# Dynamic Response Analysis of Parallel Twin Tunnels Under Different Train Loads
## 5 Conclusions  
This study investigates the influence of train operations in Tunnel 1 on the structure of Tunnel 2 and the surrounding environment. Conditions A\({}_{1}\) to A\({}_{8}\) (from 62.4 to 131.5 kN) were established by PFC to quantitatively analyze the static and dynamic responses of the T2 structure and its surroundings under varying loadings. The main findings are summarized as follows:  
1. The \(D_{\rm V}\) of T2 sleepers is approximately three times the \(D_{\rm H}\), while the \(V_{\rm V}\) is roughly twice the \(V_{\rm H}\), highlighting the predominance of vertical responses over horizontal ones as a critical focus. The reinforcement characteristics inherent in the twin-tunnel structure enhance the stability of the intermediate region between the tunnels, resulting in relatively small responses in the T2 sleeper region closer to the vibration source. Overloading of trains may cause uneven displacements in T2 liners, potentially leading to microcracks or even structural failure. 2. The maximum \(D_{\rm V}\) and \(V_{\rm V}\) points on the surface are located slightly to the left above T1, surpassing those of the tunnel sleepers under the same conditions. The dynamic response of the surroundings under train loads is significantly influenced by the burial depth and tunnel structure, causing uneven compressive forces in the lower-right and upper-left regions of the T2 surroundings. Consequently, it causes elliptical deformation and potential liner-rock separation. When the train vibration load exceeds 92.0 kN (A\({}_{4}\)), the \(R_{\rm P}\) above the tunnel becomes significantly pronounced, emphasizing the significant impact of overload on the tunnel's surroundings, particularly near the surface. 3. The train vibration load in T1 significantly amplifies both the static and dynamic responses of T2 and its surroundings. However, a sudden decrease is observed under the A\({}_{7}\) condition. This reduction can be attributed to the dynamic amplification effect dominating the pressure effect under A\({}_{1}\) to A\({}_{6}\) conditions, leading to a progressive increase in the dynamic response of T2. Under the A\({}_{7}\) condition, the pressure effect surpasses dynamic amplification, leading to a sharp decline in T2's dynamic characteristics. When the load reaches the A\({}_{8}\) condition, the dynamic amplification effect far exceeds the pressure effect, resulting in a dramatic increase in T2's dynamic response. 4. In practical engineering applications, it is crucial to monitor the static and dynamic responses of overloaded trains on adjacent tunnel structures, with particular emphasis on the static and dynamic responses of the liners and surrounding areas on the T2 side proximate to T1. During construction, critical zones within the T2 structure must be closely monitored when T1 experiences train overloading to ensure the safety and integrity of the tunnel throughout its operational life. It is recommended that the operational load of the tunnel be maintained within the threshold of the A\({}_{4}\) condition (92.0 kN) to mitigate potential risks. This study examines the static and dynamic responses of adjacent tunnels under single train operation. However, since train loading represents a long-term condition, its adverse effects on adjacent tunnels are expected to be more pronounced. Future research will explore the impact of prolonged train loading on these responses. Conceptualization, L.W. and X.B. ; methodology, L.W. ; software, J.W. ; validation, L.W., X.B. and J.W. ; formal analysis, L.W. ; investigation, X.B. ; resources, H.G. ; data curation, H.G. ; writing--original draft preparation, J.W. ; writing--review and editing, L.W. ; visualization, J.W. ; supervision, H.G. ; project administration, X.B. ; funding acquisition, X.B. All authors have read and agreed to the published version of the manuscript. The authors declare no conflicts of interest. Not applicable. The original contributions presented in this study are included in the article.