*4.2. Acceleration Response*

**Table 4.** Comparison of peak excess pore pressure ratios. **Shaking Intensity Sand Type P1 P2 P3 P4 P5 P6 P7 P8** 0.1 g Coral sand 0.06 0.04 0.04 0.03 0.08 0.04 0.04 0.03 Fujian sand 0.07 0.06 0.05 Lost 0.09 0.06 0.04 0.04 0.2 g Coral sand 0.94 0.68 0.62 0.5 1.1 0.72 0.59 0.54 Fujian sand 1.2 1.09 0.98 Lost 1.5 1.24 1.12 0.81 Figure 9 shows the acceleration time history curves of the coral sand and Fujian sand site. Under 0.1 g shaking intensity, the shape of acceleration time history curves of two kinds of sand sites was similar to that of the input sinusoidal wave excitation, which indicated that the soil was basically in an elastic state, and there was a near-linear amplification effect on the input sinusoidal wave excitation. The acceleration amplification factors got larger when the depth decreased, as shown in Figure 10. The acceleration amplification factors of coral sand were less than that of Fujian sand, which were approximately 0.54–0.90 times of that of Fujian sand. The difference of peak values of the acceleration between two kinds of sand sites was the greatest at the A1 position and the smallest at the A3 position. *J. Mar. Sci. Eng.* **2020**, *8*, 189 10 of 17

**Figure 9.** Acceleration time history curves: (**a**) A1 position under 0.1 g intensity; (**b**) A2 position under 0.1 g intensity; (**c**) A3 position under 0.1 g intensity; (**d**) A1 position under 0.2 g intensity; (**e**) A2 position under 0.2 g intensity; and, (**f**) A3 position under 0.2 g intensity. **Figure 9.** Acceleration time history curves: (**a**) A1 position under 0.1 g intensity; (**b**) A2 position under 0.1 g intensity; (**c**) A3 position under 0.1 g intensity; (**d**) A1 position under 0.2 g intensity; (**e**) A2 position under 0.2 g intensity; and, (**f**) A3 position under 0.2 g intensity.

**Figure 10.** Acceleration amplification factors at different depth.

Depth (mm)

Under 0.2 g shaking intensity, the acceleration of Fujian sand gradually increased with time, reaching peak values at about 4.5 s, and then suddenly decreased. The acceleration change of coral sand with time was not that obvious, like Fujian sand. The shape of time history curves of coral sand was basically similar to that of input sinusoidal wave excitation. The difference of shape of acceleration time history curves between coral sand and Fujian sand was due to the liquefaction of the Fujian sand site. The shear strength of Fujian sand site sharply decreased, and the soil had an obvious attenuation effect on input acceleration excitation with the onset of liquefaction. The coral sand site was in a high pore pressure state at this time, but there was no obvious liquefaction phenomenon, the attenuation effect of soil on input acceleration was less obvious than that of Fujian sand. Figure 10 shows acceleration amplification factors at different depths of two kinds of sand sites. Acceleration amplification factors increased with the decrease of depth, which is consist with the acceleration response of general liquefaction sites. The acceleration amplification factors of coral sand were less than that of Fujian sand, which were approximately 0.79–0.90 times of that of Fujian sand. Figure 11 shows the spectrum analysis with a damping ratio of 0.05 for the white noise at the A1 position. The dominant frequencies of the coral sand and Fujian sand sites were 10 Hz before the sinusoidal wave excitation, and the spectrum distribution of two kinds of sand sites was similar, which indicated that the initial state of two kinds of sand sites was close. After 0.2 g sinusoidal wave

0.8 1.2 1.6 2.0 2.4

Acceleration amplification factor

 0.1 g, Coral sand 0.1 g, Fujian sand 0.2 g, Coral sand 0.2 g, Fujian sand

*4.3. Displacement Response* 

the Fujian sand site.

**Figure 9.** Acceleration time history curves: (**a**) A1 position under 0.1 g intensity; (**b**) A2 position under

position under 0.2 g intensity; and, (**f**) A3 position under 0.2 g intensity.

