Analytical Prediction of Ground Movements due to a Nonuniform Deforming Tunnel
Publication: International Journal of Geomechanics
Volume 16, Issue 4
Abstract
An analytical solution is presented to predict ground movement induced by a nonuniformly deforming circular tunnel in a heavy elastic half-plane. Simple expression is proposed to describe the nonuniform soil deformation around the tunnel. The tunnel-deforming components (i.e., ground loss, ovalization, vertical translation) can be determined by the solution-inherent mechanism and by fitting from measured field data. The effects of tunnel-deforming components on the resulting displacement field are discussed. Case studies from various ground conditions were used to check the capacity and applicability of the proposed solution. Although elasticity is a rough representation of the soil behavior, the proposed analytical solution can serve as a simple tool for predicting a reasonable ground settlement profile in the preliminary design of tunnels.
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References
Attewell, P. B., and Farmer, I. W. (1974). “Ground deformations resulting from shield tunnelling in London clay.” Can. Geotech. J., 11(3), 380–395.
Attewell, P. B., Yeates, J., and Selby, A. R. (1986). Soil movements induced by tunnelling and their effects on pipelines and structures, Chapman and Hall, New York.
Bakker, K. J. (2003). “Structural design of linings for bored tunnels in soft ground.” Heron, 48(1), 33–63.
Bobet, A. (2001). “Analytical solution for shallow tunnels in saturated ground.” J. Eng. Mechanics, 1258–1266.
Cheng, C. Y., Dasari, G. R., Chow, Y. K., and Leung, C. F. (2007). “Finite element analysis of tunnel–soil–pile interaction using displacement controlled model.” Tunn. Underground Space Technol., 22(4), 450–466.
Chou, W. I., and Bobet, A. (2002). “Predictions of ground deformations in shallow tunnels in clay.” Tunn. Underground Space Technol., 17(1), 3–19.
Clough, G. W., and Schmidt, B. (1981). “Design and performance of excavations and tunnels in soft clay.” Soft Clay Eng., 569–631.
Clough, G. W., Sweeney, B. P., and Finno, R. J. (1983). “Measured soil response to EPB shield tunneling.” J. Geotech. Eng., 131–149.
Deane, A. P., and Bassett, R. H. (1995). “The Heathrow Express trial tunnel.” Geotech. Eng., 113(3), 144–156.
Fu, J. Y., Yang, J. S., Yan, L., and Abbas, S. M. (2015). “An analytical solution for deforming twin-parallel tunnels in an elastic half plane.” Int. J. Numer. Anal. Methods Geomech., 39(5), 524–538.
Gonzalez, C., and Sagaseta, C. (2001). “Patterns of soil deformations around tunnels. Application to the extension of Madrid Metro.” Comput. Geotech., 28(6–7), 445–468.
ITA/AITES (Association Internationale des Tunnels et de L’Espace Souterrain/International Tunnelling and Underground Space Association). (2007). “Settlements induced by tunneling in soft ground.” Tunn. Underground Space Technol., 22(2), 119–149.
Kooi, C. B., and Verruijt, A. (2001). “Interaction of circular holes in an infinite elastic medium.” Tunn. Underground Space Technol., 16(1), 59–62.
Leca, E. (1996). “Modelling and prediction for bored tunnels.” Proc., Int. Symp. on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, the Netherlands, 27–41.
Lee, K. M., and Rowe, R. K. (1989). “Deformations caused by surface loading and tunnelling, the role of elastic anisotropy.” Géotechnique, 39(1), 125–140.
Lee, K. M., and Rowe, R. K. (1991). “An analysis of three-dimensional ground movements: the Thunder Bay tunnel.” Can. Geotech. J., 28(1), 25–41.
Lee, K. M., Rowe, R. K., and Lo, K. Y. (1992). “Subsidence owing to tunnelling. I. Estimating the gap parameter.” Can. Geotech. J., 29(1), 929–940.
Liu, B. (1992). “Theory of stochastic medium and its application in surface subsidence due to excavation.” Trans. NFsoc, 2(3), 17–24.
Loganathan, N. (2011). BP 2009 William Barclay Parsons Fellowship Monograph 25: An innovative method for assessing tunnelling-induced risks to adjacent structures, Parsons Brinckerhoff, Inc., New York.
Loganathan, N., and Poulos, H. G. (1998). “Analytical prediction for tunneling-induced ground movements in clay.” J. Geotech. Geoenviron., 846–856.
Macklin, S. R. (1999). “The prediction of volume loss due to tunnelling in overconsolidated clay based on heading geometry and stability number.” Ground Eng., 32(4), 30–33.
Mair, R. J. (1996). “Settlement effects of bored tunnels.” Proc., Int. Symp. on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, the Netherlands, 43–53.
Mair, R. J., Gunn, M. J., and O'Reilly, M. P. (1981). “Ground movements around shallow tunnel in soft clay.” Proc., 10th Int. Conf. on Soil Mechanics and Foundation Eng., Vol. 1, Balkema, Rotterdam, the Netherlands, 323–328.
Mair, R. J., Taylor, R. N., and Bracegirdle, A. (1993). “Subsurface settlement profile above tunnels in clays.” Géotechnique, 43(2), 315–320.
Moh, Z. C., Ju, D. H., and Hwang, R. N. (1996). “Ground movements around tunnels in soft ground.” Proc., Int. Symp. on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, the Netherlands, 725–730.
New, B. M., and Bowers, K. H. (1994). “Ground movement model validation at the Heathrow Express trial tunnel.” Proc., Tunnelling ′94 Symp., Institution of Mining and Metallurgy and British Tunnelling Society, Springer, Berlin, 301–329.
