Abstract
The analysis of dynamic soil–pile interaction problems requires the relation of soil resistance to lateral loading that is represented by nonlinear p–y curves in the beam on the nonlinear Winkler foundation (BNWF) approach. Current methods for p–y curves are either based on static load tests, or dynamic tests, which cannot properly consider soil nonlinearity. This study investigates the dynamic soil–pile interaction in cohesionless soils by numerical analyses to better characterize the p–y curves considering the nonlinear soil behavior under dynamic loading. A numerical pile–soil-structure model was created in FLAC3D and verified by two centrifuge tests published in the literature. The parametric analyses were performed to obtain the p–y curves for various pile diameters, soil relative densities, and degrees of nonlinearities. Based on the parametric analyses, a mathematical model was proposed for the dynamic p–y curves for cohesionless soils. The proposed model characterizes the backbone of dynamic p–y curves based on the three leading parameters (initial stiffness Kpy, ultimate resistance pu, and degree of nonlinearity n). The numerical analyses showed that the p–y curve nonlinearity mainly depends on the employed modulus reduction curves of soils. In the model, the degree of nonlinearity parameter (n) was directly related to the soil parameter γr which solely represents the modulus reduction curve of soils. In this regard, by correlating the dynamic p–y curves to the reference strain, the dependence on various dynamic soil parameters was diminished. The validation analyses performed in structural analysis software demonstrated that the proposed dynamic p–y model is capable of estimating the pile and structure response under earthquake loading more accurately by incorporating the hysteretic nonlinear soil behavior.
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The dataset generated during and/or analyzed during the current study are available from the authors on reasonable request.
Change history
28 November 2023
A Correction to this paper has been published: https://doi.org/10.1007/s10518-023-01829-1
References
Allotey N, El Naggar MH (2008) A numerical study into lateral cyclic nonlinear soil–pile response. Can Geotech J 45(9):1268–1281. https://doi.org/10.1139/T08-050
Alver O, Eseller-Bayat E (2022a) The Effect of soil damping on the soil-pile-structure interaction analyses in liquefiable and non-liquefiable soils. In: Conference on performance-based design in earthquake. Geotechnical Engineering. Springer, pp 1059–1066. https://doi.org/10.1007/978-3-031-11898-2_83
Alver O, Eseller-Bayat EE (2022b) Effect of soil damping on the soil–pile–structure interaction analyses in cohesionless soils. Appl Sci 12(18):9002. https://doi.org/10.3390/app12189002
API (1989) Recommended practice for planning, designing, and constructing fixed offshore platforms. vol 2. American Petroleum Institute
Bouc R (1971) A mathematical model for hysteresis. Acta Acust Acust 24(1):16–25
Boulanger RW, Curras CJ, Kutter BL, Wilson DW, Abghari A (1999) Seismic soil-pile-structure interaction experiments and analyses. J Geotech Geoenviron 125(9):750–759. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:9(750)
Brown DA, O'Neill M, Hoit M, McVay M, El Naggar M, Chakraborty S (2001) Static and dynamic lateral loading of pile groups. vol Project E24–9 FY'97.
