Dynamic ultimate strength for circular tube pile stiffened at pile head based on centrifuge tests of superstructure-pile-liquefied soil system

In our previous paper, centrifuge tests of superstructure-pile-liquefied soil systems have been conducted, and dynamic ultimate mechanism of steel piles subjected to the vertical force and horizontal force in the liquefied soil was clarified. It is shown that piles' ultimate strength was estimated using the M-N interaction curves. In the other hand, for real structures, reinforced concrete is filled at a pile head to fix a connection between steel piles and a reinforced concrete footing beam. It is considered that the flexural buckling length of steel piles becomes shortened because pile head filled with concrete acts as the rigid body. In this paper, centrifuge tests of superstructure-pile-liquefied soil systems are conducted to compare the dynamic ultimate mechanism of steel piles reinforced at pile heads with that of non-stiffened ones. Subsequently, piles' ultimate strength is estimated using M-N interaction curves with pile's equivalent buckling slenderness ratio. Figure 1 shows a specimen of centrifuge tests. The specimen is configured by a superstructure represented consisting of a mass and a pair of spring elements, four piles and a saturated sand layer. In this paper, an aluminum cross section member is inserted into the pile head of a specimen to reproduce a real pile reinforced filled with concrete at the pile head. In Case 1, the pile cap is laterally fixed, and then only varying axial force acts on the piles. In Case 2, the pile cap can laterally move, and the vertical and horizontal forces act on the piles. The centrifuge tests were performed under centrifugal acceleration 40 g. Figures 7 and 8 show the response time histories of Case 1 specimens and table 5 shows the pile's maximum axial force. It is shown that the bucking strength becomes larger as reinforcement length at the pile head is longer. Figures 14 and 15 show the response time histories of Case 2 specimens. For all Case 2 specimens, the bending strain increased immediately after soil liquefied. For specimens of Case 1, the dynamic buckling strength of piles is evaluated. Figure 13 shows the relationship between observed pile's dynamic buckling strength subjected to only vertical load and buckling curves for Japanese limit state design of steel structures and Japanese design standard for steel structures. Here, the equivalent slenderness ratio is calculated by the ratio of pile's elastic flexural buckling load to the yield load. For a pile reinforced at the pile head, elastic flexural buckling load developed by the energy method in Section 3.3 is applied. The buckling curve of Japanese recommendations for limit state design of steel structures is lower bound of flexural buckling strength of piles in the liquefied soil. As the results, it is shown that the buckling stress curve with the equivalent slenderness ratio can be applied to estimate flexural buckling stress of pile reinforced at the pile head. Next, for piles subjected to lateral and vertical forces, ultimate strength is evaluated using Japanese current design criteria. Figure 19 shows the relationship between ultimate strength of piles on centrifuge tests and the M-N interaction curves for the design criteria. The axial force of piles is divided by elastic-plastic buckling stress of piles obtained from buckling curve of Japanese recommendations for limit state design of steel structures as shown in Fig. 13, and the bending moment at the maximum bending strain position is divided by the full plastic moment of piles. It is shown that the M-N interaction curves of Japanese recommendations for design of building foundation is lower bound of pile's ultimate strength in the liquefied soil at the maximum bending strain.