水下浅埋双孔平行隧道渗流场的解析研究

郭玉峰; 王华宁; 蒋明镜

doi:10.11779/CJGE202106012

水下浅埋双孔平行隧道渗流场的解析研究 English Version

郭玉峰¹,
王华宁^{1, 2, ,},
蒋明镜^{2, 3}

1.
同济大学航空航天与力学学院,上海　200092
2.
同济大学土木工程防灾国家重点实验室,上海　200092
3.
天津大学土木工程学院,天津　300072

基金项目:

国家自然科学基金项目 11872281

同济大学土木工程防灾国家重点实验室自主课题 SLDRCE19-A-06

详细信息

作者简介:
王华宁(1975—),女,教授,博士生导师,主要从事地下工程中的解析理论与方法、数值方法的耦合分析、离散元在地下工程中的应用等方面的教学和科研。E-mail: wanghn@tongji.edu.cn

通讯作者:
王华宁, E-mail: wanghn@tongji.edu.cn

中图分类号: TU462
计量
- 文章访问数: 264
- HTML全文浏览量: 44
- PDF下载量: 163
出版历程
- 收稿日期: 2020-08-01
- 网络出版日期: 2022-12-02
- 刊出日期: 2021-05-31

Analytical solutions of seepage field for underwater shallow-buried parallel twin tunnels

1.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
2.
State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
3.
Department of Civil Engineering, Tianjin University, Tianjin 300072, China

摘要

摘要: 目前对于双孔隧道渗流场的解析求解多基于单孔隧道渗流场的简单叠加,未真实满足洞周边界条件,所得结果存在误差。基于质量守恒定律和达西定律,采用保角变换法和Schwartz迭代法对水下双线平行隧道稳态渗流场进行了推导,经过2～3次迭代后获得了高精度的解答。采用Comsol软件对该问题进行数值模拟,并将数值模拟结果与本文解析解进行对比,发现在全域范围二者均吻合良好。与叠加法解答的对比显示,本解答与叠加法解答在远区一致；而隧道附近叠加法的误差较大。最后,讨论了隧道间距、埋深和相对大小对双孔平行隧道渗流场水头分布、渗流量的影响。
- 双孔平行隧道 /
- 渗流场 /
- 解析解 /
- Schwartz迭代法 /
- 保角变换
Abstract: Most of the current analytical solutions of seepage field for twin tunnels are directly obtained by the superposition of seepage fields of two single tunnels, which does not really satisfy the conditions at the tunnel boundary and has the deviation from the actual seepage field. Based on the mass conservation law and the Darcy’s law, an analytical solution of seepage field for underwater twin parallel tunnels is derived by the Schwartz alternating method combined with the conformal mapping. After two to three iterations, an analytical solution of the problem with high accuracy is obtained. The numerical software Comsol is used to simulate the problem, and the simulated results are compared with the analytical solutions proposed in this study. It is found that they are in good agreement throughout the entirety of the ground. Compared with the direct superposition results, the two results are consistent in the region far from the tunnel, while there is a large error of the superposition results near the tunnel boundary. Finally, the influences of tunnel spacing, buried depth and relative size on the distribution of hydraulic head and the water inflow of the tunnel are discussed.
- twin parallel tunnels /
- seepage field /
- analytical solution /
- Schwartz alternating method /
- conformal mapping

HTML全文

图 1 双线平行隧道示意图

Figure 1. Schematic diagram of twin parallel tunnels

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图 2 迭代中的边界条件及附加水头

Figure 2. Boundary conditions and generated additional heads in alternating iterations

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图 3 保角映射

Figure 3. Conformal mapping

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图 4 迭代中的附加水头

Figure 4. Additional heads in each iterative step

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图 5 数值模拟结果

Figure 5. Numerical results

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图 6 总水头等值线图(解析解)

Figure 6. Contours of hydraulic head (analytical results)

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图 7 与有限元结果的对比

Figure 7. Comparison between analytical and FEM results

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图 8 本文解析解与镜像叠加法结果对比

Figure 8. Comparison between mirror image superposition and Schwartz alternating method

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图 9 隧道横剖面地层分布

Figure 9. Cross section of tunnel and distribution of strata

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图 10 隧道间距对渗流场的影响

Figure 10. Influence of tunnel spacing on seepage field

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图 11 两隧道中点处水头随隧道间距的变化

Figure 11. The hydraulic head at the midpoint of two tunnels versus tunnel spacing

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图 12 不同间距下隧道1渗流量沿洞周分布

Figure 12. Distribution of specific discharge around tunnel 1 under different tunnel spacings

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图 13 比流量最小值及出现位置随隧道间距的变化

Figure 13. The minimum value of specific discharge around tunnel 1 and the location where it occurs versus tunnel spacing

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图 14 隧道2不同埋深下隧道1渗流量沿洞周分布

Figure 14. Distribution of specific discharge around tunnel 1 under different buried depths of tunnel 2

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图 15 隧道1比流量最小值及出现位置随隧道2埋深的变化

Figure 15. The minimum specific discharge around tunnel 1 and its location versus buried depth of tunnel 2

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图 16 不同相对大小下隧道1渗流量沿洞周分布

Figure 16. Distribution of specific discharge around tunnel 1 under various relative tunnel sizes

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表 1 算例参数

Table 1 Parameters of example

隧道编号i	半径 $r_{i}$ $r_{i}$ /m	埋深 $h_{i}$ $h_{i}$ /m	洞周水压 $p_{i}$ $p_{i}$ /Pa	隧道间距l/m	地表水头H/m
1	5	15	0	20	36
2	5	15	0	20	36

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