**Figure 10.** Acceleration amplification factors at different depth. **Figure 10.** Acceleration amplification factors at different depth.

Under 0.2 g shaking intensity, the acceleration of Fujian sand gradually increased with time, reaching peak values at about 4.5 s, and then suddenly decreased. The acceleration change of coral sand with time was not that obvious, like Fujian sand. The shape of time history curves of coral sand was basically similar to that of input sinusoidal wave excitation. The difference of shape of acceleration time history curves between coral sand and Fujian sand was due to the liquefaction of the Fujian sand site. The shear strength of Fujian sand site sharply decreased, and the soil had an obvious attenuation effect on input acceleration excitation with the onset of liquefaction. The coral sand site was in a high pore pressure state at this time, but there was no obvious liquefaction phenomenon, the attenuation effect of soil on input acceleration was less obvious than that of Fujian sand. Figure 10 shows acceleration amplification factors at different depths of two kinds of sand sites. Acceleration amplification factors increased with the decrease of depth, which is consist with the acceleration response of general liquefaction sites. The acceleration amplification factors of coral sand were less than that of Fujian sand, which were approximately 0.79–0.90 times of that of Fujian sand. Under 0.2 g shaking intensity, the acceleration of Fujian sand gradually increased with time, reaching peak values at about 4.5 s, and then suddenly decreased. The acceleration change of coral sand with time was not that obvious, like Fujian sand. The shape of time history curves of coral sand was basically similar to that of input sinusoidal wave excitation. The difference of shape of acceleration time history curves between coral sand and Fujian sand was due to the liquefaction of the Fujian sand site. The shear strength of Fujian sand site sharply decreased, and the soil had an obvious attenuation effect on input acceleration excitation with the onset of liquefaction. The coral sand site was in a high pore pressure state at this time, but there was no obvious liquefaction phenomenon, the attenuation effect of soil on input acceleration was less obvious than that of Fujian sand. Figure 10 shows acceleration amplification factors at different depths of two kinds of sand sites. Acceleration amplification factors increased with the decrease of depth, which is consist with the acceleration response of general liquefaction sites. The acceleration amplification factors of coral sand were less than that of Fujian sand, which were approximately 0.79–0.90 times of that of Fujian sand.

Figure 11 shows the spectrum analysis with a damping ratio of 0.05 for the white noise at the A1 position. The dominant frequencies of the coral sand and Fujian sand sites were 10 Hz before the sinusoidal wave excitation, and the spectrum distribution of two kinds of sand sites was similar, which indicated that the initial state of two kinds of sand sites was close. After 0.2 g sinusoidal wave Figure 11 shows the spectrum analysis with a damping ratio of 0.05 for the white noise at the A1 position. The dominant frequencies of the coral sand and Fujian sand sites were 10 Hz before the sinusoidal wave excitation, and the spectrum distribution of two kinds of sand sites was similar, which indicated that the initial state of two kinds of sand sites was close. After 0.2 g sinusoidal wave excitation, the high frequency component attenuation and low frequency component amplification occurred in both coral sand and Fujian sand sites although the dominant frequency of the two kinds of sand sites were still 10 Hz, which illustrated that the two kinds of sand sites had softened and the stiffness of model foundation was reduced when compared with the initial state. *J. Mar. Sci. Eng.* **2020**, *8*, 189 11 of 17 excitation, the high frequency component attenuation and low frequency component amplification occurred in both coral sand and Fujian sand sites although the dominant frequency of the two kinds of sand sites were still 10 Hz, which illustrated that the two kinds of sand sites had softened and the stiffness of model foundation was reduced when compared with the initial state.

