## 4 Methodology for Weathering Evaluation
Among these, the weathering coefficient \(K\), based on the rates of ultrasonic velocity, changes between fresh and weathered rocks; it can be customized by considering the rock type of a stone architectural heritage [48]. In case of the weathering coefficient, once the ultrasonic velocity of fresh rock in the provenance of a stone architectural heritage is determined, the relative weathering after construction can be determined. Additionally, the coefficient can compare the absolute strength between rocks regardless of the rock type using the ultrasonic velocity of a universal hard rock (5000 m/s) without considering that of a fresh rock in the provenance. Therefore, this study classified the weathering coefficient \(K\) as the relative and absolute weathering grades according to the standard ultrasonic velocities of the fresh rocks. These grades were applied to the analysis of the stone block foundation of the Sungmyemun Gate. To determine the relative weathering of the stone block foundation of the Sungmyemun Gate, the ultrasonic velocities of fresh pink feldspar granite and leucogranite were measured at the provenance site (quarry). The site is reported as the Namsan mountain in Seoul, Republic of Korea by [PERSON] et al. [38] and [PERSON] and [PERSON] [49]. The ultrasonic measurements of the rocks at the provenance were conducted using same methods and procedures as those used for analyzing the stone block foundation. The average ultrasonic velocity of fresh pink feldspar granite was 3829 m/s (3659-4000 m/s), and that of fresh leucogranite was 4036 m/s (3911-4286 m/s), indicating that the overall physical properties of leucogranite were somewhat high (Table 3). These ultrasonic velocities were used as fresh standards for evaluating the relative weathering of the two types of rock that constituted the stone block foundation of the Sungmyemun Gate. The rocks that constitute the stone architectural heritage include granite, gneiss, marble, and sandstone. At the time of this study, these rocks exhibit different physical properties and strengths from those at the time of their creation. Therefore, the ultrasonic velocity of a universal hard rock needs to be determined to compare the absolute strengths observed in various types of rocks. In this study, a database was established by analyzing a Republic of Korean and foreign research that provided the ultrasonic velocity of fresh rock (Table 4). Each rock type exhibited a different ultrasonic velocity; even rocks of the same type can possess different ultrasonic velocities based on the corresponding provenance sites. The granites in the database exhibit ultrasonic velocities that are similar to those observed at the provenance site of the stone block foundation of the Sungmyemun Gate. In this study, the absolute weathering used a 5000 m/s ultrasonic velocity [32], which was extensively used as the standard for fresh rock, among the various ultrasonic velocities observed based on the type of rock. Table 5 presents the relative weathering grade using the ultrasonic velocity of fresh rock in the provenance site of the stone block foundation of the Sungmyemun Gate and absolute weathering grade based on a 5000 m/s velocity. Although the relative weathering grade differs with the type of rock, the absolute weathering grade is standard regardless of the type of rock. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rock Types** & **Mean** & **Min.** & **Max.** & **SD** \\ \hline Pink feldspar granite & 3829 & 3659 & 4000 & 91 \\ Leucogranite & 4036 & 3911 & 4286 & 115 \\ Total & 3932 & 3659 & 4286 & 147 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The mean, minimum, and maximum ultrasonic velocities (m/s) and standard deviations of fresh rocks in the provenance site.