## 1 Introduction  
In the field of urban transportation, the integration of a high-capacity rapid public transportation system, centered around subway projects, assumes a pivotal role in the establishment of a contemporary and all-encompassing transportation network. Benefiting from the policy support, the urban rail transit sector in China is experiencing a rapid and comprehensive expansion, evidenced by substantial growth in both the length and quantity of operational routes. By the end of 2022, a total of 308 operational urban rail transit lines had been inaugurated across 55 cities in China, reflecting an annual rise of 8.8%. Impressively, the cumulative length of these operational lines had expanded to reach 10,287.45 km, marking a noteworthy year-on-year increase of 11.7%. This substantial mileage places China at the forefront globally in terms of total operational urban rail transit network length. In 2016, China issued and implemented Seismic Ground Motion Parameters Zonation Map of China (GB18306-2015) [1], which completely eliminated the non-seismic zones. Most cities with a subway under construction in China are currently located in strong seismic activity zones, which means that underground structures in service, under construction, or proposed face seismic threats at any time. The historical records of seismic damage to structures demonstrate a noteworthy resemblance between underground constructions and surface buildings. When subjected to the effects of strong seismic events, underground structures are susceptible to varying degrees of damage and disruption [2]. For example, the Great Hanshin earthquake in 1995 caused the complete destruction of more than 30 columns in the Daikai subway station in Kobe City, resulting in the collapse of and damage to the overall structure [3]. In addition, the Wenchuan earthquake and the Chi-Chi earthquake caused damage to numerous urban underground structures and mountain tunnels [4; 5]. In response to the complete collapse of the Daikai subway station in the Great Hanshin earthquake, scholars around the world have carried out research work from theoretical analysis, model tests, and numerical simulations [6; 7; 8; 9; 10]. Regarding the seismic damage mechanism of the Daikai station, many scholars believe that the overburden on the underground structure tends to lose its structural stability under the action of ground shaking, especially the inertial force of the vertical component effects of earthquakes. The incongruuous deformation capacity of the sidewalls and center columns caused by the change in force distribution results in damage to the structure [11; 12]. In order to protect underground structures from earthquake damage, the traditional seismic design generally aims to strengthen the structure itself. For example, in the structural design of the Daikai station, the safety factor of the center column is about 3. In addition, the seismic control techniques for underground structures can be divided into two main categories: one is used to install seismic damping materials around the structure; the other is used to install appurtenant devices to protect key components. [PERSON] et al. [13] analyzed the effect of damping materials on the dynamic response of tunnels, and concluded that the smaller the ratio of elastic modulus between the damping layer and the surrounding rock, the more obvious the seismic damping effect. [PERSON] et al. [14] and [PERSON] et al. [15] proposed a seismic isolation layer for underground structures and carried out theoretical analyses and experimental studies. Starting from the Daikai station, [PERSON] et al. [16] and [PERSON] et al. [17] studied the seismic damping effect of friction bearings at the top of the center column. [PERSON] et al. [18; 19] discussed the damping effect of the shear plate damper and lead-core rubber bearing installed on the center columns in subway stations and found that they could effectively reduce the structural internal forces. [PERSON] et al. [20] and [PERSON] et al.