Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass

  • Zou, Jin-Feng (School of Civil Engineering, Central South University) ;
  • Yang, Tao (School of Civil Engineering, Central South University) ;
  • Ling, Wang (School of Civil Engineering, Central South University) ;
  • Guo, Wujun (Guizhou Zhongjiao Tonghuai Expressway Co., Ltd.) ;
  • Huang, Faling (Guizhou Expressway Group Co., Ltd.)
  • Received : 2019.01.16
  • Accepted : 2019.05.28
  • Published : 2019.06.30
⟨ Previous Next ⟩

Abstract

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

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. Meth. Geomech., 27(13), 1153-1185. https://doi.org/10.1002/nag.315.
  2. Bernier, F., Li, X.L. and Bastiaens, W. (2007), "Twenty-five years' geotechnical observation and testing in the tertiary boom clay formation", Geotechnique, 57(2), 229-237. https://doi.org/10.1680/geot.2007.57.2.229.
  3. Cao, L.F., Teh, C.I. and Chang, M.F. (2001), "Undrained cavity expansion in modified Cam clay I: Theoretical analysis", Geotechnique, 51(4), 323-334. https://doi.org/10.1680/geot.2001.51.4.323
  4. Chao, M.S., Gao, M., Zhang, J.Y. and Chen, Q.S. (2016), "An analytic solution for spherical cavity expansion based on energy dissipation theory", Rock Soil Mech., 37(7), 1986-1993.
  5. Chen, S.L. and Abousleiman, Y.N. (2013), "Exact drained solution for cylindrical cavity expansion in modified Cam Clay soil", Geotechnique, 63(6), 510-517. http://dx.doi.org/10.1680/geot.11.P.088.
  6. Cheng, T., Yu, Z., Zheng, J., Du, J., Zhang, Y., Garg, A. and Garg, A. (2018), "Improvement of the cavity expansion theory for the measurement of strain softening in over consolidated saturated clay", Measurement, 119, 156-166. https://doi.org/10.1016/j.measurement.2018.01.069.
  7. Chen, G.H., Zou, J.F. and Qian, Z.H. (2019a), "An improved collapse analysis mechanism for the face stability of shield tunnel in layered soils", Geomech. Eng., 17(1), 97-107. https://doi.org/10.12989/gae.2019.17.1.097.
  8. Chen, G.H., Zou, J., Min, Q., Guo, W.J. and Zhang, T.Z. (2019b), "Face stability analysis of a shallow square tunnel in non-homogeneous soils", Comput. Geotech., In Press.
  9. Carter, J.P., Booker, J.R. and Yeung, S.K. (1986), "Cavity expansion in cohesive frictional soils", Geotechnique, 36(3), 349-358. https://doi.org/10.1680/geot.1986.36.3.349
  10. Carter, J.P. and Yeung, S.K. (1985), "Analysis of cylindrical cavity expansion in a strain weakening material", Comput. Geotech., 1(3), 161-180. https://doi.org/10.1016/0266-352X(85)90021-7.
  11. Collins, I.F. and Yu, H.S. (1996), "Undrained cavity expansions in critical state soils", Int. J. Numer. Anal. Meth. Geomech., 20(7), 489-516. https://doi.org/10.1002/(SICI)1096-9853(199607)20:7%3C489::AID-NAG829%3E3.0.CO;2-V.
  12. Dalton, J. and Hawkins, P.G. (1982), "Fields of stress - some measurements of the in-situ stress in a meadow in the cambridgeshire countryside", Ground Eng., 15(4).
  13. Fahimifar, A., Ghadami, H. and Ahmadvand, M. (2015), "The ground response curve of underwater tunnels, excavated in a strain-softening rock mass", Geomech. Eng., 9(1), 115-124. http://dx.doi.org/10.12989/gae.2015.8.3.323.
  14. Huang, Q., Zou, J.F. and Qian, Z.H. (2019), "A stability analysis approach for tunnel face excavating in the longitudinally inclined and anisotropic cohesive soils", J. Central South Univ.
  15. 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. Technol., 23(5), 588-599. https://doi.org/10.1016/j.tust.2007.11.002.
  16. Li, C., Zou, J.F. and Zhou H. (2019a), "Cavity expansions in k0 consolidated clay", Eur. J. Environ. Civ. Eng., https://doi.org/10.1080/19648189.2019.1605937.
  17. Li, C. and Zou, J.F. (2019b), "Closed-form solution for undrained cavity expansion in anisotropic soil mass based on the spatially mobilized plane failure criterion", Int. J. Geomech., 19(7), 04019075. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001458.
  18. Luo, Z.Y., Zhu, X.R. and Gong, X.N. (2007), "Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression", J. Zhejiang Univ. Sci. A, 8(9), 1380-1387. https://doi.org/10.1631/jzus.2007.A1380.
  19. Nanda, S. and Patra, N.R. (2015), "Undrained cylindrical cavity expansion in critical state soils considering soil structure", Indian Geotech. J., 45(2), 169-180. https://doi.org/10.1007/s40098-014-0125-3.
  20. 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. Technol., 23(2), 151-159. https://doi.org/10.1016/j.tust.2007.03.002.
  21. Sharan, S.K. (2008), "Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock", Int. J. Rock Mech. Min. Sci., 45(1), 78-85. http://dx.doi.org/10.1016%2Fj.ijrmms.2007.03.002. https://doi.org/10.1016/j.ijrmms.2007.03.002
  22. Silvestri, V. and Abou-Samra, G. (2012), "Analytical solution for undrained plane strain expansion of a cylindrical cavity in modified cam clay", Geomech. Eng., 4(1), 19-37. http://dx.doi.org/10.12989/gae.2012.4.1.019.
  23. Vesic, A.S. (1972), "Expansion of cavities in infinite soil mass", J. Geotech. Eng., 98(SM3), 265-290.
  24. Vrakas, A. (2016), "Relationship between small and large strain solutions for general cavity expansion problems in elasto-plastic soils", Comput. Geotech., 76, 147-153. https://doi.org/10.1016/j.compgeo.2016.03.005.
  25. Wang, F. and Zou, J.F. (2018), "A simple prediction procedure of strain-softening surrounding rock for a circular opening", Geomech. Eng., 16(6), 619-626. https://doi.org/10.12989/gae.2018.16.6.619.
  26. Wang, L., Zou, J.F. and Sheng, Y.M. (2019), "An improved stress and strain-increment-approaches for circular tunnel in strain-softening surrounding rock considering the seepage force", Adv. Mater. Sci. Eng. https://doi.org/10.1155/2019/2075240.
  27. Wang, S., Yin, K., Tang, Y.H. and Ge, X. (2010), "A new approach for analyzing circular tunnel in strain-softening rock masses", Int. J. Rock Mech. Min. Sci., 47(1), 170-178. http://dx.doi.org/10.1016%2Fj.ijrmms.2009.02.011. https://doi.org/10.1016/j.ijrmms.2009.02.011
  28. Wang, S., Yin, S. and Wu, Z. (2012), "Strain-softening analysis of a spherical cavity", Int. J. Numer. Anal. Meth. Geomech., 36(2), 182-202. https://doi.org/10.1002/nag.1002.
  29. Yang, X.L. and Yin, J.H. (2010), "Slope equivalent Mohr- Coulomb strength parameters for rock masses satisfying the Hoek-Brown criterion", Rock Mech. Rock Eng., 43(4), 505-511. https://doi.org/10.1007/s00603-009-0044-2
  30. Yang, X.L. and Zou, J.F. (2011), "Cavity expansion analysis with non-linear failure criterion", Proc. Inst. Civ. Eng. Geotech. Eng., 164(1), 41-49. https://doi.org/10.1680/geng.2011.164.1.41.
  31. Yu, H.S. and Carter, J.P. (2002), "Rigorous similarity solutions for cavity expansion in cohesive-frictional soils", Int. J. Geomech., 2(2), 233-258. https://doi.org/10.1061/(ASCE)1532-3641(2002)2:2(233).
  32. Yu, H.S. (2000), Cavity Expansion Methods in Geomechanics, Kluwer Academic Publishers.
  33. Zheng, H., Liu, D.F., Lee, C.F. and Ge, X.R. (2005), "Principle of analysis of brittle-plastic rock mass", Int. J. Solids Struct., 42(1), 139-158. https://doi.org/10.1016/j.ijsolstr.2004.06.050.
  34. Zheng, J.J, Peng, H. and Nie, C.J. (2004), "Analytical solutions to expansion of cylindrical cavity in linear softening soil", Acta Mechanica Solida Sinica, 17(4), 353-360. https://doi.org/10.1007/s10338-004-0443-6
  35. Zhou, H., Liu, H. and Kong, G. (2014), "Influence of shear stress on cylindrical cavity expansion in undrained elastic-perfectly plastic soil", Geotechnique Lett., 4(3), 203-210. http://dx.doi.org/10.1680/geolett.14.00034.
  36. Zou, J.F., Liu, S.X., Li, J.B. and Qian, Z.H. (2019a), "Face stability analysis for a shield-driven tunnel with non-linear yield criterion", Proc. Inst. Civ. Eng. Geotech. Eng., 172(3), 243-254. https://doi.org/10.1680/jgeen.17.00222.
  37. Zou, J.F., Wang, F. and Wei, A. (2019b), "A semi-analytical solution for shallow tunnels with radius-iterative-approach in semi-infinite space", Appl. Math. Model., 73, 285-302. https://doi.org/10.1016/j.apm.2019.04.007.
  38. Zou, J.F. and Xia, M.Y. (2017), "A new approach for the cylindrical cavity expansion problem incorporating deformation dependent of intermediate principal stress", Geomech. Eng., 12(2), 257-263. https://doi.org/10.12989/gae.2017.12.2.257.
  39. Zou, J.F., Xia, Z.Q. and Dan, H.C. (2016), "Theoretical solutions for displacement and stress of a circular opening reinforced by grouted rockbolt", Geomech. Eng., 11(3), 439-455. https://doi.org/10.12989/gae.2016.11.3.439.