## 5 Conclusions  
In the present study, the tunnel sidewall stress release method was utilized to obtain the elastic strain at finite measurement points on the tunnel surface. By integrating it with the developed SMARS algorithm, a stress-field inversion method for the stresses around a tunnel was proposed based on surface strain measurements. The results were applied to the inversion of the stress data from a deep tunnel and its surrounding rock mass in Macheng Iron Mine. Through validation and field application, the following conclusions can be drawn:  
1. The utilization of the equilibrium stress subroutine can avoid errors caused by artificial stress or displacement boundary conditions. Secondly, by directly inverting the stress field based on strain measurements, it circumvents the secondary errors introduced by calculating stresses based on elastic principles. Additionally, by considering the excavation-induced plastic damage to the surrounding rock, severe distortion of the results arising from use of the governing constitutive model can be prevented.  
Figure 14: Collapsed zone of the tunnel at the field site.  
Figure 13: The inverted stress field around the tunnel.  
Based on accuracy verification through examples and field applications in the Ma Cheng iron mine, the proposed stress inversion method can achieve an accuracy of over 90% in practical applications. Particularly for deeply buried rock masses, this method proves to be a simple and cost-effective approach.  
According to the in situ stress measurement method proposed in this study, the maximum principal stress, intermediate principal stress, and minimum principal stress in the rock at the Ma Cheng iron mine were calculated as 38.78 MPa, 25.68 MPa, and 11.63 MPa, respectively. The ratio between the maximum and minimum principal stresses is 3.33:1, and the maximum principal stress is 1.43 times greater than the intermediate principal stress. The concentration of stress is evident in the left-hand side of the tunnel arch. These findings are consistent with the observed collapse phenomena.  
In practice, we often encounter challenges related to the difficulty and high cost of measuring strain or stress, especially when measuring stress fields in deeply buried tunnels. The inversion method developed in the present study provides an effective solution to this problem. Through a small amount of measurement data, the stress distribution within the problem domain can be revealed without the need for extensive on-site measurements, saving valuable time and costly resources. The proposed method also shows certain limitations; when the rock mass surface is highly fractured or characterized by significant joint development, the accuracy of strain measurements may be compromised, leading to larger errors in the inversion results. Therefore, it is crucial to obtain accurate surface strains under special geological conditions and construct the corresponding geological models with precision. This will be the key to improving the accuracy of stress inversion and an important focus of future research.  
Conceptualization, Q.H. and F.Z.; methodology, Q.H.; software, Q.H.; validation, R.Y., J.P. and S.T.; investigation, Q.H.; resources, R.Y.; data curation, Q.H.; writing--original draft preparation, Q.H.; writing--review and editing, J.P. and F.Z.; visualization, R.Y. and J.P.; supervision, X.Y.; project administration, X.Y.; funding acquisition, F.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 52274114).  
Not applicable.  
That data that support the findings of this study are available from the corresponding author, [Q.H.], upon reasonable request.  
The authors declare no conflict of interest.