# Calculation Method for Settlement Deformation of Existing Tunnel Induced by Underpass Construction
## 7 Conclusions  
A deformation calculation method for existing tunnels considering construction factors and soil loss is proposed, which can provide some theoretical support for analyzing the impact of shield tunnels passing through existing tunnels. The main conclusions are as follows:  
(1) The additional stress induced by the excavation of the existing tunnel is determined using the Mindlin stress solution and the three-dimensional Loganathan formula. Subsequently, the settlement of the existing tunnel caused by the underpassing new tunnel is calculated by integrating this stress analysis with the energy variational method. Field tests and numerical simulations have been conducted for the sewage pipe project in the Macao New Port area, and the results have been compared and verified against theoretical calculations. Compared with the existing method, which mainly considers soil loss, this paper considers the influence of construction factors on the deformation of existing tunnels, and the proposed calculation method fits well with the measured data and numerical simulation results, with an error of only 14.8%, compared to the existing method with an error of 31.3%.  
(2) The settlement of the existing tunnel is primarily attributed to the loss of soil resulting from the utilization of the shield tunnel boring machine. The tunnel in question exhibits gradual settlement, with the maximum settlement observed at the centerline of the tunnel. As the excavation surface of the shield gradually approaches the existing tunnel, the rate of change of settlement increases. Upon reaching the existing tunnel directly below, the rate of change reaches its maximum. Once the tail section of the shield machine has passed through the existing tunnel, the settlement tends to stabilize. The final settlement was calculated to be 2.52 mm.  
(3) A parameter sensitivity analysis was carried out for the depth of the new tunnel, its diameter, and the loss rate of the strata. The existing tunnel's level of settlement is reduced in proportion as the new tunnel's depth increases. Conversely, an increase in the new tunnel's diameter or the rate of strata loss results in greater settlement of the existing tunnel. The diameter has the most significant effect on the settlement, with a sensitivity factor of 1.87, which is higher than the ground loss rate of 1 and the new tunnel depth of 0.53.  
Conceptualization, L.C. and Y.-L.L.; methodology, L.C., J.Z., J.-H.X., Y.-L.L. and G.-L.Y.; validation, L.C.; formal analysis, L.C.; investigation, L.C.; resources, Y.-L.L.; data curation, L.C. and Y.-L.L.; writing--original draft preparation, L.C.; writing--review and editing, Y.-L.L. and L.C.; visualization, L.C.; supervision, Y.-L.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Science and Technology Research and Development Program Project of China Railway Group Limited (Grant No. 2023-Major-03).  
Not applicable.  
The data presented in this study may be available on reasonable request from the corresponding author.  
The authors would like to acknowledge the China Railway Sixth Group Co., Ltd. and the China Railway Tunnel Group Co., Ltd. for providing detailed information about the design, construction as well as the monitoring data of project.  
The authors declare no conflicts of interest.