Wave-Induced Response of Seepage Pressure around Shield Tunnel in Sand Seabed Slope
Publication: International Journal of Geomechanics
Volume 23, Issue 10
Abstract
With the increasing demand of transport construction in coastal areas, seabed instability around tunnels subjected to ocean waves and protection of the tunnels are becoming increasingly important. Current analytical solutions on the seepage field around subsea shield tunnels induced by waves are generally based on the impermeable lining, without considering the permeability. Furthermore, previous studies seldom take account of the influence of nonlinear wave loads under the sloping seabed terrain. For better tunnel stability, this paper presents a new set of analytical solutions for predicting Stokes wave-induced seepage pressure responses around a shield tunnel in a sloping seabed considering the influence of the permeable tunnel lining. The accuracy of the presented solutions is then verified by comparison with the numerical solution and experimental data, showing reasonable alignments. Moreover, parametric analyses are also performed to assess the influence of wave characteristics, seabed properties, and tunnel lining permeability on seepage pressure responses, in which the distribution of the excess pore pressure response outside the lining and excess pore pressure around the tunnel circumference is described in detail. In general, the analytical solutions provide an effective insight into the wave-induced seepage pressure response around a shield tunnel, which can serve as a credible theoretical basis in the preliminary design of tunnels.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors acknowledge the financial support provided by the National Natural Science Foundation of China for the Key Program and the General Program (No. 42177145 and No. 41977247), the Project of State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures (No. KF2022-07), the Project of Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Natural Resources (Fujian Key Laboratory of Geohazard Prevention, No. FJKLGH2020K004), and the Project of Shandong Provincial Key Laboratory of Marine Ecological Environment and Disaster Prevention and Mitigation (No. 201703).
References
Bayraktar, D., J. Ahmad, B. E. Larsen, S. Carstensen, and D. R. Fuhrman. 2016. “Experimental and numerical study of wave-induced backfilling beneath submarine pipelines.” Coastal Eng. 118: 63–75. https://doi.org/10.1016/j.coastaleng.2016.08.010.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 12: 155–164. https://doi.org/10.1063/1.1712886.
Chen, R. P., L. Y. Wu, B. Zhu, and D. Q. Kong. 2019. “Numerical modelling of pipe-soil interaction for marine pipelines in sandy seabed subjected to wave loadings.” Appl. Ocean Res. 88: 233–245. https://doi.org/10.1016/j.apor.2019.04.021.
Chen, W., D. Fang, G. Chen, D. Jeng, J. F. Zhu, and H. Zhao. 2018. “A simplified quasi-static analysis of wave-induced residual liquefaction of seabed around an immersed tunnel.” Ocean Eng. 148: 574–587. https://doi.org/10.1016/j.oceaneng.2017.11.049.
Cheng, A. H. D., and P. L. F. Liu. 1986. “Seepage force on a pipeline buried in a poroelastic seabed under wave loadings.” Appl. Ocean Res. 8 (1): 22–32. https://doi.org/10.1016/S0141-1187(86)80027-X.
Conte, E., and A. Troncone. 2008. “Soil layer response to pore pressure variations at the boundary.” Géotechnique 58 (1): 37–44. https://doi.org/10.1680/geot.2008.58.1.37.
Fan, N., J. X. Jiang, Y. K. Dong, L. Guo, and L. F. Song. 2022. “Approach for evaluating instantaneous impact forces during submarine slide-pipeline interaction considering the inertial action.” Ocean Eng. 245: 110466. https://doi.org/10.1016/j.oceaneng.2021.110466.
Fu, C. J., G. Y. Li, and T. L. Zhao. 2018. “Research on the calculation of seepage force on buried pipelines in shallow water.” [In Chinese.] Chin. J. Comput. Mech. 35 (1): 76–81. https://doi.org/10.7511/jslx20161207003.
Fu, Y. B., D. Q. Zeng, H. Xiong, X. H. Li, and Y. L. Chen. 2022. “Seepage effect on failure mechanisms of the underwater tunnel face via CFD-DEM coupling.” Comput. Geotech. 146: 104591. https://doi.org/10.1016/j.compgeo.2021.104591.
