Analytical Solutions to Interaction Factors of Two Unequal Length Piles under Horizontal Loads
Publication: International Journal of Geomechanics
Volume 19, Issue 4
Abstract
The technical note presents analytical solutions to interaction factors of two unequal length piles (ULPs) under horizontal loads by using the fictitious pile method. The bending moments along the fictitious piles and the horizontal displacements of the pile heads/bottoms were obtained based on a simplified Fredholm integral equation of the second kind. The proposed analytical solutions were validated against the three-dimensional finite-element simulations considering different pile slenderness ratios. Parametrical studies were then conducted to show the influence of some key parameters on the pile-to-pile interaction factors for ULPs.
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Acknowledgments
Financial support for this study from the Innovation Project of Shanghai Education Committee (15ZZ103) and the Key Science Research of Shanghai Open University (KX1806) is gratefully acknowledged.
References
Abdrabbo, F. M., and A. Z. El-wakil. 2015. “Behavior of pile group incorporating dissimilar pile embedded into sand.” Alexandria Eng. J. 54 (2): 175–182. https://doi.org/10.1016/j.aej.2014.11.001.
Algin, H. M. 2016. “Optimised design of jet-grouted raft using response surface method.” Comput. Geotech. 74 (Apr): 56–73. https://doi.org/10.1016/j.compgeo.2015.12.012.
Algin, H. M. 2017. “Optimised design of jet-grouted rafts subjected to nonuniform vertical loading.” KSCE J. Civ. Eng. 22 (2): 494–508. https://doi.org/10.1007/s12205-017-0841-1.
Anderson, J. B., F. C. Townsend, and B. Grajales. 2003. “Case history evaluation of laterally loaded piles.” J. Geotech. Geoenviron. Eng. 129 (3): 187–196. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:3(187).
Banerjee, P. K., and T. G. Davis. 1978. “The behaviour of axially and laterally loaded single piles embedded in nonhomogeneous soils.” Géotechnique 28 (3): 309–326. https://doi.org/10.1680/geot.1978.28.3.309.
Basile, F. 1999. “Non-linear analysis of pile groups.” Proc. Inst. Civ. Eng. Geotech. Eng. 137 (2): 105–115. https://doi.org/10.1680/gt.1999.370205.
Basu, D., R. Salgado, and M. Prezzi. 2009. “A continuum-based model for analysis of laterally loaded piles in layered soils.” Géotechnique 59 (2): 127–140. https://doi.org/10.1680/geot.2007.00011.
Chen, S. L., and L. Z. Chen. 2008. “Note on the interaction factor for two laterally loaded piles.” J. Geotech. Geoenviron. Eng. 134 (11): 1685–1690. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:11(1685).
Chow, Y. K. 1986. “Analysis of vertically loaded pile groups.” Int. J. Numer. Anal. Methods Geomech. 10 (1): 59–72. https://doi.org/10.1002/nag.1610100105.
Davisson, M. T., and H. L. Gill. 1963. “Laterally loaded piles in a layered soil system.” J. Soil Mech. Found. Div. 89 (3): 63–94.
El Sharnouby, B., and M. Novak. 1990. “Stiffness constants and interaction factors for vertical response of pile groups.” Can. Geotech. J. 27 (6): 813–822. https://doi.org/10.1139/t90-094.
Guo, W. D., and F. H. Lee. 2001. “Load transfer approach for laterally loaded piles.” Int. J. Numer. Anal. Methods Geomech. 25 (11): 1101–1129. https://doi.org/10.1002/nag.169.
Hetenyi, M. 1946. Beams on elastic foundations: Theory with applications in the fields of civil and mechanical engineering. Ann Arbor, MI: University of Michigan Press.
Kim, B. T., N. K. Kim, W. J. Lee, and Y. S. Kim. 2004. “Experimental load-transfer curves of laterally loaded piles in Nak-Dong River sand.” J. Geotech. Geoenviron. Eng. 130 (4): 416–425. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:4(416).
Kim, K. N., S. H. Lee, K. S. Kim, C. K. Chung, M. M. Kim, and H. S. Lee. 2001. “Optimal pile arrangement for minimizing differential settlements in piled raft foundations.” Comput. Geotech. 28 (4): 235–253. https://doi.org/10.1016/S0266-352X(01)00002-7.
Kumar, A., D. Choudhury, and R. Katzenbach. 2016. “Effect of earthquake on combined pile–raft foundation.” Int. J. Geomech. 16 (5): 04016013. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000637.
Leung, C. F., and Y. K. Chow. 1987. “Response of pile groups subjected to lateral loads.” Int. J. Numer. Anal. Methods Geomech. 11 (3): 307–314. https://doi.org/10.1002/nag.1610110307.
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.
Liang, F. Y., L. Z. Chen, and J. Han. 2009. “Integral equation method for analysis of piled rafts with dissimilar piles under vertical loading.” Comput. Geotech. 36 (3): 419–426. https://doi.org/10.1016/j.compgeo.2008.08.007.
Liang, F. Y., and Z. Song. 2014. “BEM analysis of the interaction factor for vertically loaded dissimilar piles in saturated poroelastic soil.” Comput. Geotech. 62 (Oct): 223–231. https://doi.org/10.1016/j.compgeo.2014.07.016.
Matlock, H. 1970. “Correlations for design of laterally loaded piles in soft clay.” In Proc., 2nd Offshore Technology Conf., 577–594. Houston, TX: Offshore Technology Conf.
Mindlin, R. D. 1936. “Force at a point in the interior of a semi-infinite solid.” Physics 7 (5): 195–202. https://doi.org/10.1063/1.1745385.
Muki, R. 1960. “Asymmetric problems of the theory of elasticity for a semi-infinite solid and a thick plate.” In Vol. 1 of Progress in Solid Mechanics, edited by I. N. Sneddon and R. Hill, 339–349. Amsterdam: North-Holland Publishing.
Muki, R., and E. Sternberg. 1968. “On the diffusion of load from a transverse tension bar into a semi-infinite elastic sheet.” J. Appl. Mech. 35 (4): 737–746. https://doi.org/10.1115/1.3601299.
Muki, R., and E. Sternberg. 1970. “Elastostatic load-transfer to a half-space from a partially embedded axially loaded rod.” Int. J. Solids Struct. 6 (1): 69–90. https://doi.org/10.1016/0020-7683(70)90082-X.
Mylonakis, G., and G. Gazetas. 1998. “Settlement and additional internal force of group piles in layered soil.” Géotechnique 48 (1): 55–72. https://doi.org/10.1680/geot.1998.48.1.55.
Pak, R. Y. S. 1989. “On the flexure of a partially embedded bar under lateral loads.” J. Appl. Mech. 56 (2): 263–269. https://doi.org/10.1115/1.3176077.
Poulos, H. G. 1968. “Analysis of the settlement of pile groups.” Géotechnique 18 (4): 449–471. https://doi.org/10.1680/geot.1968.18.4.449.
Poulos, H. G. 1971a. “Behavior of laterally loaded piles: I—Single piles.” J. Soil Mech. Found. Div. 97 (5): 711–731.
Poulos, H. G. 1971b. “Behavior of laterally loaded piles: II—Pile groups.” J. Soil Mech. Found. Div. 97 (5): 733–751.
Poulos, H. G., and E. H. Davis. 1974. Elastic solutions for soil and rock mechanics. New York: Wiley.
Poulos, H. G., and E. H. Davis. 1980. Pile foundation analysis and design. New York: Wiley.
Randolph, M. F. 1981. “The response of flexible piles to lateral loading.” Géotechnique 31 (2): 247–259. https://doi.org/10.1680/geot.1981.31.2.247.
Reese, L. C., and W. R. Cox. 1969. “Soil behavior from analysis of tests of uninstrumented piles under lateral loading.” In Performance of Deep Foundations, edited by R. Lundgren and E. D’Appolonia, 160–176. Philadelphia: American Society for Testing and Materials.
Reese, L. C., Cox, W. R., and Koop, F. D. 1974. “Analysis of laterally loaded pile in sand.” In: Proc, 6th Annual Offshore Technology Conf., 2080. Houston: Offshore Technology Conf.
Reese, L. C., Cox, W. R. and Koop, F. D. 1975. “Field testing and analysis of laterally loaded piles in stiff clay.” In: Proc., 7th Annual Offshore Technology Conf., 671–690. Houston: Offshore Technology Conf.
Reese, L. C., and Matlock, H. 1956. “Non-dimensional solutions for laterally-loaded piles with soil modulus assumed proportional to depth.” In Proc., 8th Texas Conf. on Soil mechanics and Foundation Engineering, 1–23. Dallas: Association of Drilled Shaft Contractors.
Reese, L. C., and R. C. Welch. 1975. “Lateral loading of deep foundations in stiff clay.” J. Geotech. Geoenviron. Eng. Div. 101 (7): 633–649.
Shen, S. L., L. Ma, Y. S. Xu, and Z. Y. Yin. 2013a. “Interpretation of increased deformation rate in aquifer IV due to groundwater pumping in Shanghai.” Can. Geotech. J. 50 (11): 1129–1142. https://doi.org/10.1139/cgj-2013-0042.
Shen, S. L., Z. F. Wang, and W. C. Cheng. 2017. “Estimation of lateral displacement induced by jet grouting in clayey soils.” Géotechnique 67 (7): 621–630. https://doi.org/10.1680/jgeot.16.P.159.
Shen, S. L., Z. F. Wang, S. Horpibulsuk, and Y. H. Kim. 2013b. “Jet-Grouting with a newly developed technology: The Twin-Jet method.” Eng. Geol. 152 (1): 87–95. https://doi.org/10.1016/j.enggeo.2012.10.018.
Shen, S. L., and Y. S. Xu. 2011. “Numerical evaluation of land subsidence induced by groundwater pumping in Shanghai.” Can. Geotech. J. 48 (9): 1378–1392. https://doi.org/10.1139/t11-049.
Small, J. C., and H. H. Zhang. 2002. “Behavior of piled raft foundations under lateral and vertical loading.” Int. J. Geomech. 2 (1): 29–45. https://doi.org/10.1061/(ASCE)1532-3641(2002)2:1(29).
Southcott, P. H., and J. C. Small. 1996. “Finite layer analysis of vertically loaded piles and pile groups.” Comput. Geotech. 18 (1): 47–63. https://doi.org/10.1016/0266-352X(95)00019-7.
Sun, K. 1994. “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).
Trochanis, A. M., J. Bielak, and P. Christiano. 1991. “Three-dimensional nonlinear study of piles.” J. Geotech. Eng. 117 (3): 429–447. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:3(429).
Wong, S. C., and H. G. Poulos. 2005. “Approximate pile-to-pile interaction factors between two dissimilar piles.” Comput. Geotech. 32 (8): 613–618. https://doi.org/10.1016/j.compgeo.2005.11.001.
Zhang, L., H. Ernst, and H. H. Einstein. 2000. “Nonlinear analysis of laterally loaded rock-socketed shafts.” J. Geotech. Geoenviron. Eng. 126 (11): 955–968. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:11(955).
Zhang, Q. Q., and Z. M. Zhang. 2011. “Study on interaction between dissimilar piles in layered soils.” Int. J. Numer. Anal. Methods Geomech. 35 (1): 67–81. https://doi.org/10.1002/nag.893.
Zhao, M., L. Zhang, and M. Yang. 2006. “Settlement calculation for long-short composite piled raft foundation.” J. Cent. South Univ. Technol. 13 (6): 749–754. https://doi.org/10.1007/s11771-006-0026-4.
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Published In
International Journal of Geomechanics
Volume 19 • Issue 4 • April 2019
Copyright
© 2019 American Society of Civil Engineers.
History
Received: Jun 13, 2018
Accepted: Sep 14, 2018
Published online: Jan 29, 2019
Published in print: Apr 1, 2019
Discussion open until: Jun 29, 2019
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