The effects of roughness and normal stress on hydraulic properties of fractures are significant during the coupled shear flow test. Knowing the laws of fluid flow and solute transport in fractures is essential to ensure the nature and safety of geological projects. Although many experiments and numerical simulations of coupled shear flow test have been conducted, there is still a lack of research on using the full Navier-Stokes (N-S) equation to solve the real flow characteristics of fluid in three-dimensional rough fractures. The main purpose of this paper is to study the influence of roughness and normal stress on the fluid flow and solute transport through fractures under the constant normal stiffness boundary condition. Based on the corrected successive random addition (SRA) algorithm, fracture surfaces with different roughness expressed by the Hurst coefficient ( ) were generated. By applying a shear displacement of 5 mm, the sheared fracture models with normal stresses of 1 MPa, 3 MPa, and 5 MPa were obtained, respectively. The hydraulic characteristics of three-dimensional fractures were analyzed by solving the full N-S equation. The particle tracking method was employed to obtain the breakthrough curves based on the calculated flow field. The numerical method was verified with experimental results. It has been found that, for the same normal stress, the smaller the fracture value is (i.e., more tough the fracture is), the larger the mechanical aperture is. The ratio of hydraulic aperture to mechanical aperture ( ) decreases with the increasing of normal stress. The smaller the value, the effect of the normal stress on the ratio is more significant. The variation of transmissivity of fractures with the flow rate exhibits similar manner with that of . With the normal stress and value increasing, the mean velocity of particles becomes higher and more particles move to the outlet boundary. The dispersive transport behavior becomes obvious when normal stress is larger.

中文翻译：

---

不同法向应力下粗糙裂缝中流体流动和溶质运移的数值研究

在耦合剪切流试验中，粗糙度和法向应力对裂缝水力特性的影响是显着的。了解裂缝中流体流动和溶质运移规律对于保证地质工程的性质和安全至关重要。尽管已经进行了大量的耦合剪切流试验的实验和数值模拟，但对于利用完整的纳维-斯托克斯(NS)方程求解三维粗糙裂缝中流体的真实流动特征仍然缺乏研究。本文的主要目的是研究在常法向刚度边界条件下粗糙度和法向应力对流体流动和溶质通过裂缝输运的影响。基于修正的连续随机加法（SRA）算法，产生了用 Hurst 系数 ( ) 表示的不同粗糙度的断面。通过施加5 mm的剪切位移，分别得到法向应力为1 MPa、3 MPa和5 MPa的剪切断裂模型。通过求解全NS方程，分析了三维裂缝的水力特性。基于计算出的流场，采用粒子跟踪方法获得穿透曲线。数值方法得到了实验结果的验证。已经发现，对于相同的法向应力，断裂值越小（即断裂越坚韧），机械孔径越大。液压孔径与机械孔径之比 ( ) 随法向应力的增加而减小。值越小，正应力对比率的影响更为显着。裂缝导水率随流速的变化规律与 相似。随着法向应力和值的增加，粒子的平均速度变高，更多的粒子移动到出口边界。当正应力较大时，弥散输运行为变得明显。