Abstract
A new practical formulation of the load-transfer P-Y curves to analyze the load–deflection response of a single pile under lateral loads is proposed in this paper. Parameters of the P-Y curves, namely the lateral reaction modulus and the lateral soil resistance, were correlated to the pre-bored pressuremeter (PMT) data as well as to the pile/soil stiffness ratio. A total of 16 full-scale monotonic lateral loading tests carried out in six experimental sites in France, representing a variety of soil conditions, were interpreted focused on the construction of the experimental P-Y curves along the test pile.
For practical purposes, a methodology of construction of the P-Y curves was proposed. Moreover, the paper highlights the new concept of the critical deflection, which is the threshold of the nonlinear pile/soil response, as well as a classification of piles based on the pile/soil stiffness ratio.
The process of validation of the proposed P-Y curve-based method was undertaken by comparing the predicted load–deflection curves to the experimental curves of several test piles within a medium-sized database, and a very good predictive capability was noticed.
At last, the concept of the normalized load–deflection curve was introduced to estimate the pile deflection during a preliminary stage of pile design.
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References
Adam M, Lejay J (1971) Etude des pieux sollicités horizontalement- Déterminationdu module de réaction dans un sol donné (in French). J Ann de l’ITBTP N° 280, pp : 127–155, Paris.
AFNOR (2012) "Justification des ouvrages géotechniques : Norme nationale d’application de l’Eurocode 7- Fondations profondes" (In French), French standard NF P94–262, 205
Ambrosino R, Bru J-P, Ledoux J-L. (1973) Comportement d’un pieu sollicité horizontalement (in French). Bulletin des LPC No. 67, pp : 151–167, Laboratoire Central des Ponts et Chaussées, Paris, France.
API (2014) ISO 19901–4 (modified)-Geotechnical and foundation design considerations, 138 pages.
Baguelin F, Frank R, Said Y (1977) Theoretical study of lateral reaction mechanism of piles. Journal Géotechnique 27:3
Baguelin F, Jézéquel J-F (1972) Etude expérimentale du comportement des pieux chargés latéralement (in French). Ann de l’ITBTP N° 297 155-200, ITBTP, Paris, France
Baguelin F, Jézéquel J-F., Shields D-H (1978) The pressuremeter and foundation engineering. Series on rock and soil mechanics, Vol. 2, N° 4, 1st edition, 1978 Trans Tech Publications, Germany, 615 p.
Baguelin F, Frank R, Jézéquel J-F (1990) The Ménard pressuremeter test and the behaviour of laterally loaded piles in sand, Proceedings of ISP3 the 3rd International Symposium on Pressuremeters, Oxford University, 2–6 April 1990, pp 381–391.
Baguelin F (1982) Règles de calcul des fondations à partir de l’essai au pressiomètre auto-foreur (in French). Proceedings of the symposium "La pressiométrie et ses applications en mer", Paris,19–20 April 1982, pp 359–371, editions LCPC-IFP.
Banerjee P, Davies T (1978) The behaviour of axially and laterally loaded single piles embedded in non-homogeneous soils. Géotechnique 28(3):309–326
Bouafia A (1995) Bouguerra A (1995) Modélisation en centrifugeuse du comportement d’un pieu flexible chargé horizontalement à proximité d’une pente (in French). Can Geotech J 32(2):324–335
Bouafia A (2007) Single piles under horizontal loads-determination of the P-Y curves from the prebored pressuremeter. Int J Geotech Geol Eng 25:283–301 (Springer-Verlag, ISSN: 0960-3182)
Bouafia A, Bouguerra A (1996) Effet de la proximité du talus sur un pieu court et rigide chargé horizontalement (in French). French Geotech J RFG No. 75, 2nd trimester 1996, pp : 47–56.
Bouafia, A., Lachenani, A., (2005) Analysis of P-Y curves for single piles from the prebored pressuremeter, Proceedings of the 16th International Conference on Soil Mechanics and Geotechnical Engineering, September 12–16, 2005, Osaka, Japan, pp: 1955–1958, Edition: Millpress Science Publishers Rotterdam, The Netherlands.
