Geomechanics and Engineering

  • 제25권4호
  • /
  • Pages.283-294
  • /
  • 2021
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A semi-analytical solution to spherical cavity expansion in unsaturated soils

  • Tang, Jianhua (Department of Civil Engineering, Tongji University) ;
  • Wang, Hui (Department of Civil Engineering, Tongji University) ;
  • Li, Jingpei (Department of Civil Engineering, Tongji University)
  • 투고 : 2020.12.18
  • 심사 : 2021.04.29
  • 발행 : 2021.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a rigorous solution for spherical cavity expansion in unsaturated soils under constant suction condition. The hydraulic behavior that describes the saturation-suction relationship is modeled by a void ratio-dependent soil-water characteristic curve, which allows the hydraulic behavior to fully couple with the mechanical behavior that is described by an extended critical state soil model for unsaturated soil through the specific volume. Considering the boundary condition and introducing an auxiliary coordinate, the problem is formulated to a system of first-order differential equations with three principal stress components and suction as basic unknowns, which is solved as an initial value problem. Parameter analyses are conducted to investigate the effects of suction and the overconsolidation ratio on the overall expansion responses, including the pressure-expansion response, the distribution of the stress components around the cavity, and the stress path of the soil during cavity expansion. The results reveal that the expansion pressures and the distribution of the stress components in unsaturated soils are generally higher than those in saturated soils due to the existence of suction.

