A Procedure for Nonlinear Analysis of Laterally Loaded Single Piles and Pile Groups
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This research introduces an analytical procedure for simulating the nonlinear behavior of single piles and pile groups under lateral loads in multi-layered, heterogeneous soil. The methodology combines the finite element method, the p-y technique, and the p-multiplier concept. Duncan and Chang's hyperbolic equation, characterized by three parameters, was employed to represent the soil reaction for sand and clay soils. A newly proposed equation to derive p-multipliers as a function of a pile's location and spacing within a pile group. Its predictions show satisfactory agreement with those from existing methods. The procedure was implemented in a computer program to enable rapid and accurate computation. The proposed program validation involved comprehensive comparisons against results from field load tests and sophisticated 3D finite element analyses. These comparisons confirm that the developed program is both reliable and efficient, making it well-suited for preliminary design stages. A subsequent parametric study on a single pile revealed that replacing soft upper clay with a compacted sand layer significantly decreases lateral deflection and bending moment. For the cases examined, an optimal compacted layer thickness of three pile diameters and a stiffness 5.6 times that of the native soft clay were identified.
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[1] Brown, D. A., & Shie, C. F. (1991). Some numerical experiments with a three dimensional finite element model of a laterally loaded pile. Computers and Geotechnics, 12(2), 149–162. doi:10.1016/0266-352X(91)90004-Y.
[2] Hidayawanti, R., Latief, Y., & Gaspersz, V. (2024). Risk-Based Method-Technology Integration on Spun Pile Production for Product and Service Quality. Civil Engineering Journal, 10(11), 3683–3698. doi:10.28991/CEJ-2024-010-11-015.
[3] Gui, M. W., & Alebachew, A. A. (2025). Numerical investigation of laterally loaded pile groups at the crest of slopes. Scientific Reports, 15(1), 22670. doi:10.1038/s41598-025-07715-x.
[4] Elsiragy, M., Azzam, W., & Kassem, E. M. (2025). Experimental and Numerical Study of Enlarged-Head Monopile Under Lateral Load in Soft Clay. Civil Engineering Journal (Iran), 11(2), 453–471. doi:10.28991/CEJ-2025-011-02-04.
[5] Poulos, H. G. & Davis, E. H. (1980). Pile foundation analysis and design (1st Ed.), John Wiley and Sons, New York, United States.
[6] Matlock, H., & Reese, L. C. (1960). Generalized Solutions for Laterally Loaded Piles. Journal of the Soil Mechanics and Foundations Division, 86(5), 63–92. doi:10.1061/jsfeaq.0000303.
[7] Reese, L. C., Cox, W. R., & Koop, F. D. (1974). Analysis of Laterally Loaded Piles in Sand. Offshore Technology Conference. doi:10.4043/2080-ms.
[8] Reese, L. C., & Welch, R. C. (1975). Lateral Loading of Deep Foundations in Stiff Clay. Journal of the Geotechnical Engineering Division, 101(7), 633–649. doi:10.1061/ajgeb6.0000177.
[9] Reese, L. C., Wang, S. T., Isenhower, W. M., Arrellaga, J. A., & Hendrix, J. (2000). A program for the analysis of piles and drilled shafts under lateral loads. LPILE version, 4, Ensoft, Inc., Austin, United States.
[10] Ashford, S. A., & Juirnarongrit, T. (2003). Evaluation of Pile Diameter Effect on Initial Modulus of Subgrade Reaction. Journal of Geotechnical and Geoenvironmental Engineering, 129(3), 234–242. doi:10.1061/(asce)1090-0241(2003)129:3(234).
[11] Castelli, F., & Maugeri, M. (2009). Simplified Approach for the Seismic Response of a Pile Foundation. Journal of Geotechnical and Geoenvironmental Engineering, 135(10), 1440–1451. doi:10.1061/(asce)gt.1943-5606.0000107.
[12] Alver, O., & Eseller-Bayat, E. E. (2024). A new p-y model for soil-pile interaction analyses in cohesionless soils under monotonic loading. Soils and Foundations, 64(2), 101441. doi:10.1016/j.sandf.2024.101441.
[13] El Gendy, M. (2025). Analyzing laterally loaded piles in multi-layered cohesive soils: a hybrid beam on nonlinear Winkler foundation approach with case studies and parametric study. Discover Civil Engineering, 2(1), 1-34. doi:10.1007/s44290-025-00240-w.
[14] Ashour, M., Norris, G., & Pilling, P. (1998). Lateral Loading of a Pile in Layered Soil Using the Strain Wedge Model. Journal of Geotechnical and Geoenvironmental Engineering, 124(4), 303–315. doi:10.1061/(asce)1090-0241(1998)124:4(303).
