1. School of Resources and Safety Engineering, Central South University, Changsha 410083, China 2. Three Gorges Base Development Limited Company, Yichang 443002, China
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.
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.
Fig.1Calculation model for seepage field of tunnel
Fig.2Location relationship of point source and sink
Fig.3Bipolar coordinate system with focusz1 and z2
Fig.4Equipotential lines at boundary in calculation model
Fig.5FLAC3D 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.1Structural 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.2Water head difference between arch top and arch bottom in FLAC3D simulation results
Fig.6Influence of tunnel buried depth on external water pressure PC of initial support
Fig.7Influence of permeability coefficient of initial support on external water pressure of initial support
Fig.8Relationship between water head of initial support and thickness of initial support
Fig.9Relationship between seepage discharge and initial support thickness
Fig.10Relationship between water head difference and initial support thickness
Fig.11Relationship between water head of initial support and permeability coefficient of initial support
Fig.12Relationship between seepage discharge and permeability coefficient of initial support
Fig.13Relationship between water head difference and permeability coefficient of initial support
[1]
VERRUIJT A A complex variable solution for a deforming circular tunnel in elastic half plane[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1997, 21: 77- 89
doi: 10.1002/(SICI)1096-9853(199702)21:2<77::AID-NAG857>3.0.CO;2-M
[2]
MOHAMED E T Circular tunnel in a semi-infinite aquifer[J]. Tunnelling and Underground Space Technology, 2003, 18 (1): 49- 55
doi: 10.1016/S0886-7798(02)00102-5
[3]
KOLYMBAS D, WAGNER P Groundwater ingress to tunnels: the exact analytical solution[J]. Tunnelling and Underground Space Technology, 2007, 22 (1): 23- 27
doi: 10.1016/j.tust.2006.02.001
[4]
PARK K H, ADISORN O, Lee J G Analytical solution for steady-state groundwater inflow into a drained circular tunnel in a semi-infinite aquifer: a revisit[J]. Tunnelling and Underground Space Technology, 2008, 23 (2): 206- 209
doi: 10.1016/j.tust.2007.02.004
[5]
HUANGFU M, WANG M S, TAN Z S, et al Analytical solutions for steady seepage into an underwater circular tunnel[J]. Tunnelling and Underground Space Technology, 2010, 25 (4): 391- 396
doi: 10.1016/j.tust.2010.02.002
[6]
杜朝伟, 王梦恕, 谭忠盛 水下隧道渗流场解析解及其应用[J]. 岩石力学与工程学报, 2011, 30 (Suppl.2): 3567- 3573 DU Chao-wei, WANG Meng-shu, TAN Zhong-sheng Analytical solution for the seepage field of subsea tunnel and its application[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30 (Suppl.2): 3567- 3573
[7]
朱成伟, 应宏伟, 龚晓南. 任意埋深水下隧道渗流场解析解[J]. 岩土工程学报, 2017, 39(11): 1984-1991. ZHU Cheng-wei, YING Hong-wei, GONG Xiao-nan. Analytical solutions for seepage fields of underwater tunnels with arbitrary burial depth[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(11): 1984-1991.
[8]
YING H W, ZHU C W, SHEN H W, et al Semi-analytical solution for groundwater ingress into lined tunnel[J]. Tunnelling and Underground Space Technology, 2018, 76 (3): 43- 47
[9]
朱成伟, 应宏伟, 龚晓南, 等 水下双线平行隧道渗流场解析研究[J]. 岩土工程学报, 2019, 41 (2): 355- 360 ZHU Cheng-wei, YING Hong-wei, GONG Xiao-nan, et al Analytical solutions to seepage field of underwater twin parallel tunnels[J]. Chinese Journal of Geotechnical Engineering, 2019, 41 (2): 355- 360
[10]
潘以恒, 罗其奇, 周斌, 等 半无限平面含注浆圈深埋隧道渗流场解析研究[J]. 浙江大学学报:工学版, 2018, 52 (6): 1114- 1122 PAN Yi-heng, LUO Qi-qi, ZHOU Bin, et al Analytical study on seepage field of deep tunnel with grouting circle in half plane[J]. Journal of Zhejiang University: Engineering Science, 2018, 52 (6): 1114- 1122
[11]
HARR M E. Groundwater and seepage[M]. New York: McGraw-Hill, 1962.
[12]
LEI S An analytical solution for steady flow into a tunnel[J]. Ground Water, 1999, 37 (1): 23- 26
doi: 10.1111/j.1745-6584.1999.tb00953.x
[13]
张炳强 半无限平面双孔平行隧道渗流场解析研究[J]. 铁道学报, 2017, 39 (1): 125- 131 ZHANG Bing-qiang Analytical solution for seepage field of twin-parallel tunnels in semi-infinite plane[J]. Journal of the China Railway Society, 2017, 39 (1): 125- 131
doi: 10.3969/j.issn.1001-8360.2017.01.018
[14]
王秀英, 谭忠盛 水下隧道复合式衬砌水压特征研究[J]. 现代隧道技术, 2015, 52 (1): 89- 97 WANG Xiu-ying, TAN Zhong-sheng Study on the characteristics of water pressure on the composite lining in underwater tunnels[J]. Modern Tunnelling Technology, 2015, 52 (1): 89- 97
[15]
李鹏飞, 张顶立, 赵勇, 等 海底隧道复合衬砌水压力分布规律及合理注浆加固圈参数研究[J]. 岩石力学与工程学报, 2012, 31 (2): 280- 288 LI Peng-fei, ZHANG Ding-li, ZHAO Yong, et al Study of distribution law of water pressure acting on composite lining and reasonable parameters of grouting circle for subsea tunnel[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31 (2): 280- 288
doi: 10.3969/j.issn.1000-6915.2012.02.007
[16]
程林松. 高等渗流力学: 第1版[M]. 北京: 石油工业出版社, 2011.
[17]
张兆夺. 弹性半平面问题解析解的双极坐标和复变函数解法研究[D]. 重庆: 重庆大学, 2017. ZHANG Zhao-duo. An analytical study on the half-plane elasticity using the methods of bi-polar coordinates and complex variables[D]. Chongqing: Chongqing University, 2017.
[18]
应宏伟, 朱成伟, 龚晓南 考虑注浆圈作用水下隧道渗流场解析解[J]. 浙江大学学报:工学版, 2016, 50 (6): 1018- 1023 YING Hong-wei, ZHU Cheng-wei, GONG Xiao-nan Analytical solution on seepage field of underwater tunnel considering grouting circle[J]. Journal of Zhejiang University: Engineering Science, 2016, 50 (6): 1018- 1023
[19]
李林毅, 阳军生, 张峥, 等 深埋式中心水沟排水隧道渗流场解析研究[J]. 浙江大学学报:工学版, 2018, 52 (11): 2050- 2057 LI Lin-yi, YANG Jun-sheng, ZHANG Zheng, et al Analytical study of seepage field of deep-buried central ditch drainage tunnel[J]. Journal of Zhejiang University: Engineering Science, 2018, 52 (11): 2050- 2057
doi: 10.3785/j.issn.1008-973X.2018.11.002
[20]
高新强, 艾旭峰, 孔超 高水压富水区裂隙岩体隧道渗流场的特征[J]. 中国铁道科学, 2016, 37 (6): 42- 49 GAO Xin-qiang, AI Xu-feng, KONG Chao Characteristics of seepage field of fractured rock mass tunnel in high water pressure and rich water zone[J]. China Railway Science, 2016, 37 (6): 42- 49
doi: 10.3969/j.issn.1001-4632.2016.06.06
