## 2 Numerical Analysis Setup
### Boundary Conditions and Input Ground Motion  
The numerical simulations in this paper consist of two stages: static and dynamic analysis. It is assumed that the utility tunnel is located in a semi-infinite space, so appropriate boundary conditions need to be applied to the finite model. In the first stage (i.e., the static analysis), the four lateral boundaries are fixed in the normal direction, the bottom of the model is fixed horizontally and in the normal direction, and the ground surface is flat and unloaded. In static analysis, boundaries can be placed at some distance from the main study area. In dynamic analysis, however, fixed boundary conditions can cause the reflection of outward propagating waves back into the model [27]. Therefore, the free-field boundaries provided by Flac3D are used in the second stage to represent the lateral expansion of the far field. The free-field boundary of the model consists of four plane free-field grids at the sides and four column free-field grids at the corners, and the grid points of the free-field boundary correspond to the main grid one by one, as shown in Figure 3a. The plane free-field grid is a two-dimensional calculation and is assumed to extend infinitely in the normal direction of the plane. The column free-field grid is a one-dimensional calculation, which is assumed to extend infinitely in two horizontal directions [24]. The properties and initial conditions of the free-field boundaries are transferred from the adjacent main grid zones. The main grid zones are coupled to the free-field boundary grids by viscous dashpots, and the unbalanced forces from the free-field grids are applied to the main grids, the viscous dashpots on the boundary provide viscous traction that can absorb the waves propagating to the boundary [28], in this way, the use of free-field boundaries in the dynamic analysis minimizes wave reflection. Ground motion is applied in the form of a velocity wave in the horizontal direction at the bottom of the model.  
The geological exploration data of Beijing Daxing International Airport Utility Tunnel shows that this is a Class III site with a design seismic grouping of Group One and an eight-degree site earthquake fortification intensity. The Uniform Hazard Spectrum (UHS) curve for the site is established according to the Chinese Code for Seismic Design of Buildings [29] (CCSDB). Ground motion matched to the UHS was selected from the Pacific Earthquake Engineering Research Centre (PEER) ground motion database. The earthquake data were obtained from records at the Port Hueneme monitoring station during the 1973 Point Mugu earthquake. The original seismic data was processed according to a similar study on the  
Figure 5: Shear modulus reduction curve for sand compared with [PERSON] and [PERSON] (1970) [26].  
seismic response of underground stations in Chen [16]. The original ground motion was linearly matched to the UHS, then baseline corrected and low-pass filtered using the FISH function with a cut-off frequency of 15 Hz to remove high-frequency components that adversely affect wave propagation, resulting in the input ground motion, as shown in Figure 6, which correspond to the 10% in 50-year hazard level in the Daxing area of Beijing.