## 5 Conclusions  
A series of centrifuge tests in tunnels located at cover over diameter (C/D) ratios equal to 0.5, 1.0 and 1.5 were carried out to investigate the ground deformation induced by the variation of excess/insufficient support pressure. The soil pressure, pore pressure, maximum surface displacement and the ground movement induced by reduced/increased support pressure were investigated. Based on the centrifuge test, the ground deformation mechanism was analyzed compared with previous studies and a supporting pressure control coefficient was proposed to conduct quantitative analysis of surface deformation induced by support pressure. Finally, the control of support pressure based on the surface deformation was discussed to provide some advice for practical engineering. The numerical investigation will be carried out in the future. The key findings in this paper are summarized as follow:  
1. The ground disturbance range induced by excess support pressure is approximately fishtail-shaped. When the burial depth is shallow (<1.5D), the surface disturbance range can extend horizontally to about twice buried depth beyond the front of the face and the maximum heave occurred at a distance of approximately buried depth beyond the front of the excavation face. However, when the burial depth is large (\(\geq\)1.5D), the ground deformation caused by the excess support pressure is difficult to extend to the surface, but it will cause great disturbance in the ground.
2. The ground disturbance range induced by insufficient support pressure is approximately chimney-shaped. The range of ground disturbance area in water-rich sand soil induced by insufficient support pressure was observed to extend horizontally to about buried depth beyond the front of the face which was larger than that in dry sand soil. The shallower the buried depth, the more sensitive the ground deformation as well as the greater the range of ground surface settlement.
3. A supporting pressure control coefficient which is related to buried depth is proposed to quantitatively describe the relationships between the surface displacement with support pressure and the relationship was found linear before the excavation face reaching the limit state.
4. The effect of reducing the initial settlement by increasing the support pressure is limited, and may even further cause greater surface settlement directly above the excavation surface. In comparison, the ground deformation is more sensitive in the case of insufficient support pressure. For shallow tunnels, the support pressure needs to be strictly controlled to avoid being insufficient while for deep tunnels, if the supporting pressure is insufficient, it is necessary to pay attention to the discharge amount of soil to avoid further accelerating the ground deformation disturbance.  
Conceptualization, W.L. and D.Y.; methodology, P.L.; software, W.L.; validation, P.L. and D.J.; formal analysis, W.L.; investigation, W.L. and P.L.; resources, J.C. and G.Y.; data curation, W.L. and P.L.; writing--original draft preparation, W.L.; writing--review and editing, P.L.; visualization, D.J.; supervision, D.Y.; project administration, J.C.; funding acquisition, D.Y. and D.J. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China under Grant No. 52008021, the Key Project of High-speed Rail Joint Fund of National Natural Science Foundation of China under Grant No. U1834208.  
Not applicable.  
The data presented in this study are available from the corresponding author upon request.  
The authors gratefully acknowledge financial support from the National Natural Science Foundation of China under Grant No. 52008021, the Key Project of High-speed Rail Joint Fund of National Natural Science Foundation of China under Grant No. U1834208. Appreciate for the support by the CSC scholarship.  
The authors declare no conflict of interest.