## 4 Effect of Burial Depth of Utility Tunnels
### Structure-Soil Interactions  
The structure-soil interaction and the state of the soil impact structures' seismic response during the earthquake. This section discusses the effect of burial depth on the structural seismic response by analyzing the normal forces on the left and right walls and the liquefaction ratio of the soil beneath the structure.  
Figure 15 shows the distribution of the initial normal force on the left and right walls and the residual normal force at the end of the earthquake for five burial depths. The normal force on the wall is calculated over a longitudinal range of 1 m and is obtained by integrating the lateral earth pressure of the soil along the height of the wall. It can be seen that the normal force distribution on the wall at the end is larger than the initial state, and the growth of the normal force at the bottom of the wall is larger. Both normal force and normal force increment increase with burial depth, and the normal force increment at the bottom of the right wall of the model with a 3.5 m burial depth is 1.9 times that under 2 m burial depth, which increases the shear force of the structure.  
Figure 14: Residual vertical displacement of the ground surface under five burial depth conditions.  
Underground structures are kept in balance under the action of uplift forces and anti-buoyancy forces, of which excess pore water pressure is an important part of the uplift forces. The development of excess pore water pressure in liquefiable soil beneath the structure during the earthquake alters the original balance, and the structure is uplifted under the action of vertical unbalance forces. Figure 16a,b show the time histories of the pore pressure ratio of the soils beneath the structure, and the vertical displacement at the midpoint of the top slab for the five burial depth conditions, respectively. As the burial depth increases, the liquefaction ratio of the soil beneath the structure decreases, and the structure's uplift also decreases the combined effect of excess pore water pressure and vertical effective stress.  
The rationality of the seismic behavior analysis of the utility tunnel is verified by comparing it with the research results in the existing literature. [PERSON] et al. (2020) [PERSON] et al. (2020) investigated the uplift response of the typical underground access structures in homogeneous liquefiable sands with different burial depths under seismic action by developing numerical models. The soils were loosely saturated sand with a relative density of 20%, and the 1988 Saguenay earthquake record (the earthquake amplitude was multiplied by a constant value to be compatible with the largest seismic zone in Quebec) was used as the  
Figure 16: Five burial depth conditions: (**a**) time histories of excess pore water pressure in the soils beneath the structure, and (**b**) vertical displacement at the midpoint of the top slab.  
Figure 15: Normal force distribution of the left and right walls at the initial state and the end of the earthquake, the data in (**a-e**) are from numerical models for 2 m, 2.5 m, 3 m, 3.5 m and 4 m burial depths, respectively.  
seismic load to study the effect of the 0-1 m burial depth range on the uplift displacement of the underground access structures. Figure 17a shows the vertical displacement of the midpoint of the top slab and the surrounding soil in [PERSON]'s calculation, and Figure 17b shows the uplift displacement of the underground access structure under different burial depth conditions. Comparing Figures 11 and 17a, it can be seen that the uplift of different types of underground structures and the settlement of the surrounding soil at the liquefied site under seismic loading are in good agreement, from Figures 16b and 17b, it also can be seen that the response of the uplift of the underground structure decreases with increasing burial depth is also consistent, so it can be considered that the numerical calculation results of this study for the seismic response of the underground utility tunnel are reasonable.