## 1 Introduction  
In recent years, a large number of marine engineering projects have been constructed in China, such as transmission line towers, drilling platforms, cross-sea bridges, port terminals, wind turbines, etc., among which the development of offshore wind power projects is particularly rapid [1, 2, 3, 4, 5]. To tackle the challenges posed by the intricate offshore environment, these structures often rely on the pile group, as the preferred choice for foundation design [6, 7]. The oceanic environment necessitates that the pile foundations for offshore structures be engineered to endure not only the gravitational forces of the superstructure, but also the onslaught of horizontal cyclic loads, including wind, waves, and currents. These cyclical loads often vary in direction and magnitude throughout the lifespan of the project, posing a significant challenge to the safe operation of the structure [8]. The complex loads acting on the offshore wind turbine foundation can cause permanent lateral deformation of the structure [9]. According to the opinions of some scholars, the marine clay layer is prone to long-term cyclic loads, which triggers a constant remodeling of the soil around the pile foundation. This, in turn, leads to a gradual decline in the stiffness and shear strength of the soil, ultimately causing cumulative deformation of the pile foundation [10]. Moreover, the creation and release of surplus pore water pressure at the periphery of offshore pile groups during the application of cyclic horizontal loads could potentially impact the operational functionality of the foundation [11, 12]. Therefore, examining the long-term response of the pile group to cyclic horizontal loading is critical in developing effective design approaches for offshore wind turbine foundations. While there have been numerous numerical simulations conducted to investigate the dynamic response of offshore structures [13, 14, 15, 16], inaccurate parameter selection during such simulations might result in predictive errors. Therefore, in order to thoroughly examine the long-term loading characteristics of pile group foundations in saturated clay soil under horizontal cyclic loading, the most effective approach is the implementation of long-term loading tests. These tests are comprised of both field and model experiments. Notably, [PERSON] et al. [17] and [PERSON] et al. [18] have successfully carried out such tests, proposing the force characteristics of the pile group foundation under horizontal cyclic loads, as well as the correlation between the pile group effect and the spacing of piles. The field tests can truly reflect the cyclic loading characteristics of pile foundations in the actual working conditions and verify the feasibility of numerical analysis. However, this kind of method usually takes a long time and has high costs. Therefore, in attempts to explore the behavior of the pile group foundation under long-term loading, indoor model tests have become a routine method. These tests typically comprise centrifugal tests and 1 g model tests. Numerous scholars have undertaken centrifugal tests on the pile group foundation as a means to rectify the issue of stress-strain state inconsistency between prototypes and models [19; 20; 21; 22; 23]. Although these tests are able to effectively replicate the working conditions of the prototypes, they are accompanied by notable constraints stemming from the limitations in the construction scale of core equipment, such as centrifuges and vibration tables. Consequently, the execution of these model tests has been more challenging. In contrast to field tests and centrifugal model tests, the 1 g model tests have the characteristics of high controllability, good repeatability, and high-test efficiency. Significant findings have been achieved through 1 g model tests since the 1970s. [PERSON] et al.