Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Dynamic response of vertically loaded rectangular barrettes in multilayered viscoelastic soil

  • Cao, Geng (Key of Laboratory for RC and PRC Structure of Education Ministry, Southeast University) ;
  • Zhu, Ming X. (Key of Laboratory for RC and PRC Structure of Education Ministry, Southeast University) ;
  • Gong, Wei M. (Key of Laboratory for RC and PRC Structure of Education Ministry, Southeast University) ;
  • Wang, Xiao (School of Civil Engineering, Southeast University) ;
  • Dai, Guo L. (Key of Laboratory for RC and PRC Structure of Education Ministry, Southeast University)
  • Received : 2020.06.06
  • Accepted : 2020.10.26
  • Published : 2020.11.10
⟨ Previous Next ⟩

Abstract

Rectangular barrettes have been increasingly used as foundations for many infrastructure projects, but the vertical vibration of a barrette has been rarely addressed theoretically. This paper presents an analysis method of dynamic response for a rectangular barrette subjected to a time-harmonic vertical force with the aid of a modified Vlasov foundation model in multilayered viscoelastic soil. The barrette-soil system is modeled as a continuum, the vertical continuous displacement model for the barrette and soil is proposed. The governing equations of the barrette-soil system and the boundary conditions are obtained and the vertical shaft resistance of barrette is established by employing Hamilton's principle for the system and thin layer element, respectively. The physical meaning of the governing equations and shaft resistance is interpreted. The iterative solution algorithm flow is proposed to obtain the dynamic response of barrette. Good agreement of the analysis and comparison confirms the correctness of the present solution. A parametric study is further used to demonstrate the effects of cross section aspect ratio of barrettes, depth of soil column, and module ratio of substratum to the upper soil layers on the complex barrette-head stiffness and the resistance stiffness.

Keywords

Acknowledgement

The study presented herein is supported by the National Natural Science Foundation of China (Nos. 51808112; 51678145), the Natural Science Foundation of Jiangsu Province (BK20180155), and the Six Talent Peaks Project in Jiangsu Province (No. XNY-047). The authors are grateful for their support.

