## 4 Methodology for Weathering Evaluation  
The evaluation of the weathering of the rock by measuring its ultrasonic velocity has been performed for a long time. Because this evaluation is a highly reliable method of non-destructive testing, several countries use it as the geological standard. Many researchers quantitatively categorize weathering grades into three to five stages according to various types of rocks, such as natural stone [41], acidic volcanic rock [37], limestone [42], andesite [36], marble [43], and granite [44] (Table 2). Among these, the durability of the natural stone does not only depend on the alteration factors, and it also depends on the mineralogy, the rock fabric, and the pore system [45]. To determine the weathering status of a stone architectural heritage based on ultrasonic velocity, we can use the already reported standards. However, [PERSON] [35] reported that the physical and structural changes of a weathered stone could be analyzed by comparing its ultrasonic velocity with that of a fresh rock, based on which \(K\), the weathering coefficient, can be determined as follows:  
\[K=\frac{V_{f}-V_{w}}{V_{f}}\]  
where \(V_{f}\) and \(V_{w}\) are the P-wave velocities of a fresh and weathered rock, respectively. As the stone weathers, \(K\) increases uniformly. Further, \(K\) encompasses the overall effect of various factors, such as the density, porosity, and expansion of micro-cracks, which are \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Spots** & **Si** & **Al** & **Fe** & **Ca** & **Mg** & **Na** & **K** & **P** & **S** & **Cl** & **C** & **O** \\ \hline
1 & 14.8 & 8.8 & - & - & - & - & - & - & 4.2 & - & 13.0 & 59.2 \\
2 & - & - & - & 25.9 & - & - & - & - & 22.3 & - & 2.8 & 49.0 \\
3 & 6.8 & 3.8 & 33.6 & - & - & - & 0.6 & - & - & - & 16.7 & 38.6 \\
4 & 11.6 & 5.0 & 37.9 & 2.0 & - & - & 1.0 & 2.8 & 1.9 & 1.1 & 2.9 & 33.7 \\
5 & 7.1 & 2.4 & - & 20.2 & 1.0 & 2.3 & 1.3 & - & 17.4 & 0.9 & 0.5 & 46.9 \\
6 & 3.3 & 1.3 & - & 39.8 & - & - & 1.1 & - & 26.8 & - & 4.3 & 23.4 \\
7 & 5.8 & - & - & 28.9 & - & - & - & - & 19.1 & - & - & 46.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of SEM-EDS analysis for surface contaminants (wt.%). The analysis spots are similar to those in Figure 4. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multirow{2}{*}{**Rock Types**} & \multicolumn{6}{c}{**Weathering Classification**} \\ \cline{3-8}  & & **1 (FR)** & **II (SW)** & **III (MW)** & **IV (HW)** & **V (CW)** \\ \hline [PERSON] et al. (1979) [41] & Natural stones & \textgreater{}5000 & 4000\(\sim\)5000 & 3500\(\sim\)4000 & 2500\(\sim\)3500 & \textgreater{}2500 \\ [PERSON] et al. (2007) [34] & Acidic volcanic rock & \textgreater{}3862 & 3242\(\sim\)3861 & 2623\(\sim\)3242 & \textgreater{}2623 & - \\ [PERSON] and [PERSON] (1990) [42] & Limestone & 3900\(\sim\)4100 & 3000\(\sim\)3900 & 2000\(\sim\)3000 & 1000\(\sim\)2000 & \textgreater{}1000 \\ [PERSON] (1966) [32] & Monzononite & \textgreater{}5000 & 4000\(\sim\)5000 & 3000\(\sim\)4000 & 2000\(\sim\)3000 & \textgreater{}2000 \\ [PERSON] (1997) [33] & Andesite & \textgreater{}3900 & 3050\(\sim\)3900 & 2250\(\sim\)3050 & 1350\(\sim\)2250 & \textgreater{}1350 \\ [PERSON] (1991) [43] & Marble & \textgreater{}5000 & 3000\(\sim\)5000 & 2000\(\sim\)3000 & 1500\(\sim\)2000 & \textgreater{}1500 \\ [PERSON] and [PERSON] (2005) [44] & Granite & 4220\(\sim\)5100 & 2480\(\sim\)4120 & 1450\(\sim\)2400 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The weathering classifications based on ultrasonic velocity (m/s). highly sensitive to weathering. It is a relatively simple and highly applicable measure of weathering [46; 47]. Thus, applying the already reported standards or calculating the weathering coefficient, \(K\), is required to evaluate the weathering of a stone architectural heritage using ultrasonic measurements.