Modeling of coupled Darcy-Forchheimer flow in fractured porous media and its engineering application
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摘要: 针对裂隙-孔隙双重介质非线性渗流问题,采用压力交换函数描述孔隙Darcy渗流和裂隙Forchheimer渗流耦合特性,推导了渗流方程有限体积的数值格式,并编制了相应的计算程序。通过与单裂隙和相交裂隙渗流的Frih和Arraras解对比,验证了新方法的合理性。对富水深埋裂隙型围岩隧道非线性渗流问题的计算表明,所提算法对复杂裂隙系统问题具有很强的适用性。进一步分析隧道围岩渗流特征：越接近隧道位置,水压梯度越大,流量也越大；隧道周围水压梯度呈现“底部大,顶部小”的特点,最大相差2.5倍,因此隧道底部的流量大于顶部流量；裂隙方向均匀性和密度是影响隧道围岩水力特性的重要因素。在一定水力梯度下,裂隙方向越集中于水力梯度方向且密度越大时,围岩导水性越大,隧道流量越大,越容易发生涌水事故。研究成果为裂隙型围岩隧道防水设计及工程实践提供参考。
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关键词:
- 裂隙-孔隙双重介质 /
- Darcy-Forchheimer耦合流动 /
- 有限体积法 /
- 隧道非线性渗流
Abstract: Aiming to solve the nonlinear flow in fractured porous media, the coupling characteristics between Darcy flow in pores and Forchheimer flow in fractures are described by means of the pressure transfer function. The finite volume numerical form of seepage equations is derived, and the corresponding numerical code is written. The flow solution by the proposed method for single fracture and intersecting fracture is verified against Frih and Arraras’ solution. Based on this method, the fluid flow behavior of a fractured rock deep-buried tunnel is simulated, which shows it has strong applicability to flow in complex fracture system. The nonlinear flow of tunnel is also analyzed. The results show that the hydraulic gradient of surrounding rock is characterized by "large at bottom and small at top", with the maximum difference of 2.5 times. Therefore, the flow rate at the bottom of the tunnel is greater than that at the top. The distribution homogeneity and density of fracture are the important factors that affect the hydraulic behavior of fractured rock tunnels. At certain water pressure, the more fractures concentrated in the direction of water pressure and the greater the density is, the greater the surrounding rock conductivity is and the greater the flow rate of tunnel is. In this condition, water-inflow accident of tunnels will be prone to occur. The research results may provide reference for the waterproof design and engineering practice of fractured rock tunnels. -
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图 8 相交裂隙1新方法计算的压力
Figure 8. Distribution of pressure calculated by proposed method for intersecting fracture case 1
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图 9 相交裂隙2新方法计算的压力
Figure 9. Distribution of pressure calculated by proposed method for intersecting fracture case 2
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图 10 相交裂隙网格大小与误差的关系
Figure 10. Relationship between error and mesh size for intersecting fracture model
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图 11 相交裂隙单元比率与误差的关系
Figure 11. Relationshp between error and mesh ratio for intersecting fracture model
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图 13 不同κ值下隧道围岩[30, 50]段压力分布
Figure 13. Distribution of water pressure of tunnel rock at [30, 50] range under different values of κ
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图 14 不同κ值下裂隙流量分布
Figure 14. Distribution of fracture flow rate under different values of κ
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图 15 不同裂隙数量下隧道围岩[30, 50]段压力分布
Figure 15. Distribution of water pressure of tunnel rock at [30, 50] range under different fracture numbers
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图 16 不同裂隙数量下裂隙流量分布
Figure 16. Distribution of fracture flow rate under different fracture numbers
表 1 裂隙几何参数
Table 1 Geometrical parameters of fractures
长度/m 开度/mm 倾角 数量N lmin lmax λ b μ κ 1.0 60.0 1.0 0.1 50° [0,8] [10,300] 
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