References

  1. Ai, Z.Y. and Li, Z.X. (2015), "Dynamic analysis of a laterally loaded pile in a transversely isotropic multilayered half-space", Eng. Anal. Bound Elem., 54, 68-75. https://doi.org/10.1016/j.enganabound.2015.01.008.
  2. Anoyatis, G. and Mylonakis, G. (2012), "Dynamic Winkler modulus for axially loaded piles", Geotechnique, 62(6), 521-536. https://doi.org/10.1680/geot.11.P.052.
  3. Basu, D., Prezzi, M., Salgado, R. and Chakraborty, T. (2008), "Settlement analysis of piles with rectangular cross sections in multi-layered soils", Comput. Geotech., 35(4), 563-575. https://doi.org/10.1016/j.compgeo.2007.09.001.
  4. Cai, Y., Liu, Z., Li, T., Yu, J. and Wang, N. (2020), "Vertical dynamic response of a pile embedded in radially inhomogeneous soil based on fictitious soil pile model", Soil Dyn. Earthq. Eng., 132, 106038. https://doi.org/10.1016/j.soildyn.2020.106038.
  5. Cui, C.Y., Zhang, S.P., Yang, G. and Li, X.F. (2016), "Vertical vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock", J. Cent. South U., 23(1), 220-232. https://doi.org/10.1007/s11771-016-3065-5.
  6. Cui, C.Y., Meng, K., Wu, Y.J., Chapman, D. and Liang, Z.M. (2018a), "Dynamic response of pipe pile embedded in layered visco-elastic media with radial inhomogeneity under vertical excitation", Geomech. Eng., 16(6), 609-618. https://doi.org/10.12989/gae.2018.16.6.609.
  7. Cui, C., Zhang, S., Chapman, D. and Meng, K. (2018b), "Dynamic impedance of a floating pile embedded in poro-visco-elastic soils subjected to vertical harmonic loads", Geomech. Eng., 15(2), 793-803. https://doi.org/10.12989/gae.2018.15.2.793.
  8. Das, Y.C. and Sargand, S.M. (1999), "Forced vibrations of laterally loaded piles", Int. J. Solids Struct., 36(33), 4975-4989. https://doi.org/10.1016/S0020-7683(98)00231-5.
  9. Dym, C.L. and Shames, I.H. (1973), Solid Mechanics: A Variational Approach, McGraw-Hill, New York, U.S.A.
  10. El Gendy, M., Ibrahim, H. and El Arabi, I. (2018), "Modeling single barrettes as elastic support by CCT", Malaysian J. Civ. Eng., 30(2),296-312. https://doi.org/10.11113/mjce.v30n2.481.
  11. El Gendy, M., Ibrahim, H. and El Arabi, I. (2019), "Composed coefficient technique for barrette group", Malaysian J. Civ. Eng., 31(1), 23-33. https://doi.org/10.11113/mjce.v31n1.510.
  12. El Wakil, A.Z. and Nazir, A.K. (2013), "Behavior of laterally loaded small scale barrettes in sand", Ain Shams Eng. J., 4(3), 343-350. http://doi.org/10.1016/j.asej.2012.10.011.
  13. Fellenius, B.H., Altaee, A., Kulesza, R. and Hayes, J. (1999), "Ocell testing and FE analysis of 28-m-deep barrette in Manila, Philippines", J. Geotech. Geoenviron. Eng., 125(7), 566-575. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:7(566).
  14. Gan, S., Zheng, C., Kouretzis, G. and Ding, X. (2020), "Vertical vibration of piles in viscoelastic non-uniform soil overlying a rigid base", Acta Geotech., 15, 1321-1330. https://doi.org/10.1007/s11440-019-00833-7.
  15. Guo, W.D. and Lee, F.H. (2001), "Load transfer approach for laterally loaded piles", Int. J. Numer. Anal. Meth. Geomech., 25(11), 1101-1129. https://doi.org/10.1002/nag.169.
  16. Gupta, B.K. and Basu, D. (2016a), "Analysis of laterally loaded rigid monopiles and poles in multilayered linearly varying soil", Comput. Geotech., 72, 114-125. https://doi.org/10.1016/j.compgeo.2015.11.008.
  17. Gupta, B.K. and Basu, D. (2016b), "Response of laterally loaded rigid monopiles and poles in multi-layered elastic soil", Can. Geotech. J., 53(8), 1281-1292. https://doi.org/10.1139/cgj-2015-0520.
  18. Gupta, B.K. and Basu, D. (2017), "Analysis of laterally loaded short and long piles in multilayered heterogeneous elastic soil", Soils Found., 57(1), 92-110. https://doi.org/10.1016/j.sandf.2017.01.007.
  19. Gupta, B.K. and Basu, D. (2018), "Applicability of Timoshenko, Euler-Bernoulli and rigid beam theories in analysis of laterally loaded monopiles and piles", Geotechnique, 68(9), 772-785. https://doi.org/10.1680/jgeot.16.P.244.
  20. Gupta, B.K. and Basu, D. (2018), "Dynamic analysis of axially loaded end-bearing pile in a homogeneous viscoelastic soil", Soil Dyn. Earth. Eng., 111, 31-40. https://doi.org/10.1016/j.soildyn.2018.04.019.
