## 1 Introduction
[24] developed a simplified analytical approach to predict how existing tunnels would respond to nearby foundation pit excavations. They validated their method by comparing it to a finite element software simulation and two sets of measured data. [PERSON] [25] analyzed 14 case studies of tunnel excavation engineering and delineated the patterns of structural construction's impact on tunnel deformation. [PERSON] et al. [26] performed long-term monitoring of highway tunnels adjacent to the building of vast foundation pits, documenting the effects of sectional excavation and soil improvement on mitigating displacement in existing tunnels. Diverse investigations have been undertaken concerning the development of new tunnels over pre-existing lines. Primary research methods encompass model testing [27; 28; 29], analyses of measured data [30; 31; 32], theoretical calculations [33; 34; 35; 36; 37; 38], and numerical simulations [39; 40]. [PERSON] et al. [27] applied centrifuge model tests to analyze the impact of highway tunnel construction on the uplift and bending moment of the shield tunnel beneath. [PERSON] et al. [28] investigated the effects of constructing new shield tunnels on horizontal and parallel existing tunnels using a scaled model. [PERSON] et al. [30] and [PERSON] et al. [31] were the first to report a case in which a sewage pipe constructed using the shield method crossed an existing subway line at a short distance. [PERSON] et al. [32] investigated the additional stress and deformation imposed by newly constructed adjacent tunnels using data from existing tunnel monitoring. [PERSON] et al. [33] examined the [PERSON] [34] and [PERSON] [35] foundation models, [PERSON]'s expression [36], and [PERSON]'s expression [37] and introduced a simplified nonlinear analysis method to quickly assess the response of an existing tunnel to a newly constructed overhead tunnel. [PERSON] et al. [38] investigated the interaction between tunnels and soil under unloading stress using the Winkler foundation model, calculating the unloading stress caused by the tunnel's location through the Mindlin solution. [PERSON] et al. [39] employed 3D finite element software to examine the mutual effects of adjacent tunnel construction. [PERSON] et al. [40] utilized finite element software to model a large section of pipe jacking above an existing tunnel, validating the numerical results against field monitoring data. References [18; 19] used finite element software to analyze the influence of foundation pit excavation on an existing tunnel directly below the site. In reference [10], the PLAXIS software was used to analyze the influence of foundation pit excavation on an existing side tunnel, but the research focused on the interaction mechanism between soil unloading caused by foundation pit excavation and the existing tunnel; the degree of influence and the temporal effect of the different construction stages on the tunnel were different; and the protective effect of the reasonable division of the excavation sequence on the existing structure was emphasized. References [17; 20] compared the results of a centrifuge test to those calculated using finite element software, focusing on selecting a reasonable soil constitutive model. The research in reference [21; 22] focused on the change in soil strength and pressure after foundation pit excavation. Reference [23] used a semi-analytical method to verify the influence of basement uplift on an existing tunnel directly below a foundation pit excavation site. In reference [24], the theoretical formula was simplified to predict the influence of foundation pit excavation on existing tunnels. Reference [25] collected 14 domestic foundation pit engineering examples and carried out a statistical analysis on the measured data, but the engineering examples summarized the displacement laws of the existing tunnels penetrating the foundation pit at different angles.