## 4 Conclusions  
The ABGPR-MC reliability method of an initial support structure for a deep rock tunnel was proposed in this study. The LHS method was employed to generate the sampling points for obtaining the geo-mechanical parameter dataset of the ABGPR. CRBF was constructed and selected as the kernel function in the ABGPR-MCS reliability calculation. The efficiency and feasibility of the proposed method were illustrated and analyzed by ABGPR-MC and PRSM. The conclusions are as follows. 1. A comparison among the prediction abilities of RBF, K1.5, K2.5, RBFK1.5, RBFK2.5, and CRBF indicates that the prediction ability of CRBF is the strongest. It is denoted \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Iteration Number** & **\(\boldsymbol{E/GPa}\)** & \(\boldsymbol{\mu}\) & \(\boldsymbol{c/MPa}\) & \(\boldsymbol{\varphi}^{\text{\tiny{G}}}\) & \(\boldsymbol{\beta}\) \\ \hline
0 & 0.3306 & 0.338 & 0.1896 & 32.795 & \\
1 & 0.3271 & 0.338 & 0.1874 & 32.483 & 2.87 \\
2 & 0.3288 & 0.338 & 0.1864 & 32.424 & 2.94 \\
3 & 0.3281 & 0.338 & 0.1864 & 32.507 & 2.77 \\
4 & 0.3291 & 0.338 & 0.1860 & 32.484 & 2.80 \\
5 & 0.3287 & 0.338 & 0.1863 & 32.491 & 2.77 \\
6 & 0.3288 & 0.338 & 0.1863 & 32.514 & 2.64 \\
7 & 0.3284 & 0.338 & 0.1867 & 32.560 & 2.40 \\
8 & 0.3278 & 0.338 & 0.1873 & 32.480 & 2.68 \\
9 & 0.3288 & 0.338 & 0.1864 & 32.484 & 2.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Iteration results of PRSM. that the prediction ability of the ABGP model can be greatly improved through the design of the combined kernel functions. 2. A comparison between the reliability indices obtained from the proposed ABGPR-MCS method and the PRSM indicates that ABGPR-MCS is an efficient method for the probabilistic analyses of deep rock tunnel engineering. The most distinct advantage of the proposed method is that it can establish an optimized surrogate model for the numerical simulation calculation and obtain the mean value, variance, and confidence interval of geo-mechanical parameters. 3. For deep rock tunnel structure systems with fewer failure elements, using the proposed ABGPR-MCS reliability analysis method and the system reliability theory can estimate its failure probability range and determine its comprehensive reliability index. The proposed method can quickly assess the chances of large deformation disasters in deep soft rock non-circular tunnels. 4. From the system reliability calculation results obtained by using the proposed reliability method, it can be denoted that the support structure of the tunnel in this study is safe, which is consistent with the actual situation. For zones of the initial support structure of the tunnel with low reliability, the reliability and safety of the tunnel can be improved by strengthening the initial support measures. 5. Using the ABGPR method to establish a surrogate model of the nonlinear mapping relationship between geo-mechanical parameters and their responses can significantly reduce the time needed for numerical simulation calculations. There are obvious advantages regarding the prediction error and the prediction ability of the proposed method (ABGPR) compared with Kriging and XGBoost. The selection of kernel functions in this study mainly considers model performance, and the next step of research needs to combine data characteristics, computational resources, and parameter adjustments. Due to the fact that it took over two months for more than 1000 rounds of 3D numerical simulation calculations by using ABAQUS, we only conducted sampling using the LHS method in this study. In further research, we will incorporate a bootstrapping technique to conduct the sampling to eliminate the effect of randomness in DoE. The dynamic loads and weakening of the rock mass due to the presence of water have a significant impact on the stability of deep-buried soft rock tunnels. Our numerical simulation did not consider them, which is the main limitation of this study.