**2. Shaking Table Test**

The test was performed using ANCO shaking table, which is sourced from ANCO company, Los Angeles, America. The shaking table can simultaneously carry out horizontal and vertical shaking, with a dimension of 1200 mm × 1200 mm in plane, as shown in Figure 1. The maximum proof model mass, horizontal displacement, and base excitation is 1000 kg, 100 mm, and 2.0 g, respectively. A soil container with size of 950 mm in length, 850 mm in width, and 550 mm in depth was used. The soil container changes from a laminar shear type to a rigid type when the controls at the four corners of the soil container are tightened (Figure 1). Two DHDAS acquisition instruments with 96 channels were used to collect sensor signal data simultaneously in this test. The DHDAS acquisition instruments is sourced from Donghua Testing Technology Co., Ltd., Jingjiang, China.

*J. Mar. Sci. Eng.* **2020**, *8*, 189 3 of 17

(**a**) Shaking table (**b**) Soil container

#### *2.1. Similitude Ratio 2.1. Similitude Ratio*

The geometric similarity ratio is set as 1:40 based on the maximum load of the shaking table and the size of the soil container. According to the Buckingham theory [31,32] and scaling laws [33], length *l*, elastic modulus *E*, and equivalent density *ρ* were chosen as the basic physical quantities. The similarity ratio of elastic modulus *S<sup>E</sup>* is obtained by comparing the elastic modulus of the model building material and the prototype building material. The similarity ratio of equivalent density *S<sup>ρ</sup>* is calculated by equation (1), when the preset acceleration similarity ratio *S<sup>a</sup>* is 1. The other physical quantities, such as time, acceleration, and displacement, were derived based on the similarity relations, as shown in Table 1. The geometric similarity ratio is set as 1:40 based on the maximum load of the shaking table and the size of the soil container. According to the Buckingham theory [31,32] and scaling laws [33], length *l*, elastic modulus *E*, and equivalent density ρ were chosen as the basic physical quantities. The similarity ratio of elastic modulus *S<sup>E</sup>* is obtained by comparing the elastic modulus of the model building material and the prototype building material. The similarity ratio of equivalent density *S*<sup>ρ</sup> is calculated by Equation (1), when the preset acceleration similarity ratio *S<sup>a</sup>* is 1. The other physical quantities, such as time, acceleration, and displacement, were derived based on the similarity relations, as shown in Table 1.

$$\mathcal{S}\_{d} = \frac{\mathcal{S}\_{E}}{\mathcal{S}\_{\rho} \cdot \mathcal{S}\_{l}} \tag{1}$$


**Table 1.** Similitude laws of shaking table test.

#### Linear displacement *r Sr=S<sup>l</sup>* 1:40 *2.2. Preparation of the Model*

*2.2. Preparation of the Model*  The soil container was separated into two halves along the orientation of shaking, half of which was for preparing the coral sand foundation and the other half was for preparing Fujian sand foundation. The rigid soil container was used in the test to prevent the two sands from interacting with each other. Relatively compressible foam cushions with thicknesses of 100 mm were attached to the inner walls of the soil container perpendicular to the shaking direction to reduce the energy that was reflected by the container. The foam was made of polystyrene. The density, water absorption, and compressive strength of the foam were 30 kg·m−<sup>3</sup> , 1%, and 150 kPa. A foam board was installed at the middle of the soil container to prevent the mix of the two kinds of sands. Coral sand that was The soil container was separated into two halves along the orientation of shaking, half of which was for preparing the coral sand foundation and the other half was for preparing Fujian sand foundation. The rigid soil container was used in the test to prevent the two sands from interacting with each other. Relatively compressible foam cushions with thicknesses of 100 mm were attached to the inner walls of the soil container perpendicular to the shaking direction to reduce the energy that was reflected by the container. The foam was made of polystyrene. The density, water absorption, and compressive strength of the foam were 30 kg·m−<sup>3</sup> , 1%, and 150 kPa. A foam board was installed at the middle of the soil container to prevent the mix of the two kinds of sands. Coral sand that was used in the test was taken from a reef in the South China Sea, and the quartz sand used was Fujian standard sand.

Figure 2 presents the grain-size distribution of the two kinds of sands, which shows that the grain-size distributions of the two kinds of sands are similar. Table 2 illustrates the basic physical parameters of the two kinds of sands. standard sand. Figure 2 presents the grain-size distribution of the two kinds of sands, which shows that the grain-size distributions of the two kinds of sands are similar. Table 2 illustrates the basic physical parameters of the two kinds of sands.

