4.1 Strain response of the pile
The fibre Bragg gratings (FBGs) were arranged on two opposite lateral surfaces of piles. Measuring-point numbers are shown in Fig. 5A. Based on the measured strains at each measuring point of the pile, according to Eq. 1, the bending moment at each measuring point of the pile can be calculated as
$$M=\frac{{EI({\varepsilon _t} - {\varepsilon _c})}}{d}$$
1
,
where EI is the bending rigidity of the pile, d is the side length of the square pile, and \({\varepsilon _t}\) and \({\varepsilon _c}\) are the measured strains of the FBGs on two opposite lateral surfaces of the pile at the same depth. In this study, the bending moment with the tension on the right side of the pile is defined as positive, whereas the tension on the left side of the pile is negative. Figure 12 shows the measured strain-response time-history curves at each measuring point on the lateral surfaces of the middle pile.
As shown in Fig. 12, the strain responses of the middle pile indicate that a residual deformation of the pile was found at most of the measuring points, whether the input PGA was 0.1 g or 0.2 g. Especially, when the input PGA is 0.2 g, the dynamic cumulative strains at the top of the pile (E5-1 and E5-2) present a rapid unidirectional accumulation trend after the main vibration stage of the input ground motion. According to the limiting compress strain of the micro-concrete (about 1µε) (Liu et al., 2021) and the pile physical condition after the test, the pile should not be damaged by itself concrete. However, the large lateral residual deformation of the pile can be induced by the unrecovered lateral deformation of the liquefied soil foundation under the pile cap.
As depicted in Fig. 13A, when the input PGA was 0.1 g (non-liquefied foundation) and the bending moment at the top end of the middle pile reached its maximum value, the bending-moment amplitude at the top end of the middle pile was positive, and the negative bending moment at the middle-upper part of the pile was the largest (point E6). As shown in Fig. 13B, the changing pattern of the bending moment amplitude from top to bottom of the pile increased and then decreased, and the maximal amplitude took place at the middle-upper part of the pile.
When the input PGA was 0.2 g (liquefied foundation), as shown in Fig. 13A, the bending-moment amplitude at the top end of the pile changed from a positive bending moment to a negative one, and the absolute value of its amplitude increased approximately 6.2 times the absolute value with an input PGA of 0.1 g. As shown in Fig. 13B, in this test condition, the bending moment amplitude decreased from from top to the middle-upper part of the pile, and then increased at point E7 where is near to the inerface between the liquefied soil layer and the under clay soil layer.At last, the bending moment amplitude decreased to the mimimum value at the bottom end of the pile.
To further analyse the strain responses of piles at different positions after the soil foundation liquefied, a comparison between the strain responses of the corner pile and that of the middle pile is shown in Fig. 14. Because the variation laws of the strain response with an input PGA of 0.1 g were consistent with those of the input PGA of 0.2 g, the relevant results are not given in this paper. The strain-response amplitude at the top end of the corner pile was significantly smaller than that of the middle pile, while the strain responses of the corner pile were significantly greater than those of the middle pile at its middle and lower bodies. This phenomenon indicates that the middle body of the corner pile and the top end of the middle pile are more prone to seismic damage under soil liquefaction. The seismic responses of the pile group on the liquefied soil foundation by the numerical modelling of Liu et al. also showed that the bending-moment responses of piles at different positions were different (Liu et al., 2015). In general, the moment response amplitude of the corner pile was the largest, while that of the middle pile was the smallest before the soil foundation liquefied. Meanwhile, the maximum bending moment of the middle pile appears at its top end, and the maximal moment amplitude of the corner pile appeared at the adjacent interace between the non-liquefied soil layer and the liquefied soil layer.
