Stochastic generation and numerical gridding of dissolved pore-fracture composite networks
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摘要:
煤层底板岩溶裂隙含水层导致底板突水问题受到广泛关注, 掌握含水层渗流特征是减少此类事故发生的关键, 而在此之前应首先建立合理的含水层模型。岩溶裂隙含水层具有裂隙和岩溶两种复合网络介质特征, 针对此类问题主要采用数值模拟方法进行研究, 而多数成果仅对含水层中的裂隙网络进行分析, 忽略了其中随机分布的溶孔等岩溶现象, 与实际情况差异较大。重点对灰岩含水层中随机分布的溶孔进行模拟, 并将其与裂隙网络模型结合, 得到准确度较高的灰岩含水层网络模型, 并将其数值化。为此选取了钻孔揭露及露头资料, 用AutoCAD软件描绘溶孔轮廓建立了溶孔形态库, 为溶孔的随机生成提供了足够的样本支撑, 溶孔样本足够多时, 溶孔形态库就具有很高的真实性; 其次利用多因素定向块体切割技术建立了溶孔储存空间, 随机从中提取溶孔, 按照一定比例缩放并置于储存空间内, 就可以实现随机溶孔模型的生成。随后将其与基于蒙特卡洛法生成的裂隙网络叠加, 从而得到具有一定溶孔率和裂隙密度、间距的灰岩含水层复合网络模型。最后基于AutoCAD软件将网络模型转化为FLAC3D数值网格, 即建立灰岩含水层数值模型, 由此生成具有不同溶孔率和裂隙密度、间距的复合网络模型。对裂隙网络中的裂隙密度和延展性分别按低、较低、中等、较高、高进行分类; 将溶孔模型中的溶孔率设为0.05, 0.10, 0.15, 0.20, 0.25, 0.35。以高密度-低延展性裂隙网络为例, 选取了溶孔率为0.05和0.25的溶孔模型与其叠加, 对复合网格中的裂隙迹长、溶孔长轴比和倾角进行统计, 结果符合预期, 从而证明所生成模型的有效性。研究成果对于三维随机溶孔模型的建立具有一定参考意义, 为后续基于数值模拟分析岩溶裂隙含水层的渗流特征奠定了模型基础。
Abstract:Objective The problem of water inrush caused by karst fissure aquifers in coal seam floor has been widely concerned. The key to reduce the occurrence of such accidents is mastering the seepage characteristics of aquifer. Before that, an accurate and reasonable aquifer model should be established first.
Methods The karst fractured aquifer has the characteristics of composite network. At present, the numerical simulation method is mainly used to resolve this kind of problem. However, most of the existing numerical models only simulate the fracture network of aquifer, ignoring the karst phenomena such as dissolved pores with stochastic distribution, which is different from the practice. Therefore, this paper focuses on the simulation of randomly distributed dissolution pores in limestone aquifers, and combines them with the existing fracture network to obtain a more accurate karst featured aquifer network model, then convert it into a numerical ones. For this reason, firstly, some drilling and outcrop data are selected, and the contour of dissolved pores is depicted by AutoCAD software to establish corresponding morphological library, which provides sufficient samples for the stochastic generation of dissolved pore. When there are enough dissolved pore samples, the authenticity of the morphological library of dissolved pores are maintained. Secondly, the multi-factor directional block cutting technology is used to establish a storage space for the subsequent random dissolved pores. The dissolved pores are randomly extracted from corresponding morphological library, after scaling and rotating these samples into the storage space according to a certain scaling ratio, and finally the stochastic generation of dissolved pores can be realized. Subsequently, superimposed it with the fracture network generation based on the Monte Carlo method to obtain a randomly generated limestone aquifer composite grid model with a certain dissolved porosity, fracture density and spacing. Finally, the network model is transformed into FLAC3D numerical gird based on AutoCAD software, and the numerical model of limestone can be established.
Results According to the above method, the composite network model of limestone aquifer with different solution porosity, fracture density and spacing can be generated. The density and ductility of the fractures in the fracture network are labelled as low, moderately low, medium, moderately high and high respectively. The dissolution rate of dissolved pore is classified into 0.05, 0.10, 0.15, 0.20, 0.25 and 0.35 respectively. Taking high density-low ductility fracture network as an example. Two models with dissolved pore rate of 0.05 and 0.25 are superimposed, and statistial analysis was carried out on the trace length of fracture, long axis ratio and dip angle of dissolved pore. The obtained results are in line with expectations, which proves the effectiveness of the generated model.
Conclusion The research results have certain significance for the establishment of three-dimensional random dissolution pore model, and lay a foundation for the subsequent analysis of seepage characteristics of karst fracture aquifer based on numerical simulation.
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图 2 溶孔形态特征的计算与统计示意图
o(x, y). 中心点坐标；a, b. 溶孔边框矩形的长轴，短轴；θ. 溶孔长轴与竖直方向的夹角
Figure 2. Calculation and statistical diagram of dissolved pore morphology characteristics
图 3 多因素定向切割示意图
a. 椭圆块体切割示意; b. 最终地层定向块体切割
Figure 3. Schematic diagram of multi-factor directional cutting
图 4 溶孔模型生成流程图
a. 溶孔生成流程示意; b. 填充溶孔的岩体
Figure 4. Flow chart of dissolved pore model generation
图 5 高密度-低延展性裂隙网络及裂隙迹长统计图
a. 裂隙网络; b. 第Ⅰ组裂隙迹长; c. 第Ⅱ组裂隙迹长
Figure 5. High density-low ductility fissure network and fissure track length statistics
图 6 裂隙网络修剪与不同子区域数值网格
a. 修剪后的裂隙网络与子区域框选; b. 4.0 m×4.0 m; c. 3.0 m×3.0 m; d. 1.0 m×1.0 m; e. 0.4 m×0.4 m; f. 0.2 m×0.2 m
Figure 6. Fissure network pruning and numerical grids of different sub-regions
图 7 溶孔率为0.05的溶孔岩体
a. 随机生成的溶孔; b. 长轴比统计直方图; c. 溶孔倾角统计直方图
Figure 7. Dissolution pore rock mass with a dissolved porosity ratio of 0.05
图 8 溶孔边界几何数据集及其数值网格化
a. 溶孔率0.05的几何集; b. 溶孔率0.25的几何集; c. 溶孔率0.05的数值网格; d. 溶孔率0.25的数值网格
Figure 8. Boundary geometry dataset and numerical gridding of the dissolved pore
图 9 不同溶孔率的随机溶孔-裂隙网络数值网格
a. 溶孔率0.05; b. 溶孔率0.25
Figure 9. Numerical grid of the random dissolved pore-fracture network with different dissolved porosity
图 10 不同子区域下的数值网格实现
a. 16 m×16 m; b. 12 m×12 m; c. 8.0 m×8.0 m; d. 4.0 m×4.0 m
Figure 10. Numerical grid implementation of different subregions
表 1 高密度-低延展性裂隙参数
Table 1. Parameters of high density-low ductility fractures
几何参数 分布类型 平均值 标准差 最小值 最大值 Ⅰ 迹长/m 对数正态 0.5 0.1 0.4 0.6 走向/(°) 正态 45 2 43 47 平均间距/m 0.05 Ⅱ 迹长/m 对数正态 0.5 0.1 0.4 0.6 走向/(°) 正态 135 2 133 137 平均间距/m 0.05 
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