**Figure 11.** Fourier analysis of white noise: (**a**) coral sand; and, (**b**) Fujian sand. **Figure 11.** Fourier analysis of white noise: (**a**) coral sand; and, (**b**) Fujian sand.

oscillation amplitude of buildings in the two kinds of sand sites was basically similar with time. Both of the building horizontal displacements of coral sand and Fujian sand experienced a rapid increase in a short time (about 1.5 s) and remained stable. The variation law of building oscillation amplitude with time was consistent with the input sinusoidal wave excitation. At this time, there was no liquefaction in the two kinds of sand sites, no obvious reduction of soil stiffness and shear strength, and the horizontal displacement oscillation amplitude of the building changed with the input sinusoidal wave excitation. When the shaking ended, the horizontal displacement of building in coral sand site was 0.02 mm, and that in the Fujian sand site was 0.22 mm. The horizontal displacement in coral sand site was less than that in Fujian sand site, which was approximately 0.09 times of that in

(**a**) 0.1 g shaking intensity

sand site.

times of that in the Fujian sand site.

### *4.3. Displacement Response 4.3. Displacement Response*  Figure 12 shows the horizontal displacement time history curves of buildings in coral sand and

Figure 12 shows the horizontal displacement time history curves of buildings in coral sand and Fujian sand sites. Under 0.1 g shaking intensity, the variation law of horizontal displacement oscillation amplitude of buildings in the two kinds of sand sites was basically similar with time. Both of the building horizontal displacements of coral sand and Fujian sand experienced a rapid increase in a short time (about 1.5 s) and remained stable. The variation law of building oscillation amplitude with time was consistent with the input sinusoidal wave excitation. At this time, there was no liquefaction in the two kinds of sand sites, no obvious reduction of soil stiffness and shear strength, and the horizontal displacement oscillation amplitude of the building changed with the input sinusoidal wave excitation. When the shaking ended, the horizontal displacement of building in coral sand site was 0.02 mm, and that in the Fujian sand site was 0.22 mm. The horizontal displacement in coral sand site was less than that in Fujian sand site, which was approximately 0.09 times of that in the Fujian sand site. Fujian sand sites. Under 0.1 g shaking intensity, the variation law of horizontal displacement oscillation amplitude of buildings in the two kinds of sand sites was basically similar with time. Both of the building horizontal displacements of coral sand and Fujian sand experienced a rapid increase in a short time (about 1.5 s) and remained stable. The variation law of building oscillation amplitude with time was consistent with the input sinusoidal wave excitation. At this time, there was no liquefaction in the two kinds of sand sites, no obvious reduction of soil stiffness and shear strength, and the horizontal displacement oscillation amplitude of the building changed with the input sinusoidal wave excitation. When the shaking ended, the horizontal displacement of building in coral sand site was 0.02 mm, and that in the Fujian sand site was 0.22 mm. The horizontal displacement in coral sand site was less than that in Fujian sand site, which was approximately 0.09 times of that in the Fujian sand site.

(**a**) (**b**)

*J. Mar. Sci. Eng.* **2020**, *8*, 189 11 of 17

excitation, the high frequency component attenuation and low frequency component amplification occurred in both coral sand and Fujian sand sites although the dominant frequency of the two kinds of sand sites were still 10 Hz, which illustrated that the two kinds of sand sites had softened and the

stiffness of model foundation was reduced when compared with the initial state.

**Figure 12.** Horizontal displacement time history curves of building. **Figure 12.** Horizontal displacement time history curves of building.

The horizontal displacement of buildings in the two kinds of sand sites changed with time similarly under 0.2 g shaking intensity, while the horizontal displacement oscillation amplitude in the coral sand site was obviously smaller than that in the Fujian sand site. The horizontal displacement oscillation amplitude in the two kinds of sand sites decreased abruptly at around 4.8 s, at this moment, the excess pore pressure ratio reached its peak value (Figure 8). The coral sand site was in high pore pressure state, and the research of Chen et al. [37] showed that the soil under that condition exhibited shear thinning non-Newtonian fluid characteristics, even if the soil did not The horizontal displacement of buildings in the two kinds of sand sites changed with time similarly under 0.2 g shaking intensity, while the horizontal displacement oscillation amplitude in the coral sand site was obviously smaller than that in the Fujian sand site. The horizontal displacement oscillation amplitude in the two kinds of sand sites decreased abruptly at around 4.8 s, at this moment, the excess pore pressure ratio reached its peak value (Figure 8). The coral sand site was in high pore pressure state, and the research of Chen et al. [37] showed that the soil under that condition exhibited shear thinning non-Newtonian fluid characteristics, even if the soil did not liquefy, so the attenuation

liquefaction. When shaking ended, the horizontal displacement of building in coral sand site was 0.53 mm, and that in Fujian sand site was 2.96 mm. The horizontal displacement of building in coral sand site was less than that in Fujian sand site, which was approximately 0.18 times of that in the Fujian