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**Figure 2.** Grain-size distribution curves of coral sand and Fujian sand. **Figure 2.** Grain-size distribution curves of coral sand and Fujian sand.

**Table 2.** Physical properties of sand. **Table 2.** Physical properties of sand.


The model foundation consisted of two parts along the vertical direction, above and below the water level. The soil layer below the water level was prepared while using the water sedimentation method. The water surface is about 10 cm above the sand surface throughout the process. The main factor affecting the relative density of the model foundation that was prepared by the water sedimentation method is the fall distance [34]. The two kinds of sands fall to the water surface at the same height during sample preparation, and other influencing factors, such as the speed and flow of the sand ejection head, should be consistent, in order to make the relative density of the coral sand and quartz sand sites approximately the same. During the preparation of the model foundation, a calibrated aluminum box was used for sampling analysis in time to ensure that the uniformity and relative density of the two sand model foundations were approximately similar. The soil layer above the water level with a thickness of 30 mm was prepared to keep consistent with the actual engineering situation. The relative density of the whole model foundation is 0.67. The model foundation consisted of two parts along the vertical direction, above and below the water level. The soil layer below the water level was prepared while using the water sedimentation method. The water surface is about 10 cm above the sand surface throughout the process. The main factor affecting the relative density of the model foundation that was prepared by the water sedimentation method is the fall distance [34]. The two kinds of sands fall to the water surface at the same height during sample preparation, and other influencing factors, such as the speed and flow of the sand ejection head, should be consistent, in order to make the relative density of the coral sand and quartz sand sites approximately the same. During the preparation of the model foundation, a calibrated aluminum box was used for sampling analysis in time to ensure that the uniformity and relative density of the two sand model foundations were approximately similar. The soil layer above the water level with a thickness of 30 mm was prepared to keep consistent with the actual engineering situation. The relative density of the whole model foundation is 0.67.

The prototype of the structures were three-story concrete frame buildings with a nine-pile foundation. The buildings are used to store large equipment and heavy machinery on coral sand sites. The organic glass was selected to prepare the model buildings and piles, because the geometric dimensions of the model building were too small after shrinking according to the similar law and there were practical operation difficulties in concrete pouring. The three-story model building with side length of 180 mm, net height of 100 mm for the bottom floor, and 90 mm for the other floors is made of organic glass, as shown in Figure 3. The organic glass plates with the thickness of 5 mm were used as slabs, under which rectangular organic glass bars with geometry of 5 mm × 5 mm × 160 mm were installed to simulate the beam. The cross-sectional dimension of the model column was 10 mm × 10 mm, and the outer edge of which was leveled with the outer edge of the model beam. The geometry of the model raft was 220 mm in length and 15 mm in thickness. The diameter and length of the model pile were 20 mm and 400 mm, respectively. The organic glass can be changed into liquid state by dropping acetone on it. Each component of the model building was dissolved in order to connect by the special adhesive of organic glass. In the connection process, the verticality among the The prototype of the structures were three-story concrete frame buildings with a nine-pile foundation. The buildings are used to store large equipment and heavy machinery on coral sand sites. The organic glass was selected to prepare the model buildings and piles, because the geometric dimensions of the model building were too small after shrinking according to the similar law and there were practical operation difficulties in concrete pouring. The three-story model building with side length of 180 mm, net height of 100 mm for the bottom floor, and 90 mm for the other floors is made of organic glass, as shown in Figure 3. The organic glass plates with the thickness of 5 mm were used as slabs, under which rectangular organic glass bars with geometry of 5 mm × 5 mm × 160 mm were installed to simulate the beam. The cross-sectional dimension of the model column was 10 mm × 10 mm, and the outer edge of which was leveled with the outer edge of the model beam. The geometry of the model raft was 220 mm in length and 15 mm in thickness. The diameter and length of the model pile were 20 mm and 400 mm, respectively. The organic glass can be changed into liquid state by dropping acetone on it. Each component of the model building was dissolved in order to connect by the special adhesive of organic glass. In the connection process, the verticality among the components

connection after the organic glass dissolved.