[15] Ashour, M., & Norris, G. (2000). Modeling Lateral Soil-Pile Response Based on Soil-Pile Interaction. Journal of Geotechnical and Geoenvironmental Engineering, 126(5), 420–428. doi:10.1061/(asce)1090-0241(2000)126:5(420).
[16] Ashour, M., Pilling, P., & Norris, G. (2004). Lateral Behavior of Pile Groups in Layered Soils. Journal of Geotechnical and Geoenvironmental Engineering, 130(6), 580–592. doi:10.1061/(asce)1090-0241(2004)130:6(580).
[17] Reese, L. C., & Van Impe, W. F. (2010). Single Piles and Pile Groups Under Lateral Loading. CRC Press, London, United Kingdom. doi:10.1201/b17499.
[18] API. (2014). Recommended Practice 2A-WSD- Planning, Designing, and Constructing Fixed Offshore Platforms Working Stress Design. American Petroleum Institute (API), Washington, united States.
[19] AASHTO. (2000). Bridge design specifications. American Association of State Highway and Transportation Officials (AASHTO), Washington, United States.
[20] Matlock, H. (1970). Correlation for Design of Laterally Loaded Piles in Soft Clay. Offshore Technology Conference. doi:10.4043/1204-ms.
[21] Kim, Y., & Jeong, S. (2011). Analysis of soil resistance on laterally loaded piles based on 3D soil-pile interaction. Computers and Geotechnics, 38(2), 248–257. doi:10.1016/j.compgeo.2010.12.001.
[22] Bhuiyan, F. M. (2022). Development of a New Load Analysis Tool and a Unified Py Method for Lateral Analysis of Large-Diameter Drilled Shafts Validated Using Load Tests. PhD Thesis, University of Nevada, Reno, United States.
[23] Yang, K., & Liang, R. (2006). Numerical Solution for Laterally Loaded Piles in a Two-Layer Soil Profile. Journal of Geotechnical and Geoenvironmental Engineering, 132(11), 1436–1443. doi:10.1061/(asce)1090-0241(2006)132:11(1436).
[24] Liam Finn, W. D., & Dowling, J. (2016). Modelling effects of pile diameter. Canadian Geotechnical Journal, 53(1), 173–178. doi:10.1139/cgj-2015-0119.
[25] McVay, M. C., & Niraula, L. (2004). Development of PY curves for large diameter piles/drilled shafts in limestone for FBPIER. No. Final Report, University of Florida, Gainesville, United States.
[26] Murchison, J. M., & O’Neill, M. W. (1984). Evaluation of p-y relationships in cohesionless soils, analysis and design of pile foundations. Proceedings of the Symposium in Conjunction with the ASCE National Convention, 1-5 October, 1984, San Francisco, United States.
[27] Choi, J. I., Kim, M. M., & Brandenberg, S. J. (2015). Cyclic p-y Plasticity Model Applied to Pile Foundations in Sand. Journal of Geotechnical and Geoenvironmental Engineering, 141(5), 8216001. doi:10.1061/(asce)gt.1943-5606.0001261.
[28] Rahmani, A., Taiebat, M., Finn, W. D. L., & Ventura, C. E. (2018). Evaluation of p-y springs for nonlinear static and seismic soil-pile interaction analysis under lateral loading. Soil Dynamics and Earthquake Engineering, 115, 438–447. doi:10.1016/j.soildyn.2018.07.049.
[29] Wang, L., & Ishihara, T. (2022). New p-y model for seismic loading prediction of pile foundations in non-liquefiable and liquefiable soils considering modulus reduction and damping curves. Soils and Foundations, 62(5), 101201. doi:10.1016/j.sandf.2022.101201.
[30] Georgiadis, M., Anagnostopoulos, C., & Saflekou, S. (1992). Centrifugal testing of laterally loaded piles in sand. Canadian Geotechnical Journal, 29(2), 208–216. doi:10.1139/t92-024.
[31] Kondner, R. L. (1963). Hyperbolic Stress-Strain Response: Cohesive Soils. Journal of the Soil Mechanics and Foundations Division, 89(1), 115–143. doi:10.1061/jsfeaq.0000479.
[32] Tak Kim, B., Kim, N.-K., Jin Lee, W., & Su Kim, Y. (2004). Experimental Load–Transfer Curves of Laterally Loaded Piles in Nak-Dong River Sand. Journal of Geotechnical and Geoenvironmental Engineering, 130(4), 416–425. doi:10.1061/(asce)1090-0241(2004)130:4(416).
[33] Papadopoulou, M. C., & Comodromos, E. M. (2014). Explicit extension of the p-y method to pile groups in sandy soils. Acta Geotechnica, 9(3), 485–497. doi:10.1007/s11440-013-0274-z.