Bouafia A (1990) Modélisation des pieux chargés latéralement en centrifugeuse (in French), Doctorate thesis of the University of Nantes, France, 267 p.
Bouafia A (1997) Etude en centrifugeuse du comportement d’un pieu chargé horizontalement (in French). Proceedings of the 14th ICSMFE, 6–12 September, pp : 771–776, A.A. Balkema publications.
Bouafia A (2002a) Analysis of lateral reaction modulus for piles in sand from CPT test. Proceedings of the international symposium PARAM’02, Paris, 2–3 September 2002, Presses de l’ENPC.
Bouafia A (2002b) Response of a flexible pile under lateral loads in dense sand in centrifuge. Proceedings of ICPMG’02 International Conference on Physical Modelling in Geotechnics, St-John’s, Newfoundland, Canada July 10–12 2002c, edited by the Canadian Geotechnical Society.
Briaud J-L (1997) SALLOP: simple approach for lateral loads on piles. J Geotech Geoenviron Eng 123(10):958–964
A pressuremeter method for laterally loaded piles, Proceedings of the International Conference on Soil Mechanics and Foundation Engineering, San- Francisco 1985, Vol. 3, pp 1353-1356
Briaud J-L, Smith T, Meyer B (1983) Laterally loaded piles and the pressuremeter-comparison of existing methods. Proceedings of the Symposium "Laterally loaded deep foundations-Analysis and performance", ASCE, STP-835, ed. Longer, Mosley and Thompson, pp: 97–111.
Briaud J-L (2013) Geotechnical engineering: unsaturated and saturated soils, edited by John Wiley & Sons, Inc., 1022 p.
Broms B (1964) Lateral resistance of piles in cohesive soils. J ASCE 90(SM2):27–63
Budhu M, Davies T (1987) Nonlinear analysis of laterally loaded piles in cohesionless soils. Can Geotech J N 24:289–298
Canépa Y, Depresle D, Leipp J, Smirr JL (1987) Essais de sollicitations horizontales de tubes de différents diamètres fichés dans une fosse de sable de Fontainebleau (in French). Testing report to the LREP, Code F.A.E.R 1.15.06.6, file 8670, 32 pages.
Carter DP (1984) A nonlinear soil model for predicting lateral pile response, Master of Engineering Thesis, University of Auckland.
Cassan M (1988) Les essais in-situ en mécanique des sols (in French), Volumes No. 1 and 2, edited by Eyrolles, Paris
Combarieu O (1995) L’essai pressiométrique et la résistance au cisaillement des sols (In French). Bulletin de liaison des LPC, No. 196, pp :43–51, Paper ID : 3886, Laboratoire Central des Ponts et Chaussées, Paris.
Djoneidi Dj, Frank R (1983) Contribution à l’étude théorique en grandes déformations du poinçonnement dans les sols (in French). Research report GT-2, 151 pages, edited by LCPC, Paris.
Dunand M (1981) Etude expérimentale du comportement des fondations soumises au renversement (in French). PhD dissertation of the University of Grenoble IMG, France
Frank R (1984) Etudes théoriques des fondations profondes et d’essais en place par auto-forage dans les LPC et résultats pratiques (in French). Research Report to the LCPC, N° 128
Hadjadji, T., Frank, R., Degny, E., (2002) Analyse du comportement expérimental de pieux sous chargements horizontaux (in French), Series: Géotechnique et risques naturels (Geotechnics and natural Hazards), No. GT-74, 303, ed: LCPC, Paris, France
Hansen B (1961) The ultimate resistance of rigid piles against transversal forces. Bulletin N°12, The Danish Geotechnical Institute, pp: 1–9.
Haouari H, Bouafia A (2023a) Single piles under cyclic lateral loads - Full scale tests and numerical modelling. Geotech Eng 32(1):21–34. https://doi.org/10.12989/gae.2023.32.1.021
Haouari H, Bouafia A (2023b) Single piles under monotonic lateral loads-Full scale tests and numerical modelling. J Geomec Geoeng 1(1):11–25. https://doi.org/10.38208/jgg.v1i1.441
Kérisel J, Adam A (1967) Calcul des forces horizontales applicables aux fondations profondes dans les argiles et limons (in French). J Ann de l’ITBTP N° 239:1655–1694
Kim Y, Jeong S, Lee S (2011) Wedge failure analysis of soil resistance of laterally loaded piles in clay. J Geotech Geo-Environ Eng 137(7):633–729
Matlock H, Reese L (1960) Generalized solutions for laterally loaded piles. JSMFE, ASCE, SM5, pp: 83–91.
