The seepage field around twin noncircular tunnels in anisotropic sloping
Tóm tắt
A new and efficient theoretical model for studying the seepage field around two noncircular tunnels in sloping ground is proposed through analytical derivation. The model considers the exact interaction between two tunnels with arbitrary shapes and locations, as well as the permeability anisotropy, whose principal orientation is along any direction. By applying the Schwartz alternating method and conformal mapping, the analytical solutions of the hydraulic head and pore pressure can be obtained. These solutions strictly satisfy all governing equations and conditions. The correctness and accuracy of the analytical solutions are verified by the good agreement between the theoretical and numerical results. The proposed theoretical model can be applied to the cases with any tunnel shape, slope angle, anisotropic direction and degree. The quantitative influences of the anisotropy ratio, slope angle and tunnel shape on the seepage field are obtained, and some useful charts are provided. The proposed model can efficiently and quickly predict the seepage flow around tunnels in anisotropic sloping ground.
Từ khóa
Tài liệu tham khảo
Dong XJ, Karrech A, Basarir H, Elchalakani M, Qi CC (2020) Closed-form solution to the poromechanics of deep arbitrary-shaped openings subjected to rock mass alteration. Int J Geomech 20(12):04020223. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001875
El Tani M (2003) Circular tunnel in a semi-infinite aquifer. Tunn Undergr Space Technol 18(1):49–55. https://doi.org/10.1016/S0886-7798(02)00102-5
Fogang PM, Liu Y, Zhao JL, Ka TA, Xu S (2023) Analytical prediction of tunnel deformation beneath an inclined plane complex potential analysis. Appl Sci-Basel 13(5):3252. https://doi.org/10.3390/app13053252
Guo YF, Wang HN, Jiang MJ (2021) Efficient iterative analytical model for underground seepage around multiple tunnels in semi-infinite saturated media. J Eng Mech 147(11):04021101. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001999
Guo YF, Wang HN, Jiang MJ (2023) An exact analytical approach for determining the seepage field around underwater twin tunnels with linings. Transp Geotech 42:101050. https://doi.org/10.1016/j.trgeo.2023.101050
Harr ME (1962) Groundwater and seepage. McGraw-Hill, New York
Huangfu M, Wang MS, Tan ZS, Wang XY (2010) Analytical solutions for steady seepage into an underwater circular tunnel. Tunn Undergr Space Technol 25(4):391–396. https://doi.org/10.1016/j.tust.2010.02.002
Kolymbas D, Wagner P (2007) Groundwater ingress to tunnels–: the exact analytical solution. Tunn Undergr Space Technol 22(1):23–27. https://doi.org/10.1016/j.tust.2006.02.001
Kong FC, Lu DC, Du XL, Li CP (2018) Displacement analytical prediction of shallow tunnel based on unified displacement function under slope boundary. Int J Numer Anal Methods Geomech 43(1):183–211. https://doi.org/10.1002/nag.2859
Lee IM, Nam SW (2001) The study of seepage forces acting on the tunnel lining and tunnel face in shallow tunnels. Tunn Undergr Space Technol 16(1):31–40. https://doi.org/10.1016/S0886-7798(01)00028-1
Lee SW, Jung JW, Nam SW, Lee IM (2007) The influence of seepage forces on ground reaction curve of circular opening. Tunn Undergr Space Technol 22(1):28–38. https://doi.org/10.1016/j.tust.2006.03.004
Li PF, Wang F, Long YY, Zhao X (2018) Investigation of steady water inflow into a subsea grouted tunnel. Tunn Undergr Space Technol 80:92–102. https://doi.org/10.1016/j.tust.2018.06.003
Li Z, He C, Chen ZQ, Yang SZ, Ding JJ, Pen Y (2019) Study of seepage field distribution and its influence on urban tunnels in water-rich regions. Bull Eng Geol Environ 78:4035–4045. https://doi.org/10.1007/s10064-018-1417-0
