The permeability evolution of fractal-based two-dimensional discrete fracture networks (DFNs) during shearing under constant normal stiffness (CNS) boundary conditions is numerically modeled and analyzed based on a fully coupled hydromechanical (HM) model. The effects of fractal dimension, boundary normal stiffness and hydraulic pressure on the evolutions of mechanical behaviors, aperture distributions and permeability are quantitatively investigated. The results show that with increasing confining pressure from 0 to 30 MPa, the permeability decreases from the magnitude of 10−13 m2 to 10−16 m2, which is generally consistent with previous models reported in the literature. With the increment of shear displacement from 0 to 500 mm, the variations in shear stress, normal stress and normal displacement exhibit the same patterns with the conceptual model. As shear advances, the permeability evolution exhibits a three-stage behavior. In the first stage, the permeability decreases due to the compaction of fractures induced by the increasing shear stress from 0 to the peak value. In the second stage, the permeability holds almost constant values under constant normal load (CNL) boundary conditions, whereas that under CNS boundary conditions decreases by approximately one order of magnitude. Under CNS boundary conditions, although the aperture of shearing fracture increases enhancing its own permeability, the apertures of surrounding fractures are compacted due to the simultaneous increases in the normal and shear stresses, which result in the decrease in the total permeability of DFNs. When the fractal dimension increases from 1.4 to 1.5, the permeability increases following exponential functions in the early stage of shear, which fail to characterize the permeability in the residual stage due to the complex flow path distributions. At the start of shear, the ratio of permeability perpendicular to the shear direction to that parallel to shear decreases approximately from 1.0 to 0.5 and then gradually decreases from 0.5 to 0.3 in the residual stage. The hydraulic pressure tends to open up the fractures and enhances the permeability. The magnitude in permeability enhancement is of approximately the same order with the increase in the hydraulic pressure.

中文翻译：

---

恒定法向刚度边界条件下二维断裂网络渗透率演化

基于全耦合流体力学 (HM) 模型对恒定法向刚度 (CNS) 边界条件下剪切过程中基于分形的二维离散裂缝网络 (DFN) 的渗透率演化进行了数值建模和分析。定量研究了分形维数、边界法向刚度和液压对力学行为、孔径分布和渗透率演变的影响。结果表明，随着围压从 0 增加到 30 MPa，渗透率从 10-13 m2 减少到 10-16 m2，这与之前文献报道的模型基本一致。随着剪切位移从 0 到 500 mm 的增加，剪切应力的变化，法向应力和法向位移表现出与概念模型相同的模式。随着剪切的推进，渗透率演化表现出三阶段行为。在第一阶段，由于剪切应力从 0 增加到峰值引起的裂缝压实，渗透率下降。在第二阶段，渗透率在恒定法向载荷 (CNL) 边界条件下几乎保持不变，而在 CNS 边界条件下，渗透率下降了大约一个数量级。在 CNS 边界条件下，虽然剪切裂缝的孔径增大提高了其自身的渗透率，但由于法向应力和剪切应力同时增加，周围裂缝的孔径被压实，导致 DFN 的总渗透率降低。当分形维数从 1.4 增加到 1.5 时，渗透率在剪切早期遵循指数函数增加，由于流路分布复杂，不能表征剩余阶段的渗透率。在剪切开始时，垂直于剪切方向的渗透率与平行于剪切方向的渗透率之比大约从 1.0 减小到 0.5，然后在残余阶段从 0.5 逐渐减小到 0.3。液压往往会打开裂缝并提高渗透率。渗透率增强的幅度与液压的增加大致相同。由于复杂的流路分布，无法表征剩余阶段的渗透率。在剪切开始时，垂直于剪切方向的渗透率与平行于剪切方向的渗透率之比大约从 1.0 减小到 0.5，然后在残余阶段从 0.5 逐渐减小到 0.3。液压往往会打开裂缝并提高渗透率。渗透率增强的幅度与液压的增加大致相同。由于复杂的流路分布，无法表征剩余阶段的渗透率。在剪切开始时，垂直于剪切方向的渗透率与平行于剪切方向的渗透率之比大约从 1.0 减小到 0.5，然后在残余阶段从 0.5 逐渐减小到 0.3。液压往往会打开裂缝并提高渗透率。渗透率增强的幅度与液压的增加大致相同。液压往往会打开裂缝并提高渗透率。渗透率增强的幅度与液压的增加大致相同。液压往往会打开裂缝并提高渗透率。渗透率增强的幅度与液压的增加大致相同。