## 4 Correlation Analysis Result Summary  
As mentioned previously, weathering grade system proposed by [PERSON] [28] can be implemented for rocks with similar strength and stiffness of granite. Granite is one of the mostly distributed rock types. Due to its wide distribution mixed with other rock minerals, granites have wide ranges of compressive strength and stiffness. The uniaxial compressive strengths of granites are reported within ranges of 26-485 MPa [62; 63; 64; 65; 66; 67; 68; 69; 70; 71] and elastic modulus exists within a range of 20-81 GPa [62; 64; 65; 66; 67; 68; 70; 71; 72; 73; 74; 75]. Dolomite has uniaxial compressive strength of 32-500 MPa [62; 64; 76; 67; 68; 77; 78; 79; 80; 81] and elastic modulus of 38-70 GPa [62; 64; 79; 81], while quartzite has uniaxial compressive strength of 215-320 MPa [62; 82] and elastic modulus of 88.3 GPa [62]. Therefore, the weathering grades suggested by [PERSON] [29] can be also implemented for the samples (domolite and quartzite) used in this study and this classification is used in the prediction of weathering by rock type, discussed in the next section.  
As shown in Figure 2 through Figure 4, R\({}^{2}\) values of relationships among UCS, S\({}_{\text{h}}\), and A\({}_{\text{bs}}\) exhibit weak correlations. This weak correlation of observed mechanical and physical properties has also been reported by other investigators [57; 58], suggesting the need for quantification using a coefficient other than freeze-thaw cycles in order to predict the course of weathering as freeze-thaw progresses. From the correlation analyses of rock properties' correlations during freeze-thaw weathering, it was found that the relationships (Figures 5 and 6) of USC and S\({}_{\text{h}}\), which parameters showed high uncertainties, with V\({}_{\text{P}}\) provided a slightly better correlations compared to those (Figures 3 and 4) with A\({}_{\text{bs}}\). Figure 7 is the cross-plot showing the correlation between A\({}_{\text{bs}}\) and V\({}_{\text{P}}\) measured in the same specimens every 150 cycles. As shown in Figure 2 through Figure 6, the relationships among A\({}_{\text{bs}}\), V\({}_{\text{P}}\), S\({}_{\text{h}}\), and UCS showed large variance, whereas Figure 7 of A\({}_{\text{bs}}\) against V\({}_{\text{P}}\) and Figure 8 of UCS against V\({}_{\text{P}}\)/UCS presented relatively constant attenuation with less uncertainty as freeze-thaw progressed.  
Despite of poor correlation between UCS and V\({}_{\text{P}}\) in Figure 5, effort was made to find a good equation representing their relationship (equations in Figure 8) for Locations A and B. The plot of UCS against UCS/V\({}_{\text{P}}\) in Figure 8 shows a relatively steep slope compared to the graph in Figure 5, and R\({}^{2}\) for rocks from Locations A and B are 0.8974 and 0.9858, respectively, demonstrating strong correlations. The inconsistent attenuation of changes in physical properties with increasing number of freeze-thaw cycles is thought to reflect the variance in UCS in Figures 2, 3 and 5. Thus, the cross-plot of UCS against UCS/P-wave velocity has the drawback that it is difficult to directly calculate hardness characteristics and the attenuation of freeze-thaw weathering from the number of freeze-thaw cycles.  
Figure 8: Relationship between uniaxial compressive strength and “normalized P-wave velocity with uniaxial compressive strength” for every 150 freeze–thaw cycles and initial state prior to freeze–thaw test.