Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

The ground response curve of underwater tunnels, excavated in a strain-softening rock mass

  • Fahimifar, Ahmad (Department of Civil and Environmental Engineering, Amirkabir University of Technology) ;
  • Ghadami, Hamed (Department of Civil Engineering, Science and Research Branch, Islamic Azad University) ;
  • Ahmadvand, Masoud (Department of Civil Engineering, Tafresh University)
  • Received : 2013.12.28
  • Accepted : 2014.12.02
  • Published : 2015.03.25
⟨ Previous Next ⟩

Abstract

This paper presents an elasto-plastic model for determination of the ground response curve of a circular underwater tunnel excavated in elastic-strain softening rock mass compatible with a nonlinear Hoek-Brown yield criterion. The finite difference method (FDM) was used to propose a new solution to calculate pore water pressure, stress, and strain distributions on periphery of circular tunnels in axisymmetric and plain strain conditions. In the proposed solution, a modified non-radial flow pattern, for the hydraulic analysis, is utilized. To evaluate the effect of gravitational loads and variations of pore water pressure, the equations concerning different directions around the tunnel (crown, wall, and floor) are derived. Regarding the strain-softening behavior of the rock mass, the stepwise method is executed for the plastic zone in which parameters of strength, dilatancy, stresses, strains, and deformation are different from their elasto-plastic boundary values as compared to the tunnel boundary values. Besides, the analytical equations are developed for the elastic zone. The accuracy and application of the proposed method is demonstrated by a number of examples. The results present the effects of seepage body forces, gravitational loads and dilatancy angle on ground response curve appropriately.

