## 5 Conclusions  
This paper proposed a longitudinal deformation profile (LDP) considering the rock quality and the initial stress conditions. For LDP analysis, a numerical analysis method using FLAC 3D was employed, and 35 analysis results were evaluated by combining the RMR and the initial stress conditions. This study expanded the empirical equation for the LDP proposed by [PERSON] [8], which showed the best fit for the measured values of tunnel internal displacement reported by [PERSON] et al. [9]. This previous study can lead to an error in forecasting the ratio of the preceding displacement while ignoring the rock conditions. Due to this, a comprehensive tunnel behavior analysis cannot be understood. To avoid such error, an expanded longitudinal deformation profile (ELDP) is developed according to the rock mass conditions. The results of this study can be summarized as follows:  
1. An LDP equation considering tunnel excavation conditions was proposed in a generalized form, including the parameters \(\alpha\) and \(\beta\) from the empirical equation put forth by [PERSON] [8]. The parameters are expressed as a function of the RMR and the initial stress, where \(\alpha\) is a log function and \(\beta\) is an exponential function with excellent correlation coefficient. \[\frac{u_{r}}{u_{r}^{m}}=\left[1+\exp\left(\frac{-x/R_{T}}{\alpha}\right) \right]^{-\beta}\] (16) where \(\alpha=0.305\ln(\text{Po}/\text{RMR}^{1.5})+2.419\); \(\beta=2.926\,\exp(-0.01\,\text{RMR})\). 2. For the empirical formula of [PERSON] [8], which showed the best fit for the tunnel internal displacements reported by [PERSON] et al. [9], the values of \(\alpha\) and \(\beta\) were 1.1 and 1.7, respectively. However, in the present study, \(\alpha=0.898\)-2.416 and \(\beta=1.361\)-2.851 depending on the rock quality and the initial stress conditions. 3. The ratio of the preceding displacement was analyzed in the range of 0.1 to 0.35. When the rock quality was poor, the LDP varied according to the initial stress condition. However, for an RMR of 70 or more, the LDP remained the same regardless of the initial stress conditions. These results are considered to be related to the plastic area formed according to the quality of the rock. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(P_{0}=3\) MPa & A-1 & B-1 & C-1 & D-1 & E-1 & F-1 & G-1 \\ \hline \(\alpha\) & 1.94 & 1.89 & 1.81 & 1.33 & 0.91 & 0.90 & 0.90 \\ \(\beta\) & 2.82 & 2.72 & 2.51 & 1.69 & 1.37 & 1.36 & 1.36 \\ \hline \(P_{0}=5\) MPa & A-2 & B-2 & C-2 & D-2 & E-2 & F-2 & G-2 \\ \hline \(\alpha\) & 2.05 & 1.99 & 1.88 & 1.51 & 0.96 & 0.90 & 0.90 \\ \(\beta\) & 2.85 & 2.85 & 2.73 & 1.83 & 1.41 & 1.36 & 1.36 \\ \hline \(P_{0}=10\) MPa & A-3 & B-3 & C-3 & D-3 & E-3 & F-3 & G-3 \\ \hline \(\alpha\) & 2.18 & 2.16 & 2.03 & 1.84 & 1.43 & 0.90 & 0.90 \\ \(\beta\) & 2.70 & 2.78 & 2.86 & 2.18 & 1.74 & 1.36 & 1.36 \\ \hline \(P_{0}=15\) MPa & A-4 & B-4 & C-4 & D-4 & E-4 & F-4 & G-4 \\ \hline \(\alpha\) & 2.29 & 2.20 & 2.15 & 1.90 & 1.60 & 0.91 & 0.90 \\ \(\beta\) & 2.70 & 2.68 & 2.79 & 2.43 & 1.87 & 1.36 & 1.36 \\ \hline \(P_{0}=20\) MPa & A-5 & B-5 & C-5 & D-5 & E-5 & F-5 & G-5 \\ \hline \(\alpha\) & 2.42 & 2.31 & 2.00 & 1.95 & 1.80 & 0.92 & 0.90 \\ \(\beta\) & 2.74 & 2.70 & 2.65 & 2.62 & 2.01 & 1.37 & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Regression analysis results for \(\alpha\) and \(\beta\). **Author Contributions:** [PERSON]-g.H. developed the research concept and wrote the paper. [PERSON] performed the numerical analyses. [PERSON] conducted an analysis and consultation of the rock conditions for numerical analysis. [PERSON]-[PERSON] and [PERSON]-[PERSON] performed statistical analyses on the results of the numerical analysis. [PERSON]-[PERSON] reviewed the final paper. [PERSON]-[PERSON] supervised the research and provided important suggestions and recommendations for paper revision. All authors have read and agreed to the published version of the manuscript.