## Materials and Methods
### Characterization and Classification of Rock Mass Based on \(Rmr_{89}\)
For graphical rating, which is a more precise method of characterization, the range of \(RQD\) rating for \(RMR_{89}\) is clarified [23], and after this clarification the continuous rating of \(RQD\) can be determined from Equation (3):  
\[R_{2}=0.22 RQD-0.0002 RQD^{2} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{8}{c}{_RMR_} \\ \cline{2-10}  & **1973** & **1974** & **1975** & **1979** & **1989** & **2011** & **2013** & **2014** \\ \hline \multirow{2}{*}{Intact rock strength (MPa)} & 0–10 & 0–10 & 0–15 & 0–15 & 0–15 & 0–15 & 0–15 & 0–15 & 0–15 \\  & \(RQD\) (\%) & 3–16 & 3–20 & 3–20 & 3–20 & 3–20 & 0–20 & - & - \\ Joint spacing (mm) & 5–30 & 5–30 & 5–30 & 5–20 & 5–20 & 0–20 & - & - \\ Discontinuity density (joints/m) & - & - & - & - & - & - & 0–40 & 0–40 \\ Separation of joints (mm) & 1–5 & - & - & - & - & - & - & - \\ Continuity of joints (m) & 0–5 & - & - & - & - & - & - & - \\ Weathering & 1–9 & - & - & - & - & - & - & - \\ Condition of joints & - & 0–15 & 0–25 & 0–30 & 0–30 & 0–30 & 0–30 & 0–20 \\ Groundwater & 2–10 & 2–10 & 0–10 & 0–15 & 0–15 & 0–15 & 0–15 & 0–15 \\ Alterability (\%) & - & - & - & - & - & - & - & 0–10 \\  & F\({}_{0}\) & 3–15 & 3–15 & 0\(-\)(\(-12\)) & 0\(-\)(\(-12\)) & 0\(-\)(\(-12\)) & 0\(-\)(\(-12\)) & 0\(-\)(\(-12\)) & 0\(-\)(\(-12\)) \\ Adjustment & F\({}_{e}\) & - & - & - & - & - & - & - & 1–1.32 \\  & F\({}_{\text{s}}\) & - & - & - &The discontinuity spacing rating (\(R_{3}\)) is applicable for a rock mass having three joint sets. When less than three sets of discontinuities are present, \(R_{3}\) should be increased by 30%. However, without this, a conservative assessment is performed [6]. Like \(RQD\), the range of ratings for joint spacing is from 5 to 20 based on the average value. However, the range of graphical ratings for joint spacing in \(RMR_{89}\) is also clarified as with \(RQD\)[23], and after this clarification, the continuous rating of joint spacing (\(x\)) in \(RMR_{89}\) can be determined from Equation (4):  
\[R_{3}=2.281\times\ln(x)-3.41,\,(x=5\text{-}200\text{ mm}); \tag{4a}\] \[R_{3}=4.175\times\ln(x)-13.51,\,(x=200\text{-}900\text{ mm});\] (4b) \[R_{3}=6.250\times\ln(x)-27.55,\,\,(x=900\text{-}2000\text{ mm}). \tag{4c}\]  
A modified criterion, introduced for \(RMR_{b}\) calculation, replaced \(RQD\) and the discontinuity spacing by the number of joints per meter (frequency) in the excavation face. The joint frequency (\(\lambda\)) parameter, consisting of \(RQD\) and joint spacing parameters, is evaluated with the chart provided by [PERSON] and [PERSON] [15]. The joint spacing and \(RQD\) are functions of the fracture frequency and can be determined either directly or indirectly. The first indirect method used for fracture frequency determination is a mathematical equation between the fracture frequency and \(RQD\), as given by Equation (5) [31]:  
\[RQD=100\times e^{-0.1\lambda}(1+0.1\lambda). \tag{5}\]  
When data are available, both in terms of the number of joint sets and average spacing between joints of each joint set, the joint frequency is determined using Equation (6):  
\[\lambda=\frac{No.s\,of\,\,joint\,\,sets}{Average\,\,spacing\,\,(m)} \tag{6}\]  
The continuous rating for joint frequency (\(R_{2\text{-}3}\)) can be determined using Equation (7) for \(\lambda\) = 1-50. If the joint frequency is less than 1, the rating will be maximum, i.e., 40. \[RMR_{89}=R_{1}+R_{2}+R_{3}+R_{4}+R_{5}+R_{6}. \tag{1}\]0 \[RMR_{89}=R_{1}+R_{2}+R_{3}+R_{4}+R_{5}+R_{6}. \tag{1}\]1  
The joint condition term and its corresponding rating (\(R_{4}\)) are the function of the discontinuity length (m), separation (mm), roughness, infilling (mm), and weathering. The rating \(R_{4}\) can be selected for \(RMR_{89}\) using the detail listed in Table 2, but some conditions are mutually exclusive; i.e., in the case of the infilling material, the roughness is overshadowed by the infilling influence [6]. However, this aspect is missing when calculating ratings for joint conditions [24].