[34] Lim, H., Jeong, S., & Chung, M. (2018). Analysis of Soil Resistance on Laterally Loaded Offshore Piles in Inchon Marine Clay. Innovations in Geotechnical Engineering, 147–159. doi:10.1061/9780784481639.009.
[35] Zhou, P., Zhou, H., Liu, H., Li, X., Ding, X., & Wang, Z. (2020). Analysis of lateral response of existing single pile caused by penetration of adjacent pile in undrained clay. Computers and Geotechnics, 126, 103736. doi:10.1016/j.compgeo.2020.103736.
[36] Lu, W., Kaynia, A. M., & Zhang, G. (2021). Centrifuge study of p-y curves for vertical-horizontal static loading of piles in sand. International Journal of Physical Modelling in Geotechnics, 21(6), 275–294. doi:10.1680/jphmg.19.00030.
[37] Amar Bouzid, D. (2021). Analytical Quantification of Ultimate Resistance for Sand Flowing Horizontally around Monopile: New p-y Curve Formulation. International Journal of Geomechanics, 21(3), 4021007. doi:10.1061/(asce)gm.1943-5622.0001927.
[38] Liang, R. Y., Shatnawi, E. S., & Nusairat, J. (2007). Hyperbolic P-Y criterion for cohesive soils. Jordan Journal of Civil Engineering, 1(1), 38–58.
[39] Brown, D. A., Morrison, C., & Reese, L. C. (1988). Lateral load behavior of pile group in sand. Journal of Geotechnical Engineering, 114(11), 1261–1276. doi:10.1061/(ASCE)0733-9410(1988)114:11(1261).
[40] Hoit, M., Hays, C., & McVay, M. (1997). The Florida Pier Analysis Program Methods and Models for Pier Analysis and Design. Transportation Research Record: Journal of the Transportation Research Board, 1569(1), 1–7. doi:10.3141/1569-01.
[41] Ruesta, P. F., & Townsend, F. C. (1997). Evaluation of Laterally Loaded Pile Group at Roosevelt Bridge. Journal of Geotechnical and Geoenvironmental Engineering, 123(12), 1153–1161. doi:10.1061/(asce)1090-0241(1997)123:12(1153).
[42] Rollins, K. M., Peterson, K. T., & Weaver, T. J. (1998). Lateral Load Behavior of Full-Scale Pile Group in Clay. Journal of Geotechnical and Geoenvironmental Engineering, 124(6), 468–478. doi:10.1061/(asce)1090-0241(1998)124:6(468).
[43] Zhang, X. (1999). Comparison of lateral group effect between bored and PC driven pile groups in sand. Master Thesis, University of Houston, Houston, United States.
[44] Duncan, J. M., & Chang, C.-Y. (1970). Nonlinear Analysis of Stress and Strain in Soils. Journal of the Soil Mechanics and Foundations Division, 96(5), 1629–1653. doi:10.1061/jsfeaq.0001458.
[45] Poulos, H. G. (1989). Pile behaviour - theory and application. Geotechnique, 39(3), 365–415. doi:10.1680/geot.1989.39.3.365.
[46] Yu, Y., Shen, M., & Hsein Juang, C. (2019). Assessing Initial Stiffness Models for Laterally Loaded Piles in Undrained Clay: Robust Design Perspective. Journal of Geotechnical and Geoenvironmental Engineering, 145(10), 4019073. doi:10.1061/(asce)gt.1943-5606.0002074.
[47] Callanan, J. F. (1984). Evaluation of procedures for predicting foundation uplift movements. Cornell University, Report EL-4107 Electric Power Research Institute, Palo Alto, California, United States.
[48] Bowles, J.E. (1996) Foundation Analysis and Design (5th Ed.). McGraw-Hill Companies, Inc., New York, United States.
[49] Kulhawy, F. H., & Mayne, P. W. (1990). Manual on estimating soil properties for foundation design. No. EPRI-EL-6800, Electric Power Research Inst., Palo Alto, United States.
[50] Duncan, J. M., & Bursey, A. (2013). Soil Modulus Correlations. Foundation Engineering in the Face of Uncertainty, 321–336. doi:10.1061/9780784412763.026.
[51] Wagh, J. D., & Bambole, A. N. (2024). Improved correlation of soil modulus with SPT N values. Open Engineering, 14(1), 1–17. doi:10.1515/eng-2024-0046.
[52] Jeong, S., Kim, Y., & Kim, J. (2011). Influence on lateral rigidity of offshore piles using proposed p-y curves. Ocean Engineering, 38(2–3), 397–408. doi:10.1016/j.oceaneng.2010.11.007.
