Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Simple solutions of an opening in elastic-brittle plastic rock mass by total strain and incremental approaches

  • Park, Kyungho (Department of Civil Engineering, A'Sharqiyah University)
  • Received : 2016.06.05
  • Accepted : 2017.04.03
  • Published : 2017.10.25
⟨ Previous Next ⟩

Abstract

This study deals with simple solutions for a spherical or circular opening excavated in elastic-brittle plastic rock mass compatible with a linear Mohr-Coulomb (M-C) or a nonlinear Hoek-Brown (H-B) yield criterion. Based on total strain approach, the closed-form solutions of stresses and displacement are derived simultaneously for circular and spherical openings using original H-B and M-C yield criteria. Two simple numerical procedures are proposed for the solution of generalized H-B and M-C yield criteria. Based on incremental approach, the similarity solution is derived for circular and spherical openings using generalized H-B and M-C yield criteria. The classical Runge-Kutta method is used to integrate the first-order ordinary differential equations. Using three data sets for M-C and H-B models, the results of the radial displacements, the spreading of the plastic radius with decreasing pressure, and the radial and circumferential stresses in the plastic region are compared. Excellent agreement among the solutions is obtained for all cases of spherical and circular openings. The importance of the use of proper initial values in the similarity solution is discussed.

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", I. J. Numer. Anal. Meth. Geomech., 27(13), 1153-1185. https://doi.org/10.1002/nag.315
  2. 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)
  3. Carranza-Torres, C. (2004), "Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion", I. J. Rock Mech. Min. Sci., 41(3), 480-481. https://doi.org/10.1016/j.ijrmms.2003.12.014
  4. Carranza-Torres, C. and Fairhurst, C. (1999), "The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion", I. J. Rock Mech. Min. Sci., 36(5), 777-809.
  5. Chapra, S.C. and Canale, R.P. (2002), Numerical Methods for Engineers, 4th Edition, McGraw-Hill, New York, U.S.A.
  6. Detournay, E. (1986), "Elastoplastic model of a deep tunnel for a rock with variable dilatancy", Rock Mech. Rock Eng., 19(2), 99-108. https://doi.org/10.1007/BF01042527
  7. Fahimifar, A., Ghadami, H. and Ahmadvand, M. (2015), "The ground response curve of underwater tunnels excavated in a strain-softening rock mass", Geomech. Eng., J., 8(3), 323-359. https://doi.org/10.12989/gae.2015.8.3.323
  8. Nawel, B. and Salah, M. (2015), "Numerical modeling of two parallel tunnels interaction using threedimensional finite elements method", Geomech. Eng., 9(6), 775-791. https://doi.org/10.12989/gae.2015.9.6.775
  9. Osgoui, R. and Oreste, P. (2010), "Elasto-plastic analytical model for the design of grouted bolts in a hoekbrown medium", I. J. Numer. Anal. Met. Geomech., 34(16), 1651-1686.
  10. Park, K.H. (2014a), "Similarity solution of a spherical or circular opening in elastic-strain softening rock mass", I. J. Rock Mech. Min. Sci., 71, 151-159.
  11. Park, K.H. (2014b), "Large strain similarity solution for a spherical or circular opening excavated in elasticperfectly plastic media", I. J. Numer. Anal. Met. Geomech., 39(7), 724-737. https://doi.org/10.1002/nag.2333
  12. Park, K.H. and Kim, Y.J. (2006), "Analytical solution for a circular opening in an elastic-brittle-plastic rock", I. J. Rock Mech. Min. Sci., 43(4), 616-622. https://doi.org/10.1016/j.ijrmms.2005.11.004
  13. Serrano, A., Olalla, C. and Reig, I. (2011), "Convergence of circular tunnels in elastoplastic rock masses with non-linear failure criteria and non-associated flow laws", I. J. Rock Mech. Min. Sci., 48(6), 878-887. https://doi.org/10.1016/j.ijrmms.2011.06.008
  14. Sharan, S.K. (2003), "Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media", I. J. Rock Mech. Min. Sci., 40(6), 817-824. https://doi.org/10.1016/S1365-1609(03)00040-6
  15. Sharan, S.K. (2005), "Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic hoek-brown rock", I. J. Rock Mech. Min. Sci., 42(4), 542-549. https://doi.org/10.1016/j.ijrmms.2005.03.019
  16. Sharan, S.K. (2008), "Analytical solutions for stresses and displacements around a circular opening in a generalized hoek-brown rock", I. J. Rock Mech. Min. Sci., 45(1), 78-85. https://doi.org/10.1016/j.ijrmms.2007.03.002
  17. Shin, Y.J., Song, K.I, Lee, I.M. and Cho, G.C. (2011), "Interaction between tunnel supports and ground convergence consideration of seepage forces", I. J. Rock Mech. Min. Sci., 48(3), 394-405. https://doi.org/10.1016/j.ijrmms.2011.01.003
  18. Vrakas, A. and Anagnostou, G. (2014), "A finite strain closed-form solution for the elastoplastic ground response curve in tunneling", I. J. Numer. Anal. Met. Geomech., 38(11), 1131-1148. https://doi.org/10.1002/nag.2250
  19. Wang, S.L. and Yin, S.D. (2011), "A closed-form solution for a spherical cavity in the elastic-brittle-plastic medium", Tunn. Underg. Sp. Tech., 26(1), 236-241. https://doi.org/10.1016/j.tust.2010.06.005
  20. Wang, S.L., Yin, S.D. and Wu, Z.J. (2012), "Strain-softening analysis of a spherical cavity", I. J. Numer. Anal. Met. Geomech., 36(2), 182-202. https://doi.org/10.1002/nag.1002
  21. Zhang, W. and Goh, A.T.C. (2016), "Predictive models of ultimate and serviceability performances for underground twin caverns", Geomech. Eng., 10(2), 175-188. https://doi.org/10.12989/gae.2016.10.2.175

Cited by

  1. Tunnel lining load with consideration of the rheological properties of rock mass and concrete vol.21, pp.1, 2020, https://doi.org/10.12989/gae.2020.21.1.053
  2. Shear failure and mechanical behavior of flawed specimens containing opening and joints vol.23, pp.6, 2017, https://doi.org/10.12989/gae.2020.23.6.587
  3. Deformation behavior analysis of tunnels opened in various rock mass grades conditions in China vol.26, pp.2, 2017, https://doi.org/10.12989/gae.2021.26.2.191