Abstract In this note, the non-linear fluid flow through rough fracture is investigated experimentally. The rough surface of fracture is generated synthetically based on the fractal dimension (D) and standard deviation (σ). 3D printing technique is used to produce the fracture specimen, in which, different components of the specimen are printed and assembled so that the fracture roughness and aperture can be easily controlled. After that, the self-designed apparatus is used to conduct the fluid flow test on the fractured specimens under various pressure gradients. It is found that, the surface roughness imposes an important impact on the nonlinear characteristics of fluid flow through fracture; and the root-mean-square of the first derivative of profile, Z2, is found effective in characterizing the fracture roughness. Based on the test results and the derived parameters in Forchheimer equation, an empirical equation is proposed to relate the hydraulic aperture (eh) to Z2 and mechanical aperture (em). Furthermore, the correlation among the nonlinear coefficient β , em and Z2 is established.

中文翻译：

---

基于分形理论和3D打印技术的非线性流体通过粗糙裂缝的实验研究

摘要 在这篇文章中，通过实验研究了通过粗糙裂缝的非线性流体流动。根据分形维数 (D) 和标准差 (σ) 综合生成断裂的粗糙表面。3D打印技术用于生产断裂试样，其中试样的不同部件被打印和组装，从而可以轻松控制断裂粗糙度和孔径。之后，利用自行设计的装置对不同压力梯度下的破裂试样进行流体流动试验。研究发现，表面粗糙度对流体流经裂缝的非线性特性有重要影响；并且发现轮廓的一阶导数 Z2 的均方根可有效表征断裂粗糙度。基于测试结果和 Forchheimer 方程中的导出参数，提出了一个经验方程，将液压孔径 (eh) 与 Z2 和机械孔径 (em) 联系起来。此外，还建立了非线性系数β、em 和Z2 之间的相关性。