Gao, F. P., X. Y. Gu, D. S. Jeng, and H. T. Teo. 2002. “An experimental study for wave-induced instability of pipelines: The breakout of pipelines.” Appl. Ocean Res. 24 (2): 83–90. https://doi.org/10.1016/S0141-1187(02)00012-3.
Gao, F. P., and Y. X. Wu. 2006. “Non-linear wave-induced transient response of soil around a trenched pipeline.” Ocean Eng. 33: 311–330. https://doi.org/10.1016/j.oceaneng.2005.05.008.
Gao, Y., J. S. Zhang, L. L. Tong, Y. K. Guo, and D. Lam. 2022. “Wave induced silty seabed response around a trenched pipeline.” Ocean Eng. 245: 110527. https://doi.org/10.1016/j.oceaneng.2022.110527.
Guo, X. S., T. K. Nian, N. Fan, and Y. G. Jia. 2021. “Optimization design of a honeycomb-hole submarine pipeline under a hydrodynamic landslide impact.” Mar. Georesour. Geotechnol. 39 (9): 1055–1070. https://doi.org/10.1080/1064119X.2020.1801919.
Han, S., D. S. Jeng, and C. C. Tsai. 2019. “Response of a porous seabed around an immersed tunnel under wave loading: Meshfree model.” J. Mar. Sci. Eng. 7 (10): 369. https://doi.org/10.3390/jmse7100369.
Hsu, J. R. C., and D. S. Jeng. 1994. “Wave-induced soil response in an unsaturated anisotropic seabed of finite thickness.” Int. J. Numer. Anal. Methods Geomech. 18 (11): 159–167. https://doi.org/10.1002/nag.1610181104.
Kasper, T., J. S. Steenfelt, L. M. Pedersen, P. G. Jackson, and R. W. M. G. Heijmans. 2008. “Stability of an immersed tunnel in offshore conditions under deep water wave impact.” Coastal Eng. 55 (9): 753–760. https://doi.org/10.1016/j.coastaleng.2008.02.021.
Kokkinowrachos, K., and S. Asorakos. 1985. “Hydrodynamic analysis of large offshore structure on porous elastic seabed.” In Vol. 2 of Proc., 4th Offshore Mechanics and Artic Engineering Symp., 172–181. New York: ASME.
Kong, F. C., D. C. Lu, X. L. Du, X. Q. Li, and C. C. Su. 2021. “Analytical solution of stress and displacement for a circular underwater shallow tunnel based on a unified stress function.” Ocean Eng. 219 (6): 108352. https://doi.org/10.1016/j.oceaneng.2020.108352.
Kong, F. C., D. C. Lu, X. L. Du, and C. P. Shen. 2019. “Elastic analytical solution of shallow tunnel owing to twin tunnelling based on a unified displacement function.” Appl. Math. Modell. 68: 422–442. https://doi.org/10.1016/j.apm.2018.11.038.
Li, P. F., F. Wang, Y. Y. Long, and X. Zhao. 2018. “Investigation of steady water inflow into a subsea grouted tunnel.” Tunnelling Underground Space Technol. 80: 92–102. https://doi.org/10.1016/j.tust.2018.06.003.
Liam, W. D., R. Siddharthan, and G. R. Martin. 1983. “Response of seafloor to ocean waves.” J. Geotech. Eng. 109 (4): 556–572. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:4(556).
Liu, X. L., H. N. Cui, D. S. Jeng, and H. Y. Zhao. 2019. “A coupled mathematical model for accumulation of wave-induced pore pressure and its application.” Coastal Eng. 154: 103577. https://doi.org/10.1016/j.coastaleng.2019.103577.
Lu, D. C., F. C. Kong, X. L. Du, C. P. Shen, C. C. Su, and J. Wang. 2020. “Fractional viscoelastic analytical solution of shallow tunnel based on a time-dependent unified displacement function.” Comput. Geotech. 117: 103284. https://doi.org/10.1016/j.compgeo.2019.103284.
Madsen, O. S. 1978. “Wave-induced pore pressure and effective stresses in a porous bed.” Géotechnique 28 (4): 377–393. https://doi.org/10.1680/geot.1978.28.4.377.
