Technical Notes
Jun 18, 2018

Analytical Solution for Steady-State Groundwater Inflow into a Circular Tunnel in Anisotropic Soils

Publication: Journal of Engineering Mechanics
Volume 144, Issue 9

Abstract

An analytical solution for groundwater flow through a circular tunnel in anisotropic soils is derived based on conformal mapping and can be used to calculate the water flow rate into the tunnel and predict the pore water pressure distribution in surrounding soils. If the vertical and horizontal permeabilities are equal, this analytical solution is reduced to the solution for the isotropic flow condition. This proposed analytical solution is verified by numerical simulations. The water flow rate into the tunnel decreases with a decreasing value of soil permeability in the horizontal direction, and the pore water pressure distribution is distorted due to the anisotropy of soil. This proposed analytical solution provides an efficient approach for estimating the groundwater inflow into a circular tunnel accounting for anisotropic soils.

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Acknowledgments

This research is supported by Alberta Innovation Technology Futures (AITF) Graduate Student Scholarship and China Scholarship Council (CSC). The authors also acknowledge the support from Natural Sciences and Engineering Research Council of Canada (NSERC).

References

Bear, J. 1972. Dynamics of fluids in porous media. New York: American Elsevier.
Cui, Y., D. Chan, and A. Nouri. 2017. “Coupling of solid deformation and pore pressure for undrained deformation: A discrete element method approach.” Int. J. Num. Anal. Methods Geomech. 41 (18): 1943–1961. https://doi.org/10.1002/nag.2708.
Cui, Y., A. Nouri, D. Chan, and E. Rahmati. 2016. “A new approach to DEM simulation of sand production.” J. Pet. Sci. Eng. 147: 56–67. https://doi.org/10.1016/j.petrol.2016.05.007.
El Tani, M. 2003. “Circular tunnel in a semi-infinite aquifer.” Tunnelling Underground Space Technol. 18 (1): 49–55. https://doi.org/10.1016/S0886-7798(02)00102-5.
Fernández, G., and T. A. Alvarez. 1994. “Seepage-induced effective stresses and water pressures around pressure tunnels.” J. Geotech. Eng. 120 (1): 108–128. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:1(108).
GEO-SLOPE International Ltd. 2012. Seepage modeling with SEEP/W. Calgary, AB, Canada: GEO-SLOPE International Ltd.
Guo, S., T. Zhang, Y. Zhang, and D. Z. Zhu. 2012. “An approximate solution for two-dimensional groundwater infiltration in sewer systems.” Water Sci. Technol. 67 (2): 347–352. https://doi.org/10.2166/wst.2012.568.
Harr, M. E. 1962. Groundwater and Seepage. New York: McGraw-Hill.
Huangfu, M., M.-S. Wang, Z.-S. Tan, and X.-Y. Wang. 2010. “Analytical solutions for steady seepage into an underwater circular tunnel.” Tunnelling Underground Space Technol. 25 (4): 391–396. https://doi.org/10.1016/j.tust.2010.02.002.
Kolymbas, D., and P. Wagner. 2007. “Groundwater ingress to tunnels-the exact analytical solution.” Tunnelling Underground Space Technol. 22 (1): 23–27. https://doi.org/10.1016/j.tust.2006.02.001.
Lei, S. 1999. “An analytical solution for steady flow into a tunnel.” Ground Water 37 (1): 23–26. https://doi.org/10.1111/j.1745-6584.1999.tb00953.x.
Mitchell, J. K., and K. Soga. 2005. Fundamentals of soil behavior. New York: Wiley.
Moon, J., and S. Jeong. 2011. “Effect of highly pervious geological features on ground-water flow into a tunnel.” Eng. Geol. 117 (3): 207–216. https://doi.org/10.1016/j.enggeo.2010.10.019.
Palmer, J., and D. J. Belshaw. 1980. “Deformations and pore pressures in the vicinity of a precast, segmented, concrete-lined tunnel in clay.” Can. Geotech. J. 17 (2): 174–184. https://doi.org/10.1139/t80-021.
Park, K.-H., A. Owatsiriwong, and J.-G. Lee. 2008. “Analytical solution for steady-state groundwater inflow into a drained circular tunnel in a semi-infinite aquifer: A revisit.” Tunnelling Underground Space Technol. 23 (2): 206–209. https://doi.org/10.1016/j.tust.2007.02.004.
Shin, J. H. 2010. “Analytical and combined numerical methods evaluating pore water pressure on tunnels.” Géotechnique 60 (2): 141–145. https://doi.org/10.1680/geot.8.T.035.
Shin, J. H., T. I. Addenbrooke, and D. M. Potts. 2002. “A numerical study of the effect of groundwater movement on long-term tunnel behaviour.” Géotechnique 52 (6): 391–403. https://doi.org/10.1680/geot.2002.52.6.391.
Tang, Y., D. H. Chan, D. Z. Zhu, and S. Guo. 2018. “An analytical solution for steady seepage into a defective pipe.” Water Sci. Technol. Water Supply 18 (3): ws2017168. https://doi.org/10.2166/ws.2017.168.
Vladimirov, V. S. 1966. Methods of the theory of functions of many complex variables. Cambridge, MA: MIT Press.
Wongsaroj, J., K. Soga, and R. J. Mair. 2007. “Modelling of long-term ground response to tunnelling under St James’s Park, London.” Géotechnique 57 (1): 75–90. https://doi.org/10.1680/geot.2007.57.1.75.
Yang, Y., D. Z. Zhu, T. Zhang, W. Liu, and S. Guo. 2016. “Improved model for contaminant intrusion induced by negative pressure events in water distribution systems.” J. Hydraul. Eng. 142 (10): 06016012. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001176.
Yoo, C. 2005. “Interaction between tunneling and groundwater: Numerical investigation using three dimensional stress-pore pressure coupled analysis.” J. Geotech. Geoenviron. Eng. 131 (2): 240–250. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:2(240).
Zhang, D., L. Ma, H. Huang, and J. Zhang. 2012. “Predicting leakage-induced settlement of shield tunnels in saturated clay.” Comput. Model. Eng. Sci. 89 (3): 163–188.
Zhang, D., L. Ma, J. Zhang, P. Hicher, and C. Juang. 2015. “Ground and tunnel responses induced by partial leakage in saturated clay with anisotropic permeability.” Eng. Geol. 189: 104–115. https://doi.org/10.1016/j.enggeo.2015.02.005.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 144Issue 9September 2018

History

Received: Oct 8, 2017
Accepted: Mar 15, 2018
Published online: Jun 18, 2018
Published in print: Sep 1, 2018
Discussion open until: Nov 18, 2018

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Authors

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Postdoctoral Fellow, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB, Canada T6G 2W2 (corresponding author). Email: [email protected]
Dave H. Chan [email protected]
Professor, College of Civil and Architecture, Three Gorges Univ., Yichang, Hubei, China; Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB, Canada T6G 2W2. Email: [email protected]
David Z. Zhu, M.ASCE [email protected]
Professor, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB, Canada T6G 2W2. Email: [email protected]

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