Keywords

References

  1. Alonso, E., Alejano, L.R., Varas, F., Fdez-Manin, G. and Carranza-Torres, C. (2003), "Ground response curves for rock masses exhibiting strain-softening behavior", Int. J. Numer. Anal. Method. Geomech., 27(13), 1153-1185. https://doi.org/10.1002/nag.315
  2. Brown, E.T. and Bray, J.W. (1982), "Rock-lining interaction calculations for pressure shafts and tunnels", ISRM Symposium, Aachen, Germany, pp. 26-28.
  3. Brown, E.T., Bray, J.W., Ladanyi, B and Hoek, E. (1983), "Ground response curves for rock tunnels", J. Geotech. Eng., 109(1), 15-39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15)
  4. Carranza-Torres, C. (2004), "Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion", Int. J. Rock. Mech. Min. Sci., 41, 480-481. https://doi.org/10.1016/j.ijrmms.2003.12.014
  5. Carranza-Torres, C. and Fairhurst, C. (1999), "On the stability of tunnels under gravity loading, with post-peak softening of the ground", Int. J. Rock. Mech. Min. Sci., 34(3-4), 75.e1-75.e18. https://doi.org/10.1016/S1365-1609(97)00253-0
  6. Detournay, E. and Fairhurst, C. (1987), "Two dimensional elastoplastic analysis of along, cylindrical cavity under non-hydrostatic loading", Int. J. Rock. Mech. Min. Sci. Geomech. Abs., 24(4), 197-211. https://doi.org/10.1016/0148-9062(87)90175-6
  7. Fahimifar, A. and Zareifard, M.R. (2009), "A theoretical solution for analysis of tunnels below groundwater considering the hydraulic-mechanical coupling", Tunn. Undergr. Sp. Tech., 24(6), 634-646. https://doi.org/10.1016/j.tust.2009.06.002
  8. Fahimifar, A., Ghadami, H. and Ahmadvand, M. (2014), "The influence of seepage and gravitational loads on elastoplastic solution of circular tunnels", Sci Iran., 21(6), 1821-1832.
  9. Fahimifar, A., Ghadami, H. and Ahmadvand, M. (2015), "An elasto-plastic model for underwater tunnels considering seepage body forces and strain-softening behaviour", Eur. J. Environ. Civ. Eng., 19(2), 129-151. https://doi.org/10.1080/19648189.2014.939305
  10. Fernandez, G. (1994), "Behavior of pressure tunnels and guidelines for liner design", J. Geotech. Eng., 120(10), 1768-1791. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:10(1768)
  11. Hoek, E. and Brown, E. (1980), "Empirical strength criterion for rock masses", J. Geotech. Eng., 106(GT9), 1013-1035.
  12. Kolymbas, D. and Wagner, P. (2007), "Groundwater ingress to tunnels - the exact analytical solution", Tunn. Undergr. Sp. Tech., 22(1), 23-27. https://doi.org/10.1016/j.tust.2006.02.001
  13. Lee, Y-K. and Pietruszczak, S. (2008), "A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass", Tunn. Undergr. Sp. Tech., 23(5), 588-599. https://doi.org/10.1016/j.tust.2007.11.002
  14. Lee, S.W., Jung, J.W., Nam, S.W. and Lee, I.M. (2006), "The influence of seepage forces on ground reaction curve of circular opening", Tunn. Undergr. Sp. Tech., 22(1), 28-38.
  15. Ming, H., Meng-Shu, W., Tan, Z-S. and Xiu-Ying, W. (2010), "Analytical solution for steady seepage into an underwater circular tunnel", Tunn. Undergr. Sp. Tech., 25(4), 391-396. https://doi.org/10.1016/j.tust.2010.02.002
  16. Park, K-H. and Kim, Y-J. (2006), "Analytical solution for a circular opening in, an elasto-brittle-plastic rock", Int. J. Rock. Mech. Min. Sci., 43(4), 616-622. https://doi.org/10.1016/j.ijrmms.2005.11.004
  17. Park, K-H., Tontavanich, B. and Lee, J.-G. (2008), "A simple procedure for ground response Curve of circular tunnel in elastic-strain softening rock masses", Tunn. Undergr. Sp. Tech., 23(2), 151-159. https://doi.org/10.1016/j.tust.2007.03.002
  18. Sharan, S.K. (2003), "Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media", Int. J. Rock. Mech. Min. Sci., 40(6), 817-824. https://doi.org/10.1016/S1365-1609(03)00040-6
  19. Sharan, S.K. (2005), "Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic Hoek-Brown rock", Int. J. Rock. Mech. Min. Sci., 42(4), 542-549. https://doi.org/10.1016/j.ijrmms.2005.03.019
  20. Shin, J.H., Shin, Y.S., Kim, S.H. and Shin, H.S. (2007), "Evaluation of residual pore water pressures on linings for undersea tunnels", Chin. J. Rock. Mech. Eng., 26(2), 3682-3688.
  21. Shin, Y.J., Kim, B.M., Shin, J.H. and Lee, I.M. (2010), "The ground reaction curve of underwater tunnels considering seepage forces", Tunn. Undergr. Sp. Tech., 25(4), 315-324. https://doi.org/10.1016/j.tust.2010.01.005
  22. Shin, J.H., Lee, I.M. and Shin, Y.J. (2011), "Elasto‐plastic seepage‐induced stresses due to tunneling", Int. J. Numer. Anal. Method. Geomech., 35(13), 1432-1450. https://doi.org/10.1002/nag.964
  23. Skempton, A.W. (1961), "Effective stress in soils, concrete and rock", In: Pore Pressure and Suction in Soils, Butterworth, London, UK, pp. 4-16.
  24. Terzaghi, K. (1923), "Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungerscheinungen", Sitz. Akad. Wissen. Wien, Math. Naturwiss. Kl., Abt. IIa, 132, 125-138.
  25. Timoshenko, S.P. and Goodier, J.N. (1982), Theory of Elasticity, McGraw-Hill, New York, NY, USA.
  26. Wang, Y. (1996), "Ground response of circular tunnel in poorly consolidated rock", J. Geotech. Eng., 122(9), 703-708. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:9(703)
  27. Zareifard, M.R. and Fahimifar, A. (2012), "A new solution for shallow and deep tunnels by considering the gravitational Loads", Acta. Geotech. Slov., 2012(2).

