可能会被低估。将非线性参数与无因次有效水力孔径联系起来，提出了一个新模型来预测粗糙裂缝的临界水力行为。还评估了Forchheimer定律以量化非线性裂缝流动。Forchheimer线性透射率与固有线性透射率之间的相对差约为1-3％。假设Forchheimer线性透射率等于本征线性透射率，则线性压降可能会被低估。将非线性参数与无因次有效水力孔径联系起来，提出了一个新模型来预测粗糙裂缝的临界水力行为。