*4.4. Dynamic Bending Moment Response*

The bending moment of the column and pile foundation is obtained by the following equation:

$$M = \frac{EI(\varepsilon\_t - \varepsilon\_c)}{h} \tag{2}$$

where *M* is the bending moment, ε*<sup>t</sup>* and ε*<sup>c</sup>* are tensile and compressive strain, respectively, *h* is the length of the section side for square cross-section columns, and *h* is the diameter of the pile for circular cross-section piles.

Figure 14 shows the peak values of the dynamic column bending moments in the coral sand and Fujian sand sites. The dynamic column moments in two kinds of sand sites were the largest at the bottom of column, followed by the second story column, which was consistent with the general law of dynamic moment response of building columns under earthquake. Under 0.1 g shaking intensity, the peak column moments in the coral sand site were smaller than that in the Fujian sand site. From top to bottom (S1–S4), the peak column moments in coral sand site were approximately 0.98, 0.88, 0.82, and 0.98 times of that in Fujian sand site. The peak column moments in the coral sand site were also smaller than that in Fujian sand site under 0.2 g shaking intensity. When compared with 0.1 g shaking intensity, the dynamic column moments in the coral sand site increased by 3.11–3.61 times, and by 4.41-5.93 times in Fujian sand site under 0.2 g shaking intensity. The dynamic moment amplification effect of building columns in coral sand site was smaller than that in Fujian sand site when the shaking intensity increased. *J. Mar. Sci. Eng.* **2020**, *8*, 189 14 of 17

**Figure 14.** Peak column bending moments at different height: (**a**) 0.1 g shaking intensity; and, (**b**) 0.2 g shaking intensity. **Figure 14.** Peak column bending moments at different height: (**a**) 0.1 g shaking intensity; and, (**b**) 0.2 g shaking intensity.

Figure 15 shows the peak values of the dynamic pile moments in coral sand and Fujian sand sites. The dynamic moments of corner pile, edge pile, and center pile similarly varied with buried depth. The peak values of moments were the largest at the top and the smallest at the bottom of pile. When 0.1 g shaking excitation was input, the peak moments of corner piles in coral sand site were less than that in the Fujian sand site, which were approximately 0.69–0.94 times of that in the Fujian sand site. The peak moments of edge piles and center piles in coral sand site were also less than that in Fujian sand site, respectively. When 0.2 g shaking excitation was input, the moments of pile groups in coral sand site were less than that in Fujian sand site, which were about 0.62–0.93 times of that in Figure 15 shows the peak values of the dynamic pile moments in coral sand and Fujian sand sites. The dynamic moments of corner pile, edge pile, and center pile similarly varied with buried depth. The peak values of moments were the largest at the top and the smallest at the bottom of pile. When 0.1 g shaking excitation was input, the peak moments of corner piles in coral sand site were less than that in the Fujian sand site, which were approximately 0.69–0.94 times of that in the Fujian sand site. The peak moments of edge piles and center piles in coral sand site were also less than that in Fujian sand site, respectively. When 0.2 g shaking excitation was input, the moments of pile groups in coral sand site were less than that in Fujian sand site, which were about 0.62–0.93 times of that in Fujian sand site.

**Figure 15.** Peak pile bending moments at different depth: (**a**) corner pile; (**b**) edge pile; and (**c**) center

Shaking table tests of three-story buildings with nine-pile foundation in the coral sand and Fujian sand sites were carried out in this research. The similarities and differences of dynamic responses of coral sand and Fujian sand sites were studied through testing and analyzing the physical quantities, such as pore water pressure, acceleration, displacement, and dynamic bending moment.

1) The peak values of excess pore pressure ratio of coral sand and Fujian sand were far less than 1 under 0.1 g shaking intensity, there was no liquefaction in two kinds of sand sites. The peak values of excess pore pressure ratio of coral sand were basically less than that of Fujian sand,

2) The development rate of excess pore pressure ratio of coral sand was smaller than that of Fujian sand and the peak values of excess pore pressure ratio of coral sand were less than that of Fujian sand, which were about 0.53–0.78 times of that of Fujian sand. The coral sand sites were more difficult to liquefy than Fujian sand sites under the same relative density and similar grain-size

which were approximately 0.67–1.00 times of that of Fujian sand.

g shaking intensity.

**Figure 14.** Peak column bending moments at different height: (**a**) 0.1 g shaking intensity; and, (**b**) 0.2

Figure 15 shows the peak values of the dynamic pile moments in coral sand and Fujian sand sites. The dynamic moments of corner pile, edge pile, and center pile similarly varied with buried depth. The peak values of moments were the largest at the top and the smallest at the bottom of pile. When 0.1 g shaking excitation was input, the peak moments of corner piles in coral sand site were less than that in the Fujian sand site, which were approximately 0.69–0.94 times of that in the Fujian sand site. The peak moments of edge piles and center piles in coral sand site were also less than that in Fujian sand site, respectively. When 0.2 g shaking excitation was input, the moments of pile groups

**Figure 15.** Peak pile bending moments at different depth: (**a**) corner pile; (**b**) edge pile; and (**c**) center **Figure 15.** Peak pile bending moments at different depth: (**a**) corner pile; (**b**) edge pile; and (**c**) center pile.

#### pile. **5. Summary and Conclusions**

**5. Summary and Conclusions** Shaking table tests of three-story buildings with nine-pile foundation in the coral sand and Fujian sand sites were carried out in this research. The similarities and differences of dynamic responses of coral sand and Fujian sand sites were studied through testing and analyzing the physical quantities, such as pore water pressure, acceleration, displacement, and dynamic bending moment. Shaking table tests of three-story buildings with nine-pile foundation in the coral sand and Fujian sand sites were carried out in this research. The similarities and differences of dynamic responses of coral sand and Fujian sand sites were studied through testing and analyzing the physical quantities, such as pore water pressure, acceleration, displacement, and dynamic bending moment. The following conclusions are drawn:


**Author Contributions:** Conceptualization, Q.W. and X.D.; Data curation, Q.W.; Formal analysis, Y.Z.; Funding acquisition, X.D.; Investigation, X.D.; Methodology, Q.W.; Project administration, X.D.; Resources, X.D.; Supervision, X.D.; Validation, Q.W., Y.Z. and Z.C.; Visualization, Y.Z.; Writing—original draft, Q.W.; Writing—review & editing, Z.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China (grant number 51622803, grant number 41831282 and grant number 51878103).

**Acknowledgments:** The authors appreciate the assistant of our group members in the experiments.

**Conflicts of Interest:** The authors declare no conflict of interest.