Choi JI, Kim MM, Brandenberg SJ (2016) Cyclic p-y plasticity model applied to pile foundations in sand. J Geotech Geoenviron 142(6):08216001. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001261
Correia AA, Pecker A (2021) Nonlinear pile-head macro-element for the seismic analysis of structures on flexible piles. Bull Earthq Eng 19(4):1815–1849. https://doi.org/10.1007/s10518-020-01034-4
CSI (2016) SAP2000 integrated software for structural analysis and design. Ver. 18.2. Berkeley, California
Darendeli MB (2001) Development of a new family of normalized modulus reduction and material damping curves. The university of Texas at Austin
Desai C, Kuppusamy T (1980) Application of a numerical procedure for laterally loaded structures. In: Numerical methods in offshore piling. Thomas Telford Publishing, London, pp 93–99
Di Laora R, Rovithis E (2015) Kinematic bending of fixed-head piles in nonhomogeneous soil. J Geotech Geoenviron 141(4):04014126
El Naggar M, Novak M (1996) Nonlinear analysis for dynamic lateral pile response. Soil Dyn Earthq Eng 15(4):233–244. https://doi.org/10.1016/0267-7261(95)00049-6
Finn W (2005) A study of piles during earthquakes: issues of design and analysis. Bull Earthq Eng 3(2):141–234. https://doi.org/10.1007/s10518-005-1241-3
Finn W, Fujita N (2002) Piles in liquefiable soils: seismic analysis and design issues. Soil Dyn Earthq Eng 22(9–12):731–742. https://doi.org/10.1016/S0267-7261(02)00094-5
Fleming K, Weltman A, Randolph M, Elson K (1992) Piling engineering. Taylor & Francis, Milton Park
Gazetas G, Dobry R (1984) Horizontal response of piles in layered soils. J Geotech Eng 110(1):20–40. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:1(20)
Georgiadis M, Anagnostopoulos C, Saflekou S (1992) Centrifugal testing of laterally loaded piles in sand. Can Geotech J 29(2):208–216. https://doi.org/10.1139/t92-024
Gerolymos N, Gazetas G (2005) Constitutive model for 1-D cyclic soil behaviour applied to seismic analysis of layered deposits. Soils Found 45(3):147–159. https://doi.org/10.3208/sandf.45.3_147
Gerolymos N, Gazetas G (2006a) Development of Winkler model for static and dynamic response of caisson foundations with soil and interface nonlinearities. Soil Dyn Earthq Eng 26(5):363–376. https://doi.org/10.1016/j.soildyn.2005.12.002
Gerolymos N, Gazetas G (2006b) Static and dynamic response of massive caisson foundations with soil and interface nonlinearities—validation and results. Soil Dyn Earthq Eng 26(5):377–394. https://doi.org/10.1016/j.soildyn.2005.12.001
Gerolymos N, Escoffier S, Gazetas G, Garnier J (2009) Numerical modeling of centrifuge cyclic lateral pile load experiments. Earthq Eng Eng Vib 8(1):61–76. https://doi.org/10.1007/s11803-009-9005-8
Giannakos S, Gerolymos N, Gazetas G (2012) Cyclic lateral response of piles in dry sand: Finite element modeling and validation. Comput Geotech 44:116–131. https://doi.org/10.1016/j.compgeo.2012.03.013
Gohl WB (1991) Response of pile foundations to simulated earthquake loading: experimental and analytical results volume I. PhD Dissertation, University of British Columbia
Groholski DR, Hashash YM, Kim B, Musgrove M, Harmon J, Stewart JP (2016) Simplified model for small-strain nonlinearity and strength in 1D seismic site response analysis. J Geotech Geoenviron 142(9):04016042. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001496
Haldar S, Babu GS (2010) Failure mechanisms of pile foundations in liquefiable soil: Parametric study. Int J Geomech 10(2):74–84
Hardin BO, Black WL (1968) Vibration modulus of normally consolidated clay. J Soil Mech Found Div 94(2):353–369
Hardin BO, Drnevich VP (1972) Shear modulus and damping in soils: measurement and parameter effects (terzaghi leture). J Soil Mech Found Div 98(6):603–624
Hashash YMA MM, Harmon J et al (2017) DEEPSOIL 7.0, User manual.
Hussein AF, El Naggar MH (2022) Seismic behaviour of piles in non-liquefiable and liquefiable soil. Bull Earthq Eng 20(1):77–111. https://doi.org/10.1007/s10518-021-01244-4
Ishibashi I, Zhang X (1993) Unified dynamic shear moduli and damping ratios of sand and clay. Soils Found 33(1):182–191. https://doi.org/10.3208/sandf1972.33.182
Itasca Consulting Group I (2019) FLAC3D—fast lagrangian analysis of continua in three-dimensions. Ver. 7.0. Minneapolis: Itasca
Kagawa T, Kraft LM (1980) Lateral load-deflection relationships of piles subjected to dynamic loadings. Soils Found 20(4):19–36
Kokusho T (1980) Cyclic triaxial test of dynamic soil properties for wide strain range. Soils Found 20(2):45–60
Kondner RL (1963) A hyperbolic stress-strain formulation for sands. In: Proceedings of 2nd Pan Am. Conf. on Soil Mech. and Found. Eng., Brazil, 1963, vol 1.