  21. Hirai, H. (2014), "Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach", Int. J. Numer. Anal. Meth. Geomech., 38(12), 1298-1320. https://doi.org/10.1002/nag.227.
  22. Kim, Y.S. and Choi, J.I. (2017), "Nonlinear numerical analyses of a pile-soil system under sinusoidal bedrock loadings verifying centrifuge model test results", Geomech. Eng., 12(2), 239-255. https://doi.org/10.12989/gae.2017.12.2.239.
  23. Kramer, S.L. (1996), Geotechnical Earthquake Engineering, Prentice-Hall, Upper Saddle River, New Jersey, U.S.A.
  24. Kuhlemeyer, R.L. (1979), "Static and dynamic laterally loaded floating piles", J. Geotech. Eng., 105, 289-304.
  25. Lee, K. and Xiao, Z. (1999), "A new analytical model for settlement analysis of a single pile in multi-layered soil", Soils Found., 39(5), 131-143. https://doi.org/10.3208/sandf.39.5_131.
  26. Lei, G., Hong, X. and Shi, J. (2005), "Stata-of-the-art review on barrette", China Civ. Eng. J., 38(4), 103-110 (in Chinese). https://doi.org/10.3321/j.issn:1000-131X.2005.04.017.
  27. Lei, G.H., Hong, X. and Shi, J.Y. (2007a), "Approximate threedimensional analysis of rectangular barrette-soil-cap interaction", Can. Geotech. J., 44(7),781-796. https://doi.org/10.1139/t07-017.
  28. Lei, G.H. and Ng, C.W. (2007b), "Rectangular barrettes and circular bored piles in saprolites", Proc. Inst. Civ. Eng. Geotech. Eng., 160(4), 237-242. https://doi.org/10.1680/geng.2007.160.4.237.
  29. Liu, W. and Novak, M. (1994), "Dynamic response of single piles embedded in transversely isotropic layered media", Earthq. Eng. Struct. Dyn., 23(11), 1239-1257. https://doi.org/10.1002/eqe.4290231106.
  30. Maeso, O., Aznarez, J.J. and Garcia, F. (2005), "Dynamic impedances of piles and groups of piles in saturated soils", Comput. Struct., 83(10-11), 769-782. https://doi.org/10.1016/j.compstruc.2004.10.015.
  31. Mamoon, S.M., Kaynia, A.M. and Banerjee, P.K. (1990), "Frequency domain dynamic analysis of piles and pile groups", J. Eng. Mech., 116(10), 2237-2257. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:10(2237).
  32. Michaelides, O., Gazetas, G., Bouckovalas, G. and Chrysikou, E. (1998), "Approximate non-linear dynamic axial response of piles", Geotechnique, 48(1), 33-53. https://doi.org/10.1680/geot.1998.48.1.33.
  33. Millan, M.A. and Dominguez, J. (2009), "Simplified BEM/FEM model for dynamic analysis of structures on piles and pile groups in viscoelastic and poroelastic soils", Eng. Anal. Bound Elem., 33(1), 25-34. https://doi.org/10.1016/j.enganabound.2008.04.003.
  34. Mylonakis, G. (2001), "Elastodynamic model for large-diameter end-bearing shafts", Soils Found., 41(3), 31-44. https://doi.org/10.3208/sandf.41.3_31.
  35. Mylonakis, G. and Gazetas, G. (1998), "Settlement and additional internal forces of grouped piles in layered soil", Geotechnique, 48(1), 55-72. https://doi.org/10.1680/geot.1998.48.1.55.
  36. Ng, C.W. and Lei, G.H. (2003), "Performance of long rectangular barrettes in granitic saprolites", J. Geotech. Geoenviron. Eng., 129(8), 685-696. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:8(685).
  37. Ng, C.W., Rigby, D.B., Ng, S.W. and Lei, G.H. (2000), "Field studies of well-instrumented barrette in Hong Kong", J. Geotech. Geoenviron. Eng., 126(1), 60-73. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:1(60).
  38. Nogami, T. and Konagai, K. (1987), "Dynamic response of vertically loaded nonlinear pile foundations", J. Geotech. Eng., 113(2), 147-160. https://doi.org/10.1061/(ASCE)0733-9410(1987)113:2(147).
  39. Padron, L.A., Aznarez, J.J. and Maeso, O. (2007), "BEM-FEM coupling model for the dynamic analysis of piles and pile groups", Eng. Anal. Bound Elem., 31(6), 473-484. https://doi.org/10.1016/j.enganabound.2006.11.001.
  40. Poulos, H.G. (1989), "Pile behaviour-theory and application", Geotechnique, 39(3), 365-415. https://doi.org/10.1680/geot.1989.39.3.365.
  41. Randolph, M.F. (1981), "The response of flexible piles to lateral loading", Geotechnique, 31(2), 247-259. https://doi.org/10.1680/geot.1981.31.2.247.
