## 2 Methodology
### Assessment of Pohang Earthquake-Induced Liquefaction at Youngil-Man Port Using the UBCSAND2 Model
#### 2.3.1 Study Area and Ground Motion of the Pohang Earthquake
The appropriate input motion at depth can be computed through a deconvolution analysis using the one-dimensional (1-D) wave propagation code such as the equivalent-linear program PROSHAKE [31] as shown in Figure 12. A typical soil profile at the observed site up to 50 m of depth is presented in Figure 12a, in which the data is obtained from [PERSON] et al. [11] and [PERSON] et al. [12]. Under a depth of 30 m, the bedrock is primarily distributed up to 500 m of depth as the report of [PERSON] et al. [32] and [PERSON] et al. [9]. Additionally, the corrected N\({}_{1(60),\text{cs}}\) is calculated from the data provided by the Integrated DB Center of National Geotechnical Information [33]. To simply the input parameters for both PROSHAKE and FLAC analysis (i.e., \(N_{1(60),\text{cs}}\)), [PERSON] et al. [11] and [PERSON] et al. [12] calculated the corresponding \(N_{1(60),\text{cs}}\) values of sandy soil layers by the experimental works of [PERSON] [34] and [PERSON] et al. [35] in relation to the liquefied soils due to the Pohang earthquake. The calculation procedure for the N\({}_{1(60),\text{cs}}\) value was based on a method proposed by [PERSON] et al. [36] and [PERSON] et al. [37]. The sediment and weather rock layer are assumed as \(N_{1(60),\text{cs}}=20\) and \(N_{1(60),\text{cs}}=30\), respectively. Although the bedrock is very hard for the SPT test, it can \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & \multicolumn{2}{c}{**Location**} & \multirow{2}{*}{**Distance from Epicenter (km)**} & \multirow{2}{*}{**Site Classification**} & \multicolumn{3}{c}{_PGA (g)_} \\ \cline{2-2} \cline{5-8}  & **E** & & & **N** & **EW** & **UD** \\ \hline PHA2 & 129.37080\({}^{\circ}\) & 36.19290\({}^{\circ}\) & 9 & \(S_{\text{B}}\) & 0.271200 & 0.243283 & 0.140000 \\ \hline CHS & 129.08811\({}^{\circ}\) & 36.18113\({}^{\circ}\) & 26 & \(S_{\text{B}}\) & 0.027800 & 0.021200 & 0.01900 \\ \hline DKJ & 129.10892\({}^{\circ}\) & 35.94675\({}^{\circ}\) & 29 & \(S_{\text{B}}\) & 0.048300 & 0.02500 & 0.042800 \\ \hline HAK & 129.50037\({}^{\circ}\) & 35.92955\({}^{\circ}\) & 23 & \(S_{\text{B}}\) & 0.036400 & 0.026700 & 0.030300 \\ \hline \hline \end{tabular} Note: E = east, N = north, NS = north–south, EW = east–west, UD = up–down, PGA = peak ground acceleration.  
\end{table} 
Table 2: Information of the four recording stations. be assumed as \(N_{1(60),\text{cs}}\) = 50 for the equivalent-linear analysis. From Figure 12b, there is a reasonable agreement between the corrected \(N_{1(60),\text{cs}}\) from SPT test and the simplification. Based on the simplified \(N_{1(60),\text{cs}}\), the maximum shear modulus \(G_{\text{max}}\) can be determined by the empirical function proposed by [PERSON] et al. (2018) as in Equations (15) and (16). If shear modulus \(G_{\text{max}}\) and unit weight \(\gamma\) are inputted, shear wave velocity \(V_{\text{s}}\) would be automatically calculated by PROSHAKE software. It can be seen that \(V_{\text{s}}\) is varied in the ranges 180-270 m/s for silty sand, 285 m/s for sediment, 300-330 m/s for weather rock, and 760 m/s for bedrock layer. \[G_{max}\ =\ 21,7\text{-}\ K_{2 max}\text{-}P_{a}\text{-}(\sigma^{\prime}{}_{m}/P_{a })^{0.5} \tag{15}\]  
\[K_{2 max}\ =\ 20\text{-}N_{1(60),\text{CS}}{}^{0.333} \tag{16}\]  
where \(G_{max}\) is maximum shear modulus, \(K_{2 max}\) is shear modulus number, \(P_{a}\) is atmospheric pressure (\(\approx\)100 kPa), \(\sigma^{\prime}{}_{m}\) is mean effective stress, N\({}_{1(60),\text{cs}}\) is corrected SPT number of blow counts. Figure 13 presents the numerical results obtained from the 1-D equivalent-linear analysis in PROSHAKE. By the application of deconvolution procedure as shown in Figure 13a, the outcrop motion at surface is inputted at the base at a depth of 50 m. Then, the wave propagation would be generated to the above layers depending on their properties. Three ground motions at the depth of 50 m, 25 m, and free-surface are extracted for the comparison as shown in Figure 13b-d.