Figure 13 shows the horizontal displacement time history curves of buildings in coral sand and Fujian sand sites. Under 0.1 g shaking intensity, the building settlement in two kinds of sand sites increased slowly with time. The building settlement in coral sand site was 0.07 mm, which in the Fujian sand site was 0.43 mm. The building settlement in coral sand site was less than that in the Fujian sand site, which was about 0.16 times of that in Fujian sand site. Under 0.2 g shaking intensity, the building settlement in coral sand site increased linearly with time. The building settlement development trend in the Fujian sand site was similar to that in coral sand site within 4.8 s from the beginning of shaking, while the building settlement rate in Fujian sand site suddenly increased at 4.8 s, when compared with the results of the excess pore pressure ratio of Fujian sand, as illustrated in Figure 8, it could be seen that the excess pore pressure ratio of Fujian sand reached 1 at this time and the soil was in the initial liquefaction state. The effective stress between the soil particles of Fujian sand was close to 0, which led to the soil having almost no shear strength and the bearing capacity of the foundation decreasing, consequently, the building subsided sharply. After shaking, the building settlement in coral sand site was 1.29 mm, which in the Fujian sand site was 7.98 mm. The building settlement in coral sand site was less than that in Fujian sand site, which was approximately 0.16

liquefy, so the attenuation of horizontal displacement oscillation amplitude of buildings was related

of horizontal displacement oscillation amplitude of buildings was related to a certain reduction of soil to input shaking excitation and horizontal force of pile that was caused by stiffness degradation of the coral sand site. The attenuation of building oscillation amplitude in the Fujian sand site was due to the sharp decrease of shear strength of soil that was caused by liquefaction. When shaking ended, the horizontal displacement of building in coral sand site was 0.53 mm, and that in Fujian sand site was 2.96 mm. The horizontal displacement of building in coral sand site was less than that in Fujian sand site, which was approximately 0.18 times of that in the Fujian sand site.

Figure 13 shows the horizontal displacement time history curves of buildings in coral sand and Fujian sand sites. Under 0.1 g shaking intensity, the building settlement in two kinds of sand sites increased slowly with time. The building settlement in coral sand site was 0.07 mm, which in the Fujian sand site was 0.43 mm. The building settlement in coral sand site was less than that in the Fujian sand site, which was about 0.16 times of that in Fujian sand site. Under 0.2 g shaking intensity, the building settlement in coral sand site increased linearly with time. The building settlement development trend in the Fujian sand site was similar to that in coral sand site within 4.8 s from the beginning of shaking, while the building settlement rate in Fujian sand site suddenly increased at 4.8 s, when compared with the results of the excess pore pressure ratio of Fujian sand, as illustrated in Figure 8, it could be seen that the excess pore pressure ratio of Fujian sand reached 1 at this time and the soil was in the initial liquefaction state. The effective stress between the soil particles of Fujian sand was close to 0, which led to the soil having almost no shear strength and the bearing capacity of the foundation decreasing, consequently, the building subsided sharply. After shaking, the building settlement in coral sand site was 1.29 mm, which in the Fujian sand site was 7.98 mm. The building settlement in coral sand site was less than that in Fujian sand site, which was approximately 0.16 times of that in the Fujian sand site. *J. Mar. Sci. Eng.* **2020**, *8*, 189 13 of 17

**Figure 13.** Settlement time history curves of building. **Figure 13.** Settlement time history curves of building.

where *M* is the bending moment, εt and εc 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

( −

ℎ

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

)

(2)

=

*4.4. Dynamic Bending Moment Response*

when the shaking intensity increased.

cross-section piles.

Fujian sand site.

pile.

**5. Summary and Conclusions**

distributions.

The following conclusions are drawn:
