## 1 Introduction  
Currently, with the rapid development of underground space and urban rail transit, the phenomenon of deep excavation adjacent to existing tunnels is increasing [1, 2, 3, 4]. Excavation can inevitably disturb the surrounding rock and soil, and then cause the displacement of the existing tunnel buried in it [5, 6, 7, 8]. This disturbed area is called the influenced zone of deep excavation. Therefore, it is important to predict the influenced zone of deep excavation and take measures to reduce the tunnel displacement in the influenced zone before excavation. At present, the simplest method to determine the influenced zone is using laws and regulations. For example, the management regulations of urban rail transit in Beijing, Shanghai, Nanjing, etc., take 50 m beyond the outer line of the subway tunnel as the protection zone for tunnel deformation. In this method, a fixed value is used to determine the scope of the influenced zone of construction, which is convenient for management departments to control risks. However, this method does not consider the effects of geological conditions, tunnel structure forms, construction workmanship, etc. In the code GB 50911-2013 [9], according to the different influence degrees, the range outside the deep excavation is divided into: I--primary influenced zone, II--secondary influenced zone, and III--possible influenced zone. This method is simple and easy to understand, but the parameter for dividing the influenced zone is only the excavation depth \(H\), without considering the other factors such as geological conditions, deformation forms and magnitudes of the retaining structures. Additionally, the intersection line of the pit wall and base slab is taken as the baseline for dividing the influenced zone, which is more suitable for the traditional shallow excavation using the retaining structure of a flexible sheet pile or without a retaining structure. For the deep and large excavations with deeply embedded retaining structures, the rationality of this simplification is debatable. [PERSON] (2009) [10] put forward another division method of the influenced zone of deep excavation considering the excavation-induced soil deformation behaviors. The range outside the pit is divided into: I--primary influenced zone, II--secondary influenced zone, and III--uninfluenced zone. Different from the triangular influenced zone in the GB 50911-2013 [9], the influenced zone in this method is simplified as a right-angled trapezoid, and the bottom of the retaining structure is taken as the baseline for dividing the influenced zone. However, the scope of the influenced zone has not been quantitively characterized. [PERSON] et al. (2016, 2017) [11; 12] studied the displacement behaviors of existing tunnels induced by adjacent deep excavation and, on this basis, the range outside the pit is divided into: I--primary influenced zone, II--secondary influenced zone, III--general influenced zone, and IV--weak influenced zone. In his method, the relationship between the displacement control standards of the tunnel and the influenced zone of deep excavation is established, and the displacement of the tunnel can be directly predicted according to the actual influenced zone where it locates. Referencing the method proposed by [PERSON] et al. (2016, 2017) [11; 12], [PERSON] et al. (2021) [13] studied the excavation-induced displacement behaviors of underlying tunnels and then divided the range below the base slab into: I--primary influenced zone, II--secondary influenced zone, III--general influenced zone, and IV--weak influenced zone. On this basis, [PERSON] and [PERSON] (2021) [14] studied the effects of ground improvement below the base slab on the underlying tunnel displacement and the influenced zone of deep excavation. The above studies played an important role in determining the influenced zone of deep excavation on tunnel displacement. However, the study on the control of the influenced zone and tunnel displacement is still limited.