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AbstractA numerical method that takes into account the coupling between the rigidities of the piles, the cap, and the column has been devel-oped for analyzing the response of pile group supported columns. Special attention is given to consideration of pile cap flexibility. A loadtransfer approach using t–z/q–z and p–y curves is used for the analysis of single piles. The finite element technique is used to combine thepile stiffness with the stiffness of the cap and column. The numerical method developed has been verified by comparing the results withother numerical methods for pile groups. 52532
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Through comparative studies, it has been found that the maximum load on the inpidual pilesin a group is highly influenced by pile cap flexibility. The prediction of the lateral loads and bending moments in the pile cap is muchmore conservative in the present analysis than in FBPier 3.0 and shows a definitely larger lateral load and bending moment for variouscap thicknesses. 2006 Elsevier Ltd. All rights reserved.Keywords: Numerical method; Coupling; Pile group supported columns; Pile cap flexibility 1. IntroductionPiles are often used in groups for the support of bridgestructures. There are numerous analytical and numericalmethods for designing pile groups. These methods can gen-erally be classified into three different types: (1) the equiv-alent single pile method [1–5], (2) the elasticity method[6–9], and (3) the general three-dimensional load transfermethod [10–14].The first type of method is based on the analysis of a sin-gle pile combined with group efficiency factors or groupamplification factors representing both the pile–soil–pileinteraction and the pile–cap interaction. The simplicity ofthis method, which uses only a spreadsheet to calculatethe design parameters, is its main advantage. However, thismethod has some restrictions in that it can be applied onlyto uniformly spaced pile groups no larger than approxi-mately 5 · 5 arrangement and does not provide the loaddistributions along the pile depths in a group [5]. The sec-ond type of method is a continuum method that models thesoil around the piles as a three-dimensional linearly elasticcontinuum. The interaction factor approach [6] usingMindlin’s solutions, and direct continuum models [8] aretypically included in this category. It should be noted thatthis method was originally an elastic method, althoughnumerous variations have been developed that permit themodeling of soil layering, pile–soil slip, three-dimensionalgeometry, and so on.
The third type of method of analysisof pile groups models all inpidual piles using beam–col-umn elements attached to nonlinear soil springs (loadtransfer curves) and the pile cap using rigid body [10–12]or finite element [13,14] methods. This method is popularbecause the modeling of randomly arranged piles is rela-tively simple and the design parameters can be easilyobtained; as a result of many load tests performed duringthe past two decades, many reliable load transfer curves(t–z/q–z and p–y curves) have been suggested. The*Corresponding author. Tel.: +82 2 2123 2807; fax: +82 2 364 5300.E-mail addresses: wjo20@yonsei.ac.kr (J. Won), koen@dweng.co.kr(S.-Y. Ahn), soj9081@yonsei.ac.kr (S. Jeong), icdij@chollian.net (J. Lee),syjang@moiza.chonnam.ac.kr (S.-Y. Jang). pile–soil–pile interaction that occurs in closely spaced pilescan be taken into account by introducing reduction factorsfor the soil reactions in the p–y curves for single piles.The general three-dimensional load transfer method wasused in the study described in this paper. To date, com-pared with the pile–soil–pile interaction, the pile–cap inter-action has not received the attention it deserves, since manycomplex geometric and loading conditions are involved inthe structural and geotechnical analyses. In recent years,however, McVay et al. [15] have reported the significanceof the fixity of the pile head, which is one of the factorsinfluencing the pile–cap interaction. According to the USArmy Manual [16], knowing the correct relationshipbetween the stiffnesses of the pile and cap is extremelyimportant for accurately designing pile groups for use inflexible base structures. Two kinds of methods are availablefor calculating the pile–cap interaction: the stiffness methodand the finite element method.The stiffness method was suggested by Hrennikoff [17],and has been extended into a general three-dimensionalmethod by Saul [18] and Reese et al. [10]. Group 6.0 [19],a commercial package which has been used for practicaldesign, is based on this stiffness method. This method canconsider the pile–cap interaction, the nonlinear behaviorof inpidual piles, and the pile–soil–pile interaction, buthas limitations in that it cannot consider the coupling ofthe rigidities of the pile cap to each other and to the col-umn, since this method assumes a pile cap to be a rigidbody. To consider these coupled pile cap rigidities, a pilecap needs to be modeled by finite elements such as beams,frames, plates, and flat-shell elements.In this study, a new numerical method that considerscoupled cap rigidities has been developed to overcomethe restrictions associated with the conventional stiffnessmethod. The conceptual methodology of the presentmethod is completely different from not only that of thegeneral structural models (FBPier 3.0 [13] and SAP2000)but also that of the stiffness method.2. New numerical method for pile group supported columns