# A Precise Prediction of Tunnel Deformation Caused by Circular Foundation Pit Excavation
## 5 Conclusions  
This paper studies the tunnel deformation caused by circular excavations; the problem is tackled numerically by means an advanced nonlinear hypoplasticity constitutive model, which is able to capture the path-dependent and strain-dependent soil stiffness, even at small strains. The numerical analysis is accompanied by an experimental calibration of the parameters based on centrifuge tests. The effect of the excavation shape and the tunnel and soil responses were analyzed. The precise prediction method is useful for practical applications and can represent a key reference the design of  
Figure 8: Additional bending strains in tunnel lining along the (**a**) transverse and (**b**) longitudinal direction. tunnel structures, accounting for the soil-structural interaction. The comparisons of the predicted results can be regarded as the verification of different design analyses, carried out by practicing engineers. Based on the comparisons between measured and computed results, the following conclusions may be drawn:  
1. Tunnel heave occurred in the existing tunnel lining, owing to stress relief above the existing tunnel. Thus, the tunnel heave caused by the circular basement excavation was 18% larger than that caused by the square basement. 2. The tunnel lining caused by both basement excavation types was elongated vertically and compressed horizontally with the basement excavation depth. The maximum tunnel diameter change caused by the circular basement excavation was 22% larger than that caused by the square basement excavation. 3. In the transverse direction, the compressive strains were recorded at the tunnel springlines, while the tensile strains arose at the other tunnel elements. The basement shape had little influence on the tunnel bending strain. In the tunnel's longitudinal direction, the symmetrical bending strain distribution could be determined with regard to the basement excavation centerline. The computed maximum tunnel bending strain caused by the circular excavation was 32% smaller than that caused by the square excavation. 4. Under identical excavation area conditions, the extent of the influence of the stress relief caused by the circular excavation was wider and deeper than that caused by the square excavation. This implies that controlling the deformation of a metro tunnel under excavation depends mainly on the length of the metro tunnel passing through the excavation area, rather than on the excavation shape. The computed data used to support the findings of this study are included within the article. Previously reported measured data were used to support this study and are available at [[[https://doi.org/10.1139/cgi-2012-0423](https://doi.org/10.1139/cgi-2012-0423)]([https://doi.org/10.1139/cgi-2012-0423](https://doi.org/10.1139/cgi-2012-0423)), [[https://doi.org/10.1139/cgi-2014-0361](https://doi.org/10.1139/cgi-2014-0361)]([https://doi.org/10.1139/cgi-2014-0361](https://doi.org/10.1139/cgi-2014-0361))]. These prior studies (and datasets) are cited at relevant places within the text as references [7; 12]. Conceptualization, H.S. ; methodology, H.S. ; software, H.S. and S.C.; validation, H.S. and L.W. ; formal analysis, H.S. and L.W. ; investigation, H.S. and H.D. ; resources, H.S. and S.C.; data curation, H.S. and H.D. ; writing--original draft preparation, H.S. and L.W. ; writing--review and editing, H.S. and J.Z. ; visualization, H.S. ; supervision, H.S. ; project administration, H.S. ; funding acquisition, H.S. This research was funded by the National Natural Science Foundation of China, grant number 51708245, the Natural Science Foundation of Jiangsu Province, grant number BK20160426, and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB620002, 17 KJB130003, 17 KJA560001). We thank the anonymous reviewers for their valuable comments and suggestions. We thank [PERSON], Edanz Editing China (www.liwenbianji.cn/ac), for editing the English text of a draft of this manuscript.