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The reason for the different lat-eral displacements in these cases of lateral loading isthought to be the difference in the modeling method forinpidual piles, as previously mentioned. Sudden changesin both the tensile displacement in pile A and the settlementin pile B occurred at a lateral load of 100 kN in loose sandand at 300 kN in medium sand, as shown in Fig. 10(c) and(d). The reason is that the tensile displacement increasessuddenly as the skin friction reaches its ultimate level.The results of an analysis of a piled pier under pinnedconditions are shown in Fig. 11 together with the resultsfor fixed head conditions in dense sand. At the pier top,the lateral displacement obtained under pinned condi-tions is somewhat larger than that for fixed head condi-tion. At a lateral load of 550 kN, yielding occurs andthen the displacement increases suddenly. This is causedby a sudden increase in the tensile displacement of pileA, as shown in Fig. 11(c). The lateral displacement ofpile head A is estimated to be smaller under pinned con-ditions than under fixed head conditions. From thesepiled pier analyses, it was concluded that the overallbehavior of a piled pier is affected significantly by thepile head condition.Fig. 12 shows the profiles of the bending moment and theshear force on a piled pier in dense sand, subjected to com-bined external loads (V = 3000 kN and H = 500 kN) at thepier top. The bending moments and shear forces calculatedby the present method and by FBPier 3.0 show differencesbetween the leading row and the trailing row near the pilehead. The differences in the bending moment and shearforce near the pile head compared with the results fromGroup 6.0 are caused by the effect of the local bending stressand membrane horizontal stress in the pile cap. 4. The effect of pile cap flexibilityFor the design of flexible base structures in which therelative difference between the stiffnesses of the pile capand the piles is small, and thus bending of the cap isexpected, use of the correct stiffness relationship betweenthe cap and the piles is extremely important for accuratelydesigning a pile group [16]. For this reason, considerationof the flexibility of the pile cap is needed in the design ofstructures that include large diameter piles.In this study, a pile group supported column (a piledpier) with large diameter piles (D = 1.5 m), as shown inFig. 13, was analyzed by the present method. To investigatethe effect of pile cap flexibility, the results predicted by thepresent method have been compared with results obtainedby the displacement method, which assumes that a pile capis a rigid body. 4.1. Problem descriptionA total of four piles are arranged in a 2 · 2 pattern andthe center-to-center spacing of the piles is three times thepile diameter D (=1.5 m). One pier is located at the centerof the pile cap. External forces are applied at the top of thepier, namely a vertical load V0 = 17,585 kN and a lateralload H0 = 938 kN. No torsional load is considered. Thethickness of the pile cap is 2 m and the pile cap is locatedabove the ground surface, so that the soil reaction beneaththe cap can be ignored. The connection between the pileand the cap is a fixed condition. The SPT-N value of thehomogeneous soil is 6, and the modulus of the lateral subgrade reaction kh is 0.974 kg/cm3, obtained by using anempirical equation suggested by the Korea Specificationfor Bridges [27]. The p-multiplier is set to one to allow com-parison with the results of the displacement method and toinvestigate the pile–cap interaction rather than the interac-tion between piles, although in this configuration (s/D =3)a reduction of the soil reaction is expected.
The pile headstiffness (c1 c5) calculated by the load transfer methodusing the present method is presented in Table 2 (case 2).In the displacement method, the calculated pile head stiff-ness was used.4.2. Pile cap displacementFig. 14 shows the distribution of the settlement of thepile cap. A larger settlement was estimated on the right-hand side of the pile cap owing to the effect of the lateralload. The settlements at both edges were similar for thetwo methods, but a somewhat larger value was calculatedby the present method at the center of the cap. Fig. 15shows the three-dimensional deformed shape of the pilecap, calculated by the present method. It is drawn with a200 times enlarged scale of the displacement for better vis-ibility of the deformed shape. The center point, at whichthe pier is located, has sunk, not only in the x–z planebut also in the y–z plane. The displacement added by thedeformation of the pile cap is smaller than that caused bythe movement of the pile cap. However, it is importantto consider the effects of the flexibility of the pile cap forcorrect estimation of the inpidual forces on the pileheads.4.3. Stress in the pile capIn general, the magnitude and the distribution of stres-ses are important parameters for the design of a pile cap.The stiffness method (displacement method, Group 6.0,etc.), in which the pile cap is assumed to be a rigid body,cannot estimate the stress in a pile cap. However, in thepresent method, using a flat-shell element, the stress in apile cap can be calculated at the integration points.Fig.