## 4 Application in Determination of Rock-Mass Properties
### Deformation Modulus of Rock Masses  
The uncertainties are associated to in-situ \(E_{m}\) calculations due to blast damage, experiment method and procedure and therefore, a good rock mass characterization may give equivalent, or possibly better \(E_{m}\) values [83]. In the literature, several correlations have been suggested for the \(E_{m}\) and the rock-mass quality (\(RMR\) and \(Q\)) values since the first empirical equation between \(RMR\) and \(E_{m}\) by [PERSON] [84] and the first empirical equation between \(Q\) and \(E_{m}\) by [PERSON] [85]. In these equations, the intact rock properties were missing. Later, it was determined that, for the calculation of rock-mass mechanical properties (\(E_{m}\), \(\sigma_{cm}\), \(\
u_{m}\), \(\hat{\phi}_{m}\), \(c_{m}\) and \(\sigma_{tm}\)), the intact rock properties (\(E_{i}\), \(\sigma_{c}\), \(\
u_{i}\), \(\hat{\phi}_{i}\), \(c_{i}\) and \(\sigma_{t}\) respectively) and rock-mass classification indexes must be involved [86]. The proposed correlations between the deformation modulus of rock mass and the \(RMR\) or \(Q\) values can be divided into two groups:  
* The \(E_{m}\) is calculated independently from the \(E_{i}\), Table 4.
* The \(E_{m}\) is calculated dependently from the \(E_{i}\), Table 5.  
Where \(\alpha\) is a constant in Equation (14) and its value varies from 0.16 to 0.3. This equation is suitable for dry conditions. \(c\) in Equation (20) is a general constant for \(Q>1.0\) that ranges from 10 to 40 with a mean value of 25 [68; 93]. The applications of Equation (12) and (13) are extended for \(RMR_{89}\). \(RMR_{76}\) and \(RMR_{79}\) are the 1976 and 1979 version of \(RMR\), respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**S. No.** & **Equation** & **Equation No.** & **Reference** \\ \hline
1 & \(E_{m}=2\times RMR_{89}-100(\text{GPa})\), \(RMR>50\) & (12) & [84] \\
2 & \(E_{m}=10^{-\frac{RMR_{89}-10}{2}}(\text{GPa})\) & (13) & [87] \\
3 & \(E_{m}=0.3\times H^{\alpha}\times 10^{(\frac{RMR_{89}-2}{8})}(\text{GPa})\), H \(>50\) m & (14) & [88] \\
4 & \(E_{m}=e^{(\frac{\alpha\alpha\pi}{100\times\frac{RMR_{89}}{10}})}(\text{GPa})\) & (15) & [89] \\
5 & \(E_{m}=0.1\times\left(\frac{RMR_{89}}{10}\right)^{3}(\text{GPa})\) & (16) & [90] \\
6 & \(E_{m}=0.0097\times RMR_{89}^{(\text{GPa})}\) & (17) & [86] \\  & \(E_{m}=0.0876\times RMR_{89}(\text{GPa})\), \(RMR\leq 50\) & (18a) (18b) & [91] \\
7 & \(E_{m}=0.0876\times RMR_{89}+1.056\times(RMR_{89}-50)+0.015\times(RMR_{89}-50)^ {2}\), & (18a) (18b) & [91] \\  & \(RMR>50\) & \(E_{m}=1.35\times e^{\alpha\beta\
u\text{FRMR}_{89}}(\text{GPa})\) & (19) & [92] \\
9 & \(E_{m}=c\times\log\left(\text{GPa}\right)\), \(Q>1\) & (20) & [85] \\
11 & \(E_{m}=10\times Q^{1}(\text{GPa})\) & (21) & [69] \\
12 & \(E_{m}=10\times(Q\times\frac{RMR_{89}}{10})^{3}=10\times Q^{1}(\text{GPa})\) & (22) & [24] \\
13 & \(E_{m}=10^{(15\times(Q\times\frac{RMR_{89}}{10})^{4/40}},Q<1.0\) and \(RMR<50\) & (23) & [24] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Equations for calculation of \(E_{m}\) without \(E_{i}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**S. No.** & **Equation** & **Equation No.** & **Reference** \\ \hline
1 & \(\frac{E_{m}}{E_{i}}=\left(0.9\times e^{\frac{RMR_{89}}{20}}+0.0028\times RMR_{79 }^{2}\right)\times\frac{1}{100}\) & (24) & [94] \\
2 & \(\frac{E_{m}}{E_{i}}=0.05\Big{(}1-\cos\pi\frac{RMR_{89}}{100}\Big{)}\) & (25) & [95] \\
2 & \(\frac{E_{m}}{E_{i}}=\frac{RMR_{89}}{100}\Big{)}\) & \(\beta=6.0\) & (26) & [96] \\
4 & \(\frac{E_{m}}{E_{i}}=\frac{RMR_{89}}{20,23,34}\) & (27) & [93] \\
5 & \(\frac{E_{m}}{E_{i}}=e^{-(0.0035)(5100-RMR_{89})}\) & (28) & [97] \\
6 & \(\frac{E_{m}}{E_{i}}=e^{(RMR_{89}-100)/36}\) & (29) & [91] \\
7 & \(\frac{E_{m}}{E_{i}}=10^{(\{MR_{89}-100\}^{2}/4000\times e^{-\{-2 MR_{89}/100\}})}\) & (30) & [98] \\
9 & \(\frac{E_{m}}{E_{i}}=e^{(-0.003520(10-3\times\log Q))}\) & (31) & [97] \\ \hline \hline \end{tabular}
\end{table}
Table 5: Equations for calculation of \(E_{m}\) with \(E_{i}\).