<p>In Japanese Recommendation for Design of Building Foundation, the method to estimate steel pile's ultimate strength in the liquefied soil at pile's collapsing due to the significant earthquake is proposed. However, there are some cases, in which steel piles do not fail and continue to carry the dead load, even though they become plastic due to the previous seismic motion. The ultimate strength of steel piles, which have already accumulated the damage due to the multiple earthquakes, may decrease and the piles may collapse when they experience the subsequent massive earthquake. In this paper, centrifugal tests for the case where piles are subjected to multiple earthquakes are conducted to clarify pile's collapse mechanism in the liquefied soil and pile's ultimate strength. Furthermore, the estimation method of pile's cumulative damage is presented based on results of centrifugal tests and numerical analyses.</p><p>Fig. 1 shows the model and instruments. The specimen consisted of a superstructure and a footing beam with mass, two bending plates, four piles, and a saturated sand layer. Table 2 shows specimen parameters, which are pile's diameter, the relative density of the soil and the height-to-width aspect ratio of the superstructure. The centrifugal tests were performed under the centrifugal acceleration of 40 g.</p><p>Figs. 11(b), (c)-16(b), (c) show response time histories of Case 4. The bending strain at the pile head for the first shaking reached εlc after the soil liquefied and superstructure's inertial force became maximum. The piles became inelastic although they kept their ability to carry the dead load even after shaking. The maximum value of superstructure's acceleration and pile's varying axial force during the second shaking were almost the same as that of first shaking. On the other hand, the bending strain gradually increased and reached the maximum value, εb,max, at 35 s. As shown in Fig. 19, the bending strain exceeded εyc for Case 2, but did not reach it in Case 1, Case 3, and Case 4. For all specimens, the local buckling occurred at the pile head, as well as at the bottom and the center of the pile as presented in Photo 1.</p><p>Fig. 20 shows the relationship between pile's strength on centrifugal tests and the M-N interaction curves of design criteria. For Case 2, Case 5-Case 8, which collapsed during the first shaking, results at εb,max exceeded the M-N interaction curve of Japanese Recommendation for Design of Building Foundation and were distributed roughly following the ultimate strength curve. However, for Case 1, Case 3-Case 4, which collapsed subjected to multiple shaking events, the values at εb,max did not reach the ultimate strength curve and were smaller than those of Case 2, Case 5-Case 8.</p><p>Fig. 21 represents the calculation flow of pile's accumulated plastic strain amplitude, ∑εpa, which is defined as pile's cumulative damage indicator in this paper. Mechanical characteristics' relationships (as shown in Figs. 26(a)-(c)), as well as regression equations (Eqs. (15)-(18)) are obtained based on analysis results of Figs. 22-25. Eq. (19), which is derived from Eqs. (15)-(18), shows the relationship between normalized ∑εpa and plastic deformation capacity μcmax. Fig. 27 describes the comparison between the values of centrifugal tests, numerical analyses, and Eq. (19). It is concluded that the cumulative damage of the steel pile, which collapses subjected to multiple earthquakes, can be evaluated using Eq. (19).</p>
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