## 5 Conclusions  
From the findings of the current work, the following conclusions can be drawn:  
* The theoretical method developed in this work can calculate the compensation for rectifying the horizontal displacement of existing tunnels by grouting. It can also be used to determine the amount of horizontal displacement of tunnels corrected by grouting. The reliability of the method was verified by comparing the calculated results with actual engineering data. The nonuniform expansion model and the uniform expansion model function similarly in simulating the compensation for rectifying the horizontal displacement of tunnels by grouting. Moreover, both the original method and the revised simplified method proposed herein can properly calculate the horizontal displacement of existing tunnels caused by grouting. The revised simplified method has higher computational efficiency and thus is more suitable for promotion and application. * The variation of the grouting volume and the grouting distance in a small range has a more significant impact on rectification of the horizontal displacement of existing tunnels; beyond a certain range, the impact of the grouting volume and the grouting distance lessens. At a constant length of grouting section, setting the bottom of the grouting section at the same depth as the lower end of the tunnel maximizes the effect of grouting correction. * The method proposed herein can help guide actual construction in two ways. First, by substituting the relevant parameters of grouting into this model, the maximum horizontal displacement of the tunnel and the influence range of grouting can be calculated; thus, the results can determine whether the grouting scheme is appropriate. Second, the impact of grouting on rectification of the horizontal displacement of the tunnel can be adjusted by tuning the grouting parameters. * Finally, a single-factor analysis of the grouting volume, the grouting distance, and the grouting depth was conducted, which resulted in an understanding of the influence law of these parameters and some conclusive suggestions that are of great significance in guiding actual construction projects. The current work simplified the influence of sleeve valve pipe grouting on the volume expansion of the grouting area; moreover, it took into account neither the variations in mechanical properties of the surrounding soil that may be caused by grouting, nor the volume expansion of the grout slurry over time. This study chiefly focused on analyzing the maximum corrective effect of grouting on the horizontal displacement of an existing tunnel. Therefore, herein, we assumed that the grouting efficiency was equal to one, i.e., \(\xi_{\text{inj}}=1\). In a follow-up research, variation in the grouting efficiency and in the corrective effect of grouting with time will be examined. In addition, the reference value of the correction coefficient (\(q\)) was obtained by inverse calculation based on measured data. In order to define ranges of the correction coefficient under different conditions, collation and inverse calculation of more similar project data need to be further developed. At present, due to the limited engineering data available, only a reference value of \(q=\)1.25 was given. The injection of a large amount of grout may cause the soil around the grouting area to change from an elastic state to a plastic state, which will affect calculation accuracy of the additional stress on the tunnel to a certain extent, although this effect is relatively small. On the other hand, considering the elastoplastic problem of soil will make the theoretical calculation method particularly complicated, which is not conducive to research and application of theoretical methods. Therefore, research on the influence of soil plasticization on the effect of grouting correction needs to be carried out in the future. Conceptualization, Y.Q. ; methodology, Y.Q. ; software, Y.Q. ; validation, Y.Q., G.W., and F.F. ; data curation, Y.Q. ; writing--original draft preparation, Y.Q.