## 2 Materials and Methods
The authors of [43; 44] provided a quantitative base to evaluate the GSI system using proposed ratings of rock mass structure and surface condition (SCR), and a structure rating (SR) based on the volumetric joint count (Jv), and the roughness, weathering, and infilling nature of joints. A new testing procedure was proposed in [45] to estimate rock mass deformation using the GSI, based on Hoek-Brown's empirical constants and the Mohr-Coulomb failure criterion. The available equations allowing calculations of rock mass deformation considering the GSI are summarised in Table 1.  
Figure 4: Relationship between rheological deformation and time, obtained by experimental and analytical approaches. Based on the listed equations in Table 1, the authors adopted Formula (24) to estimate the rock mass strain modulus, as proposed by [36]. Combining Equation (6) and Formula (24) we obtain:  
\[E_{t}=E\bigg{[}0.02+\frac{1-D/2}{1+e^{((60+15D-GSI)/11)}}\bigg{]} \tag{25}\]  
Currently, to characterise rock masses, rock mass classification systems can be divided into two main groups, qualitative and quantitative. The qualitative classification comprises the GSI (geological strength index); rock load; and SIA 199, while the Q; RMR; RSR; and RQD systems are quantitative in their nature [3; 34; 36; 46; 47]. Since the first rock mass classification was proposed, together with a new experimental approach to tunnel design, the system has been adopted and enhanced and now comprises a huge number of challenging factors to establish parameters [35; 36; 37; 48; 49; 50]. Rock mass classification schemes are used to support the design of underground supporting structures such as RMR, Q and GSI. Some well-known classification systems are listed in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**References** & **Formulas** & **Number** \\ \hline
[41] & \(E_{rm}[GPa]=(1-D/2)\sqrt{\frac{e_{rm}}{10}}10^{\frac{GSI-10}{60}}\) & (20) \\ \hline
[41] & \(E_{rm}[GPa]=(1-D/2)10^{\frac{G(1-D)}{60}}\) & (21) \\ \hline
[46] & \(E_{rm}[GPa]=0.1451e^{(0.0654 GSI)}\) & (22) \\ \hline
[36] & \(E_{rm}[GPa]=100\Big{(}\frac{1-D/2}{1+e^{(60+15D-GSI)/11}}\Big{)}\) & (23) \\ \hline
[36] & \(E_{rm}[GPa]=E\Big{(}0.02+\frac{1-D/2}{1+e^{(60+15D-GSI)/11}}\Big{)}\) & (24) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Established formulas for rock mass strain modulus calculations, considering GSI. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rock Mass Classification System** & **Reference** & **Application Areas** \\ \hline Rock Load & [29] & Tunnels with steel support \\ \hline Stand-up time & [1] & Tunnelling \\ \hline New Austrian Tunnelling & & \\ Method (NATM) & [51] & Tunnelling \\ \hline Rock Quality Designation (RQD) & [34] & Core logging, tunnelling \\ \hline Rock Structure Rating (RSR) & [49] & Tunnelling \\ \hline Rock Mass Rating (RMR) & [36] &
\begin{tabular}{c} Tunnels, mines, \\ (slopes, foundations) \\ \end{tabular} \\ \hline Modified Rock Mass Rating (M-RMR) & [52] & Mining \\ \hline Rock Mass Quality (Q) & [37] & Tunnels, mines, foundations \\ \hline Strength-Block size & [53] & Tunnelling \\ \hline Basic Geotechnical Classification & [54] & General \\ \hline Rock Mass Strength (RMS) & [55] & Metal mining \\ \hline Unified Rock Mass Classification & [56] & General \\ System (URCS) & [57] & Coal mining \\ \hline Communication Weakening Coefficient & & \\ System (WCS) & [57] & Coal mining \\ \hline Rock Mass Index (RMI) & [58] & Tunnelling \\ \hline Geological Strength Index (GSI) & [38] & All underground excavations \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rock mass classification systems (modified after [3]). [PERSON] and [PERSON] [58] established the experimental relationships for rock mass mechanical parameters such as compression strength, and strain modulus, which increase exponentially along with an increase in rock mass quality. In accordance with [59], a database of GSI was proposed, where values of the GSI were adopted from the range of 13 to 80.