Matlock H (1970) Correlations for the design of laterally loaded piles in soft clays. Proceedings of the Offshore Technology Conference, Dallas, TX, Paper No. 1204
Ménard L (1957) Mesures in-situ des propriétés physiques des sols (in French). J Ann des Ponts Chaussées Paper 24:358–377
Ménard L, Gambin M, Bourdon G (1969) Méthode générale de calcul d’un rideau ou d'un pieu sollicité horizontalement en fonction des résultats pressiométriques (in French). J Sols/Soils Vol. 1, No. 20/23, 1969, pp : 16–28.
Moussard H, Kersale J-F (2011) Etude expérimentale du comportement d'un pieu isolé sous l'effet de sollicitations horizontales de freinage et de démarrage de circulations ferroviaires (in French), Revue Française de Géotechnique No. 134-135, 1e-2e trimestres 2011, pp 87–98
Pouget P (1988) Etude du comportement de deux pieux métalliques sollicités rapidement par un effort horizontal (in French). Report to LRPC of Clermont-Ferrand, LCPC N°63/85/0545, Code FAER :1.05.05.6, 50 p.
Poulos HG, Davis EH (1980) Pile foundation analysis and design. Edited by John Wiley and Sonc. Inc. New- York.
Poulos H, Hull T (1992) Analytical geomechanics in foundation engineering- a study of laterally loaded piles. Research report No. R667 to the University of Sydney, Australia, 40 p
Randolph M (1981) The response of flexibles piles to lateral loading. Géotechnique 81(2):247–259
Randolph M, Houlsby T (1984) The limiting pressure on a circular pile loaded laterally in cohesive soil. J Géotechnique 34(4):613–623
Reese L, Van Impe W (2001) Single piles and pile groups under lateral loading, edited by Francis and Taylor/Balkema, 463 p.
Reese L, Cox W, Koop F (1974) Analysis of laterally loaded piles in sand. Proceedings of the 6th Annual Offshore Technology Conference, Houston, Texas, 473–485.
Robertson P, Hughes J, Campanella R (1984) Design of laterally loaded displacement piles using a driven pressuremeter. Laterally Loaded Deep Foundations- Analysis and Performance, ASTM Special Technical Publications No 835(1984):229–238
Ruesta P, Townsend F-C (1997) Evaluation of laterally loaded pile group at Roosevelt bridge. J Geotech Geoenviron Eng 123:1153–1161
Scott R (1981) Foundation analysis. Prentice Hall Inc, Englewood Cliffs, N.J.
Smith T (1983) Pressuremeter design method for single piles subjected to static lateral loading. Ph.D dissertation, Texas A & M University, 446 pages.
Smith T (1987) Friction mobilisation F-Y curves for laterally loaded piles from the pressuremeter. Proceedings of the International Symposium on Predictions and Performance in Geotechnical Engineering, Calgary, Canada, 17–19 June 1987, pp 89–95, A. A. Balkema.
Terzaghi K (1955) Evaluation of coefficients of subgrade reaction. J Géotechnique 5(4):297–326
Vesic AS (1961) Bending of beams resting on isotropic elastic solid. J Eng Mech ASCE 87(2):35–53
Acknowledgements
The author is grateful to Mr. Jacques Roudier, General Manager of the LCPC Laboratory, for authorizing him to access to the experimental data of full-scale lateral loading tests of piles carried out by the LCPC, as well as to the Ph.D and M.Sc students team who worked for many years on this topic under supervision of the author.
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Ali, B. New P-Y curve formulation for laterally loaded single piles based on the pre-bored pressuremeter. Arab J Geosci 16, 684 (2023). https://doi.org/10.1007/s12517-023-11804-4
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DOI: https://doi.org/10.1007/s12517-023-11804-4