## 2 Methodology
### Assessment of Pohang Earthquake-Induced Liquefaction at Youngil-Man Port Using the UBCSAND2 Model
#### 2.3.2 Numerical Modeling
Steady-state seepage analysis was then performed to develop the initial phreatic surface. Boundary conditions for seismic analysis: A quiet boundary condition in the \(x\)- and \(y\)-directions was applied to the bottom of the model to minimize the reflection of outward propagating waves back into the model and does not allow the necessary energy radiation [30; 39; 40]. Along the side boundaries of the grid should not be assigned as the quiet boundaries because the wave energy can leak out of the sides. Alternatively, free-field boundaries can be used in this situation [30]. During the seismic analysis, the side boundary zones were assigned to be elastic elements with appropriate stiffness (three columns of elements on each side) to prevent free-field boundary conditions from element distortions \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{\(\gamma_{d}\) (\(\Delta\)N/m\({}^{3}\))} & \multirow{2}{*}{\(N_{1(60)}\)} & \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Parameters for Non-Liquefied Soils**} & \multirow{2}{*}{**Remarks**} \\ \cline{4-4} \cline{6-9}  & & & & \(G\) & \(B\) & \(c\) & \(\phi\) & \(k\) & \(\
u\) & \(k\) \\  & & & & (\(\mathbf{k}\)Pa) & (\(\mathbf{k}\)Pa) & (\(\mathbf{k}\)Pa) & (\(\mathbf{k}\)Pa) & (\(\mathbf{k}\)Pa) & (\(\mathbf{m}\)s) & \\ \hline Silty sand 1 & 19.00 & 15.00 & UBC2 & - & - & - & - & - & Liquefied \\ \hline Silty sand 2 & 19.00 & 15.00 & UBC2 & - & - & - & - & - & Liquefied \\ \hline Sediment & 19.00 & 20.00 & M-C & \(1.43\times 10^{3}\) & \(3.72\times 10^{3}\) & 0.00 & 30.0 & \(1\times 10^{-5}\) & 0.33 & Non-liquefied \\ \hline Weather rock & 20.60 & 50.00 & M-C & \(2.85\times 10^{3}\) & \(7.43\times 10^{3}\) & 0.00 & 30.0 & \(1\times 10^{-4}\) & 0.25 & Non-liquefied \\ \hline Rippap & 18.00 & 50.00 & M-C & \(2.49\times 10^{3}\) & \(6.49\times 10^{3}\) & 0.00 & 40.0 & \(1\times 10^{-1}\) & 0.33 & Non-liquefied \\ \hline Gravel & 20.00 & 50.00 & M-C & \(7.22\times 10^{3}\) & \(7.22\times 10^{3}\) & 0.00 & 33.0 & \(1\times 10^{-4}\) & 0.33 & Non-liquefied \\ \hline Concrete & 23.00 & - & elastic & \(1.00\times 10^{3}\) & \(1.67\times 10^{3}\) & - & - & - & 0.25 & Elastic \\ \hline Steel pipe pile & 78.5 & - & elastic & \(\text{E}=2.1\times 10^{3}\) kPa \(\
u=02\), A = 0.01671 m\({}^{2}\), I = \(7.3\times 10^{-5}\) m\({}^{4}\), D = 1.884 m & Elastic \\ \hline \hline \end{tabular} Note: \(\gamma_{d}=\text{dry}\) unit weight of, \(N_{1(60)}\) = corrected SPT number of blow counts, \(G\) = shear modulus, \(B\) = bulk modulus, \(c\) = cohesion, \(\phi\) = friction angle, \(k\) = hydraulic conductivity, \(\
u\) = Poisson’s ratio, UBC2 = UBCSAND2 model, M-C = Mohr-Coulomb model, E = Young’s modulus, A = area of cross-section, I = inertia moment, and D = perimeter.  
\end{table} 
Table 3: Material properties used. and increase the spurious reflections off the boundary. This kind of technique can minimize wave reflections if dynamic loading is applied to the model boundaries [30]. To achieve dynamic loading at the base, the ground motions were transformed to equivalent shear waves (i.e., horizontal motion) for the weathered rock layer as follows:  
\[\sigma_{s}\ =\ 2\cdot(\rho\text{-}C_{s})\cdot v_{s} \tag{19}\]  
where \(\sigma_{s}\) is the applied shear stress, \(\rho\) is the mass density, \(C_{s}\) is the velocity of the s-wave propagation through medium, and \(v_{s}\) is the input velocity. Viscous damping: Rayleigh damping was used for the seismic analysis in FLAC. The predominant frequency of the ground motions (= 1.05 Hz, as in Figure 14d) was considered as the center of frequency in the analysis. The numerical results obtained from the equivalent linear analysis using PROSHAKE software were extracted for silty sand, sediment, weather rock, and gravel as shown in Figure 16. The selected layer corresponds to the maximum shear strain, which is approximately 0.03% for silty sand, 0.01% for sediment, 0.01% for weather rock, and 0.01% for gravel.