components was ensured by the triangular rule and the integrity of model was guaranteed by the

was ensured by the triangular rule and the integrity of model was guaranteed by the connection after the organic glass dissolved. *J. Mar. Sci. Eng.* **2020**, *8*, 189 5 of 17

**Figure 3.** Model structure details. **Figure 3.** Model structure details.

While considering the gravity effect on the prototype structure, steel plates weighing 3.5 kg with geometry of 150 mm in length, 150 mm in width, and 20 mm in height were glued on each floor of the model structure, and steel plates weighing 6.2 kg with geometry of 150 mm in length, 150 mm in width, and 35.5 mm in height was glued on the model raft. A total additional mass of 16.7 kg or 81% of the enough artificial mass was placed on the model structure. The density of the model building is increased by adding enough artificial mass to meet the similarity rate. The gravity effect of pile foundation was ignored in this test. While considering the gravity effect on the prototype structure, steel plates weighing 3.5 kg with geometry of 150 mm in length, 150 mm in width, and 20 mm in height were glued on each floor of the model structure, and steel plates weighing 6.2 kg with geometry of 150 mm in length, 150 mm in width, and 35.5 mm in height was glued on the model raft. A total additional mass of 16.7 kg or 81% of the enough artificial mass was placed on the model structure. The density of the model building is increased by adding enough artificial mass to meet the similarity rate. The gravity effect of pile foundation was ignored in this test.

### *2.3. Instrumentation and Experimental Program 2.3. Instrumentation and Experimental Program*

wave excitation input.

The coral sand and Fujian sand sites adopt the same sensor arrangement, as shown in Figure 4. Laser displacement sensors with heights of 150 mm and 330 mm from the ground of model foundation were installed on the shaking table using the rigid brackets, respectively, and the rigid targets point were installed on the floors of the structure. The horizontal displacement sensor was 280 mm from the vertical center line of the structure. The model foundation stood for 24 h before the test. The capillarity action is considered and the water level is consistent with Figure 4(b) during 24 h. The experimental program was arranged as a comparative study of the dynamic response of pilesoil-structure system in coral sand and Fujian sand sites, while considering the influence of shaking intensity. Table 3 summarizes the specific experimental program. Figure 5 shows the time history curves of sinusoidal wave excitation. The sinusoidal wave has a simpler law than the seismic wave, and it is easy to analyze the dynamic response of the model foundation and structure, many scholars have used sinusoidal wave as excitation, especially in the liquefaction condition [35,36]. The white The coral sand and Fujian sand sites adopt the same sensor arrangement, as shown in Figure 4. Laser displacement sensors with heights of 150 mm and 330 mm from the ground of model foundation were installed on the shaking table using the rigid brackets, respectively, and the rigid targets point were installed on the floors of the structure. The horizontal displacement sensor was 280 mm from the vertical center line of the structure. The model foundation stood for 24 h before the test. The capillarity action is considered and the water level is consistent with Figure 4b during 24 h. The experimental program was arranged as a comparative study of the dynamic response of pile-soil-structure system in coral sand and Fujian sand sites, while considering the influence of shaking intensity. Table 3 summarizes the specific experimental program. Figure 5 shows the time history curves of sinusoidal wave excitation. The sinusoidal wave has a simpler law than the seismic wave, and it is easy to analyze the dynamic response of the model foundation and structure, many scholars have used sinusoidal wave as excitation, especially in the liquefaction condition [35,36]. The white noise with an amplitude of 0.02 g and a duration of 20 s was input before and after each sinusoidal wave excitation input.

noise with an amplitude of 0.02 g and a duration of 20 s was input before and after each sinusoidal

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**Figure 4.** General configuration of model tests. **Figure 4.** General configuration of model tests.

**Table 3.** Summary of shake table tests conducted.

**Acceleration (g) Duration (s) Frequency (Hz)**

**Case Relative Density Input Motions Peak**

1 0.67 Sine wave 0.1 10 5 2 0.67 Sine wave 0.2 10 5

**Table 3.** Summary of shake table tests conducted.

**Figure 5.** Time history curves of base excitation: (**a**) 0.1 g; and, (**b**) 0.2 g. **Figure 5.** Time history curves of base excitation: (**a**) 0.1 g; and, (**b**) 0.2 g.

### **3. Macroscopic Phenomena of Soil and Structure 3. Macroscopic Phenomena of Soil and Structure**

g shaking excitation.

