## 3 Numerical Analysis  
To design a discontinuity, both the shear strength of the discontinuity and the joint orientation of the discontinuity are required. However, since the research subject is a cultural heritage management area, shear strength tests cannot be performed. Therefore, the ground properties used in the numerical analysis were the results of the boring investigation of the Jeju Island Natural Cave Conservation and Management Plan [16]. The investigation results of the NCB-4 borehole closest to Jaemcheon lava tube were used. The stratum was 0.2 m of sand, and the bottom was composed of soft rock (basalt). The sand layer was not considered in the numerical analysis. Table 2 shows the numerical analysis parameters of the continuum of the sand and soft rock. The orientations of the main discontinuities were 66/70, 238/72, and 80/72, and most of them consisted of elevation angles greater than 70 degrees.  
To model a discontinuity, the shear strength of the discontinuity is required. However, since the Jaemcheon lava tube is a cultural property management area and cannot be tested for shear strength, the joint shear strength of the Manjang lava tube calculated in the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & **Cover Depth** & \multirow{2}{*}{**Aspect Ratio**} & **Vehicle Speed** & \multirow{2}{*}{**Joint Orientation**} \\  & **(m)** & & & \\ \hline \multirow{4}{*}{Condition} & 2 & 0.5 & \multirow{4}{*}{40} & No joint \\ \cline{2-2} \cline{5-5}  & & 1.0 & & Horizontal joint \\ \cline{2-2} \cline{5-5}  & & 1.5 & 80 &
\begin{tabular}{c} Vertical joint \\ \end{tabular} \\ \cline{2-2} \cline{5-5}  & & 1.5 & \multirow{2}{*}{80} & Compound joint \\ \cline{5-5}  & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Influence factors and levels.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & **Unit Weight** & **Elastic Modulus** & **Cohesion** & **Friction Angle** & **Poisson’s Ratio** \\  & **(kN/m\({}^{3}\))** & **(kN/m\({}^{2}\))** & **(kN/m\({}^{2}\))** & **(\({}^{\circ}\))** & **Poisson’s Ratio** \\ \hline Soft rock & 21.0 & 1,000,000 & 100.0 & 35.0 & 0.27 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Continuum material properties of soft rock.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & **Shear Wave** & **Dynamic Shear** & **Dynamic Elastic** & **Dynamic** \\  & **Velocity** & **Modulus** & **Modulus** & **Modulus** \\  & **(m/sec)** & \(\left(\mathbf{k}\mathbf{N}/\mathbf{m}^{2}\right)\) & \(\left(\mathbf{k}\mathbf{N}/\mathbf{m}^{2}\right)\) & **Poisson’s Ratio** \\ \hline Soft rock & 760 & 1,240,000 & 3,372,000 & 0.36 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Dynamic parameters of soft rock.  
Figure 3: Cross sectional of boring investigation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & **Cohesion** & **Inner Friction** & **ks** & **kn** \\  & **(kN/m\({}^{2}\))** & \(\left({}^{\circ}\right)\) & **(kPa/mm)** & **(kPa/mm)** \\ \hline Soft rock & 48.0 & 27.0 & 2536 & 4985 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Discontinuity material properties of soft rock.  
Vehicles passing through the upper road of Jaeamcheon lava tube were identified as cars, buses, freight cars and dump trucks. Since the vehicle with the largest load is a dump truck, the dump truck (DB-24) was selected as the vehicle scale to be used for numerical analysis (Table 6). DB-24 had a uniformly distributed load of 13.0 kN/m, and it applied to the vehicle speed of 40 km/h and 80 km/h as a live load. To consider the time history, it was modeled so that the load was activated only at certain times and deactivated at other times. This process is shown in Figure 4.