Abstract
The soil in nature will form anisotropic soil due to the arrangement of soil particles and constitutive elements, resulting in differences in the properties of the soil in the vertical direction and the horizontal direction. The vertical modulus of the soil is often smaller than the horizontal modulus, but the horizontal modulus presents isotropic characteristics. Therefore, it is more suitable to treat this kind of soil as transversely isotropic soil. Considering the influence of soil anisotropy and three-dimensional wave effect, the soil around the pile is regarded as transversely isotropic soil. The horizontal vibration of transversely isotropic soil layer is solved by using the separated variable method, and the analytical solution expression of soil damping factor is obtained. Considering the effect of transversely isotropic soil around the pile on pile foundation, the horizontal dynamic impedance at pile top in transversely isotropic soil is obtained by using the boundary conditions of the problem and the orthogonality of trigonometric function. The results show that the horizontal impedance factor of transversely isotropic soil layer and the horizontal dynamic impedance of pile foundation in transversely isotropic soil can degenerate to homogeneous soil. For transversely isotropic soil, there is a resonance point in the curve of soil impedance factor and dynamic impedance at pile top varying with frequency at low frequency, which is much sharper than that of homogeneous soil. The dimensionless frequencies interval between the resonance points of the horizontal stiffness factor is about 3, and the dimensionless frequencies interval between the resonance points of the damping factor is about 4.The anisotropy of soil has a great influence on the horizontal vibration of pile foundation, which should not be ignored. With the increase of pile length, the influence of pile length on the horizontal vibration of pile foundation in transversely isotropic soil will decrease. When the pile length is more than 100 times of the pile diameter, the influence of pile length on the horizontal dynamic impedance is very small.
Similar content being viewed by others
Data Availability
The data used to support the findings of this study are included within the article.
References
Chen G, Cai YQ, Liu FY, Sun HL (2008) Dynamic response of a pile in a transversely isotropic saturated soil to transient torsional loading. Comput Geotech 35(2):165–172
Cui CY, Meng K, Xu CS, Liang ZM, Li HJ, Pei H (2021) Analytical solution for longitudinal vibration of a floating pile in saturated porous media based on a fictitious saturated soil pile model. Comput Geotech 131:103942
Ding XM, Hanlong Liu HL, Chu J, Cheng K (2015) Time-domain solution for transient dynamic response of a large-diameter thin-walled pipe pile. Earthq Eng Eng Vib 14(2):239–251
Ding HJ, Chen WQ, Zhang L (2006) Elasticity of transversely isotropic materials. Springer Science & Business Media.
Li Y, Ai ZY (2020) Transient analysis of a fixed-head pile group in multi-layered transversely isotropic media due to horizontal loadings. Comput Geotech 127:103772
Ma WJ, Shan Y, Wang BL, Zhou SH (2021) Torsional vibration of a pile in transversely isotropic saturated soil considering its construction disturbance effect. Int J Struct Stab Dy 2021:2250044
Maeso O, Aznarez JJ, Garcı́a F (2005) Dynamic impedances of piles and groups of piles in saturated soils. Comput Struct 83:769–782
Mylonakis G, Gazetas G (1999) Lateral vibration and internal forces of grouped piles in layered soils. J Geotech Geoenviron 125(1):16–25
Nogami T, Novak M (1976) Soil-pile interaction in vertical vibration. Earthq Eng Struct D 4(3):277–293
Novak M (1974) Dynamic stiffness and damping of piles. Can Geotech J 11(4):574–598
Novak M, Nogami T (1977) Soil-pile interaction in horizontal vibration. Earthq Eng Struct D 5(3):263–281
Shahmohamadi M, Khojasteh A, Rahimian M, Pak RYS (2013) Dynamics of a cylindrical pile in a transversely isotropic half-space under axial excitations. J Eng Mech-Asce 139(5):568–579
Wu WB, Liu H, El Naggar MH, Mei GX, Jiang GS (2016) Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model. Comput Geotech 80:190–198
Ye Z, Ai ZY (2022) Vertical dynamic response of a pile embedded in layered transversely isotropic unsaturated soils. J Geotech Geoenviron 148(1):04021169
Zhang SP, Cui CY, Yang G (2019) Vertical dynamic impedance of pile groups partially embedded in multilayered, transversely isotropic, saturated soils. Soil Dyn Earthq Eng 117:106–115
Zheng CJ, Gan SS, Kouretzis G, Ding XM, Luan LB (2020) Vertical vibration of a large diameter pile partially-embedded in poroelastic soil. Soil Dyn Earthq Eng 139:106211
Zheng CJ, Hua JM, Ding XM (2016) Torsional vibration of a pipe pile in transversely isotropic saturated soil. Earthq Eng Eng Vib 15(3):509–517
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant No. U1504505) and the Key Scientific Research Projects of Colleges and Universities in Henan Province (Grant No. 23B560001).
Funding
The research received funding from the National Natural Science Foundation of China (Grant No. U1504505) and the Key Scientific Research Projects of Colleges and Universities in Henan Province (Grant No. 23B560001).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflicts of interest
The authors declare that they have no conflicts of interest to report regarding the present study.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Yan, Q., Liu, L. Horizontal Vibration of Pile Foundation in Transversely Isotropic Soil Considering Three-Dimensional Wave Effect. Geotech Geol Eng 41, 819–829 (2023). https://doi.org/10.1007/s10706-022-02307-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10706-022-02307-2