## 1 Introduction  
For the purposes of rock engineering design, eight modeling methods have been categorized, including pre-existing standard methods, analytical methods, basic and extended numerical methods, precedent type analysis, empirical classification systems, the basic system approach, and the combined system approach [1]. The empirical classification systems that have been developed for rock mass are the backbone for empirical support design in tunnels, and are currently widely used. These systems have been continuously updated for this particular purpose. In 1946, [PERSON] was the first to develop a rock mass classification system, which was known as rock load factor classification, and a number of systems for rock mass quality determination have been developed since. These systems consider the most essential parameters affecting the rock mass behavior to rate its quality. In designing tunnel supports, the geomechanical classifications, which are also known as the Rock Mass Rating (RMR) system, the tunneling quality index (\(Q\)) system, and the Rock Mass index (\(RMi\)), are currently internationally accepted, and are widely used in the field of tunneling for preliminary support designs [2]. Originally, these empirical classification systems were developed, refined, and updated for the tunnel support [3]. However, they also have applications in other engineering projects such as mining [4; 5; 6; 7], slopes [8; 9; 10; 11; 12], and tunnel-boring machine (TBM) tunnels [13; 14]. Comparing the application of these systems for tunneling in high-stress environments, the \(Q\) and \(RMi\) systems are preferred over the RMR, because their parameters are more relevant for the purpose [15]. The \(Q\)-system classification was developed in 1974 [16], and major changes in its characterizations and classifications were made in 1993 and 2002 [17; 18]. In characterization, the foremost changes include the modification of the stress reduction factor (\(SRF\)) and intact rock uniaxial compressive strength (\(\sigma_{\text{c}}\)), respectively. The system was initially developed for tunneling cases in hard and jointed rock mass [19], and thus, this system is more often applied in jointed rock mass [20]. However, its application in tunnel support design is limited to an equivalent dimension (D\({}_{\text{e}}\)) ranging from 2.5 to 30, and a \(Q\) value ranging from 0.1 to 40 [21]. The Rock Mass index (\(RMi\)) system was proposed by [PERSON] in 1995 primarily for the reduced rock mass strength caused by jointing [22] and for rock support estimation in tunneling. The system was revised, and major developments and simplifications were made after five years of successful use and experience based on practical applications [23]. These simplifications are in terms of reduction in the input parameters and correlation between block volume (\(V_{b}\)) and volumetric joint count (\(J_{v}\)). This leads to easier and quicker calculations of the tunnel support parameters; i.e., the ground condition factor \(G_{c}\) and size ratio factor \(S_{r}\), especially cases where limited field investigations have been performed. In tunneling, in situ stresses are the key factors--besides rock mass and project-related features--that control the ground behavior, but empirical classification systems have limitations in application in high stress-environments [15; 24]. The limitations of empirical classification systems, which are based on the ground behavior for underground excavation in rock engineering, are shown in Table 1. In comparing the \(Q\) system and \(RMi\) for preliminary tunnel support design in the case of high in-situ stresses, the \(Q\) system has a stress reduction factor (\(SRF\)) for the purpose, but it is limited to massive rock (Table 2) [17; 25]. The \(RMi\) system uses stress level (SL) for the first three conditions of Table 2 for jointed rock mass, and has an inverse relation with \(SRF\); it can also reveal that a high stress has a positive impact on the ground condition [22; 23].