Vertical vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock

Abstract

An axisymmetrical analytical solution is developed to investigate the vertical time-harmonic vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock. The soil is described by porous medium model established by Boer, while the pile is described by a beam vibration theory. By using separation theory of differential operator and variables to solve the dynamic governing equations for the soil, the fundamental solutions for the soil reactions on side and bottom of the pile are obtained. The dynamic impedance of the pile head is then derived by solving the vibration equation for the pile according to the compatibility condition between the pile and the soil. The proposed model is validated by comparing special cases of our model with the existing results. Numerical examples are presented to analyze the vibration characteristics of the pile.

Keywords

floating pile / vertical vibration / saturated viscoelastic soil / Boer’s porous medium model / separation theory

References

[1] YuJ, ChenH-m, YangZ, LiuCheng. Dynamic analysis of vertical loaded single pile in multilayered saturated soils [J]. Computational Structural Engineering, 2009, 1: 761-769

[2] WangK-h, ZhangZ-q, LeoC-j, XieK-he. Dynamic torsional response of an end bearing pile in saturated poroelastic medium [J]. Computers and Geotechnics, 2008, 35: 450-458

[3] WangK-h, ZhangZ-q, LeoC-j, XieK-he. Dynamic torsional response of an end bearing pile in transversely isotropic saturated soil [J]. Journal of Sound and Vibration, 2009, 327: 440-453

[4] HuW-t, XiaT-d, ZhangZ-qing. Dynamic torsional response of pre-strained end bearing pile embedded in pre-strained isotropic saturated soil medium [J]. Applied Mathematics and Mechanics, 2013, 34(12): 1521-1534

[5] LiuH-l, ZhengC-j, DingX-m, QinH-yu. Vertical dynamic response of a pipe pile in saturated soil layer [J]. Computers and Geotechnics, 2014, 61: 57-66

[6] ZengX, RajapakseR K N D. Vertical vibrations of a rigid disk embedded in a poroelastic medium [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1999, 23: 2075-2095

[7] JinB, ZhouD, ZhongZ. Lateral dynamic compliance of pile embedded in poroelastic half space [J]. Soil Dynamics and Earthquake Engineering, 2001, 21: 519-525

[8] LuJ-f, JengD-s, NieW-dong. Dynamic response of a pile embedded in a porous medium subjected to plane SH waves [J]. Computers and Geotechnics, 2006, 33: 404-418

[9] LuJ-f, XuB, WangJ-h, JengD-sheng. Dynamic responses of a pile embedded in a layered poroelastic half-space to a harmonic axial loading [J]. Acta Mech, 2009, 207: 29-49

[10] CaiY-q, ChenG, XuC-j, WuD-zhi. Torsional response of pile embedded in a poroelastic medium [J]. Soil Dynamics and Earthquake Engineering, 2006, 26: 1143-1148

[11] WangG-c, GeW, PanX-d, WangZhi. Torsional vibrations of single piles embedded in saturated medium [J]. Computers and Geotechnics, 2008, 35: 11-21

[12] ZhouX-l, WangJ-h, JiangL-f, XuBo. Transient dynamic response of pile to vertical load in saturated soil [J]. Mechanics Research Communications, 2009, 36: 618-624

[13] XuB, LuJ-f, WangJ-hua. Numerical analysis of the isolasion of the vibration due to Rayleigh waves by using pile rows in the poroelastic medium [J]. Arch Appl Mech, 2010, 80: 123-142

[14] CaiY-q, ChenG, LiuF-yu. Torsional pile subjected to transient loading in viscoelastic poroelastic medium [C]//. International Conference on Computational Science, 20071188-1196

[15] ChenG, CaiY-q, LiuF-y, SunHong. Dynamic response of a pile in a transversely isotropic saturated soil to transient torsional loading [J]. Computers and Geotechnics, 2008, 35: 165-172

[16] LiQ, ZhengH, WangK-hua. Analytical solution and its application of vertical vibration of a friction pile in saturated soil [J]. Engineering Mechanics, 2011, 28(1): 157-170

[17] EdelmanI, WilmanskiK. Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces [J]. Continuum Mech Thermodyn, 2002, 14: 25-44

[18] BoerD R. Some issues in the macroscopic porous media theory [M]. Siekmann-Festschrift: University-GH Essen, 1995310-323

[19] BoerD R, LiuZ F. Propagation of acceleration waves in incompressible saturated porous solids [J]. Transport in Porous Media, 1995, 21: 163-173

[20] BoerD R, LiuZ F. Plane waves in a semi-infinite fluid saturated porous medium [J]. Transport in Porous Media, 1994, 16: 147-173

[21] BoerD R, LiuZ F. Growth and decay of acceleration waves in incompressible saturated porous elastic solids [J]. J Appl Math Mech, 1996, 76(6): 341-347

[22] LiuZ-f, LiD-y, YanBo. Inhomogeneous plane waves in a saturated porous medium [J]. Rock and Soil Mechanics, 1999, 20(4): 31-35

[23] YangX, CheJ-lan. Plane waves and their energy dissipations in a saturated viscoelastic porous medium [J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(5): 579-585

[24] SenjuntichaiT, RajapakseRKND. Transient response of a circular cavity in a poroelastic medium [J]. Int J Numer Anal Meth Geomech, 1993, 17: 357-383

[25] LiuL-c, YangXiao. Study of vertical coupled vibrations of piles in saturated soils using porous medium theory [J]. China Civil Engineering Journal, 2009, 42(9): 89-95

[26] WuW-bingVertical vibration theory of pile-soil system based on fictitious soil pile method and its application [D], 2012HangzhouZhejiang University