Fractal model of shear-induced rough fracture flow by cross-scale description of its geometry
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摘要: 甘肃北山为高放废物深地质处置库场址的主预选区。针对场址区花岗岩受剪切破坏形成裂隙的渗流特性进行研究，具有重要的工程建设指导意义。为探究北山花岗岩多尺度粗糙裂隙几何特征对非线性渗流场演化的影响规律，对剪切条件下花岗岩裂隙断面的几何特征及渗流特性进行了分形建模研究。结果表明，粗糙裂隙的粗糙程度和开度在模型尺度变化过程中存在完全的自相似性，二者的分布特征在分布空间尺度变化过程中始终保持一致；渗流速度场、梯度场及散度场只存在局部特征的延续，尤其是不同尺度下对应的数量场均服从于正态分布；随着观察尺度的增大场内空间起伏逐渐减小，三场内的尖锐突变逐渐消失且向平滑过渡，这意味着观察尺度越大，粗糙裂隙渗流被误判为平行板渗流的概率越大，即粗糙断面渗流特性的精准描述依赖于几何尺度。Abstract: The Beishan area in Gansu province is the main pre-selected site for deep geological disposal of high-level radioactive waste, it therefore bears implications for the study of fracture seepage characteristics of granite caused by shear failure. This paper investigated the fractal modeling of the geometric and seepage characteristics of granite fracture sections under shear conditions, with the aim to explore the effect of the geometric characteristics of multi-scale rough fractures on the evolution of nonlinear seepage field in Beishan granite. Results show that the roughness height and aperture of rough fractures have complete self-similarity in the process of model scale change, whose distribution are always consistent in the process of spatial scale change. The seepage velocity field, gradient field and divergence field only demonstrate the continuation of local characteristics, in particular, the corresponding quantity fields at different scales are subject to normal distribution. As the observation scale increases, the spatial fluctuation in the field gradually decreases, the sharp mutations in the three fields gradually disappear and are smoothed. This indicates that the larger the observation scale, the greater the probability that the seepage of rough fracture is misjudged as the seepage of parallel plate, therefore the seepage characteristics of rough section would be more accurately described by taking the geometric scale into account.
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Key words:
- orthogonal shearing /
- rough section /
- roughness /
- multiscale /
- fractal seepage model
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图 5 样品剪切表面相对粗糙高度的正态分布
Figure 5. Normal distribution of relative roughness height of sample shear surface
图 6 样品剪切表面倾斜角度的正态分布
Figure 6. Normal distribution of tilt angle of sample shear surface
图 7 样品剪切表面连接线长度的正态分布
Figure 7. Normal distribution of the length of the connecting line on the shear surface of the sample
图 16 渗流速度梯度场的分形建模
Figure 16. Fractal modeling of gradient field describing the seepage velocity
图 18 渗流速度散度场的分形建模
Figure 18. Fractal modeling of dispersion field describing seepage velocity
表 1 COMSOL软件模拟所需定量参数
Table 1. Quantitative parameters for COMSOL simulation
名称 取值 描述 rho 1 000 kg/m3 流体密度 mu 0.001 Pa·s 流体动力黏度 
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表 2 COMSOL软件模拟所需变量参数
Table 2. Variable for COMSOL simulation
名称 表达式 单位 描述 a data(x，y)/1 000 m 裂隙开度 KS a2·rho·g_const/mu m/s 水利传导率 TS KSa m2/s 导水系数 u -KSΗx m/s x方向速度 v -KSΗy m/s y方向速度 U sqrt(u2+v2) m/s 速度 注：Η—因变量。
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