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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (11): 2142-2150    DOI: 10.3785/j.issn.1008-973X.2021.11.015
    
Analytical solution of seepage field and reasonable support parameters of tunnel in water rich area
Jian-ping ZHAO1(),Jian-wu LI1(),Lin Bi1,Bei-bei CHENG2
1. School of Resources and Safety Engineering, Central South University, Changsha 410083, China
2. Three Gorges Base Development Limited Company, Yichang 443002, China
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Abstract  

Based on the theory of complex potential function and groundwater hydraulics, the analytical solution of seepage field of tunnel in water rich area, which is composed of surrounding rock, grouting circle and initial support, was derived by introducing bipolar coordinate to describe equipotential line, and the formula of hydraulic head difference of hydraulic head around initial support before and after grouting was obtained. The rationality of the analytical method was verified, compared with conformal mapping method, image method and numerical simulation results. The determination method of reasonable seepage parameters of tunnel structure was proposed, by studying the relationship between the seepage parameters of grouting circle and initial support and the external hydraulic head, water inflow and hydraulic head difference of initial support. Results show that decreasing the permeability coefficient or increasing the thickness of the initial support can lead to the decrease of water inflow and the increase of hydraulic head. The hydraulic head difference first increases and then decreases with the increase of permeability coefficient or thickness of initial support. When the head difference is at the peak, the grouting circle can play a great role, and the external hydraulic head of the initial support can be reduced to 30%±6% of full hydraulic head.

Key words： tunnel engineering      complex potential function      bipolar coordinate      seepage field      seepage parameter     
Received: 31 December 2020      Published: 05 November 2021
CLC:  TU 45  
Fund:  国家自然科学基金青年基金资助项目(51104178)；湖南省重点研发计划资助项目(2015SK2086)
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Jian-ping ZHAO
Jian-wu LI
Lin Bi
Bei-bei CHENG
Cite this article:

Jian-ping ZHAO,Jian-wu LI,Lin Bi,Bei-bei CHENG. Analytical solution of seepage field and reasonable support parameters of tunnel in water rich area. Journal of ZheJiang University (Engineering Science), 2021, 55(11): 2142-2150.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.11.015     OR     https://www.zjujournals.com/eng/Y2021/V55/I11/2142


富水区隧道渗流场解析解及合理支护参数

以复势函数和地下水力学理论为基础，引入双极坐标描述等势线，推导由围岩、注浆圈和初期支护组成的富水地区隧道渗流场解析解，获得隧道注浆前后初期支护外水头的水头差公式. 通过与保角变换法、镜像法和数值模拟计算结果对比，验证所提解析方法的合理性. 通过研究隧道注浆圈、初期支护的渗流参数与初期支护外水头、渗水量及水头差的关系，提出隧道结构合理渗流参数的确定方法. 结果表明：减小初期支护渗透系数或增大初期支护厚度都可致渗水量减小且水头增大；水头差随初期支护渗透系数或厚度增大先增大后减小，当水头差处于峰值时，注浆圈能发挥较大的作用，初期支护外水头可以降至全水头的30%±6%.


关键词： 隧道工程,  复势函数,  双极坐标,  渗流场,  渗流参数 
Fig.1 Calculation model for seepage field of tunnel
Fig.2 Location relationship of point source and sink
Fig.3 Bipolar coordinate system with focusz1 and z2
Fig.4 Equipotential lines at boundary in calculation model
Fig.5 FLAC3D model of tunnel buried depth of 100 m
区域 k/(m·s?1) RS/m
围岩 1.5×10?6 ?
注浆圈 1×10?7 7.25
初期支护 1×10?8 2.25
隧道净空 ? 2.00
Tab.1 Structural geometric parameters and permeability coefficient in FLAC3D model
h/m ΔHP/m ΔHT/m ω/%
10 4.422 0.078 1.317
20 4.429 0.071 0.664
30 4.429 0.071 0.461
40 4.417 0.083 0.414
50 4.440 0.060 0.243
60 4.452 0.049 0.164
70 4.471 0.030 0.086
80 4.435 0.065 0.167
90 4.408 0.092 0.213
100 4.489 0.011 0.024
Tab.2 Water head difference between arch top and arch bottom in FLAC3D simulation results
Fig.6 Influence of tunnel buried depth on external water pressure PC of initial support
Fig.7 Influence of permeability coefficient of initial support on external water pressure of initial support
Fig.8 Relationship between water head of initial support and thickness of initial support
Fig.9 Relationship between seepage discharge and initial support thickness
Fig.10 Relationship between water head difference and initial support thickness
Fig.11 Relationship between water head of initial support and permeability coefficient of initial support
Fig.12 Relationship between seepage discharge and permeability coefficient of initial support
Fig.13 Relationship between water head difference and permeability coefficient of initial support
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