## 1 Introduction  
Convergence-confinement is a broadly applied method to design underground structures. In this method, a ground reaction curve (GRC) is applied to evaluate the interaction between the rock mass and the support system near the tunnel's face at the time of construction [1; 2; 3]. The classical problem of a circular tunnel constructed in the rock mass medium is illustrated in Figure 1b (according to [4]). This problem uses two well-known rock mass strength criteria: Mohr-Coulomb and Hoek-Brown. These criteria are usually adopted to investigate the behavior of materials. As described in references [4; 5; 6], the governing equilibrium equation of this problem is as presented in Figure 1d. In Figure 1, \(\sigma_{r}\) is the radial stress, and \(\sigma_{\theta}\) represents the tangential (hoop) stress, while the distance from the center of tunnel is shown using the \(r\) parameter. Thus, compatibility equations are simultaneously used to solve the stress-strain around the tunnel. In this regard, a plastic potential function and associated/non-associated flow rules are applied to find the governing relationship between the radial and tangential plastic strains [1; 4; 5; 7; 8; 9; 10; 11; 12; 13]. The stress-strain around the tunnel is also calculated, considering the strength parameters in different zones (the peak, residual, and softening parameters), as presented in Figure 1a,c, according to reference [4]. As explained in reference [4], using different yield and potential functions, the non-associated flow rule is the modeled and adopted as the flow rule in all the cases. Also, starting from the peak strength parameters, the deterioration of the strength parameters of the material (referred to as the softening behavior of the rock mass around the tunnel) begins and continues. For softening parameter values higher than the critical value, the residual parameters are taken into the considerations. As shown in Figure 1a,c, \(\omega(\eta)\) represents each of the strength parameters of the rock mass, and \(\eta\) and \(\eta^{*}\), respectively, are the softening and the critical softening parameters. In this figure, \(\sigma_{0}\) is the far-field in situ rock stress. In addition, Mohr-Coulomb and Hoek-Brown strength criteria are commonly used as two appropriate criteria to correctly evaluate the post-elastic behavior of rock mass. These criteria are, also, broadly applied in the literature for the development of the GRC. Hence, in this paper, available solutions with regard to the described problem are gathered, and rigorous datasets for both Mohr-Coulomb and Hoek-Brown strength criteria are obtained. As presented in the following sections, the collected  
Figure 1: Description of: (**a**) different zones and corresponding strength parameters; (**b**) a circular tunnel in an elastic-plastic, strain-softening rock mass; (**c**) corresponding relationships for strength parameters; (**d**) governing equilibrium equation; (**e**) schematic view of a typical ground reaction curve (GRC) and parameters (Hoek–Brown case) affecting on the curve. datasets are fed into the different types of artificial neural networks (ANNs). The main reason of ANN modeling of the tunnels' support pressure (\(P_{i}\)) is to save time and still obtain high accuracy in the predicted results. Previously, the evolutionary polynomial regression technique (EPR) was used by the authors to predict the \(P_{i}\) and to develop the GRC [4]. Nevertheless, there still exist some considerable prediction errors specially in the case of the Hoek-Brown strength criterion. Thus, we suppose that, in this case, ANNs may be more accurate. In this regard, available datasets should be sorted in the way shown in Figure 1e (a typical dataset for the case of the Hoek-Brown strength criterion). As depicted, each data pair stands for a point in the \(U_{i}-P_{i}\) space. \(U_{i}\) is the tunnel's radial convergence and \(P_{i}\) represents the corresponding required internal \(P_{i}\).