# Seismic Response of Shield Tunnel with Double-Layer Lining
## 1 Introduction  
The seismic load-bearing capacity of shield tunnels is of great importance. Currently, the commonly used approach involves a single-layer lining, which consists of segments and connecting bolts to form an assembled structure. [PERSON] et al. [1] studied the seismic interaction behavior between above-ground structures and circular tunnels. [PERSON] et al. [2] presented an efficient and reasonable methodology to evaluate the seismic fragility of shield tunnels based on a detailed investigation of the seismic performance of segments and joints in detail. [PERSON] et al. [3] developed a two-dimensional saturated soil-structure dynamic interaction model for shield tunnel lining structures and investigated the interaction mechanism between the liquefiable soil layer and the tunnel. [PERSON] et al. [4] conducted a large-scale shaking table test and studied the seismic performance of shield tunnels under near-field ground motion. [PERSON] et al. [5] proposed a refined lining model to simulate the mechanical behavior of segmental joints and investigated the seismic response of a shieldtunnel passing saturated sand deposits with different relative densities. [PERSON] et al. [6] studied the interaction of cross tunnels with different angles at close range during earthquakes, indicating that ground acceleration, internal force, and deformation of tunnel structure increase with the crossing angle between tunnels. Based on an undersea shield tunnel, [PERSON] et al. [7] created and validated a series of refined models and investigated the development of crack and damage in shield tunnel lining under seismic loading. [PERSON] et al. [8] carried out finite element simulation analyses of centrifuge shaking table tests to investigate the influence of segmental joints on seismic responses. [PERSON] et al. [9] studied the dynamic response characteristics of the bottom soil layer of a shield tunnel with different structural stiffness under different seismic loads, using the finite difference method. [PERSON] et al. [10] investigated the damage pattern of the concrete lining in a large-diameter subsea shield tunnel under different seismic loading intensities. A shield tunnel with single-layer lining possesses good seismic performance. However, there remains a risk of damage under conditions of high-intensity or adverse geological conditions. In order to enhance the seismic performance of shield tunnels, secondary linings are applied to the inner side of the tunnel. Based on the existing numerical models of the shield tunnel with double-layer lining, [PERSON] et al. [11] developed an improved numerical model and verified it with a similar model test. [PERSON] et al. [12] established a three-dimensional finite element model to analyze the stress distribution and deformation characteristics of the prestressed composite lining when the tunnel is under the completed segment assembly condition. Using a similarity model test and the engineering background of the Shiziyang Tunnel, [PERSON] et al. [13] studied the influence of the joint surface type on the mechanical behaviors and failure characteristics of the lining structure. Taking the Shiziyang shield tunnel as a case study, [PERSON] et al. [14] investigated the interaction between shield segmental lining and secondary lining under different construction times, using similar model tests. Based on the model tests, [PERSON] et al. [15] pointed out that under the high internal water pressure, structure fractures appeared first at the hance of the secondary lining, then at the vault and the arch bottom. Other scholars have also investigated the static load-bearing capacity of the shield tunnel with double-layer lining [16; 17; 18; 19; 20; 21; 22]. Building upon these understandings, scholars have further studied the seismic response characteristics of the shield tunnel with double-layer lining. [PERSON] et al. [23] explored polypropylene fiber-reinforced concrete as a secondary lining to reduce the seismic response intensity of tunnel structures. [PERSON] et al.