Li L, Chen HH, Li JP, Sun DA (2021) A semi-analytical solution to steady-state groundwater inflow into a circular tunnel considering anisotropic permeability. Tunn Undergr Space Technol 116:104115. https://doi.org/10.1016/j.tust.2021.104115
Park KH, Owatsiriwong A, Lee JG (2008) Analytical solution for steady-state groundwater inflow into a drained circular tunnel in a semi-infinite aquifer: a revisit. Tunn Undergr Space Technol 23(2):206–209. https://doi.org/10.1016/j.tust.2007.02.004
Qin ZG, Wang Y, Song Y, Dong Q (2020) The analysis on seepage field of grouted and shotcrete lined underwater tunnel. Math Probl Eng. https://doi.org/10.1155/2020/7319054
Qin ZG, He WG, Zhou HG (2022) Analytical study on seepage field of subsea twin tunnels constructed by NATM, Ocean Eng. https://doi.org/10.1016/j.oceaneng.2022.112345
Tang Y, Chan DH, Zhu DZ (2018) Analytical solution for steady-state groundwater inflow into a circular tunnel in anisotropic soils. J Eng Mech 144(9):06018003. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001502
Wang HN, Wu L, Jiang MJ, Song F (2018) Analytical stress and displacement due to twin tunneling in an elastic semi-infinite ground subjected to surcharge loads. Int J Numer Anal Methods Geomech 42(6):809–828. https://doi.org/10.1002/nag.2764
Wang JC, Huang WM, Xu RQ, Yang ZX, Xu RQ (2020) Analytical approach for circular-jointed shield tunnel lining based on the state space method. Int J Numer Anal Methods Geomech 44(5):575–595. https://doi.org/10.1002/nag.3012
Wei FR, Wang HN, Zeng GS, Jiang MJ (2022) Analytical solution to the seepage field of two parallel noncircular tunnels in permeable anisotropic ground. KSCE J Civ Eng 26:5328–5341. https://doi.org/10.1007/s12205-022-0054-0
Wei FR, Wang HN, Zeng GS, Jiang MJ (2023) Seepage flow around twin tunnels in anisotropic ground revealed by an analytical solution. Undergr Space 10:1–14. https://doi.org/10.1016/j.undsp.2022.08.003
Xu CJ, Liang LJ, Ding WX (2018) Analytical solutions on steady seepage field of deep buried circular tunnel after considering anisotropic flow (in Chinese). J Shanghai Jiao Tong Univ 52(12):27–32. https://doi.org/10.16183/j.cnki.jsjtu.2018.12.004
Ying HW, Zhu CW, Shen HW, Gong XN (2018) Semi-analytical solution for groundwater ingress into lined tunnel. Tunn Undergr Space Technol 76:43–47. https://doi.org/10.1016/j.tust.2018.03.009
Yu HT, Cai C, Bobet A, Guan XF, Yuan Y (2016) Analytical solution for long lined tunnels subjected to travelling loads. Tunn Undergr Space Technol 58:209–215. https://doi.org/10.1016/j.tust.2016.05.008
Yu HT, Cai C, Bobet A, Zhao X, Yuan Y (2019) Analytical solution for longitudinal bending stiffness of shield tunnels. Tunn Undergr Space Technol 83:27–34. https://doi.org/10.1016/j.tust.2018.09.011
Zeng GS, Cai H, Lu AZ (2019) An analytical solution for an arbitrary cavity in an elastic half-plane. Rock Mech Rock Eng 52(11):4509–4526. https://doi.org/10.1007/s00603-019-01844-2
Zeng GS, Wang HN, Wu L, Jiang MJ (2021) A generalized analytical model for mechanical responses of rock during multiple-tunnel excavation in viscoelastic semi-infinite ground. Int J Geomech 21(11):04021202. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002151
Zhang ZG, Zhang MX, Zhao QH, Fang L, Ding Z, Shi MZ (2020) Interaction analyses between existing pipeline and quasi-rectangular tunneling in clays. KSCE J Civ Eng 25(1):326–344. https://doi.org/10.1007/s12205-020-2366-2
Zhang ZG, Zhang MX, Zhao QH, Fang L, Ma SK, Lv XL (2021) A simplified analytical solution for deformation behavior of existing tunnels subjected to influences of landslides. Bull Eng Geol Environ 80:4651–4672. https://doi.org/10.1007/s10064-021-02230-5