## 2 Numerical Analysis Setup
### Materials Properties and Parameters  
In this study, the liquefiable soil is an 8 m-thick medium-saturated sand with a relative density of 45%, and the non-liquefiable soil above and below is silty clay in a plastic state. In the first stage (i.e., the static analysis), the excavation pit, underground utility tunnel application, and soil backfill are simulated [23]. The elastic-perfect-plastic Mohr-Coulomb damage criterion can represent the elastic and plastic characteristics of geotechnical materials with few and easily accessible parameters and is widely used in the numerical simulation of geotechnical materials. Therefore, the soils in the static analysis are modeled using the Mohr-Coulomb model for simplification. In the dynamic analysis, liquefiable sand is simulated using the Finn model. The Finn model establishes a relationship between cyclic shear strain and volumetric strain increments and can calculate the rise in pore pressure during shaking, thus providing a good simulation of the cyclic shear properties of sand [24]. The sand properties and liquefaction parameters are obtained from experiments on typical liquefiable sand from the study of [PERSON] [25]; the silty clay parameters are obtained based on the results of geological exploration in Beijing, as shown in Table 1.  
Figure 3: Illustrations: (**a**) numerical model for the 2 m burial depth case, and (**b**) grid of the control surface S and control point locations. The members of the underground utility tunnel (top slab, bottom slab, side walls, and internal partition walls) are continuous in the longitudinal direction, so the strength indices of each member are calculated on a per-meter basis and the moment capacity and shear capacity are calculated based on the cross-sectional area, reinforcement distribution and material strength of the structural members. The bending moment capacities of the side walls and the internal partition walls are 226 kN\(\cdot\)m/m and 90 kN\(\cdot\)m/m, respectively, and the shear capacities are 374 kN/m and 191 kN/m, respectively. The underground structure is assumed to be elastic material with the elastic modulus and Poisson ratio of 32.5 GPa and 0.2, respectively. The top and bottom slabs and side walls of the utility tunnel are modeled with liner elements (a type of Shell-Type structural element in Flac3D) and the internal partition walls are modeled with shell elements (a type of Shell-Type structural element in Flac3D). The plastic hinges are set at the member connection. The plastic hinge allows for rotational discontinuities when the ultimate plastic moment is reached and is suitable for modeling the large strain, post-damage behavior of the structure. In this paper, the moment capacities of the members are used as the moment limit for the plastic hinges. To verify the plastic hinge, a wall of height 3.5 m with a cross-sectional area of 0.4 m \(\times\) 1 m is built, as shown in Figure 4a, with the bottom connected to a fixed support with plastic hinges and horizontal displacement loads applied at the top. Figure 4b shows the relationship between the bending moment at the plastic hinge and the horizontal displacement load. The value of the moment at the plastic hinge remains constant after reaching the design capacity value and exhibits as elastic-perfectly plastic. The liner elements control the shear and normal behavior of the structure-soil interface through the strength properties (T\({}_{\text{S}}\), S\({}_{\text{S}}\), \(\delta\)) and stiffness properties (\(k_{s}\), \(k_{n}\)) of the normal and shear springs.