Kuhlemeyer RL, Lysmer J (1973) Finite element method accuracy for wave propagation problems. J Soil Mech Found Div 99(5):421–427
Kwon SY, Yoo M (2020) Study on the dynamic soil-pile-structure interactive behavior in liquefiable sand by 3D numerical simulation. Appl Sci 10(8):2723. https://doi.org/10.3390/app10082723
Di Laora R, Rovithis E (2021) Design of piles under seismic loading. In: Analysis of pile foundations subject to static and dynamic loading. CRC Press, Boca Raton, pp 269–300
Lee M, Bae K-T, Lee I-W, Yoo M (2019) Cyclic py curves of monopiles in dense dry sand using centrifuge model tests. Appl Sci 9(8):1641. https://doi.org/10.3390/app9081641
Lim H, Jeong S (2018) Simplified p-y curves under dynamic loading in dry sand. Soil Dyn Earthq Eng 113:101–111. https://doi.org/10.1016/j.soildyn.2018.05.017
López Jiménez GA, Dias D, Jenck O (2019) Effect of the soil–pile–structure interaction in seismic analysis: case of liquefiable soils. Acta Geotech 14(5):1509–1525
Makris N, Gazetas G (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
Masing G (1926) Eigenspannungen und Verfestigung beim Messing [Fundamental stresses and strengthening with brass]. International Congress of Applied Mechanics, 2d, Zurich.
Matasović N, Vucetic M (1993) Cyclic characterization of liquefiable sands. J Geotech Eng 119(11):1805–1822. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:11(1805)
McGann CR, Arduino P, Mackenzie-Helnwein P (2011) Applicability of conventional p-y relations to the analysis of piles in laterally spreading soil. J Geotech Geoenviron 137(6):557–567. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000468
Nguyen BN, Tran NX, Han J-T, Kim S-R (2018) Evaluation of the dynamic p–yp loops of pile-supported structures on sloping ground. Bull Earthq Eng 16(12):5821–5842. https://doi.org/10.1007/s10518-018-0428-3
Nogami T, Otani J, Konagai K, Chen H-L (1992) Nonlinear soil-pile interaction model for dynamic lateral motion. J Geotech Eng 118(1):89–106. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:1(89)
Novak M (1991) Piles under dynamic loads. Second international conference on recent advances in geotechnical earthquake engineering and soil dynamics, University of Missouri-Rolla.
Pender M (1993) Aseismic pile foundation design analysis. Bull N Z Soc Earthq Eng 26(1):49–160. https://doi.org/10.5459/bnzsee.26.1.49-160
Poulos HG (1971) Behavior of laterally loaded piles: I-single piles. J Soil Mech Found Div 97(5):711–731. https://doi.org/10.1061/JSFEAQ.0001592
Rahmani A, Taiebat M, Finn WL, Ventura CE (2018) Evaluation of p-y springs for nonlinear static and seismic soil-pile interaction analysis under lateral loading. Soil Dyn Earthq Eng 115:438–447. https://doi.org/10.1016/j.soildyn.2018.07.049
Ramberg W, Osgood W (1943) Description of stress-strain curves by three parameters. National Advisory Committee for Aeronautics, Washington, DC
Reese LC, Cox, William R., Koop FD (1974) Analysis of laterally loaded piles in sand. In: Offshore technology conference, 1974. OTC-2080-MS. https://doi.org/10.4043/2080-MS
Reese LC, Van Impe WF (2000) Single piles and pile groups under lateral loading. CRC Press. https://doi.org/10.1201/b17499
Richart FE, Hall JR, Woods RD (1970) Vibrations of soils and foundations. Englewood Cliffs, New Jersey: Prentice-Hall.