O’Reilly, M. P., and New, B. M. (1982). “Settlements above tunnels in the United Kingdom–their magnitude and prediction.” Proc., Tunnelling '82, Institution of Mining and Metallurgy, London, 173–181.
Palmer, J. H., and Belshaw, D. J. (1980). “Deformations and pore pressures in the vicinity of a precast, concrete-lined tunnel in clay.” Can. Geotech. J., 17(2), 174–184.
Panet, M., and Guenot, A. (1982). “Analysis of convergence behind the face of a tunnel.” Proc., Int. Symp., Tunnelling ′82, Institution of Mining and Metallurgy, London, 187–204.
Park, K. H. (2004). “Elastic solution for tunneling-induced ground movement in clays.” Int. J. Geomech., 310–318.
Park, K. H. (2005). “Analytical solution for tunnelling-induced ground movement in clays.” Tunn. Underground Space Technol., 20(3), 249–261.
Peck, R. B. (1969). “Deep excavations and tunneling in soft ground.” Proc., 7th Int. Conf. on Soil Mechanics and Foundation Eng., State of the Art Volume, Balkema, Rotterdam, the Netherlands, 225–290.
Phienwej, N. (1997). “Ground movements in shield tunnelling in Bangkok subsoils.” Proc., 14th Int. Conf. on Soil Mechanics and Foundation Eng., Balkema, Rotterdam, the Netherlands, 1469–1472.
Pinto, F., and Whittle, A. J. (2006). “Discussion of 'Elastic Solution for Tunneling-Induced Ground Movements in Clays' by K. H. Park.” Int. J. Geomech., 72–73.
Puzrin, A. M., Burland, J. B., and Standing, J. R. (2012). “Simple approach to predicting ground displacements caused by tunnelling in undrained anisotropic elastic soil.” Géotechnique, 62(4), 341–352.
Rowe, R. K., and Kack, G. J. (1983). “A theoretical examination of the settlements induced by tunnelling: Four case histories.” Can. Geotech. J., 20(2), 299–314.
Rowe, R. K., and Lee, K. M. (1992). “Subsidence owing to tunnelling. II. Evaluation of a prediction technique.” Can. Geotech. J., 29(6), 941–954.
Rowe, R. K., Lo, K. Y., and Kack, G. J. (1983). “A method of estimating surface settlement above tunnels constructed in soft ground.” Can. Geotech. J., 20(1), 11–22.
Sagaseta, C. (1987). “Analysis of undrained soil deformation due to ground loss.” Géotechnique, 37(3), 301–320.
Simpson, B., Atkinson, J. H., and Jovicic, V. (1996). “The influence of anisotropy on calculations of ground settlements above tunnels.” Proc., Int. Symp. on Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, the Netherlands, 591–594.
Sokolnikoff, I. S. (1956). Mathematical theory of elasticity, McGraw-Hill, New York.
Stallebrass, S. E., Grant, R. J., and Taylor, R. N. (1996). “A finite element study of ground movement measured in centrifuge model test of tunnels.” Proc., Geotechnical Aspects of Underground Construction in Soft Ground, Balkema, Rotterdam, the Netherlands, 595–600.
Strack, O. E., and Verruijt, A. (2000). “A complex variable solution for the ovalization of a circular tunnel in an elastic half-plane.” GeoEng 2000, an Int. Conf. on Geotechnical and Geological Eng., Technomics, Melbourne, VIC, Australia.
Strack, O. E., and Verruijt, A. (2002). “A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane.” Int. J. Numer. Anal. Methods Geomech., 26(12), 1235–1252.
Sugiyama, T., et al. (1999). “Observations of ground movements during tunnel construction by slurry shield method at the Docklands Light Railway Lewisham Extension–east London.” Soils Found., 39(3), 99–112.
Verruijt, A. (1997). “A complex variable solution for a deforming circular tunnel in an elastic half-plane.” Int. J. Numer. Anal. Methods Geomech., 21(2), 77–89.
Verruijt, A. (1998). “Deformations of an elastic half plane with a circular cavity.” Int. J. Solids. Struct., 35(21), 2795–2804.
Verruijt, A., and Booker, J. R. (1996). “Surface settlements due to deformation of a tunnel in an elastic half plane.” Géotechnique, 46(4), 753–756.
Verruijt, A., and Booker, J. R. (1998). “Surface settlements due to deformation of a tunnel in an elastic half plane.” Géotechnique, 48(5), 709–713
Verruijt, A., and Booker, J. R. (2000). “Complex variable analysis of Mindlin’s tunnel problem.” Proc., Booker Memorial Symp., Developments in Theoretical Geomechanics, Balkema, Rotterdam, the Netherlands, 3–22.
Verruijt, A., and Strack, O. E. (2008). “Buoyancy of tunnels in soft soils.” Géotechnique, 58(6), 513–515.
Wang, L.-Z., Li, L.-L., and Lv, X.-J. (2009). “Complex variable solutions for tunneling-induced ground movement.” Int. J. Geomech., 63–72.
Yang, J. S., Liu, B. C., and Wang, M. C. (2004). “Modeling of tunneling-induced ground surface movements using stochastic medium theory.” Tunn. Underground Space Technol., 19(2), 113–123.
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Published In
International Journal of Geomechanics
Volume 16 • Issue 4 • August 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Mar 12, 2015
Accepted: Jul 2, 2015
Published online: Dec 31, 2015
Discussion open until: May 31, 2016
Published in print: Aug 1, 2016
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