Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Elasto-plastic solution for cavity expansion problem in anisotropic and drained soil mass

  • Li, Chao (School of Civil Engineering, Central South University) ;
  • Zou, Jin-feng (School of Civil Engineering, Central South University) ;
  • Li, Liang (School of Civil Engineering, Central South University)
  • Received : 2018.10.31
  • Accepted : 2019.12.02
  • Published : 2019.12.30
⟨ Previous Next ⟩

Abstract

This study presents an elasto-plastic (EP) solution for drained cavity expansion on the basis of unified strength failure criterion and considers the influence of initial stress state. Because of the influence of initial consolidation of soil mass, the initial stress may be anisotropic in the natural soil mass. In addition, the undrained hypothesis is usually used in the calculation of cavity expansion problem, but most of the cases are in the drained situation in practical engineering. Eventually, the published solution and the presented solution are compared to verify the suitability of the study.

Keywords

Acknowledgement

Supported by : Central South University

This work was supported by the National Key R&D Program of China (2017YFB1201204). The first author thanks Project 2018zzts188 supported by Innovation Foundation for Postgraduate of the Central South University. The editor's and anonymous reviewer's comments have improved the quality of the study and are also greatly acknowledged.

References

  1. Andersen, K.H. (1980), "Cyclic and static laboratory tests on Drammen clay", J. Soil Mech. Found. Div., 106(5), 499-529.
  2. Carter, J.P. Booker, J.R. and Yeung, S.K. (1986), "Cavity expansion in cohesive frictional soils", Geotechnique, 36(3), 345-358. https://doi.org/10.1680/geot.1986.36.3.349.
  3. Carter, J.P., Randolph, M.F. and Wroth, C.P. (1979), "Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity", Int. J. Numer. Anal. Meth. Geomech., 3(4), 305-322. https://doi.org/10.1002/nag.1610030402.
  4. Chai, J., Carter, J. P., Miura, N. and Zhu, H. (2009), "Improved prediction of lateral deformations due to installation of soil-cement columns", J. Geotech. Geoenviron. Eng., 135(12), 1836-1845. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000155.
  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. https://doi.org/10.1680/geot.11.P.088.
  6. Chen, G.H., Zou, J.F. and Chen, J.Q. (2019a), "Shallow tunnel face stability considering pore water pressure in non-homogeneous and anisotropic soils", Comput. Geotech., 116, 103205. https://doi.org/10.1016/j.compgeo.2019.103205.
  7. Chen, G.H., Zou, J.F. and Qian, Z.H. (2019b). "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. 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.
  9. Hill, R. (1950), The Mathematical Theory of Plasticity, Clarendon Press.
  10. Li, L., Li, J. and Sun, D. (2016), "Anisotropically elasto-plastic solution to undrained cylindrical cavity expansion in K0-consolidated clay", Comput. Geotech., 73, 83-90. https://doi.org/10.1016/j.compgeo.2015.11.022.
  11. Li, C., Zou, J.F. and A, S.G. (2019a), "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.
  12. Li, C., Zou, J.F. and Zhou, H. (2019b), "Cavity expansions in k0 consolidated clay", Eur. J. Environ. Civ. Eng., 1-19. https://doi.org/10.1080/19648189.2019.1605937.
  13. Marchi, M., Gottardi, G. and Soga, K. (2014), "Fracturing pressure in clay", J. Geotech. Geoenviron. Eng., 140(2), 04013008. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001019.
  14. Mo, P.Q., Marshall, A.M. and Yu, H.S. (2016), "Interpretation of cone penetration test data in layered soils using cavity expansion analysis", J. Geotech. Geoenviron. Eng., 143(1), 04016084. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001577.
  15. Mo, P.Q. and Yu, H.S. (2016), "Undrained cavity-contraction analysis for prediction of soil behavior around tunnels", Int. J. Geomech., 17(5), 04016121. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000816.
  16. Mo, P.Q. and Yu, H.S. (2017a), "Undrained cavity expansion analysis with a unified state parameter model for clay and sand", Geotechnique, 67(6), 503-515. https://doi.org/10.1680/jgeot.15.P.261.
  17. Mo, P.Q. and Yu, H.S. (2017b), "Drained cavity expansion analysis with a unified state parameter model for clay and sand", Can. Geotech. J., 55(7), 1029-1040. https://doi.org/10.1139/cgj-2016-0695.
  18. 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.
  19. Peng, X., Yu, P., Zhang, Y. and Chen, G. (2018), "Applying modified discontinuous deformation analysis to assess the dynamic response of sites containing discontinuities", Eng. Geol., 246, 349-360. https://doi.org/10.1016/j.enggeo.2018.10.011.
  20. Randolph, M.F. (2003), "Science and empiricism in pile foundation design", Geotechnique, 53(10), 847-876. https://doi.org/10.1680/geot.2003.53.10.847.
  21. Russell, A.R. and Khalili, N. (2002), "Drained cavity expansion in sands exhibiting particle crushing", Int. J. Numer. Anal. Meth. Geomech., 26(4), 323-340. https://doi.org/10.1002/nag.203.
  22. Salgado, R. and Prezzi, M. (2007), "Computation of cavity expansion pressure and penetration resistance in sands", Int. J. Geomech., 7, 251-265. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:4(251).
  23. Seo, H.J., Jeong, K.H., Choi, H. and Lee, I.M. (2012), "Pullout Resistance Increase of Soil Nailing Induced by Pressurized Grouting", J. Geotech. Geoenviron. Eng., 138(5), 604-613. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000622.
  24. 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. https://doi.org/10.12989/gae.2012.4.1.019.
  25. Teh, C.I. and Houlsby, G.T. (1991), "Analytical study of the cone penetration test in clay", Geotechnique, 41(1), 17-34. https://doi.org/10.1680/geot.1991.41.1.17.
  26. Tolooiyan, A. and Gavin, K. (2011), "Modelling the cone penetration test in sand using cavity expansion and arbitrary Lagrangian Eulerian finite element methods", Comput. Geotech., 38(4), 482-490. https://doi.org/10.1016/j.compgeo.2011.02.012.
  27. Vesic, A.S. (1972), "Expansion of cavities in infinite soil mass", J. Soil Mech. Found. Div., 98(3), 265-290. https://doi.org/10.1061/JSFEAQ.0001740
  28. Wang, S., Wu, Z., Guo, M. and Ge, X. (2012), "Theoretical solutions of a circular tunnel with the influence of axial in situ stress in elastic-brittle-plastic rock", Tunn. Undergr. Sp. Technol., 30, 155-168. https://doi.org/10.1016/j.tust.2012.02.016.
  29. Wang, S. and Yin, S. (2011), "A closed-form solution for a spherical cavity in the elastic-brittle-plastic medium", Tunn. Undergr. Sp. Technol., 26(1), 236-241. https://doi.org/10.1016/j.tust.2010.06.005.
  30. Xiao, Y., Sun, Y., Yin, F., Liu, H. and Xiang, J. (2016), "Constitutive modeling for transparent granular soils", Int. J. Geomech., 04016150. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000857.
  31. Yang, X.L. and Pan, Q.J. (2015), "Three dimensional seismic and static stability of rock slopes", Geomech. Eng., 8(1), 97-111. http://dx.doi.org/10.12989/gae.2015.8.1.097.
  32. Yu, H.S. (2000), Cavity Expansion Methods in Geomechanics, Kluwer Academic Publishers.
  33. 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).
  34. Yu, M.H. (2004), Unified Strength Theory and Applications, Springer-Verlag.
  35. Zhang, Y., Chen, G., Zheng, L., Li, Y. and Wu, J. (2013), "Effects of near-fault seismic loadings on run-out of large-scale landslide: a case study", Eng. Geol., 166(8), 216-236. https://doi.org/10.1016/j.enggeo.2013.08.002.
  36. Zhang, Y.G. and Li, J.P. (2015), "Lateral displacements of ground caused by piles installation in soft clay", J. Tongji Univ. Nat. Sci., 43(12), 1801-1806 (in Chinese).
  37. Zhang, Y., Wang, J., Xu, Q., Chen, G., Zhao, J.X., Zheng, L. and Yu, P. (2015a), "DDA validation of the mobility of earthquake-induced landslides", Eng. Geol., 194(26), 38-51. https://doi.org/10.1016/j.enggeo.2014.08.024.
  38. Zhang, Y., Zhang, J., Chen, G., Zheng, L. and Li, Y. (2015b), "Effects of vertical seismic force on initiation of the Daguangbao landslide induced by the 2008 Wenchuan earthquake", Soil Dyn. Earthq. Eng., 73, 91-102. https://doi.org/10.1016/j.soildyn.2014.06.036.
  39. Zhao, L.H., Cheng, X., Li, D.J. and Zhang, Y.B. (2019), "Influence of non-dimensional strength parameters on the seismic stability of cracked slopes", J. Mount. Sci., 16(1), 153-167. https://doi.org/10.1007/s11629-017-4753-9.
  40. Zhou, H., Kong, G., Liu, H. and Laloui, L. (2018), "Similarity solution for cavity expansion in thermoplastic soil", Int. J. Numer. Anal. Meth. Geomech., 42(2), 274-294. https://doi.org/10.1002/nag.2724.
  41. Zhou, H., Liu, H., Randolph, M.F., Kong, G. and Cao, Z. 2017), "Experimental and analytical study of X-section cast-in-place concrete pile installation influence", Int. J. Phys. Modell. Geotech., 17(2), 1-19. https://doi.org/10.1680/jphmg.15.00037.
  42. Zou, J.F., Chen, G. and Qian, Z. (2019), "Tunnel face stability in cohesion-frictional soils considering the soil arching effect by improved failure models", Comput. Geotech., 106, 1-17. https://doi.org/10.1016/j.compgeo.2018.10.014.
  43. Zou, J.F., Chen, K.F. and Pan, Q.J. (2017), "Influences of seepage force and out-of-plane stress on cavity contracting and tunnel opening", Geomech. Eng., 13(6), 907-928. https://doi.org/10.12989/gae.2017.13.6.907.
  44. Zou, J.F. and Wei, X.X. (2018), "An improved radius-incremental-approach of stress and displacement for strain-softening surrounding rock considering hydraulic-mechanical coupling", Geomech. Eng., 16(1), 59-69. https://doi.org/10.12989/gae.2018.16.1.059.
  45. Zou, J.F., Wei, A. and Yang, T. (2018), "Elasto-plastic solution for shallow tunnel in semi-infinite space", Appl. Math. Modell., 64(12), 669-687. https://doi.org/10.1016/j.apm.2018.07.049.
  46. Zou, J.F. and Zhang, P.H. (2019), "Analytical model of fully grouted bolts in pull-out tests and in situ rock masses", Int. J. Rock Mech. Min. Sci., 113(1), 278-294. https://doi.org/10.1016/j.ijrmms.2018.11.015.

Cited by

  1. Load-displacement behaviour of tapered piles: Theoretical modelling and analysis vol.26, pp.1, 2019, https://doi.org/10.12989/gae.2021.26.1.001