## 5 Conclusions  
An analytical method for predicting the strip foundation building response induced by three-dimensional ground settlement due to shallow tunneling is presented in this paper. The tunneling process and different alignment angles are taken into account in the proposed method. The effects of six typical factors on the building response are illustrated. The main conclusions follow:  
1. The reliability of the proposed method is determined in comparison with finite element and finite difference analysis. The results obtained from the proposed method show good agreement with the two numerical results and close to those from the Winkler-based method.
2. The building settlement increases with the increase in the bending stiffness and gap parameter, and decrease as the distance from the tunnel face increases, and the elastic modulus and Poisson's ratio of the soil increase. The differential settlement of the building increases as the alignment angle decreases and the gap parameter increases, and reaches a maximum when the tunnel face is located at the middle of the building.
3. Increases in the alignment angle and soil Poisson's ratio, and the decrease in the gap parameter can decrease the rotation angles. By increasing the soil elastic modulus, the rotation angles of the left half of the building decrease while those of the right half of the building increase. The opposite trend can be observed for the bending stiffness. When the tunnel face arrives at the middle of the building, the rotation angles are symmetric with respect to the building centerline.  
Figure 14: Building response with different gap parameters: (**a**) settlement; (**b**) rotation angle; (**c**) bending moment; (**d**) shear force.  
* The maximum bending moments and the maximum shear forces gradually decrease with a larger alignment angle. The bending moments and the maximum shear forces increase as the soil elastic modulus, bending stiffness, and gap parameter increase, and decrease with the increase in the soil Poisson's ratio. The maximum bending moments occur at the middle of the building, and the maximum shear forces appear at about one-fifth and four-fifths of the building length when the tunnel face is located at the two ends of the building.
* The influence of the plastic behavior of the soil and the contact state between the building foundation and the underlying soil on the building response need to be considered in a further study.  
Conceptualization, L.Y. and Y.L.; methodology, L.Y. and G.W.; software, Y.L. and L.C.; formal analysis, L.C.; investigation, L.Y. and G.W.; data curation, G.W. and Y.L.; writing--original draft preparation, L.Y.; writing--review and editing, Q.F.; supervision, D.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Research Project of Beijing Mass Transit Railway Operation Corp. Ltd., grant number 202100058100007, and the National Natural Science Foundation of China, grant numbers 52108376 and 51738002.  
Not applicable.  
Data Availability Statement: Data are contained within this article.  
The authors thank the reviewers for their great help on the article during the review process.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.