## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & \multicolumn{5}{c}{**Range of Input Parameters**} & \multicolumn{2}{c}{**UCS Range**} \\ \cline{6-9} \# & **Empirical Relationships** & **Method** & **Reference** & \(n_{e}\) **(\%)** & \(V_{p}\) **(m/s)** & \(R_{n}\) **(\%)** & \multicolumn{2}{c}{**(MPa)**} \\ \cline{6-9}  & & & & & \multicolumn{1}{c}{**L-Type**} & **N-Type** & **From** & **To** \\ \hline
1 & UCS \(=78.22n_{t}+201\) & RA & [9] & 0.14–1.07 & – & – & – & 109.2 & 193.3 \\
2 & UCS \(=35.54V_{p}-55\) & RA & [9] & – & 4740–6690 & – & – & 109.2 & 193.3 \\
3 & UCS \(=8.36R_{n}(L)-416\) & RA & [9] & – & – & 64–72 & – & 109.2 & 193.3 \\
4 & UCS \(=2.208\omega(Mcn)\) & RA & [10] & – & – & 23.9–73.4 & 11 & 259 \\
5 & UCS \(=1.4459\omega_{0.0006R(n)}^{0.0006R(n)}\) & RA & [11] & – & – & 20.00–65.76 & – & 6.32 & 196.5 \\
6 & UCS \(=0.9165\omega_{0.006R(n)}^{0.006R(n)}\) & RA & [11] & – & – & 23.00–75.97 & 6.32 & 196.5 \\
7 & UCS \(=4.24\omega_{0.009R(n)}^{0.009R(n)}\) & RA & [12] & – & – & – & 48.30–61.80 & 60.8 & 202.9 \\
8 & UCS \(=124.28n_{t}-0.36\) & RA & [13] & 0.64–3.72 & – & – & – & 62.4 & 197 \\
9 & UCS \(=0.004V_{p}1^{2.02}\) & RA & [13] & – & 2339–5753 & – & – & 62.4 & 197 \\
10 & UCS \(=0.0040V_{p}-36.31\) & RA & [14] & – & 1941–4751 & – & – & 23.77 & 161.7 \\
11 & UCS \(=e^{2.28n_{t}(L)-4.040}\) & RA & [15] & – & – & 15–60 & – & 10.54 & 244.8 \\
12 & UCS \(=0.033V_{p}-34.83\) & RA & [16] & – & 1682–4657 & – & – & 32.51 & 133.5 \\
13 & UCS \(=2.386\omega_{0.006R(n)}^{0.006R(n)}\) & RA & [17] & – & – & 25.89–67.07 & – & 17.55 & 198.2 \\
14 & UCS \(=0.087V_{p}-355.8\) & RA & [17] & – & 5384–6250 & – & – & 91.48 & 198.2 \\
15 & UCS \(=22.26\omega_{1}-189n_{e}\) & RA & [17] & 0.06–0.4 & – & – & 91.48 & 198.2 \\
16 & UCS \(=-17.88\)ln(\(n_{e}\)) + 60.22 & BHM & [18] & 0.52–7.23 & – & – & 20.3 & 112.9 \\
17 & UCS \(=8.17\omega_{0.004 Vp}^{0.004 Vp}+3.93\) & BHM & [18] & – & 1160–5935 & – & – & 20.3 & 112.9 \\
18 & UCS \(=7.03\omega_{0.038R(n)}^{0.008R(n)}+8.39\) & BHM & [18] & – & 16.8–55.7 & – & 20.3 & 112.9 \\
19 & UCS \(=4.15\omega_{0.004 Vp}^{0.004 Vp}+3.22\) & BHM & [18] & – & 1160–5935 & 16.8–55.7 & – & 20.3 & 112.9 \\
20 & UCS \(=6.32\omega_{0.004 Vp}^{0.004 Vp}-\) & BHM & [18] & 0.52–7.23 & 1160–5935 & – & – & 20.3 & 112.9 \\
20 & UCS \(=3.62\omega_{0.008R(n)}^{0.004 Vp}+5.84\omega_{0.004 Vp}^{0.004 Vp}\) & BHM & [18] & 0.52–7.23 & 1160–5935 & – & – & 20.3 & 112.9 \\
22 & UCS \(=1.910R_{n}(N)-10.3\) & RA & [19] & – & – & – & 10–72 & 8 & 149 \\
23 & UCS \(=25.952\omega_{0.030R(n)}^{0.030R(n)}\) & RA & [20] & – & 18–61 & – & 39 & 211.9 \\
24 & UCS \(=0.005V_{p}1^{1.14}\) & RA & [20] & – & 2823–7943 & – & – & 39 & 211.9 \\
25 & UCS \(=0.004V_{p}1^{2.5972}\) & RA & [21] & – & 18.8–60 & – & 6.12 & 148 \\
26 & UCS \(=11.58\)ln(\(V_{p}\)) \(-1443.9\) & RA & [22] & – & 4108–7943 & – & – & 50.2 & 211.9 \\
27 & UCS \(=6.311R_{n}(L)-194.92\) & RA & [22] & – & – & 40–61 & – & 50.2 & 211.9 \\
28 & UCS \(=0.0367V_{p}-31.18\) & & [23] & & & & & & & \\ \hline \hline \end{tabular} Note: RA is regression analysis, and BHM is Bayesian hierarchical modelling.  
\end{table} 
Table 1: Empirical correlations between \(R_{n}\), \(V_{p}\), and \(n_{e}\) and the UCS of granite (modified from [4; 5; 6]). Triaxial tests are required in many rock engineering projects to obtain the peak and residual strength of the rock samples. Engineers typically use the results from each triaxial test to obtain the failure envelope (or peak strength envelopes) for the corresponding samples. The question would then be whether results from triaxial tests can be utilised  
to reliably estimate the UCS for the same rock samples? If the UCS can be estimated from the results of triaxial tests, it could be an additional valuable output from the triaxial tests, enriching the UCS database for the projects. This paper presents the possibility of estimating UCS from triaxial tests.