[53] Briaud, J.-L., Smith, T., & Meyer, B. (1984). Laterally Loaded Piles and the Pressuremeter: Comparison of Existing Methods. Laterally Loaded Deep Foundations: Analysis and Performance, 97–111, ASTM International, Pennsylvania, United States. doi:10.1520/stp36815s.
[54] Zhang, L. M., McVay, M. C., Han, S. J., Lai, P. W., & Gardner, R. (2002). Effects of dead loads on the lateral response of battered pile groups. Canadian Geotechnical Journal, 39(3), 561–575. doi:10.1139/t02-008.
[55] McVay, M. C., Shang, T. I., & Casper, R. (1996). Centrifuge testing of fixed-head laterally loaded battered and plumb pile groups in sand. Geotechnical Testing Journal, 19(1), 41–50. doi:10.1520/gtj11406j.
[56] Rollins, K. M., Olsen, R. J., Egbert, J. J., Jensen, D. H., Olsen, K. G., & Garrett, B. H. (2006). Pile Spacing Effects on Lateral Pile Group Behavior: Load Tests. Journal of Geotechnical and Geoenvironmental Engineering, 132(10), 1262–1271. doi:10.1061/(asce)1090-0241(2006)132:10(1262).
[57] Cox, W., Dixon, D., & Murphy, B. (1984). Lateral-Load Tests on 25.4-mm (1-in.) Diameter Piles in Very Soft Clay in Side-by-Side and In-Line Groups. Laterally Loaded Deep Foundations: Analysis and Performance, 122–139, ASTM International, Pennsylvania, United States. doi:10.1520/stp36817s.
[58] Myint Lwin, M. (1999). Why the AASHTO load and resistance factor design specifications?. Transportation Research Record, 1688(1), 173-176. doi:10.3141/1688-20.
[59] Walsh, K. D., Fréchette, D. N., Houston, W. N., & Houston, S. L. (2000). State of the practice for design of groups of laterally loaded drilled shafts. Transportation Research Record, 2000(1736), 33–40. doi:10.3141/1736-05.
[60] Brown, D. A., Reese, L. C., & O’Neill, M. W. (1987). Cyclic lateral loading of a large-scale pile group. Journal of Geotechnical Engineering, 113(11), 1326–1343. doi:10.1061/(ASCE)0733-9410(1987)113:11(1326).
[61] Mokwa, R. L., & Duncan, J. M. (2001). Laterally loaded pile group effects and p-y multipliers. Foundations and ground improvement, American Society of Civil Engineers (ASCE), Reston, United States.
[62] FEMA P-751. (2012). 2009 NEHRP Recommended Seismic Provisions: Design Examples. Federal Emergency Management Agency (FEMA), Washington, United States.
[63] Barker, R. M., & Puckett, J. A. (1987). Design of highway bridges based on AASHTO LRFD bridge design specifications. John Wiley & Sons, New York, United States.
[64] Gupta, B. K., & Basu, D. (2020). Nonlinear solutions for laterally loaded piles. Canadian Geotechnical Journal, 57(10), 1566–1580. doi:10.1139/cgj-2019-0341.
[65] Comodromos, E. M., & Pitilakis, K. D. (2005). Response evaluation for horizontally loaded fixed-head pile groups using 3-D non-linear analysis. International Journal for Numerical and Analytical Methods in Geomechanics, 29(6), 597–625. doi:10.1002/nag.428.
[66] Reese, L. C. (1986). Behavior of piles and pile groups under lateral load. No. FHWA-RD-85-106, Department of Transportation, Federal Highway Administration, Washington, United States.
[67] Wu, D., Broms, B. B., & Choa, V. (1998). Design of laterally loaded piles in cohesive soils using p-y curves. Soils and Foundations, 38(2), 17–26. doi:10.3208/sandf.38.2_17.
[68] Guo, W. D. (2013). Simple Model for Nonlinear Response of 52 Laterally Loaded Piles. Journal of Geotechnical and Geoenvironmental Engineering, 139(2), 234–252. doi:10.1061/(asce)gt.1943-5606.0000726.
[69] Rollins, K. M., Lane, J. D., & Gerber, T. M. (2005). Measured and Computed Lateral Response of a Pile Group in Sand. Journal of Geotechnical and Geoenvironmental Engineering, 131(1), 103–114. doi:10.1061/(asce)1090-0241(2005)131:1(103).
[70] Bolton, M. D. (1986). The strength and dilatancy of sands. Geotechnique, 36(1), 65–78. doi:10.1680/geot.1986.36.1.65.
[71] Eltaweila, S., Shahien, M. M., Nasr, A. M., & Farouk, A. (2021). Effect of Soil Improvement Techniques on Increasing the Lateral Resistance of Single Piles in Soft Clay (Numerical Investigation). Geotechnical and Geological Engineering, 39(6), 4059–4070. doi:10.1007/s10706-020-01534-9.
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