## 4 Conclusions and Perspectives  
The available classical methods require a broad understanding of the governing mechanisms of the convergence-confinement method and programming skills to derive the GRC for the elasto-plastic, strain-softening rock mass. Considering the proven ability of AI techniques in the prediction of the \(P_{i}\) of circular tunnels [4], the applicability of another intelligent method is investigated in this study to obtain even more accurate predictions. To do this, the performance of two different ANN types, namely, MLP and RBF, were evaluated and compared. The described methods were applied to the GRC development in both the Mohr-Coulomb and the Hoek-Brown rock mass cases. In this regard, available solutions with regard to the problem were collected, and a total of 168 and 547 datasets were compiled for the Mohr-Coulomb and the Hoek-Brown cases, respectively. Elastic rock mass properties, peak and residual strength parameters, softening and geometrical parameters, in situ stress, and the convergence of tunnel were employed as the input parameters to predict the internal \(P_{i}\). After building various one- and two-layer neural networks with the TANSIG transfer function and assessing the values of the coefficient of determination, root-mean-square error, and mean absolute error, the following conclusions were obtained:  
* The ANN-based method appeared to be a highly performant method, applicable to the the development of GRC and the estimation of the \(P_{i}\) of circular tunnels;
* The 15-5-10-1 (\(R^{2}=99.48\%\), \(RMSE=0.03883\) MPa, and \(MAE=0.02825\) MPa) and 15-15-1 (\(R^{2}=99.21\%\), \(RMSE=0.050576\) MPa, and \(MAE=0.040918\) MPa) networks were reported as the best MLP and RBF networks for the Mohr-Coulomb case, respectively;
* For the Hoek-Brown case, the 17-5-15-1 MLP (\(R^{2}=99.91\%\), \(RMSE=0.179285\) MPa, and \(MAE=0.12516\) MPa) and the 17-3-12-1 RBF (\(R^{2}=93.18\%\), \(RMSE=1.558064\) MPa, and \(MAE=1.078099\) MPa) architectures were the most accurate proposed neural networks;  
Figure 8: Comparison between the performance of (**a**) 15-5-10-1 MLP-ANN and evolutionary polynomial regression technique (EPR) model (Mohr–Coulomb case); (**b**) 17-5-15-1 MLP-ANN and EPR model (Hoek–Brown case) in the prediction of the \(P_{i}\). * It was shown that the overall performance of MLP networks was better than that of the RBF networks for both Mohr-Coulomb and Hoek-Brown cases;
* The results obtained from the comparison between neural network and EPR models proved the superiority of ANN to the EPR in the prediction of \(P_{i}\);
* The proposed networks can be effectively applied by design engineers and practitioners to accurately, time-effectively, and economically obtain the GRC using a new set of data is available;
* The proposed networks can be successfully applied in conjunction with the support characteristic curve to calculate the proper time of the installation of the tunnels' supports;
* Regarding the successful application of ANNs to the problem and as suggestion for future works, the applicability of other soft computing techniques (e.g., genetic programming, ant or bee colony, etc.) can be investigated;
* As another perspective of the current research, stress-strain and time-dependent behavior of rock masses can be studied on the basis of the implementation of viscose constitutive models;
* The formation of damaged zones around the tunnel's surface (which is the subject of new work by the authors) and new EPR and ANN methods for the prediction of pressures are other interesting perspectives suggested by the present paper. The analyses were carried out by [PERSON] This paper was written by [PERSON], [PERSON] supervised the conducted research, reviewed, and revised the paper. [PERSON] reviewed, revised, and improved the paper. The authors declare no conflict of interest. The analyses were carried out by [PERSON] This paper was written by [PERSON], [PERSON] supervised the conducted research, reviewed, and revised the paper.