Based on the analysis of above-mentioned test results, soil liquefaction should be one of the main factors that induce a significant increase in the bending-moment amplitude at the top end of the pile under a base-isolated structure. Existing studies (Dou et al., 2021) and this test all found that the lateral displacement of the soil layer at the top end of the pile increased significantly during the foundation liquefaction, as shown in Fig. 10, which further increased the bending moment response of the pile. However, compared with the existing test results and the numerical simulation on the seismic response of the pile under an non-isolated structure (Liu et al., 2015), after the soil foundation liquefied, the bending moment amplitude at the top end of the pile under the base-isolated structure increased more violently, which was much larger than those at the middle and lower bodies of the pile. As a result, when the soil foundation is liquefied, the pile under a base-isolated structure are more apt to be damaged than those under a non-isolated structure. Except the large lateral deformation of the liquefied soil layer, the rotation response of the base-isolated structure analysed in the following Section 5.1 should be another main factor inducing the great increase on the seismic response of the pile under the isolated structure.
4.2 Displacement response of the pile foundation
Laser-displacement meter HD3 was placed on the pile cap to record its horizontal displacement. Because of the large horizontal stiffness of the pile cap, its motion can be regarded as rigid, and the horizontal displacement at the top end of the pile can be obtained from the measured displacement at measuring point HD3.
The time-history curves of the horizontal displacement under different input PGAs are shown in Fig. 15. It can be seen that, when the input PGA was 0.1 g, the horizontal displacement amplitude at the top end of the pile was very small, with a maximum displacement of 7.4 mm. When the input PGA increased to 0.2 g, the horizontal displacement amplitude at the top end of the pile increased significantly to 26.5 mm. The horizontal displacement after the foundation liquefied was 3.6 times that before the foundation liquefied, which was mainly induced by the lateral spreading deformation of the liquefied soil layer.
4.3 Rotation response of the pile cap
It has been proven that the pile cap on the soft soil foundation has a large rotation response, which has a significant influence on the seismic performance of the isolated structure (Zhuang et al., 2014 and 2019). In this test, as shown in Fig. 5, vertical accelerometers VA1–VA4 were arranged on the top surface of the pile cap and the plate on the seismic isolation layer, respectively. Then, the angular acceleration of the pile cap \(\theta _{1}^{{''}}\) is calculated according to Eq. 2, from reference Huang et al. (2020), as
$$\theta _{1}^{{''}}=\frac{{V_{1}^{{''}}+V_{2}^{{''}}}}{{{L_1}}}$$
2
,
where L1 is the distance between measuring points VA1 and VA2, and \(V_{1}^{{''}}\) and \(V_{2}^{{''}}\) are the measured vertical accelerations at measuring points VA1 and VA2, respectively. Based on the above method, the angular acceleration responses of the pile cap were obtained, as shown in Fig. 16.
The peak values of \(\theta _{1}^{{''}}\) are given in Table 3, and compared with previous test results for different non-liquefied soil foundations. When the input PGA was 0.1 g, the angular acceleration response of the pile cap was relatively smaller, which was between those of the soft soil foundation (Zhuang et al., 2019) and the hard soil foundation (Zhuang et al., 2014). The reason is that the liquefiable foundation in this study was composed of loose sand soil by the “rain sink method,” while the soft soil foundation and the hard foundation adopted a saturated soft clay foundation (Zhuang et al., 2019) by the “rain sink method” and unsaturated compacted sand (Zhuang et al., 2014), respectively. The flexibility of the liquefiable soil foundation in this test should be between that of the soft soil foundation and the hard soil foundation. Therefore, the angular acceleration amplitude of the pile cap was also between the above two different soil foundations.
Owing to the liquefaction of the soil foundation, when the input PGA was 0.2 g, the pile foundation and the isolated structure underwent significant swaying seismic responses, and the peak value of \(\theta _{1}^{{''}}\) increased by approximately 170 times that before the foundation liquefied. The above analysis indicates that the rotational response of the pile cap was significantly aggravated by the liquefied foundation, which can greatly increase the dynamic bending moment response of the piles under the base-isolated structure.
Table 3
Angular acceleration amplitudes of the pile cap
Input PGA | Rigid foundation | Hard soil ground | Soft soil ground | Liquefied foundation |
0.1 g | 0.0006 | 0.0079 | 0.347 | 0.162 |
0.2 g | 0.0008 | 0.0182 | 0.821 | 27.69 |