## 2 Model Test
### Sketch of the Test Program  
The pile foundation is mainly subjected to horizontal cyclic loads such as winds and waves in the marine environment. Therefore, the amplitude, frequency, and duration of the above cyclic loads were mainly simulated by the simplified sinusoidal-type load in the indoor test. Figure 4 depicts a custom-designed horizontal cyclic loading system in this paper, comprising of a power module, sliding module, and counterforce module. The system includes a reaction steel frame, a small motor, a frequency regulator, an eccentric wheel, a connecting rod, a coupling, and other essential components. The power module consists of a motor, an eccentric wheel, and a frequency regulator, which are responsible for providing varying amplitudes and frequencies for cyclic loading in this model test. In addition, the sliding module is primarily composed of a connecting rod and a linear slide bearing, which ensures the directionality of the loading in this model test. The counterforce module mainly adopts the counterforce steel frame to support the horizontal cyclic loading device to reduce the mechanical vibration during loading and prevent the loading device from tipping over. It is worth mentioning that with reference to the experimental equipment designed by [PERSON] et al. (2018), the horizontal cyclic loading system of this study used the principle of a motor-driven eccentric wheel, driving the spring motion to realize the cyclic loading onto the pile foundation. The test loading system is capable of performing horizontal cyclic loading with varying amplitudes, frequencies, cycles, and loading paths, according to the requirements of model experiments. In Figure 5, the loading curves obtained from the tensile and compressive sensors during the test are presented. Figure 4: _Cont._  
The overall dimensions of the model box were 1.35 m \(\times\) 1.2 m \(\times\) 0.9 m. The side wall of the model box is tempered glass, and the overall frame is connected by steel plates. The sensor layout for this test is shown in Figure 6.  
In this test, data were collected using a Dong Hua DH-5922 dynamic signal acquisition system with 16 channels. This is an advanced computer-based system for intelligent dynamic signal analysis and testing, designed to provide comprehensive signal processing capabilities for a range of on-site applications. It features a complete set of hardware components required for dynamic signal testing, including signal conditioners (such as strain, vibration, etc. ), DC voltage amplifiers, anti-aliasing filters, A/D converters, sampling control, and computer communication. At the same time, it also provides user-friendly control and analysis software. The data acquisition frequency was 10 Hz in this test, and the test was terminated when the following phenomena occurred: (1) the cyclic time reached 5000 times, and (2) the lateral displacement on the mud surface exceeded 10 mm. Figure 4: Device diagrams of the horizontal cyclic loading system. (**a**) The actual experimental figure of the horizontal cyclic loading system. (**b**) The schematic diagram of the horizontal cyclic loading system. Figure 5: The variation curve of cyclic horizontal loading. (**a**) Output load of the device. (**b**) The fitting curve. The horizontal static loading test of the pile foundation is a reliable method to test the horizontal bearing capacity of the pile foundation. In this study, the slow maintenance loading method was used to apply a horizontal static force to the pile group foundation in the model test. The slow maintenance loading method is a graded loading method, which takes 1/10 of the maximum bearing capacity of the pile foundation as the loading amount of each load level. After each level of loading, the horizontal displacement of the pile foundation was observed at the time nodes of 5 min, 10 min, 15 min, 30 min, 45 min, and 60 min, and then every 30 min, and the next level of loading was applied after the horizontal displacement of pile foundation was maintained in balance.