## 6 Conclusions  
This article relies on a certain foundation pit project in Beijing's urban sub-center to study the deformation response of an existing subway tunnel under the excavation of a double foundation pit with an externally connected irregular shape using Plaxis3D numerical simulation. The following four conclusions are drawn:  
1. In terms of the overall displacement during the entire construction process, the impact of the simultaneous excavation of the double foundation pit (Plan 2) on the existing tunnel line is relatively significant, while the impact during the construction cycle of sequential excavation (Plan 1) is relatively small. The similarity in the excavation sequence results in a similarity in the trend of the impact. The early displacement trend of comprehensive excavation (Plan 3) is consistent with simultaneous excavation, and the latter displacement trend is consistent with the sequential excavation scenario.  
Figure 15: Vertical and horizontal displacement increment values for each scenario in each working condition. (**a**) P1: Incremental vertical displacement, (**b**) P1: incremental horizontal displacement, (**c**) P2: incremental vertical displacement, (**d**) P2: incremental horizontal displacement, (**e**) P3: incremental vertical displacement, (**f**) P3: incremental horizontal displacement.  
2. The excavation volume determines the displacement change values for each excavation scenario under each working condition and is the reason for the convergence of the trends. Despite the different excavation sequences and timing of the three scenarios, the increase in the volume of excavation throughout the construction cycle leads to soil relaxation and displacement. This common influence of excavation volume, regardless of the scenario used, results in the similarity of the final displacement values at the same node of the tunnel.
3. The trend of total displacement change is relatively consistent with the trend of vertical displacement change, with the change being dominated by vertical displacement, and the influence of horizontal displacement is relatively small. The impact of horizontal displacement is more pronounced in the early stages, and the different increases in vertical and horizontal displacement during the later excavation process lead to an increase in the tunnel's structural non-circularity.
4. The maximum total displacement of the tunnel occurs on the side of the tunnel close to the excavation area, and the direction is inclined towards the excavation area. The construction of supporting structures, especially the middle and bottom plates, can suppress the upward vertical deformation of the tunnel but has a less noticeable effect on horizontal displacement.  
It is worth noting that the determination of HSS constitutive model parameters in the manuscript is based on experiments on site soil and the relevant literature on soil constitutive research in Beijing, and its applicability may only be limited to Beijing and its surrounding areas. Therefore, in the future, corresponding research will be conducted in soft soil areas such as Shanghai to explore the impact of multi-pit excavation on tunnels in different regions.  
Methodology and writing, S.W.; Validation and writing, W.W. and H.Y.; Writing--review and editing, D.Z. and Y.L. All authors have read and agreed to the published version of the manuscript.  
The work presented in this paper was financially supported by the Beijing Natural Science and Foundation (No. 8222020).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Authors [PERSON], [PERSON], [PERSON] were employed by the company Second Engineering of CCCC Third Highway Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.