  42. Seo, H., Basu, D., Prezzi, M. and Salgado, R. (2009), "Loadsettlement response of rectangular and circular piles in multilayered soil", J. Geotech. Geoenviron. Eng., 135(3), 420-430. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:3(420).
  43. Sun, K. (1994a), "Laterally loaded piles in elastic media", J. Geotech. Eng., 120(8), 1324-1344. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:8(1324).
  44. Sun, K. (1994b), "A numerical method for laterally loaded piles", Comput. Geotech., 16(4), 263-289. https://doi.org/10.1016/0266-352X(94)90011-6.
  45. Tehrani, F.S., Salgado, R. and Prezzi, M. (2016), "Analysis of axial loading of pile groups in multilayered elastic soil", Int. J. Geomech., 16(2), 04015063. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000540.
  46. Ukritchon, B. and Keawsawasvong, S. (2018), "Undrained lateral capacity of rectangular piles under a general loading direction and full flow mechanism", KSCE J. Civ. Eng., 22(7), 2256-2265. https://doi.org/10.1007/s12205-017-0062-7.
  47. Vallabhan, C.G. and Das, Y.C. (1988), "Parametric study of beams on elastic foundations", J. Eng. Mech., 114(12), 2072-2082. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:12(2072)
  48. Vallabhan, C.G. and Das, Y.C. (1991a), "Modified Vlasov model for beams on elastic foundations", J. Geotech. Eng., 117(6), 956-966. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:6(956).
  49. Vallabhan, C.G. and Das, Y.C. (1991b), "Analysis of circular tank foundations", J. Eng. Mech., 117(4), 789-797. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:4(789).
  50. Vallabhan, C.G. and Mustafa, G. (1996), "A new model for the analysis of settlement of drilled piers", Int. J. Numer. Anal. Meth. Geomech., 20(2), 143-152. https://doi.org/10.1002/(SICI)10969853(199602)20:2<143::AID-NAG812>3.0.CO;2-U.
  51. Veletsos, A.S. and Dotson, K.W. (1986), "Impedances of soil layer with disturbed boundary zone", J. Geotech. Eng., 112(3), 363-368. https://doi.org/10.1061/(ASCE)0733-9410(1986)112:3(363).
  52. Wang, K., Wu, W., Zhang, Z. and Leo, C. J. (2010), "Vertical dynamic response of an inhomogeneous viscoelastic pile", Comput. Geotech., 37(4), 536-544. https://doi.org/10.1016/j.compgeo.2010.03.001.
  53. Wu, W.B., Liu, H., El Naggar, M.H., Mei, G.X. and Jiang, G.S. (2016), "Torsional dynamic response of a pile embedded in layered soil based on the fctitious soil pile model", Comput. Geotech., 80, 190-198. https://doi.org/10.1016/j.compgeo.2016.06.013.
  54. Wu, W.B., Liu, H., Yang, X.Y., Jiang, G.S., El Naggar, M.H., Mei, G.X. and Liang, R.Z. (2020), "New method to calculate apparent phase velocity of open-ended pipe pile", Can. Geotech. J., 57(1), 127-138. https://doi.org/10.1139/cgj-2018-0816.
  55. Wu, W.B., Wang, K.H., Zhang, Z.Q. and Leo, C.J. (2013), "Soilpile interaction in the pile vertical vibration considering true three-dimensional wave effect of soil", Int. J. Numer. Anal. Meth. Geomech., 37(17), 2860-2876. https://doi.org/10.1002/nag.2164.
  56. Yang, D.Y. and Wang, K.H. (2010), "Vertical vibration of pile based on fctitious soil-pile model in inhomogeneous soil", J. Zhejiang Univ., 44(10), 2021-2028 (in Chinese). https://doi.org/10.3785/j.issn.1008-973X.2010.10.030.
  57. Zhang, L.M. (2003), "Behavior of laterally loaded large-section barrettes", J. Geotech. Geoenviron. Eng., 129(7), 639-648. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:7(639).
  58. Zheng, C., Ding, X., Li, P. and Fu, Q. (2015), "Vertical impedance of an end-bearing pile in viscoelastic soil", Int. J. Numer. Anal. Meth. Geomech., 39(6), 676-684. https://doi.org/10.1002/nag.2324.
  59. Zheng, C., Liu, H., Ding, X. and Kouretzis, G. (2017a), "Resistance of inner soil to the vertical vibration of pipe piles", Soil Dyn. Earthq. Eng., 94, 83-87. https://doi.org/10.1016/j.soildyn.2017.01.002.
  60. Zheng, C., Gan, S., Ding, X. and Luan, L. (2017b), "Dynamic response of a pile embedded in elastic half space subjected to harmonic vertical loading", Acta Mech. Solida Sin., 30(6), 668-673. https://doi.org/10.1016/j.camss.2017.09.006.