## 7 Comments on the Fitting Work  
Obtained parameters for all three fitting equations (linear, parabolic, and Hoek-Brown criterion) for samples A, B, and C are presented in Table 7. As can be seen from the table, the obtained fitting parameters for the samples are fairly similar--indicating an almost homogenous behaviour between tested samples. Some comments can be made for Table 7:  
* In the linear fitting equation, the slope of the equation (parameter \(k\)) for samples A, B, and C is 10.89, 10.56, and 10.34, respectively. With these values of \(k\), the corresponding internal friction angle for the rock samples are 56, 56, and 55 degrees, respectively. * The values of \"Estimated-UCS\" obtained by the linear fitting equation (parameter \(\sigma_{ci}\)), by parabolic fitting equation (parameter \(c\)), and by the Hoek and Brown criterion equation (parameter \(\sigma_{ci}\)) are not too far from each other, as presented in Table 7;
* The obtained parameter \(m_{i}\) for samples A, B, and C are 32, 30, and 29, respectively. These values are very much comparable to the recommended \(m_{i}\)-value in such programs as RocLab and RocData [44], which is 32 \(\pm\) 3 for granite;
* The obtained fitting parameters (\(k\), \(a\), \(b\), and \(c\)) are relatively close for all samples A, B, and C. This is because the granite in this study is relatively homogenous. It is important to note that the fitting parameters are sample-dependent. Due to the inhomogeneous nature of rock, different rock types or even different samples from the same rock type have different UCS values. Consequently, they should have their own fitting parameters for each individual sample. Thus, it is not recommended to use the obtained fitting parameters in this study as general parameters for other cases. Instead, the form of equations can be used but the fitting parameters for each sample will be estimated directly from the obtained data of triaxial testing for that particular sample;
* The linear and parabolic fitting equations were obtained by built-in function in Excel. The Hoek-Brown fitting equation was obtained from commercial code RocData as mentioned or the \"Goal Seek\" in Excel can also be used. The mathematical algorithm behind both situations is the least squares method. Interested readers are recommended to refer to different mathematical books for more information on the method;
* The error between \"Estimated-UCS\" and \"True-UCS\" comes from two sources, which are (a) the sample's behaviour and (b) the selection of the fitting equation. If the sample expresses uniform behaviour at every loading step, then it is easier to find a good fitting equation for the tests and vice versa. The right choice of fitting equation will also contribute significant error to the estimate. As demonstrated above, the linear fitting equation gives a larger error than the non-linear equation for the Iddefjord granite samples performed in this research. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **Fitting Equation** & \multicolumn{2}{c}{**Fitting Parameters**} \\ \hline  & & \(k\) & \(\sigma_{ci}\) \\ \hline A & & 10.89 & 218.49 \\ B & \(\sigma_{1}=k\sigma_{3}+\sigma_{ci}\) & 10.56 & 231.12 \\ C & & 10.34 & 231.24 \\ \hline  & & \(a\) & \(b\) & \(c\) \\ \hline A & & \(-\)0.28 & 16.93 & 197.26 \\ B & \(\sigma_{1}=a\sigma_{3}{}^{2}+b\sigma_{3}+c\) & \(-\)0.27 & 16.44 & 210.48 \\ C & & \(-\)0.20 & 14.82 & 215.47 \\ \hline  & & \(m_{i}\) & \(\sigma_{ci}\) & \\ \hline A & & 32 & 201 & \\ B & \(\sigma_{1}=\sigma_{3}+\sigma_{ci}\Big{(}m_{i}\frac{\sigma_{ci}}{\sigma_{ci}}+1 \Big{)}^{1/2}\) & 30 & 216 & \\ C & & 29 & 217 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The fitting equations and obtained fitting parameters.