## 1 Introduction  
The depth of underground excavations is increasing day by day for different civil and mining engineering projects posing more challenges for safe and economic construction [1; 2; 3]. The difficulties for modelling such underground excavations due to the complex nature of rock mass are decreasing due to advancement in the research and technology, materials and systems not only in the conventional excavations methods, but also in mechanized one [4; 5; 6; 7]. In underground excavations, the issues related to the rock-mass behavior comprise the strength properties of intact rock, joint related aspects, environmental features (ground water and in situ stresses), configuration of the excavation cross section, and the excavation method; furthermore, these issues define the support required for the underground excavation [8; 9]. The ability to forecast the rock-mass quality and support pattern during the design of underground excavation is a challenging and risky task [10]. To stabilize these excavations, researchers characterize the ground in such a manner that is suitable for the support design based on past experiences, which has resulted in the development of different empirical rock-mass classification systems. Till date, empirical rock-mass classification systems have been proposed for the tunnel support system design since the earliest empirical classification proposed by [PERSON] in 1946 known as the rock load classification [4]. Some of the recommended classification systems are not favored by engineers owing to their non-practical application, but few have been frequently used owing to their reliability and practicality. The most extensively used empirical classifications of rock mass during tunnel design and construction in the world are the rock-mass rating (_RMR_) classifications and tunneling quality index (\(Q\)) systems [11; 12]. These two systems for the classification of rock masses used by engineers provide convenience in defining the preliminary support systems. The applicability of these systems has been extended with improvements in tunnel construction technology and these systems are revised extensively either in the form of characterization or support [4]. Based on ground behaviors and the available tools for underground excavation in rock engineering, the application of empirical classification systems are limited to different ground behavior during tunnel excavation and stabilization [8]. In empirical classification systems, fiber-reinforced shotcrete and rock bolts are preliminary supports that are recommended during tunnel design and construction, and _RMR_ and \(Q\) systems are effective tools for this purpose. The updated versions of these two systems suggest the shotcrete thickness and rock bolt spacing based on the same principles [13], as the excavation support ratio (ESR) in the \(Q\) system is not a parameter that is generally used worldwide, and individual countries have their own respective standards [14]. According to these principles, the fiber-reinforced shotcrete thickness is a function of the rock-mass quality (_RMR_ and \(Q\)) and tunnel span; however, the rock bolt spacing is only a function of the rock-mass quality. During tunnel stability, fiber-reinforced shotcrete and installed rock bolts act as a compound support system and the contribution of individual support depends upon its installation time and distance from the excavation face [15]. Based on the relationships of the rock-mass quality with the spacing of rock bolts (20 mm diameter) and thickness of fiber-reinforced shotcrete in the support charts of each system, a back analysis approach was established for the determination of the rock-mass quality from the tunnel span, shotcrete thickness, and rock bolt spacing in already supported tunnels [16].