The maximum bending moment calculated bythe displacement method is 519 kN m, and the bendingmoments in the leading and trailing rows calculated bythe present method are 464 kN m and 593 kN m, respec-tively. The difference in the bending moments betweenthe trailing row and the leading row is more significant inthe present method than in FBPier 3.0.Similarly, the present method has been compared withFBPier 3.0 and Group 6.0, for various thicknesses (T/T0)of the pile cap, as shown in Fig. 21. The difference in thebending moments between the trailing row and the leadingrow in the present method became more significant than inFBPier 3.0 when the thickness of the pile cap was varied.From this comparative study, it is concluded that thepresent method predicts that the effect of flexibility of thepile cap is more significant than in FBPier 3.0, and canbe regarded as a conservative method.5.2. Bending moments and shear forces in pilesFig. 22 shows profiles of the bending moment and theshear force along the pile depth for various values of theelastic modulus E of the pile cap. Four different elasticmodulus ratios (E/E0 = 0.5, 1, 2, and 10) were investigated.Except for the elastic modulus of the pile cap, all other con-ditions were identical to the conditions in Fig. 13.As shown in Fig. 22, the difference in the bendingmoment and shear force between the trailing row and theleading row decreases with increasing elastic modulus ofthe pile cap. This figure shows that there is an effect of pilecap flexibility on the bending moments and shear forces ininpidual piles and therefore represents profiles of bendingmoment and shear force different from those obtained byassuming a rigid pile cap. 6. Summary and conclusionsThe behavior of pile group supported columns (piledpiers) has been investigated by using a numerical study.The emphasis was on developing a new numerical methodto overcome the restrictions associated with the conven-tional stiffness method. A numerical method that takes intoaccount the coupling between the rigidities of the piles, thecap, and the column has been developed for analyzing theresponse of piled piers, taking account of soil nonlinearity,group effects, and the flexible pile cap.In this study, the pile cap was modeled with four-nodeflat shell elements, the pier with three-dimensional beamelements, the piles with beam-column elements, and the soilwith nonlinear load transfer curves. A nonlinear analysisalgorithm using a mixed incremental and iterative technique was proposed. The proposed method for piledpiers subjected to both axial and lateral loads was verifiedby comparing the results with other numerical methods.The conceptual methodology of the present method iscompletely different from that of general structural modelsand the stiffness method. The present method predicts wellthe general trend for pile groups, even though piles aremodeled in a simple way by using pile head stiffness matri-ces. To investigate the effects of the flexibility of the pile capon the design parameters of piled piers subjected to lateralloads, parametric studies have been conducted by the pres-ent method. From the findings of this study, the followingconclusions have been drawn:1.
The present method, based on a combination of pilehead stiffnesses for inpidual piles and finite elementmodels for the cap–pier structure, is intermediate incomplexity and theoretical accuracy between generalthree-dimensional structural models (FBPier 3.0,SAP2000, etc.) and the conventional stiffness method(Group 6.0). The lateral displacement obtained by thepresent method is similar to that obtained by the dis-placement method and Group 6.0, while it shows smal-ler values than those obtained by FBPier 3.0 owing to itsdifferent modeling methods; the overall agreementappears to be satisfactory.2. The flexibility of the pile cap affects inpidual pile headforces significantly and affects the bending moments andshear forces in inpidual piles as well, even though thedisplacement of the pile cap does not vary much. Fromparametric studies, it has been found that the presentmethod predicts well the changes in the bendingmoments and shear forces in inpidual piles and thechanges in the stresses in the pile cap when the flexibilityof the pile cap is varied.3. From comparative studies, it has been found that themaximum load on the inpidual piles in a group ishighly influenced by the flexibility of the pile cap. Theprediction of the present method is much more conser-vative than that of FBPier 3.0 and thus represents a def-initely larger lateral load and bending moment forvarious cap thicknesses.4. The present method, when used in nonlinear analysis, isuseful for predicting the displacement of a superstruc-ture such as a pier, taking account of soil nonlinearity,the flexibility of the pile cap, and the pile arrangement,since the pile cap and the pier are modeled as finiteelements.References[1] Bogard D, Matlock H. Procedures for analysis of laterally loaded pilegroups in soft clay. In: Proceedings, specialty conference of geotech-nical engineering in offshore practice, ASCE, 1983. p. 499–535.[2] Ooi PSK, Duncan JM. Lateral load analysis of groups of piles anddrilled shaft. J Geotechn Geoenviron Eng, ASCE 1994;120(6):1034–50.[3] Brown D, Morrison C, Reese LC. Lateral load behavior of pile groupin sand. J Geotech Eng, ASCE 1988;114(11):1261–76.[4] Mokwa RL, Duncan JM. Investigation of the resistance of pile capsand integral abutments to lateral loading. Research report submittedto the Virginia Transportation Research Council, Report No. VTRC00-CR4, Charlottesville, VA, 2000.[5] Ooi PSK, Chang BKF, Wang S. Simplified lateral analyses of fixed-head piles and pile groups. J Geotechn Geoenviron Eng, ASCE2004;130(11):1140–51.[6] Poulos HG. Behavior of laterally loaded piles. II: pile groups. J SoilMech Found Div, ASCE 1971;97(5):733–51.[7] Randolph MF. 考虑桩帽柔性的群桩阵列英文文献和中文翻译(7):http://www.751com.cn/fanyi/lunwen_56444.html