# Analysis of the Interaction Effects of Shield Structure Oblique Passing under an Existing Tunnel
## 1 Introduction  
With the increasing scarcity of land resources and the increasing congestion of traffic in China, the development and utilization of underground space has become a contemporary development trend, and the emergence of urban subways has greatly alleviated some traffic congestion. However, due to the rapid expansion of China's urban rail network, more and more subways are being constructed above, below, and parallel to existing tunnels. These new shield tunnels create secondary disturbances in the soil around the existing tunnels, resulting in stress increments and deformations in the existing tunnels. Large tunnel deformations can lead to the cracking of lining and track deformation and may even pose a threat to the operational safety of trains and affect the normal operation of existing tunnels. In the current golden period of urban underground space development, the construction of underground works in the presence of existing tunnels is a practical area that urgently requires research. Therefore, it is important to study the mechanical behavior and deformation of existing tunnels during the shield tunneling process. Due to the rapid development of urban rail transportation, the construction of subway tunnels will encounter a variety of engineering problems. Thus, the deformation of existing tunnels caused by the construction of urban subway tunnels has been a hot topic of research in recent years, with the internal forces and deformation of existing tunnels being predicted using theoretical derivation formulas [1; 2; 3; 4; 5; 6]. Alternatively, numerical simulation software can be used to study the interaction effects between old and new tunnels in depth [7; 8; 9; 10; 11; 12], or model test approaches can be used for prediction [13; 14; 15; 16; 17; 18; 19] before comparing the final results with the data measured in the field for analysis. Simultaneous grouting is an important means used to control surface settlement in shield method construction. [PERSON] [9] studied the construction of an EPB shield using mid-shield grouting in the Meicun to Shangmeilin tunnel of Shenzhen Metro Line 9 and found that timely mid-shield grouting is an effective method by which to control the settlement caused by excavation gaps. [PERSON] [11] investigated the settlement characteristics of existing tunnels based on monitoring data and finite difference method (FDM) numerical simulation and found that the existing tunnel deformation caused by shield underpasses is mainly a vertical settlement with some torsional deformation. [PERSON] [12] investigated the effect of a two-lane tunnel passing under an existing tunnel by varying the ratio of the existing horseshoe tunnel width to the diameter of the new circular tunnel. While theoretical analysis usually ignores the effect of ring joints, [PERSON] [15] modified the longitudinal deformation model of shield tunnels based on the Timoshenko beam theory and proposed a homogeneous solid ring-spring numerical model that considers the treatment of ring joints. In a study conducted by [PERSON] [18], the deformation and internal forces of closely overlapping shield tunnels were monitored and analyzed through a series of physical model tests and numerical simulations. [PERSON] [19] combined the TBSM with the Vlasov basis model to develop a soil-tunnel interaction model and derived a closed solution for shield tunnels using the Vlasov basis under arbitrary loads. [PERSON] [20] analyzed different culverts using CANDE software and ABAQUS software; the numerical simulation results were compared with the experimental results to determine the accuracy of both software packages in assessing the remaining structural capacity of damaged metal culverts. [PERSON] [21] performed an anti-seismic analysis of four different numerical models of soil-steel tunnels using the DINA finite element analysis software. The effect of different construction methods and different construction sequences on existing structures was found to be significant.