## 1 Introduction  
Currently, urban rail transit systems have served as a favorable means to expedite the modernization of cities [1]. An increasing number of subway tunnels have been developed to alleviate congestion in urban transportation systems [2, 3]. Shield-driven tunneling offers the advantages of high efficiency, low cost, and low interference with the surrounding environment, which makes it one of the most advanced and popular tunneling techniques [4]. Therefore, it is extensively utilized in the construction of shield tunnels in urban areas [5, 6]. With the increasing development of underground space, the construction of infrastructure in dense cities often encounters existing underground structures and facilities, such as municipal pipelines, underground corridors and interdistrict tunnels, etc. [7, 8]. Therefore, the effects of unloading caused by adjacent or above excavation on the existing structures, especially on the existing tunnels, is of increasing concern [9, 10]. However, the interaction mechanism between the existing tunnel and adjacent or above unloading action is very complex. The response of the tunnel is closely dependent on the tunnel sizes [11, 12], excavation dimensions and/or methods [13], excavation protective measures [14], and the location relationship between tunnel and excavation [15], etc. The interaction between existing tunnels and excavation have been widely investigated by employing the means of the numerical simulations [16, 17], physical model tests [18], field observations [19], and theoretical analysis [20]. [PERSON] et al. [21] reviewed the contributions to responses of existing tunnel subjected to nearby excavation, which is helpful to reveal general knowledge of the relevant problems and to provide guidance for more in-depth research. [PERSON] et al. [22] developed a 3D numerical model with ABAQUS to simulate the actual process of a new construction method (i.e., divided alternate excavation method--DAEM) in an excavation of a deep foundation pit above shield tunnels. Thereafter, the effectiveness of DAEM in controlling deformation of the underneath tunnel is confirmed by comparing the results with the other two conventional excavation methods. [PERSON] et al. [23] conducted a series of three-dimensional centrifugal tests to investigate the effects of sand density and basement wall stiffness on the basement-tunnel interaction, and then they developed a computational chart as a design tool. They reported that the excavation-induced heave and transversal strain were more sensitive to the changes in soil density in the transverse direction than those in longitudinal direction when the basement was constructed directly over the existing tunnel. Moreover, when the basement was built on the side of the existing tunnel, the diaphragm wall was more effective than the sheet pile wall in terms of controlling settlement and tensile strains of tunnels. [PERSON] et al. [24] reported that a series of hazards such as water seepage, concrete spalling, and segment cracks occurred when a station-expansion project was conducted beside the tunnels. Additionally, they further discussed the causes responsible for these hazards based on the performed numerical and theoretical investigations. [PERSON] et al. [25] examined the effects of a large excavation nearby a 6 m-diameter MRT tunnel by using field-monitoring data and finite element analysis, and confirmed that the lining stiffness possesses a significant effect on tunnel displacement induced by the adjacent excavation. They reported that the stiffer lining underwent less displacement but may experience larger bending moments. [PERSON] et al. [26] proposed a simplified analytical model for analyzing the deformation response of excavation-induced soil unloading on adjacent tunnels. The model could determine the tunnel deformation response by considering the soil unloading and Galerkin method. [PERSON] et al. [27] proposed a cracks risk assessment method for existing tunnels.