# Dynamic Response Analysis of Parallel Twin Tunnels Under Different Train Loads
## 1 Introduction  
Metro train overloading poses a significant threat to the structural integrity of tunnels. As the underground space becomes increasingly scarce and transportation demand continues to rise, the construction of closely spaced twin tunnels has become more prevalent. Train overlapping not only compromises the structural stability of the tunnels in which they operate but also poses significant safety risks to adjacent tunnels. Consequently, the impact of underground train overloading on the structure and surroundings of adjacent tunnels has attracted increasing attention. The effects of overloaded train loads on tunnels predominantly concern single tunnels. [PERSON] et al. [1] investigated the dynamic responses of heavy-haul railway tunnels under varying loads using empirical data and theoretical analysis, emphasizing that axle load is a critical factor in track bed fatigue damage, particularly at the track location. [PERSON] et al. [2] discovered that train vibrations cause elastic resonance in heterogeneous rock, significantly disturbing the surroundings and structures. [PERSON] et al. [3] utilized ABAQUS to analyze the dynamic response characteristics of heavy-haul railway tunnel surroundings, quantifying the impact of axle loads and identifying vulnerable areas under the tracks. [PERSON] et al. [4] used accelerometers to monitor tunnel displacements and segment deformations, visualizing damage caused by metro train vibrations for targeted maintenance. [PERSON] et al. [5] found that peak acceleration values of ground increased significantly in soft, medium, and dense soils compared to rock sites. Based on existing studies, heavy-haul train loads exert a more substantial influence on the structural dynamic responses of tunnels compared to conventional train loads. Research on twin-tunnel dynamics has mainly focused on conventional train loads. [PERSON] et al. [6] developed an analytical solution for twin-tunnel vibrations, demonstrating that the presence of a second tunnel substantially influences soil responses at varying distances and angles. [PERSON] et al. [7] found that the presence of an adjacent tunnel markedly amplifies soil vibrations through a three-dimensional analytical model. [PERSON] et al. [8] used LS-DYNA to analyze stress distribution in twin tunnels, identifying that floors, roofs, corners, and sidewalls are particularly susceptible to cracking under combined static and dynamic loads. [PERSON] et al. [9] used FLAC3D to investigate tunnel depth, lining thickness, and diameter effects, observing more pronounced impacts in shallower tunnels. [PERSON] et al. [10] found that high-speed train vibrations significantly affect adjacent damaged tunnels, necessitating reconstruction and anchoring for safety. [PERSON] et al. [11] conducted 50 g centrifuge tests, revealing that twin-tunnel interactions amplify dynamic responses. [PERSON] et al. [12] investigated the ground settlement and tunnel deformation induced by stacked shield tunnel construction and nearby train loads, concluding that train load exacerbates deformations in such tunnels. [PERSON] et al. [13] conducted model tests and numerical simulations to study the ground deformation caused by the construction of overlapping tunnels at different spacings (\(d/D\) = 0.50, 0.75, and 1.00) under metro train vibration loads, revealing that the patterns of ground displacement are significantly influenced by tunnel spacing. These studies primarily focused on findings obtained under standard train loading conditions. The research on the dynamic responses of twin tunnels under varying train load conditions remains limited. [PERSON] et al. [14] developed a three-dimensional finite element model (3D FEM) to investigate the influence of train axle loads on ground vibration responses in twin-tunnel configurations. Their findings indicated that ground vibrations increase with higher axle loads of both trains, especially when there are differences between the two trains. [PERSON] et al.