## 3 Relationship of Physical Parameters of Rocks Evaluated during Freeze-thaw Cycles  
Figure 2 shows relationship between UCS and shore hardness (S\({}_{\text{h}}\)) of samples from Locations A and B estimated for different freeze-thaw cycles. Triplicate tests (A-1, A-2 and A-3 for Location \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rock Strength Description** & **Uniaxial Compressive Strength (MPa)** & **Symbol** \\ \hline Extremely strong rock & higher than 250 & R6 \\ Very strong rock & 100–250 & R5 \\ Strong rock & 50–100 & R4 \\ Medium strong rock & 25–50 & R3 \\ Weak rock & 5–25 & R2 \\ Very weak rock & 1–5 & R1 \\ Extremely weak rock & 0.25–1 & R0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rock strength classification using uniaxial compressive strength for estimation of rock durability proposed by International Society for Rock Mechanics (ISRM) [28]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Rock Weathering Grade** & **P-Wave Velocity (m/s)** \\ \hline Fresh rock & higher than 5000 \\ Slightly weathered rock & 4000–5000 \\ Moderately weathered rock & 3000–4000 \\ Strongly weathered rock & 2000–3000 \\ Very strongly weathered rock & less than 2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Granite rock weathering grade based on P-wave velocity proposed by [PERSON] [29]. A; and B-1, B-2 and B-3 for Location B) were conducted for estimation of each physical parameter. Different colors were used to express different numbers of freeze-thaw cycles of 0, 150, 300, 450, 600, 750 and 900. There exists a trend of increase of UCS with increasing shore hardness; however, high scatter of data points indicates poor correlation (R\({}^{2}\) values of 0.0568 and 0.1083 for rocks from Locations A and B, respectively) between UCS and S\({}_{\text{h}}\). In addition, from a close examination of different colors, there was not a clear pattern of increase of UCS or S\({}_{\text{h}}\) with increasing freeze-thaw cycle. As mentioned earlier in this study and in part one [27] of two companion papers, the poor correlation between UCS and S\({}_{\text{h}}\) results from high uncertainties in measurement of UCS and S\({}_{\text{h}}\) due to inhomogeneity of fissures, cracks and mineral compositions [39; 40; 41; 42]. Figure 3 represents relationship between UCS and water absorption (A\({}_{\text{bs}}\)) of rock samples from Locations A and B estimated for different freeze-thaw cycles. There was a weight loss (in terms of dry weight) identified during porosity, water absorption tests with increasing freeze-thaw cycle. The dry weight of rock samples was measured at every 150 freeze-thaw cycle. Average dry rock weight losses per 150 freeze-thaw cycle for Locations A and B were 0.1 g (dry weight loss of 0.0191%) and 0.05 g (0.0102%), respectively. The dry weight losses of rocks may result from detachment of small rock fractions during freeze-thaw actions. However, calculation of A\({}_{\text{bs}}\) at each 150 freeze-thaw cycle reflects dry weight loss of the samples. There is a trend of slight decrease of UCS with increasing A\({}_{\text{bs}}\); however, due to a high inherent uncertainty in UCS and its measurement, the correlation between UCS and A\({}_{\text{bs}}\) is low. R\({}^{2}\) values for UCS and A\({}_{\text{bs}}\) correlation are 0.0124 for Location A and 0.0673 for Location B. Relationship between S\({}_{\text{h}}\) and A\({}_{\text{bs}}\) is presented in Figure 4. Similar to the relationship between UCS and A\({}_{\text{bs}}\), a slight decrease of S\({}_{\text{h}}\) with increasing A\({}_{\text{bs}}\) and their low correlation are observed. The higher values of R\({}^{2}\) of 0.1656 for Location A and 0.3014 for Location B in Figure 4 are found compared with those in Figure 3. The higher correlation (the higher R\({}^{2}\)) may result from the lower uncertainty in S\({}_{\text{h}}\) compared with that in UCS.