## 1 Introduction  
With the completion of the reservoir area and water storage, the reservoir water level periodically rises and falls, resulting in the deterioration and geotechnical damage of the reservoir bank slope subsidence zone, which has a significant impact on the stability of the bank slope [1; 2; 3; 4; 5]. The bank slope deformation and slip accumulation on the reservoir bank bridge pile foundation have a long-term lateral extrusion effect, causing the occurrence of bridge foundation, pier, and bridge span structure damage and threatening the adjacent existing bridge structure's safety and stability [6], such as pier cracking of the bridge foundation. Pier and span structures are subject to structural damage, such as pier cracking, pier tilting, and girder misalignment. Therefore, it is necessary to investigate the long-term effects of deformation and slip accumulation on the reservoir bank bridge structure under the cycle of reservoir water level rise and fall. For the problem with the periodic rise and fall of the water level in the reservoir area, many scholars have found that the stability of the reservoir bank slope is predominantly affected by the cycle of reservoir water level rise and fall. [PERSON] et al. [7], [PERSON] et al. [8], and [PERSON] et al. [9] analyzed the stability of the reservoir bank slope zone based on the centrifugal slope model, rock strength deterioration mode, geological survey analysis, dry and wet cycle tests, numerical simulation, etc., and all noted that with the increase in the reservoir water level rise and fall cycle, the geotechnical equilibrium gradually deteriorated. With the increase in the number of cycles of reservoir water level rise and fall, the balance of rock and soil bodies gradually deteriorated, leading to the instability of the reservoir bank slope. In recent years, with the cycle of water level rise and fall in the reservoir area, landslide disasters have occurred in the reservoir area, and bank slope control has become the focus of research. Scholars have studied the overall stability of bridge bank slopes based on numerical simulation by combining the geological conditions and environmental factors of bridge banks and provided corresponding suggestions for the design and prevention of pile foundations and piers of reservoir bank bridges [10]. [PERSON] et al. [11] studied the prevention and control effect of anti-slip piles under the fluctuation of reservoir water level by centrifuge model test and noted that the prevention and control effect of landslides was evident when the soil arch effect was generated between piles and soil. However, the above studies only focused on the deformation and stability of the bank slope and disregarded the effects of slope deformation and slip on the adjacent structures of the reservoir bank. These studies showed that the pile transverse bearing capacity and reliability analysis were mainly based on the pile transverse displacement as the criterion [12; 13]. In this regard, many scholars have conducted a series of studies on the pile displacement of the coupled pile-soil system of slopes under changes in the reservoir water level. [PERSON] et al. [14] obtained the trend of landslide-pile deformation under the infiltration effect when the reservoir water level fluctuated via numerical simulation based on an actual project. [PERSON] et al. [15] further investigated the influence of the pro-slope distance and slope ratio on the pile force deformation characteristics by numerical simulation and found that the pile top displacement and pile bending moment were proportional to the slope ratio. [PERSON] et al. [16] analyzed the pile displacement deformation under the reservoir water level cycle based on the stiffness decay model and soil strength degradation model in conjunction with engineering practice and noted that the cumulative pile displacement continuously increased with the number of water level cycles.