Beam–Unequal Length Piles–Soil Coupled Vibrating System Considering Pile–Soil–Pile Interaction
Publication: Journal of Bridge Engineering
Volume 26, Issue 12
Abstract
In recent years, the π-shape structure, that is, two pile shafts supporting a reinforced concrete beam and its superstructure, is increasingly used for bridge foundations. Considering the construction quality and the requirement of settlement tolerance, the pile lengths of the π-shape structure are sometimes different when passive or active. However, the effect of the unequal pile lengths on the dynamic characteristics of the π-shape structure has not been investigated. Therefore, this paper analyzes the dynamic response of the π-shape structure with unequal pile lengths. A beam–unequal length piles–soil coupled vibrating system is established in the frequency domain considering both pile–beam–pile propagation and pile–soil–pile interaction. In order to account for the pile–soil–pile interaction, a fictitious soil pile model is employed to compensate for the length difference between the piles. The developed model and the analytical results are verified through comparison with the results of rigorous finite-element analysis and a model test. The verified model and its corresponding solutions are then utilized to conduct a comprehensive parametric study. Some conclusions derived from this study can extend the application of the π-shape structure in engineering practice.
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Acknowledgments
This research was supported by the National Natural Science Foundation of China (Grant Nos. 51378464, 51579217 and 51779217). The first author was supported by the China Postdoctoral Science Foundation (Grant No. 2020M681857).
References
ASTM. 2017. Standard test method for young’s modulus, tangent modulus, and chord modulus. ASTM E111-17. West Conshohocken, PA: ASTM.
Cai, Y., Z. Liu, T. Li, J. Yu, and N. Wang. 2020. “Vertical dynamic response of a pile embedded in radially inhomogeneous soil based on fictitious soil pile model.” Soil Dyn. Earthquake Eng. 132: 106038. https://doi.org/10.1016/j.soildyn.2020.106038.
Chernauskas, L. R., and S. G. Paikowsky. 2000. “Defect detection and examination of large drilled shafts using a new cross-hole sonic logging system.” In Performance Confirmation of Constructed Geotechnical Facilities, Geotechnical Special Publication 94, edited by A. J. Lutenegger, and D. J. DeGroot, 66–83. Reston, VA: ASCE.
Chow, H. S. W., and J. C. Small. 2005. “Behaviour of piled rafts with piles of different lengths and diameters under vertical loading.” In Advances in Deep Foundations, Geotechnical Special Publication 132, edited by C. Vipulanandan, and F. C. Townsend, 1–15. Reston, VA: ASCE.
Chow, Y. K., K. K. Phoon, W. F. Chow, and K. Y. Wong. 2003. “Low strain integrity testing of piles: Three-dimensional effects.” J. Geotech. Geoenviron. Eng. 129 (11): 1057–1062. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:11(1057).
Ding, X., H. Liu, J. Liu, and Y. Chen. 2011. “Wave propagation in a pipe pile for low-strain integrity testing.” J. Eng. Mech. 137 (9): 598–609. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000263.
Dobry, R., and G. Gazetas. 1988. “Simple method for dynamic stiffness and damping of floating pile groups.” Géotechnique 38 (4): 557–574. https://doi.org/10.1680/geot.1988.38.4.557.
El Naggar, M. H. 2000. “Vertical and torsional soil reactions for radially inhomogeneous soil layer.” Struct. Eng. Mech. 10 (4): 299–312. https://doi.org/10.12989/sem.2000.10.4.299.
El Naggar, M. H., and M. Novak. 1996. “Nonlinear analysis for dynamic lateral pile response.” Soil Dyn. Earthquake Eng. 15 (4): 233–244. https://doi.org/10.1016/0267-7261(95)00049-6.
Gao, L., K. Wang, J. Wu, S. Xiao, and N. Wang. 2017. “Analytical solution for the dynamic response of a pile with a variable-section interface in low-strain integrity testing.” J. Sound Vib. 395: 328–340. https://doi.org/10.1016/j.jsv.2017.02.037.
Gazetas, G., and N. Makris. 1991. “Dynamic pile–soil–pile interaction. Part I: Analysis of axial vibration.” Earthquake Eng. Struct. Dyn. 20 (2): 115–132. https://doi.org/10.1002/eqe.4290200203.
Leung, Y. F., A. Klar, and K. Soga. 2010. “Theoretical study on pile length optimization of pile groups and piled rafts.” J. Geotech. Geoenviron. Eng. 136 (2): 319–330. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000206.
Li, D. Q., L. M. Zhang, and W. H. Tang. 2005. “Reliability evaluation of cross-hole sonic logging for bored pile integrity.” J. Geotech. Geoenviron. Eng. 131 (9): 1130–1138. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:9(1130).
Liang, F. Y., L. Z. Chen, and X. G. Shi. 2003. “Numerical analysis of composite piled raft with cushion subjected to vertical load.” Comput. Geotech. 30 (6): 443–453. https://doi.org/10.1016/S0266-352X(03)00057-0.
Liu, X., M. H. El Naggar, K. Wang, and W. Wu. 2020. “Theoretical analysis of three-dimensional effect in pile integrity test.” Comput. Geotech. 127: 103765. https://doi.org/10.1016/j.compgeo.2020.103765.
Lo, K. F., S. H. Ni, Y. H. Huang, and X. M. Zhou. 2009. “Measurement of unknown bridge foundation depth by parallel seismic method.” Exp. Tech. 33 (1): 23–27. https://doi.org/10.1111/j.1747-1567.2008.00342.x.
Lü, S. H., K. H. Wang, W. B. Wu, and C. J. Leo. 2015. “Longitudinal vibration of pile in layered soil based on Rayleigh-Love rod theory and fictitious soil-pile model.” J. Central South Univ. 22 (5): 1909–1918. https://doi.org/10.1007/s11771-015-2710-8.
Makris, N. 1994. “Soil-pile interaction during the passage of Rayleigh waves: An analytical solution.” Earthquake Eng. Struct. Dyn. 23 (2): 153–167. https://doi.org/10.1002/eqe.4290230204.
Makris, N., and G. Gazetas. 1992. “Dynamic pile–soil–pile interaction. Part II: Lateral and seismic response.” Earthquake Eng. Struct. Dyn. 21 (2): 145–162. https://doi.org/10.1002/eqe.4290210204.
Nogami, T., and M. Novak. 1976. “Soil-pile interaction in vertical vibration.” Earthquake Eng. Struct. Dyn. 4 (3): 277–293. https://doi.org/10.1002/eqe.4290040308.
Novak, M. 1977. “Vertical vibration of floating piles.” J. Eng. Mech. Div. 103 (1): 153–168. https://doi.org/10.1061/JMCEA3.0002201.
Novak, M., F. Aboul-Ella, and T. Nogami. 1978. “Dynamic soil reactions for plane strain case.” J. Eng. Mech. Div. 104 (4): 953–959. https://doi.org/10.1061/JMCEA3.0002392.
Randolph, M. F. 1992. “Dynamic and static soil models for axial pile response.” In Proc., 4th Int. Conf. on Application of Stress-Wave Theory to Piles, 3–14. Boca Raton, FL: CRC Press.
Sack, D. A., S. H. Slaughter, and L. D. Olson. 2004. “Combined measurement of unknown foundation depths and soil properties with nondestructive evaluation methods.” Transp. Res. Rec. 1868 (1): 76–80. https://doi.org/10.3141/1868-08.
Wang, K., W. Wu, Z. Zhang, and C. J. Leo. 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.
White, B., M. Nagy, and R. Allin. 2008. “Comparing cross-hole sonic logging and low-strain integrity testing results.” In Proc., 8th Int. Conf. on the Application of Stress Wave Theory to Piles, 471–476. Amsterdam, Netherlands: IOS Press.
Wolf, J. P., and G. A. von Arx. 1982. “Horizontally travelling waves in a group of piles taking pile–soil–pile interaction into account.” Earthquake Eng. Struct. Dyn. 10 (2): 225–237. https://doi.org/10.1002/eqe.4290100205.
Wu, J., M. H. El Naggar, K. Wang, and X. Liu. 2020a. “Analytical study of employing low-strain lateral pile integrity test on a defective extended pile shaft.” J. Eng. Mech. 146 (9): 04020103. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001841.
Wu, J., M. H. El Naggar, K. Wang, and W. Wu. 2019a. “Lateral vibration characteristics of an extended pile shaft under low-strain integrity test.” Soil Dyn. Earthquake Eng. 126: 105812. https://doi.org/10.1016/j.soildyn.2019.105812.
Wu, J., K. Wang, and M. H. El Naggar. 2019b. “Dynamic soil reactions around pile-fictitious soil pile coupled model and its application in parallel seismic method.” Comput. Geotech. 110: 44–56. https://doi.org/10.1016/j.compgeo.2019.02.011.
Wu, J., K. Wang, and M. H. El Naggar. 2019c. “Dynamic response of a defect pile in layered soil subjected to longitudinal vibration in parallel seismic integrity testing.” Soil Dyn. Earthquake Eng. 121: 168–178. https://doi.org/10.1016/j.soildyn.2019.03.010.
Wu, J., K. Wang, and M. H. El Naggar. 2019d. “Half-space dynamic soil model excited by known longitudinal vibration of a defective pile.” Comput. Geotech. 112: 403–412. https://doi.org/10.1016/j.compgeo.2019.05.006.
Wu, J. T., K. H. Wang, L. Gao, and S. Xiao. 2019e. “Study on longitudinal vibration of a pile with variable sectional acoustic impedance by integral transformation.” Acta Geotech. 14 (6): 1857–1870. https://doi.org/10.1007/s11440-018-0732-8.
Wu, J. T., K. H. Wang, and X. Liu. 2020b. “Effect of a nodular segment on the dynamic response of a tubular pile subjected to longitudinal vibration.” Acta Geotech. 15 (10): 2925–2940. https://doi.org/10.1007/s11440-020-00930-y.
Wu, W., M. H. El Naggar, M. Abdlrahem, G. Mei, and K. Wang. 2017. “New interaction model for vertical dynamic response of pipe piles considering soil plug effect.” Can. Geotech. J. 54 (7): 987–1001. https://doi.org/10.1139/cgj-2016-0309.
Wu, W., G. Jiang, S. Huang, and C. J. Leo. 2014. “Vertical dynamic response of pile embedded in layered transversely isotropic soil.” Math. Probl. Eng. 2014: 126916. https://doi.org/10.1155/2014/126916.
Wu, W., H. Liu, M. H. El Naggar, G. Mei, and G. Jiang. 2016. “Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model.” Comput. Geotech. 80: 190–198. https://doi.org/10.1016/j.compgeo.2016.06.013.
Yang, D. Y., and K. H. Wang. 2010. “Vertical vibration of pile based on fictitious soil-pile model in inhomogeneous soil.” J. Zhejiang Univ. 44 (10): 2021–2028.
Zheng, C., G. P. Kouretzis, X. Ding, H. Liu, and H. G. Poulos. 2015. “Three-dimensional effects in low-strain integrity testing of piles: Analytical solution.” Can. Geotech. J. 53 (2): 225–235. https://doi.org/10.1139/cgj-2015-0231.
Zheng, C., H. Liu, X. Ding, G. P. Kouretzis, and D. Sheng. 2016. “Three-dimensional effects in low-strain integrity testing of large diameter pipe piles.” J. Eng. Mech. 142 (9): 04016064. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001117.
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Published In
Journal of Bridge Engineering
Volume 26 • Issue 12 • December 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Nov 22, 2020
Accepted: Aug 4, 2021
Published online: Sep 30, 2021
Published in print: Dec 1, 2021
Discussion open until: Mar 1, 2022
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