## 1 Introduction  
China is located between the world's two major seismic belts: the Pacific Rim Seismic Belt and the Eurasian Seismic Belt. Under the compression of the Pacific, Indian, and Philippine plates, neotectonic activity in the western mountainous area is strong, and the fault zone is widely developed [1; 2]. Large active faults can extend for hundreds or even thousands of kilometers, with high seismic hazards [3; 4]. With the continuous improvement of land development intensity and the construction of basic transportation facilities along the Belt and Road, including the Sichuan-Tibet Railway [5], which has been started, more and more highways and railway bridges will inevitably have to be built next to or across large active faults. Earthquake disasters in recent decades have shown that the relative displacement of the seismogenic fault during strong earthquakes causes different ground motions on both sides of the fault, accompanied by permanent displacement of the surface rupture [6; 7]. Under the combined action of strong ground motion and surface rupture caused by the seismogenic fault, bending and shear failure of piers often occur in bridge structures adjacent to or directly crossing faults, and even beam fall or collapse of the entire bridge is severe [8]. In the 1999 Chi-Chi earthquake, the surface of the Chelongpu fault, the seismogenic fault, produced a surface rupture zone of up to 100 km, and the relative dislocation on both sides of the fault reached several meters. The huge displacement led to the failure of seven bridges near the fault, such as the Wuxi Bridge, Shiwei Bridge, and Mingzhu Bridge [9]. In the 1999 Kocaeli earthquake, the surface rupture zone of the fault passed through the piers and adjacent abutments of the Arifiye viaduct [10], and a horizontal displacement of nearly 1.5 m was generated on both sides of the ground, resulting in the collapse of the entire bridge and the complete interruption of road traffic. The 2008 Wenchuan earthquake occurred in the central fault zone of the Longmen Mountains. The Xiaoyudong Bridge and the Yingxiu Shunhe Bridge near the fault zone collapsed due to fault displacement during the earthquake. The bottom of the pier of Baihua Bridge [11] has crushing failure, and the bottom of the pier and the tie beam have severe shear failure. The above earthquake damage shows that the permanent displacement of surface fracture caused by fault dislocation is the main cause of beam fall, bearing system failure, and pier damage [12]. In order to prevent the occurrence of falling beams or to ensure the seismic safety of bearings, the measures of placing shear keys in the transverse direction of the bridge are usually adopted in bridge engineering [13; 14]. Although the shear key can reduce the seismic damage of the falling beam [15], it will also collide with the main beam, causing component damage [16]. Therefore, transverse shear key damage is a very common form of damage in post-earthquake bridge structures. For example, in the 1999 Chi-Chi earthquake and the 2001 Gujarat earthquake, there are many records of lateral movement and shear key failure of bridge superstructures [9; 17]. In the 2008 Wenchuan earthquake, the beam bridge damage was extremely severe, and the shear key failure rate was as high as 16.8%, while the pier failure rate was only 2.4% [18]. For the overall seismic design of the bridge, the main function of the transverse shear key is to limit the displacement and transfer force. Although the seismic design provisions of shear keys in different countries are not very clear, there are still many scholars who have discussed it in recent years. [PERSON] [19; 20] used the linear collision model to study the collision effect between the superstructure and the transverse shear key of the simply supported beam bridge. It is shown that the collision stiffness, initial gap, and vibration period have a great influence on the seismic response of the structure.