## 5 Conclusions  
In this paper, the seismic response of a one-story, three-span utility tunnel in a non-homogeneous liquefiable site is investigated using a finite-difference program (Flac3D). Numerical models for five burial depths of 2 m, 2.5 m, 3 m, 3.5 m, and 4 m are developed to study the effect of burial depths on seismic performance. Matching ground motion is selected as the input dynamic load in the PEER database based on the site-specific UHS. For the liquefiable layer, the Finn model is used to simulate the cyclic shear properties and the accumulation of pore water pressure. For non-liquefiable soils, the elastic-perfect-plastic Mohr-Coulomb model is used to represent the elastic and plastic characteristics of the material. Using structural elements model the utility tunnel, and plastic hinges are used at the connections of the members to simulate their plastic behavior. This paper analyzes the general force characteristics of the utility tunnel in liquefied soil and the uplift of the structure induced by excess pore water pressure, investigates the effect of burial depth on the structures' seismic response, and draws the following conclusions from the numerical results:  
1. The internal forces of the side walls in the liquefied soil are greater than the internal partition walls under the earthquake; the bottom of the side wall has a large value of bending moment and shear force. The growth of excess pore water pressure in the soil beneath the structure generates vertical unbalance forces; the soil on both sides of the structure moves towards the underside of it; the utility tunnel uplifts under the action of the surrounding liquefied soil and thus fails;
2. The burial depth of the underground utility tunnel has a great influence on its seismic response. The drift ratio, bending moment, and shear force of the structure under  
Figure 17: [PERSON] et al. (2020) [7] numerical simulation results: (**a**) time histories of vertical displacement of the midpoint of the top slab and the surrounding soil, and (**b**) vertical displacement at the midpoint of the top slab at different burial depths. the condition of 4 m burial depth are the largest, and the shear force at the bottom of the left side wall is close to the shear capacity. The internal forces of the structure increase with the burial depth, and the normal forces acting on the side walls and their increments increase with the burial depth, among which the normal forces at the bottom of the side walls increase significantly. The increase in burial depth also significantly reduces the uplift of the utility tunnel; the overburden pressure and excess pore water pressure increase with burial depth, the pore pressure ratio decreases under the combined effect of the two, and the liquefaction of the soil below the structure decreases;
3. Appropriately increasing the burial depth of the shallow-buried utility tunnel at the liquefiable site will improve its seismic stability. The following remarks can be considered in future research:
* The characteristics of ground motion such as intensity, frequency, and duration can impact the seismic response of underground structures. Use the \"Dynamic optimization with single dynamic loads\" method to reduce the impact of \"record-to-record variation\" problems in seismic engineering on the results. * The addition of haunch to the utility tunnel will improve the seismic performance of the members' joints. In the numerical simulation, the structure with haunches should be modeled according to the practical situation. * This paper investigates the seismic response of shallow-buried utility tunnels with burial depths of 2 m-4 m, and should further investigate the dynamic characteristics of deep-buried utility tunnels [32]. Methodology, T.T. and A.Y. ; Validation, T.T. and A.Y. ; Data curation, T.T. ; Writing--original draft, T.T. ; Writing--review & editing, T.T., Y.L. and Y.G. Project administration, A.Y. ; All authors have read and agreed to the published version of the manuscript.