Figure 6(a) shows the surfaces of coral sand and Fujian sand sites. When the 0.1 g sinusoidal wave excitation was input, the building on the coral sand site began to shake slightly, and no water was discharged from the model soil. The phenomenon of Fujian sand site was similar to that of the coral sand site. Figure 6(b) presents the site condition after test. When the 0.2 g sinusoidal wave excitation was input, the shaking degree of buildings in the two kinds of sand sites increased and reached the maximum at about 4.8 s, and then the shaking degree suddenly decreased. With the input of shaking excitation, the shaking degree gradually increased again. The buildings subsided and inclined, and the soil on both sides of the building rose. For coral sand, the surface of model soil was gradually getting wet, and little water accumulated after test, as shown in Figure 6(c). The water of Fujian sand site increased from the surrounding of the soil container and accumulated a little on the surface of the site (Figure 6(d)). Figure 6a shows the surfaces of coral sand and Fujian sand sites. When the 0.1 g sinusoidal wave excitation was input, the building on the coral sand site began to shake slightly, and no water was discharged from the model soil. The phenomenon of Fujian sand site was similar to that of the coral sand site. Figure 6b presents the site condition after test. When the 0.2 g sinusoidal wave excitation was input, the shaking degree of buildings in the two kinds of sand sites increased and reached the maximum at about 4.8 s, and then the shaking degree suddenly decreased. With the input of shaking excitation, the shaking degree gradually increased again. The buildings subsided and inclined, and the soil on both sides of the building rose. For coral sand, the surface of model soil was gradually getting wet, and little water accumulated after test, as shown in Figure 6c. The water of Fujian sand site increased from the surrounding of the soil container and accumulated a little on the surface of the site (Figure 6d). **Figure 5.** Time history curves of base excitation: (**a**) 0.1 g; and, (**b**) 0.2 g. **3. Macroscopic Phenomena of Soil and Structure**  Figure 6(a) shows the surfaces of coral sand and Fujian sand sites. When the 0.1 g sinusoidal wave excitation was input, the building on the coral sand site began to shake slightly, and no water was discharged from the model soil. The phenomenon of Fujian sand site was similar to that of the coral sand site. Figure 6(b) presents the site condition after test. When the 0.2 g sinusoidal wave excitation was input, the shaking degree of buildings in the two kinds of sand sites increased and reached the maximum at about 4.8 s, and then the shaking degree suddenly decreased. With the input of shaking excitation, the shaking degree gradually increased again. The buildings subsided and inclined, and the soil on both sides of the building rose. For coral sand, the surface of model soil was gradually getting wet, and little water accumulated after test, as shown in Figure 6(c). The water of Fujian sand site increased from the surrounding of the soil container and accumulated a little on the surface of the site (Figure 6(d)).

**Figure 6.** Macroscopic phenomena of the model soil and structure: (**a**) Before test; (**b**) After 0.1 g shaking excitation; (**c**) Coral sand site after 0.2 g shaking excitation; and, (**d**) Fujian sand site after 0.2 g shaking excitation. **Figure 6.** Macroscopic phenomena of the model soil and structure: (**a**) Before test; (**b**) After 0.1 g shaking excitation; (**c**) Coral sand site after 0.2 g shaking excitation; and, (**d**) Fujian sand site after 0.2 g shaking excitation.

**Figure 6.** Macroscopic phenomena of the model soil and structure: (**a**) Before test; (**b**) After 0.1 g shaking excitation; (**c**) Coral sand site after 0.2 g shaking excitation; and, (**d**) Fujian sand site after 0.2

#### **4. Result and Discussion 4. Result and Discussion**

#### *4.1. Pore Water Pressure Response 4.1. Pore Water Pressure Response*

The excess pore pressure ratio (ru) was defined here as the ratio of the difference of pore water pressure in a specified stage and initial pore water pressure over the vertical effective stress to detect the occurrence of soil liquefaction. The excess pore pressure ratio (ru) was defined here as the ratio of the difference of pore water pressure in a specified stage and initial pore water pressure over the vertical effective stress to detect the occurrence of soil liquefaction.