Mcdougal, W. G., S. H. Davidson, P. L. Monkmeyer, and C. K. Sollitt. 1988. “Wave-induced forces on buried pipelines.” J. Waterway, Port, Coastal, Ocean Eng. 114 (2): 220–236. https://doi.org/10.1061/(ASCE)0733-950X(1988)114:2(220).
Putnam, J. A. 1949. “Loss of wave energy due to percolation in a permeable sea bottom.” Eos, Trans. Am. Geophys. Union 30 (3): 349–356. https://doi.org/10.1029/TR030i003p00349.
Rafiei, A., M. S. Rahman, and M. A. Gabr. 2019. “Coupled analysis for response and instability of sloping seabed under wave action.” Appl. Ocean Res. 88: 99–110. https://doi.org/10.1016/j.apor.2019.04.017.
Sudhan, C. M., V. Sundar, and S. N. Rao. 2002. “Wave induced forces around buried pipelines.” Ocean Eng. 29 (5): 533–544. https://doi.org/10.1016/S0029-8018(01)00012-9.
Sun, K., J. S. Zhang, Y. Gao, D. S. Jeng, Y. K. Guo, and Z. D. Liang. 2019. “Laboratory experimental study of ocean waves propagating over a partially buried pipeline in a trench layer.” Ocean Eng. 173: 617–627. https://doi.org/10.1016/j.oceaneng.2019.01.022.
Tong, L. L., and P. L. F. Liu. 2022. “Transient wave-induced pore-water-pressure and soil responses in a shallow unsaturated poroelastic seabed.” J. Fluid Mech. 938: A36. https://doi.org/10.1017/jfm.2022.184.
Turcotte, B. R. 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Ithaca, NY: Cornell Univ.
Ulker, M. B. C., M. S. Rahman, and D. S. Jeng. 2009. “Wave-induced response of seabed: Various formulations and their applicability.” Appl. Ocean Res. 31 (1): 12–24. https://doi.org/10.1016/j.apor.2009.03.003.
Wang, F., and P. F. Li. 2018. “An analytical model of seepage field for symmetrical underwater tunnels.” Symmetry 10 (7): 273. https://doi.org/10.3390/sym10070273.
Wu, S., and D. S. Jeng. 2019. “Effects of dynamic soil permeability on the wave-induced seabed response around a buried pipeline.” Ocean Eng. 186: 106132. https://doi.org/10.1016/j.oceaneng.2019.106132.
Xiao, H., Y. L. Young, and J. H. Prevost. 2010. “Hydro- and morpho-dynamic modeling of breaking solitary waves over a fine sand beach.” Mar. Geol. 269 (4): 119–131. https://doi.org/10.1016/j.margeo.2009.12.008.
Xu, J. S., G. X. Li, P. Dong, and J. H. Shi. 2010. “Bedform evolution around a submarine pipeline and its effects on wave-induced forces under regular waves.” Ocean Eng. 37 (2): 304–313. https://doi.org/10.1016/j.oceaneng.2009.10.002.
Yamamoto, T., H. L. Koning, H. Sellmeijer, and E. Van Hijum. 1978. “On the response of a poro-elastic bed to water waves.” J. Fluid Mech. 87 (1): 193–206. https://doi.org/10.1017/S0022112078003006.
Ye, J. H., and K. P. He. 2021. “Dynamics of a pipeline buried in loosely deposited seabed to nonlinear wave & current.” Ocean Eng. 232: 109127. https://doi.org/10.1016/j.oceaneng.2021.109127.
Ye, J. H., D. S. Jeng, P. L. F. Liu, A. H. C. Chan, R. Wang, and C. Q. Zhu. 2014. “Breaking wave-induced response of composite breakwater and liquefaction in seabed foundation.” Coastal Eng. 85: 72–86. https://doi.org/10.1016/j.coastaleng.2013.08.003.
Ye, J. H., D. S. Jeng, R. Wang, and C. Q. Zhu. 2013. “A 3-D semi-coupled numerical model for fluid-structures-seabed-interaction (FSSI-CAS 3D): Model and verification.” J. Fluids Struct. 40: 148–162. https://doi.org/10.1016/j.jfluidstructs.2013.03.017.
Ying, H. W., C. W. Zhu, X. N. Gong, and X. Wang. 2019. “Analytical solutions for the steady-state seepage field in a finite seabed with a lined tunnel.” Mar. Georesour. Geotechnol. 37 (8): 972–978. https://doi.org/10.1080/1064119X.2018.1514446.
Ying, H. W., C. W. Zhu, H. W. Shen, and X. N. Gong. 2018. “Semi-analytical solution for groundwater ingress into lined tunnel.” Tunnelling Underground Space Technol. 76: 43–47. https://doi.org/10.1016/j.tust.2018.03.009.
Zang, Z. P., Y. F. Chen, J. F. Zhang, Y. H. Tian, and M. D. Esteban. 2021. “Experimental study on local scour and onset of VIV of a pipeline on a silty seabed under steady currents.” Appl. Ocean Res. 109: 102560. https://doi.org/10.1016/j.apor.2021.102560.
Zhai, Y. Y., J. S. Zhang, Y. K. Guo, Z. H. Tang, and T. T. Zhang. 2022. “Study of wave-induced seabed response around twin pipelines in sandy seabed through laboratory experiments and numerical simulations.” Ocean Eng. 244: 110344. https://doi.org/10.1016/j.oceaneng.2021.110344.
Zhang, Q., S. Draper, L. Cheng, and H. W. An. 2016. “Effect of limited sediment supply on sedimentation and the onset of tunnel scour below subsea pipelines.” Coastal Eng. 116: 103–117. https://doi.org/10.1016/j.coastaleng.2016.05.010.
Zhang, Y., and J. H. Ye. 2021. “Physical modelling of the stability of a revetment breakwater built on reclaimed coral calcareous sand foundation in the South China Sea-random waves and dense foundation.” Ocean Eng. 219: 108384. https://doi.org/10.1016/j.oceaneng.2020.108384.
Zhao, E. J., Y. K. Dong, Y. Z. Tang, and J. K. Sun. 2021a. “Numerical investigation of hydrodynamic characteristics and local scour mechanism around submarine pipelines under joint effect of solitary waves and currents.” Ocean Eng. 222: 108553. https://doi.org/10.1016/j.oceaneng.2020.108553.
Zhao, K., Q. Z. Wang, S. Chen, H. Y. Zhuang, and G. X. Chen. 2021b. “Dynamic response of pipelines in liquefiable seabed under nature loadings: Waves and currents.” Ocean Eng. 230: 109051. https://doi.org/10.1016/j.oceaneng.2021.109051.
Zhao, K., Q. Z. Wang, W. Y. Chen, H. Y. Zhuang, and G. X. Chen. 2020. “Uplift of immersed tunnel in liquefiable seabed under wave and current propagation.” Eng. Geol. 278: 105828. https://doi.org/10.1016/j.enggeo.2020.105828.
Zhao, K., H. Xiong, G. X. Chen, D. F. Zhao, W. Y. Chen, and X. L. Du. 2018. “Wave-induced dynamics of marine pipelines in liquefiable seabed.” Coastal Eng. 140: 100–113. https://doi.org/10.1016/j.coastaleng.2018.06.007.
Zhou, C. Y., G. X. Li, P. Dong, J. H. Shi, and J. S. Xu. 2011. “An experimental study of seabed responses around a marine pipeline under wave and current conditions.” Ocean Eng. 38 (1): 226–234. https://doi.org/10.1016/j.oceaneng.2010.10.006.
Zhu, C. W. 2020. “Study on water and soil pressure response of subaqueous tunnels under static and dynamic water level.” Ph.D. thesis, Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang Univ.
Zhu, C. W., H. W. Ying, X. N. Gong, X. Wang, and W. Wu. 2021. “Analytical solution for wave-induced hydraulic response on subsea shield tunnel.” Ocean Eng. 228: 108924. https://doi.org/10.1016/j.oceaneng.2021.108924.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 10 • October 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jun 4, 2022
Accepted: May 22, 2023
Published online: Aug 9, 2023
Published in print: Oct 1, 2023
Discussion open until: Jan 9, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.