## 2 Dynamic Centrifuge Model Testing  
Centrifuge model tests were conducted to evaluate the seismic performance of pile-supported structures with batter piles. The models were spun in the centrifuge to increase the g-level in them so that stresses in their ground were equal to those in the prototype. It is also an advantage for the theoretical verification and numerical analysis techniques as the boundary and stress conditions of the ground, which are imposed in the centrifuge model test, have been studied a lot [10; 11; 12; 13]. The tests were carried out at the Korea Advanced Institute of Science and Technology (KAIST) Geo-centrifuge Testing Center using an experimental machine with a 5 m radius and 240 g-ton maximum operating capacity [20; 21; 22]. The experiments used a square-equivalent shear beam model box (49 cm by 49 cm by 69 cm) that behaved similarly to the ground, reducing the effect of the wall reflections [23]. Certain sections of the pile-supported structures at the Port of Pohang, Korea, were modeled for the tests. This study used experimental models previously tested by [PERSON] et al. [24]. Figure 2 shows the testing procedure of the HAI55 model in detail. First, the base plate and the piles were installed to the equivalent shear beam (ESB) box, and the relative density of the ground was adjusted through the air pluviation method. The inclined ground was composited, and the test was performed after installing  
Figure 1: Pile supported structures: (**a**) a Henley beach jetty, South Australia and (**b**) a wharf [17]. the deck plate and the instrumentations. The soil was simplified to a single-component sandy soil. Figure 3 shows the four model configurations tested. Models HA45 and HAI55 had horizontal grounds with relative densities of the soil being 45% and 55%, respectively. Models IA62 and IAI58 had inclined grounds with relative densities of the soil being 62% and 58%, respectively. Models HA45 and IA62 had nine piles in the \(3\times 3\) arrangement shown in Figure 3(a,c). Models HAI55 and IAI58 had a similar \(3\times 3\) pile arrangement with four additional batter piles, as shown in Figure 3(b,d). Each model was 1/48 in scale, and the specifications were calculated by adjusting the flexural rigidity, which has the highest impact on structural behavior during an earthquake. Table 1 presents the scaling laws linking the prototype and the model, and Table 2 lists their properties. The model piles and deck plates were made of aluminum (elastic modulus, E = 68,300 MPa; Poisson's ratio, \(\
u\) = 0.3) [25; 26; 27]. Figure 4: Plan view of experimental model before installing the deck plate: (**a**) HA45 model; (**b**) HAI55 model; (**c**) IA62 model; and (**d**) IAI58 model. Figure 3: Model cross-section: (**a**) HA45 model; (**b**) HAI55 model; (**c**) IA62 model; and (**d**) IAI58 model. Artificial seismic waves (Figure 5a), suitable for Korean sites, were produced, as specified by the Ministry of Oceans Fisheries (MOF) [19]. The design ground acceleration, considering the ground characteristics, is expressed as a response spectrum curve, and a 5% damping ratio is generally applied. Figure 5b compares the response spectrum curve of the artificial seismic wave and the standard design response spectrum curve, showing their close agreement. Figure 5b also shows the natural periods of the soil-pile system of each model of the centrifuge model test. It shows the natural periods of 0.5-0.65 s. As the confining pressure of the ground near pile 3 (landward pile) was larger in the inclined ground model (IA62) than in the horizontal ground model, the ground stiffness was relatively higher than that in the horizontal ground model (HA45). This  
The tests were conducted in dry sand to minimize the effects of liquefaction and lateral spreading on the piles, which can occur when considering pore water pressure.