키워드

참고문헌

  1. Alonso, E.E., Gens, A. and Josa, A. (1990), "A constitutive model for partially saturated soils", Geotechnique, 40(3), 405-430. https://doi.org/10.1680/geot.1990.40.3.405.
  2. 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.
  3. Charlez, P.A. and Roatesi, S. (1999), "A fully analytical solution of the wellbore stability problem under undrained conditions using a linearized Cam-Clay model", Oil Gas Sci. Technol., 54(5), 551-563. https://doi.org/10.2516/ogst:1999047.
  4. 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.
  5. Chen, H.H., Li, L. and Li, J.P. (2019b), "Stress transform method to undrained and drained expansion of a cylindrical cavity in anisotropic modified cam-clay soils", Comput. Geotech., 106, 128-142. https://doi.org/10.1016/j.compgeo.2018.10.016.
  6. Chen, H.H., Li, L., Li, J.P. and Sun, D.A. (2020), "Elastoplastic solutions for cylindrical cavity expansion in unsaturated soils", Comput. Geotech., 123, 103569. https://doi.org/10.1016/j.compgeo.2020.103569.
  7. Chen, S.L. and Abousleiman, Y.N. (2012), "Exact undrained elasto-plastic solution for cylindrical cavity expansion in modified Cam Clay soil", Geotechnique, 62(5), 447-456. https://doi.org/10.1680/geot.11.P.027.
  8. 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.
  9. Collins, I.F., Pender, M.J. and Wang, Y. (1992), "Cavity expansion in sands under drained loading conditions", Int. J. Numer. Anal. Met., 16(1), 3-23. https://doi.org/10.1002/nag.1610160103.
  10. Cudmani, R. and Osinov, V.A. (2001), "The cavity expansion problem for the interpretation of cone penetration and pressuremeter tests", Can. Geotech. J., 38(3), 622-638. https://doi.org/10.1139/cgj-38-3-622.
  11. Dafalias, Y.F. (1986), "An anisotropic critical state soil plasticity model", Mech. Res. Commun., 13(6), 341-347. https://doi.org/10.1016/0093-6413(86)90047-9.
  12. Diao, H.J., Wu, Y.D., Liu, J. and Luo, R.P. (2015), "An analytical investigation of soil disturbance due to sampling penetration", Geomech. Eng., 9(6), 743-755. https://doi.org/10.12989/gae.2015.9.6.743.
  13. Hoek, E. (2001), "Big tunnels in bad rock", J. Geotech. Geoenviron. Eng., 127(9), 726-740. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:9(726).
  14. Li, C. and Zou, J.F. (2019), "Created cavity expansion solution in anisotropic and drained condition based on Cam-clay model", Geomech. Eng., 19(2), 141-151. https://doi.org/10.12989/gae.2019.19.2.141.
  15. Li, C., Zou, J.F. and Sheng Y.M. (2020), "Undrained solution for cavity expansion in strength degradation and tresca soils", Geomech. Eng., 21(6), 527-536. https://doi.org/10.12989/gae.2020.21.6.527.
  16. Li, L., Chen, H.H., Li, J.P. and Sun, D.A. (2021), "An elastoplastic solution to undrained expansion of a cylindrical cavity in SANICLAY under plane stress condition", Comput. Geotech., 132, 103990. https://doi.org/10.1016/j.compgeo.2020.103990.
  17. Li, L., Li, J.P., Sun, D.A. and Gong, W.B. (2017), "Unified solution to drained expansion of a spherical cavity in clay and sand", Int. J. Geomech., 17(8), 04017028. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000909.
  18. Li, L., Xiang, Z.C., Zou, J.F. and Wang, F. (2019), "An improved model of compaction grouting considering three-dimensional shearing failure and its engineering application", Geomech. Eng., 19(3), 217-227. https://doi.org/10.12989/gae.2019.19.3.217.
  19. Liang, F.Y., Liang, X., Zhang, H. and Wang, C. (2020), "Seismic response from centrifuge model tests of a scoured bridge with a pile-group foundation", J. Bridge Eng., 25(8), 04020054. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001594.
  20. Liang, Q.G., Li, J., Wu, X.Y. and Zhou, A.N. (2016), "Anisotropy of Q2 loess in the Baijiapo Tunnel on the Lanyu Railway, China", B. Eng. Geol. Environ., 75(1), 109-124. https://doi.org/10.1007/s10064-015-0723-z.
  21. Liu, F., Yi, J.T., Cheng, P. and Yao, K. (2020), "Numerical simulation of set-up around shaft of XCC pile in clay", Geomech. Eng., 21(5), 489-501. https://doi.org/10.12989/gae.2020.21.5.489.
  22. Lukic, D.C., Prokic, A.D. and Brcic, S.V. (2014), "Stress state around cylindrical cavities in transversally isotropic rock mass", Geomech. Eng., 6(3), 213-233. https://doi.org/gae.2014.6.3.213. https://doi.org/10.12989/gae.2014.6.3.213
  23. Mayne, P.W. (1991), "Determination of OCR in clays by piezocone tests using cavity expansion and critical state concepts", Soils Found., 31(2), 65-76. https://doi.org/10.3208/sandf1972.31.2_65.
  24. Pournaghiazar, M., Russell, A.R. and Khalili, N. (2012), "Linking cone penetration resistances measuredin calibration chambers and the field", Geotech. Lett., 2, 26-35. https://doi.org/10.1680/geolett.11.00040.
