## 3 Relationship of Physical Parameters of Rocks Evaluated during Freeze-thaw Cycles
The cross-plot of \(\rm A_{bs}\) against \(\rm V_{p}\) allows the attenuation characteristics of weathering to be calculated directly according to the number of freeze-thaw cycles; therefore, the authors surmise that the time of changes in weathering grade could be derived from the \(\rm A_{bs}\)-\(\rm V_{p}\) curves. Table 3 summarizes the linear regression equations and their \(\rm R^{2}\) values. Only the \(\rm R^{2}\) values for relationship between \(\rm A_{bs}\) and \(\rm V_{p}\) for Locations A and B are significantly higher than those of other relationships. The linear equations in Table 3 may be effective for reasonable ranges of physical parameters of UCS, \(\rm S_{h}\), \(\rm A_{bs}\) and \(\rm V_{p}\). There are studies [53; 54; 55] showing clear trends of strength drop with increasing freeze-thaw actions. However, relatively fresh rocks having UCS higher than 200 MPa do not show significant UCS decrease with increasing number of freeze-thaw cycle [56; 57]. There is a limitation on model development for estimation of one physical property of relatively fresh rock from other properties of the rock due to relatively low correlations among the physical properties. Low correlations among mechanical and physical properties of rocks are also reported from other research [57; 58]. In reality, because UCS of rock decreases with increasing weathering compared to its initial strength; therefor, UCS is often used as a good indicator of the extent of rock weathering. At the same time, UCS also is used to predict other rock properties such as Young's modulus or Poisson's ratio. The highly weathered rocks with higher porosity, larger particle size, and more-developed micro joints are likely to have more rock discontinuities. The increased surface area of highly weathered rock resulting from weathering accelerates overall weathering of the rock [59; 60; 61; 41]. In addition, as UCS is an important factor in estimation of durability of rock, research on UCS degradation with increasing freeze-thaw cycle is required for its practical use for engineers. If this study were performed for much larger number of freeze-thaw cycles and samples or implemented nondestructive tests for estimation of rock strength, more clear gradual weathering patterns in the form of destruction were observed; therefore, quantitative degrade of freeze-thaw weathering could become more apparent. However, because not all weathering processes can be assessed from laboratory tests, it will be necessary to implement a logical quantification process using existing data. In this discussion, the authors aim to analyze the required additional number of freeze-thaw cycles for chain in rock weathering grade by quantification of weathering using physical properties of rocks and the relationships. \begin{table}
\begin{tabular}{c c c} \hline
**Location** & **Regression Equations** & \(\bf R^{2}\) \\ \hline \multirow{5}{*}{A} & UCS = 5.180(\(\rm S_{h}\)) \(-\) 58.68 & 0.0568 \\  & UCS = \(-\)56.313(\(\rm A_{bs}\)) + 275.67 & 0.0012 \\  & \(\rm S_{h}\) = \(-\)9.480(\(\rm A_{bs}\)) + 64.19 & 0.1656 \\  & UCS = 0.013(\(\rm V_{p}\)) + 187.93 & 0.0170 \\  & \(\rm V_{p}\) = 91.881(\(\rm S_{h}\)) \(-\) 29.663 & 0.1791 \\  & \(\rm V_{p}\) = \(-\)4890.7(\(\rm A_{bs}\)) + 6875.5 & 0.9350 \\ \hline \multirow{5}{*}{B} & UCS = 4.968(\(\rm S_{h}\)) \(-\) 207.71 & 0.1083 \\  & UCS = \(-\)92.304(\(\rm A_{bs}\)) + 337.45 & 0.0673 \\ \cline{1-1}  & \(\rm S_{h}\) = \(-\)12.940(\(\rm A_{bs}\)) + 102.08 & 0.3014 \\ \cline{1-1}  & UCS = 0.069(\(\rm V_{p}\)) \(-\) 71.89 & 0.0478 \\ \cline{1-1}  & \(\rm V_{p}\) = 26.820(\(\rm S_{h}\)) + 1840.5 & 0.3156 \\ \cline{1-1}  & \(\rm V_{p}\) = \(-\)1066.0(\(\rm A_{bs}\)) + 5554.3 & 0.8974 \\ \hline \end{tabular}
\end{table} 
Table 3: Summary of correlations of the simple regression analysis due to freeze–thaw test (where UCS: uniaxial compressive strength, \(\rm S_{h}\): shore hardness, \(\rm A_{bs}\): water absorption, \(\rm V_{p}\): P-wave velocity).