Under 0.1 g shaking intensity, Figure 7 shows the time history curves of excess pore pressure ratio directly under the buildings (P1, P2, P3, and P4) of coral sand and Fujian sand. The signal of pore water pressure gauge was lost at P4 position in Fujian sand site. During the period of shaking (10 s), the excess pore pressure ratio of two kinds of sand sites gradually increased and the growth rate of coral sand was significantly less than that of Fujian sand. After 2 s of shaking, the excess pore pressure ratio of coral sand at P1 position was approximately 0.02, which of Fujian sand was about 0.04, and the excess pore pressure ratio of coral sand was less than that of Fujian sand. During the whole shaking period, Table 4 shows the peak values of excess pore pressure ratio. With the decrease of depth, the peak values of the two kinds of sand sites gradually increased. The peak values of excess pore pressure ratio of coral sand were less than that of Fujian sand. From top to bottom (P1–P3), the peak values of coral sand were about 0.86, 0.67, and 0.80 times of that of Fujian sand. Under 0.1 g shaking intensity, Figure 7 shows the time history curves of excess pore pressure ratio directly under the buildings (P1, P2, P3, and P4) of coral sand and Fujian sand. The signal of pore water pressure gauge was lost at P4 position in Fujian sand site. During the period of shaking (10 s), the excess pore pressure ratio of two kinds of sand sites gradually increased and the growth rate of coral sand was significantly less than that of Fujian sand. After 2 s of shaking, the excess pore pressure ratio of coral sand at P1 position was approximately 0.02, which of Fujian sand was about 0.04, and the excess pore pressure ratio of coral sand was less than that of Fujian sand. During the whole shaking period, Table 4 shows the peak values of excess pore pressure ratio. With the decrease of depth, the peak values of the two kinds of sand sites gradually increased. The peak values of excess pore pressure ratio of coral sand were less than that of Fujian sand. From top to bottom (P1–P3), the peak values of coral sand were about 0.86, 0.67, and 0.80 times of that of Fujian sand.

**Figure 7.** Excess pore pressure ratio time history curves under 0.1 g shaking intensity: (**a**) P1 position; **Figure 7.** Excess pore pressure ratio time history curves under 0.1 g shaking intensity: (**a**) P1 position; (**b**) P2 position; (**c**) P3 position; and, (**d**) P4 position.


**Table 4.** Comparison of peak excess pore pressure ratios.

(**b**) P2 position; (**c**) P3 position; and, (**d**) P4 position.

at the P1 position, the coral sand uses 2.73 s, and the Fujian sand uses 2.22 s. Table 4 shows the peak values of the excess pore pressure ratio of two kinds of sand sites. The peak values of excess pore pressure ratio of coral sand were less than that of Fujian sand. From top to bottom (P1–P3), the peak values of excess pore pressure ratio of coral sand were 0.78, 0.62, and 0.63 times of that of Fujian sand. With the increase of depth, the peak values of the excess pore pressure ratio of two kinds of sand sites gradually decreased. The liquefaction degree of coral sand site is less than that of the Fujian sand site. Figure 8 shows the time history curves of excess pore pressure ratio under 0.2 g shaking intensity, and the signal of pore water pressure gauge was lost at P4 position in the Fujian sand site. The development patterns of the excess pore pressure ratio of the two kinds of sand sites were the same with time during the shaking period (10 s). The excess pore pressure ratio reached peak value after a sharp increase of about 4 s, and then began to decrease. The growth rate of excess pore pressure ratio of coral sand was less than that of Fujian sand, when the excess pore pressure ratio reached 0.5 at the P1 position, the coral sand uses 2.73 s, and the Fujian sand uses 2.22 s. Table 4 shows the peak values of the excess pore pressure ratio of two kinds of sand sites. The peak values of excess pore pressure ratio of coral sand were less than that of Fujian sand. From top to bottom (P1–P3), the peak values of excess pore pressure ratio of coral sand were 0.78, 0.62, and 0.63 times of that of Fujian sand. With the

increase of depth, the peak values of the excess pore pressure ratio of two kinds of sand sites gradually decreased. The liquefaction degree of coral sand site is less than that of the Fujian sand site. *J. Mar. Sci. Eng.* **2020**, *8*, 189 9 of 17

**Figure 8.** Excess pore pressure ratio time history curves under 0.2 g shaking intensity: (**a**) P1 position; (**b**) P2 position; (**c**) P3 position; and, (**d**) P4 position. **Figure 8.** Excess pore pressure ratio time history curves under 0.2 g shaking intensity: (**a**) P1 position; (**b**) P2 position; (**c**) P3 position; and, (**d**) P4 position.