Rollins KM, Lane JD, Gerber TM (2005) Measured and computed lateral response of a pile group in sand. J Geotech Geoenviron 131(1):103–114. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:1(103)
Rovithis E, Kirtas E, Pitilakis K (2009) Experimental p-y loops for estimating seismic soil-pile interaction. Bull Earthq Eng 7(3):719–736. https://doi.org/10.1007/s10518-009-9116-7
Scott RF (1981) Foundation analysis. Prentice-Hall, Upper Saddle River, New-Jersey
Seed HB, and Idriss, I. M. (1970) Soil moduli and damping factors for dynamic response analysis. Rep. No. EERC 70-10, Earthquake Engineering Research Center, Berkeley, California
Stacul S, Rovithis E, Di Laora R (2022) Kinematic soil-pile interaction under earthquake-induced nonlinear soil and pile behavior: an equivalent-linear approach. J Geotech Geoenviron 148(7):04022055
Stewart J CC, Hutchinson TC, Lizundia B, Naeim F, Ostadan F (2012) Soil–structure interaction for building structures. National Institute of Standards and Technology and NEHRP Consultants Joint Venture
Terzaghi K (1955) Evalution of coefficients of subgrade reaction. Géotechnique 5(4):297–326
Thavaraj T, Liam Finn W, Wu G (2010) Seismic response analysis of pile foundations. Geotech Geol Eng 28(3):275–286. https://doi.org/10.1007/s10706-010-9311-y
Varun AD, Shafieezadeh A (2013) Soil-pile-structure interaction simulations in liquefiable soils via dynamic macroelements: formulation and validation. Soil Dyn Earthq Eng 47(Suppl 1):92–107. https://doi.org/10.1016/j.soildyn.2012.03.008
Varun (2010) A nonlinear dynamic macroelement for soil structure interaction analyses of piles in liquefiable sites. PhD Dissertation, Georgia Institute of Technology
Wang S, Kutter BL, Chacko MJ, Wilson DW, Boulanger RW, Abghari A (1998) Nonlinear seismic soil-pile structure interaction. Earthq Spectra 14(2):377–396. https://doi.org/10.1193/1.1586006
Wen Y-K (1976) Method for random vibration of hysteretic systems. J Eng Mech Div 102(2):249–263
Wilson DW (1998) Soil-pile-superstructure interaction in liquefying sand and soft clay. PhD Dissertation, University of California at Davis
Yoo M-T, Choi J-I, Han J-T, Kim M-M (2013) Dynamic p-y curves for dry sand from centrifuge tests. J Earthquake Eng 17(7):1082–1102. https://doi.org/10.1080/13632469.2013.801377
Zhang J, Andrus RD, Juang CH (2005) Normalized shear modulus and material damping ratio relationships. J Geotech Geoenviron Eng 131(4):453–464. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:4(453)
Acknowledment
The authors would like to thank Dr. Amin Rahmani and Dr. Mahdi Taiebat for providing the centrifuge test data given in Gohl (1991). The authors very much appreciate the support by Dr. Akihiro Takahashi and Dr. Dan M. Ghiocel in the scope of the research (Tubitak) project. In addition, the authors wish to thank the reviewers for greatly improving the manuscript.
Funding
This study was funded by TUBITAK (The Scientific and Technological Research Council of Turkey) under Grant No. 119M624 and project title "Development of Lateral Load Resistance-Deflection Curves for Piles in Sands under Earthquake Excitation".
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Alver, O., Eseller-Bayat, E.E. A dynamic p–y model for piles embedded in cohesionless soils. Bull Earthquake Eng 21, 3297–3320 (2023). https://doi.org/10.1007/s10518-023-01677-z
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DOI: https://doi.org/10.1007/s10518-023-01677-z