# Dynamic Response of Rectangular Tunnels Embedded at Various Depths in Spatially Variable Soils
## 5 Conclusions  
In this study, dynamic response characteristics of foundation soil and tunnel structure were studied under four kinds of tunnel depth conditions by considering soil anisotropy random field, including the analysis of soil excess pore water pressure ratio, foundation liquefaction range, tunnel floating displacement and surface deformation. Based on the results of calculation and analysis, the main conclusions were as follows:  
1. The excessive static pore pressure ratio and soil liquefaction range are greatly affected by the change in the tunnel embedment depth. With depth increasing, the soil excess pore water pressure ratio under the tunnel gradually decreases and the liquefaction degree reduces. The peak value of the foundation liquefaction range increases with the increase of embedment depth, and the time history of the liquefaction range rises faster over time in the ascending stage, while decreasing faster over time in the descending stage.
2. The tunnel depth has the same effect on the maximum uplift displacement of the tunnel and the ground surface. With the increase of embedment depth, the thickness of the overlying soil and the gravity of the soil also increase, which leads to the decrease of the maximum displacement of the tunnel and the ground surface, and the decrease of the maximum settlement of soil far away from the tunnel area.
3. When considering the anisotropy random fields of soil shear modulus, the mean response of stochastic analysis is smaller than the deterministic calculation results when the tunnel embedment depth is less than 10 m. However, when \(H\) = 10 m, it will seriously overestimate the deformation of soil and tunnel structure if the soil is regarded as a uniform field.  
The conclusions obtained in this paper are able to provide guidance for the site selection and seismic design of tunnels in the liquefaction zone. The limitations of the study primarily exist in two aspects: firstly, only one type of random field was adopted in this paper, the effect of the coefficients of variation and scales of fluctuation of random field on the tunnel behavior had not been studied; secondly, the plane strain condition was adopted in this paper, while the seismic response of the tunnel in the longitudinal direction also need to be studied. Further study is recommended to develop a 3-D random field model to investigate the dynamic response of tunnels in the longitudinal direction.  
Figure 22: Displacement vector diagram of soil around tunnel structure.  
**Author Contributions:** Conceptualization, Y.W. and Y.Z.; methodology, Y.W.; software, Y.Z. and H.Z.; validation, Y.W. and Y.Z.; formal analysis, Y.Z. and H.Z.; investigation, Y.Z., H.Z. and Y.W.; resources, Y.Z.; data curation, Y.Z. and H.Z.; writing-original draft preparation, H.Z.; writing-review and editing, Y.W. and Y.Z.; visualization, Y.Z.; supervision, Y.Z.; project administration, Y.W. and Y.Z.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the key science and technology special program of Yunnan province, grant number 202102 AF080001.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors acknowledge the financial support of the key science and technology special program of Yunnan province (No. 202102 AF080001).  
The authors declare no conflict of interest.