## 5 Conclusions  
In the present study, a large-scale model static loading experiment was carried out to explore the failure mode of the arch lining with roof voids. Based on the on-site strengthening scheme, appropriate steel plate strengthened void specimens were made to study the strengthening effect of the steel plate with a chemical anchor bolt and epoxy adhesive. Then, calculations were carried out and verified through experiments. Nine specimens were analyzed and accordingly, the following conclusions were obtained:  
1. The damage caused by vault void is mainly tensile damage and is mainly concentrated in the void boundary. This damage develops radially from the bottom surface upward. With the increase in the void range, the subsidence of the midspan relative to the void boundary gradually decreases. That is, there is a relative uplift in the middle of the span. The deformation changes from 4.74 mm downward in void height H/4 to 1.41 mm upward in void height 2H/3.
2. Compared with the unstrengthened specimens, the strengthened ones have fewer and shorter cracks under the same applied load. It is inferred that the steel plate strengthening with chemical anchor bolts and the epoxy adhesive has significantly reduced the void-induced damages. For instance, when the void height is H/4, the number of cracks after steel plate strengthening is reduced from 14 to 9, and the maximum crack length is shortened from 13.2 cm to 8.3 cm, which is a decrease of 37.12%. In addition, the steel plate strengthening also reduces the strain of the lower steel bar at the void boundary from 1130.58 \(\mu\epsilon\) to 555.12 \(\mu\epsilon\), and the strain decreases by 50.89%. When the void range is small, the whole steel plate is under tension. However, when the void range increases, the tensile force of the strengthened steel plate decreases gradually, and the compression area appears.
3. With the increase in load, the failure of the adhesive layer can be divided into two forms. At the void boundary, the adhesive layer has inclined cracks and gradually loses its function. However, due to the presence of chemical anchors here, the steel plate stress is maintained. Because there is no chemical anchor bolt in the mid-span, the stress of the steel plate decreases gradually with the expansion of the damage range of the adhesive layer.
4. A simplified calculation model is established. Considering the influence of section change on eccentricity, the bending moment, axial force, and lower surface stress of the model are obtained by integration. The results show that the voids increase the bending moment at the void boundary, reduce the axial force, and cause large tensile stress at the void boundary. The calculated results are in good agreement with the experiment.  
Although the void lining is analyzed through experiments, this experimental specimen is based on local specimens, and the experimental results may be affected by the size effect. Subsequently, we may carry out the whole lining model experiment and use the numerical model to verify the results in future studies.  
Conceptualization, Y.W.; methodology, S.S.; investigation, J.Z.; resources, K.H.; data curation, S.S.; writing--original draft preparation, S.S.; writing--review and editing, S.S.; visualization, H.W.; project administration, Y.W., and S.S.; funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the China Railway Corporation Science and Technology Research and Development Program, grant number 2018K019 and the Science and Technology Project of Zhejiang Provincial Transportation Department, grant number 2020002.  
Not applicable.  
All data are available from the author.  
The authors declare no conflict of interest.