Cited by

  1. Numerical analysis of water flow characteristics after inrushing from the tunnel floor in process of karst tunnel excavation vol.10, pp.4, 2016, https://doi.org/10.12989/gae.2016.10.4.471
  2. Explicit analytical solutions for surrounding rock stress of a shallow buried tunnel considering seepage effect 2018, https://doi.org/10.1080/19648189.2017.1388849
  3. Mechanical response features and failure process of soft surrounding rock around deeply buried three-centered arch tunnel vol.22, pp.10, 2015, https://doi.org/10.1007/s11771-015-2951-6
  4. Escape Routes Analysis after Water Inrush from the Working Face during Submarine Tunnel Excavation 2018, https://doi.org/10.1080/1064119X.2017.1313912
  5. Roof collapse of shallow tunnel in layered Hoek-Brown rock media vol.11, pp.6, 2016, https://doi.org/10.12989/gae.2016.11.6.867
  6. Limit Analysis of Active and Passive Mechanisms of Shallow Tunnels in Nonassociative Soil with Changing Water Table vol.18, pp.7, 2018, https://doi.org/10.1061/(ASCE)GM.1943-5622.0001167
  7. Collapse analysis of shallow tunnel subjected to seepage in layered soils considering joined effects of settlement and dilation vol.13, pp.2, 2015, https://doi.org/10.12989/gae.2017.13.2.217
  8. Simple solutions of an opening in elastic-brittle plastic rock mass by total strain and incremental approaches vol.13, pp.4, 2015, https://doi.org/10.12989/gae.2017.13.4.585
  9. Influences of seepage force and out-of-plane stress on cavity contracting and tunnel opening vol.13, pp.6, 2015, https://doi.org/10.12989/gae.2017.13.6.907
  10. Flow characteristics after water inrush from the working face in karst tunneling vol.14, pp.5, 2018, https://doi.org/10.12989/gae.2018.14.5.407
  11. Roof failure of shallow tunnel based on simplified stochastic medium theory vol.14, pp.6, 2015, https://doi.org/10.12989/gae.2018.14.6.571
  12. Catastrophe analysis of active-passive mechanisms for shallow tunnels with settlement vol.15, pp.1, 2015, https://doi.org/10.12989/gae.2018.15.1.621
  13. An improved radius-incremental-approach of stress and displacement for strain-softening surrounding rock considering hydraulic-mechanical coupling vol.16, pp.1, 2018, https://doi.org/10.12989/gae.2018.16.1.059
  14. EPB tunneling in cohesionless soils: A study on Tabriz Metro settlements vol.19, pp.2, 2015, https://doi.org/10.12989/gae.2019.19.2.153
  15. Elastic solutions for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface vol.19, pp.3, 2019, https://doi.org/10.12989/gae.2019.19.3.201
  16. An improved model of compaction grouting considering three-dimensional shearing failure and its engineering application vol.19, pp.3, 2019, https://doi.org/10.12989/gae.2019.19.3.217
  17. Analytical solution for steady seepage and groundwater inflow into an underwater tunnel vol.20, pp.3, 2015, https://doi.org/10.12989/gae.2020.20.3.267
  18. Experimental study on the mechanical response and failure behavior of double-arch tunnels with cavities behind the liner vol.20, pp.5, 2015, https://doi.org/10.12989/gae.2020.20.5.399
  19. A new analytical-numerical solution to analyze a circular tunnel using 3D Hoek-Brown failure criterion vol.22, pp.1, 2015, https://doi.org/10.12989/gae.2020.22.1.011
  20. Solution for surrounding rock of strain-softening considering confining pressure-dependent Young's modulus and nonlinear dilatancy vol.22, pp.4, 2015, https://doi.org/10.12989/gae.2020.22.4.277
  21. Three-dimensional finite element analysis of urban rock tunnel under static loading condition: Effect of the rock weathering vol.25, pp.2, 2015, https://doi.org/10.12989/gae.2021.25.2.099