  25. Randolph, M.F. (2003), "Science and empiricism in pile foundation design", Geotechnique, 53(10), 847-875. https://doi.org/10.1680/geot.53.10.847.37518.
  26. Rezania, M., Nezhad, M.M., Zanganeh, H., Castro, J. and Sivasithamparam, N. (2017), "Modeling pile setup in natural clay deposit considering soil anisotropy, structure, and creep effects: case study", Int. J. Geomech., 17(3), 1-13. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000774.
  27. Russell, A.R. and Khalili, N. (2006), "On the problem of cavity expansion in unsaturated soils", Comput. Mech., 37(4), 311-330. https://doi.org/10.1007/s00466-005-0672-7.
  28. Salgado, R., Mitchell, J.K. and Jamiolkowski, M. (1997), "Cavity expansion and penetration resistance in sand", J. Geotech. Geoenviron. Eng., 123(4), 344-354. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:4(344).
  29. Sheng, D., Fredlund, D.G. and Gens, A. (2008), "A new modelling approach for unsaturated soils using independent stress variables", Can. Geotech. J., 45(4), 511-534. https://doi.org/10.1139/T07-112.
  30. 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.
  31. Sivasithamparam, N. and Castro, J. (2018), "Undrained expansion of a cylindrical cavity in clays with fabric anisotropy: Theoretical solution", Acta. Geotech., 13(3), 729-746. https://doi.org/10.1007/s11440-017-0587-4.
  32. Sivasithamparam, N. and Castro, J. (2020), "Undrained cylindrical cavity expansion in clays with fabric anisotropy and structure: Theoretical solution", Comput. Geotech., 120. https://doi.org/10.1016/j.compgeo.2019.103386.
  33. Sun, D.A., Sheng, D., Li. X. and Scott W.S. (2008), "Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions", Comput. Geotech., 35(6), 845-852. https://doi.org/10.1016/j.compgeo.2008.08.002.
  34. Vesic, A.C. (1972), "Expansion of cavities in infinite soil mass", J. Soil Mech. Found. Div., 98, 265-290. https://doi.org/10.1061/JSFEAQ.0001740
  35. Vrakas, A. and Anagnostou, G. (2015), "Finite strain elastoplastic solutions for the undrained ground response curve in tunneling", Int. J. Numer. Anal. Mech. Geomech., 39(7), 738-761. https://doi.org/10.1002/nag.2335.
  36. Wang, Y., Li, L., Li, J.P. and Sun, D.A. (2020), "Jet-grouting in ground improvement and rotary grouting pile installation: Theoretical analysis", Geomech. Eng., 21(3), 279-288. https://doi.org/10.12989/gae.2020.21.3.279.
  37. Wheeler, S.J., Sharma, R.S. and Buisson, M.S.R. (2003), "Coupling of hydraulic hysteresis and stress-strain behavior in unsaturated soils", Geotechnique, 53(1), 41-54. https://doi.org/10.1680/geot.2003.53.1.41.
  38. Yang, C.Y., Chen, H.H., and Li, J.P. (2020). "Drained cylindrical cavity expansion analysis in anisotropic soils considering 3D strength" Geotech. Lett., 10, 346-352. https://doi.org/10.1680/jgele.19.00043.
  39. Yang, C.Y., Chen, H.H., Li, J.P. and Li, L. (2021b), "Undrained spherical cavity expansion in unsaturated soils: Semi-analytical solution coupling hydraulic and mechanical behaviors", Int. J. Geomech., 21(6), 04021070. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002028.
  40. Yang, C.Y., Li, J.P., Li, L. and Sun D.A. (2021a), "Expansion responses of a cylindrical cavity in overconsolidated unsaturated soils: A semi-analytical elastoplastic solution", Comput. Geotech., 130, 103922. https://doi.org/10.1016/j.compgeo.2020.103922.
  41. Yang, H. and Russell, A.R. (2015), "Cavity expansion in unsaturated soils exhibiting hydraulic hysteresis considering three drainage conditions", Int. J. Numer. Anal. Met., 39(18), 1975-2016. https://doi.org/10.1002/nag.2379.
  42. Yu, H.S. and Houlsby, G.T. (1991), "Finite cavity expansion in dilatant soils: Loading analysis", Geotechnique, 41(2), 173-183. https://doi.org/10.1680/geot.1991.41.2.173.
  43. Zhang, L.Y., Cao, P. and Radha, K.C. (2010), "Evaluation of rock strength criteria for wellbore stability analysis", Int. J. Rock Mech. Min. Sci., 47(8), 1304-1316. https://doi.org/10.1016/j.ijrmms.2010.09.001.
  44. Zhou, X.Y., Xu, Y.S., Sun, D.A., Tan, Y.Z. and Xu, Y.F. (2021), "Three-dimensional thermal-hydraulic coupled analysis in the nuclear waste repository", Ann. Nucl. Energy, 151, 107866. https://doi.org/10.1016/j.anucene.2020.107866.
  45. 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(3), 347-360. https://doi.org/10.12989/gae.2017.12.3.347.
  46. Zou, J.F., Yang, T., Ling, W., Guo, W.J. and Huang, F.L. (2019), "A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass", Geomech. Eng., 18(3), 225-234. https://doi.org/10.12989/gae.2019.18.3.225.