Analytical solutions of seepage field for underwater shallow-buried parallel twin tunnels
GUO Yu-feng1, WANG Hua-ning1,2, JIANG Ming-jing2,3
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
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.
[1] 蒋凌云, 张宏, 蒋美幸, 等. 花岗岩残积土隧道渗流效应数值模拟研究[J]. 湖南工业大学学报, 2019, 33(1): 23-30. (JIANG Ling-yun, ZHANG Hong, JIANG Mei-xing.A numerical simulation study on seepage effect of granite residual soil tunnel[J]. Journal of Hunan University of Technology, 2019, 33(1): 23-30. (in Chinese)) [2] 王众. 控制型防排水隧道渗流场数值分析[J]. 石家庄铁道大学学报(自然科学版), 2011, 24(1): 6-9. (WANG Zhong.Seepage field analysis for tunnel excavation based on drainage control[J]. Journal of Shijiazhuang Tiedao University (Natural Science), 2011, 24(1): 6-9. (in Chinese)) [3] 王建宇. 再谈隧道衬砌水压力[J]. 现代隧道技术, 2003, 40(3): 5-9. (WANG Jian-yu.Once more on hydraulic pressure upon lining[J]. Modern Tunnelling Technology, 2003, 40(3): 5-9. (in Chinese)) [4] 王秀英, 王梦恕, 张弥. 计算隧道排水量及衬砌外水压力的一种简化方法[J]. 北方交通大学学报, 2004, 28(1): 8-10. (WANG Xiu-ying, WANG Meng-shu, ZHANG Mi.A simple method to calculate tunnel discharge and external water pressure on lining[J]. Journal of Northern Jiaotong University, 2004, 28(1): 8-10. (in Chinese)) [5] 王秀英, 王梦恕, 张弥. 山岭隧道堵水限排衬砌外水压力研究[J]. 岩土工程学报, 2005, 27(1): 125-127. (WANG Xiu-ying, WANG Meng-shu, ZHANG Mi.Research on regulating water pressure acting on mountain tunnels by blocking ground water and limiting discharge[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(1): 125-127. (in Chinese)) [6] HARR M E.Groundwater and seepage[J]. Soil Science, 1963, 95(4): 289. [7] 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.Analytic solution on seepage field of underwater tunnel considering grouting circle[J]. Journal of Zhejiang University (Engineering Science), 2016, 50(6): 1018-1023. (in Chinese)) [8] PARK K H, OWATSIRIWONG A, 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, 2007, 23(2). [9] 皇甫明, 谭忠盛, 王梦恕, 等. 暗挖海底隧道渗流量的解析解及其应用[J]. 中国工程科学, 2009, 11(7): 66-70. (HUANG Fu-ming, TAN Zhong-sheng, WANG Meng-shu, et al.Analytical solutions for water inflow into an underwater tunnel and its application[J]. Journal of China Engineering Science, 2009, 11(7): 66-70. (in Chinese)) [10] 吴金刚, 谭忠盛, 皇甫明. 高水压隧道渗流场分布的复变函数解析解[J]. 铁道工程学报, 2010, 9(1): 31-36. (WU Jin-gang, TAN Zhong-sheng, HUANG Fu-ming.Analytic solution of complex function to distribution of seepage field of tunnel with high water pressure[J]. Journal of Railway Engineering Society, 2010, 9(1): 31-36. (in Chinese)) [11] 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. (in Chinese)) [12] 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. (in Chinese)) [13] TANG Y, CHAN D H, ZHU D Z.Analytical solution for steady-state groundwater inflow into a circular tunnel in anisotropic soils[J]. Journal of Engineering Mechanics, 2018, 144(9): 8. [14] ZHANG Y, ZHANG D L,FANG Q, et al.Analytical solutions of non-Darcy seepage of grouted subsea tunnels[J]. Tunnelling and Underground Space Technology, 2020, 96: 10. [15] HANSBO S.Aspects of vertical drain design: darcian or non-Darcian flow[J]. Géotechnique, 1997, 47(5): 983-992. [16] 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. (in Chinese)) [17] SU K, ZHOU Y, WU H, et al.An analytical method for groundwater inflow into a drained circular tunnel[J]. Groundwater, 2017, 55(5): 712-721. [18] WANG H N, WU L, JIANG M J, et al.Analytical stress and displacement due to twin tunneling in an elastic semi‐ infinite ground subjected to surcharge loads[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2018, 42(6): 809-828. [19] ZHANG L Q, LU A Z, YUE Z Q, et al.An efficient and accurate iterative stress solution for an infinite elastic plate around two elliptic holes, subjected to uniform loads on the hole boundaries and at infinity[J]. European Journal of Mechanics-A/Solids, 2009, 28(1): 189-193. [20] WANG H N, ZENG G S, UTILI S, et al.Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 93: 13-29. [21] WANG H N, ZENG G S, JIANG M J.Analytical stress and displacement around non-circular tunnels in semi-infinite ground[J]. Applied Mathematical Modelling, 2018, 63: 303-328. [22] 张丙强. 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. (in Chinese)) [23] 吴绍明, 孙瞻, 刘庭金, 等. 龙头山双洞八车道公路隧道地下水渗流初探[J]. 铁道建筑, 2007(12): 45-47. (WU Shao-ming, SUN Zhan, LIU Ting-jin, et al.Elementary discussion on leakage of underground water in Longtoushan mountain highway twin tunnels with 8 lanes[J]. Railway Engineering, 2007(12): 45-47. (in Chinese))