# Assessment of Pohang Earthquake-Induced Liquefaction at Youngil-Man Port Using the UBCSAND2 Model
## 2 Methodology
### UBCSAND2 Calibration for Undrained CDSS Tests on Pohang Sand
In other words, during phase (i), the two planes work together due to PSR, and then only the maximum plane works in phase (ii) for the remaining cycles because no more PSR occurs. Figure 4: Relationship of number of cycles to liquefaction (\(N_{\rm liq}\)) and cyclic stress ratio (\(CSR\)) from cyclic direct simple shear (CDSS) test results under \(\sigma^{\prime}{}_{\rm v0}\) = 100 kPa. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{2}{c}{**Generic Parameters**} & \multicolumn{2}{c}{**Calibration**} \\ \cline{2-5}  & **Function** & **Values** & **Loose** & **Dense** \\ \hline \((N_{1})_{60}\) & Normalized, corrected SPT blow counts & varies & 12.50 & 16.50 \\ \hline \(C_{\rm Dr}\) & Correlation factor between \((N_{1})_{60}\) and \(D_{\rm r}\) & Constant & 46 & 46 \\ \hline \(D_{\rm r}\) & Relative density & \([(N_{1})_{60}/C_{\rm Dr}]^{6S}\) & 0.53 & 0.61 \\ \hline \(\phi_{\rm ov}\) & Constant volume friction angle & \(33^{\circ}\) & 33.00 & 33.00 \\ \hline \(\phi_{\rm f}\) & Peak friction angle & \(\phi_{\rm cv}+(N_{1})_{60}/10\) + max(0, \((N_{1})_{60}-15)/5\) & 34.25 & 34.95 \\ \hline \(\rm k_{\rm C}\)\({}^{a}\) & Elastic shear modulus number & \(21.7\times 20\times(N_{1})_{60}\)\({}^{0.333}\) & 1006 & 1104 \\ \hline \(\rm k_{\rm S}\)\({}^{a}\) & Elastic bulk modulus number & \(0.7\times\rm k_{\rm C}\)\({}^{a}\) & 704 & 773 \\ \hline \(\rm k_{\rm C}\)\({}^{p}\) & Plastic shear modulus number & \(\rm k_{\rm C}\)\({}^{a}(N_{1})_{60}\)\({}^{\times}\)\(0.003+100\) & 572 & 1002 \\ \hline \(me\) & Elastic shear exponent & 0.5 & 0.50 & 0.50 \\ \hline \(ne\) & Elastic bulk exponent & 0.5 & 0.50 & 0.50 \\ \hline \(np\) & Plastic shear exponent & 0.4 & 0.40 \\ \hline \(R_{\rm f}\) & Failure ratio & \(\rm min(1.1\times(N_{1})_{60}-0.155,0.99)\) & 0.75 & 0.72 \\ \hline \(a\) & Factor for _flict_ calculation & \(\rm 1.05-0.03\times(N_{1})_{60}+0.04\times[(N_{1})_{60}]^{2}-0.000185\) & 1.01 & 1.03 \\ \hline \(b\) & Factor for _flict_ calculation & \(\rm 1.0(-0.424-0.259\times(N_{1})_{60}+0.00763\times[(N_{1})_{60}]^{2})\) & \(-0.4\) & \(-0.38\) \\ \hline _flfac1_ & Factor of primary hardener & \(A\times(\sigma^{\prime}_{\rm ov}P_{\rm atm})^{b}\) & 1.01/0.77 & 1.03/0.79 \\ \hline _flfac2_ & Factor of secondary hardener & 1.0 & 1.00 & 1.00 \\ \hline _flfac3_ & Factor of dilation hardener & 1.0 & 1.00 & 1.00 \\ \hline _anisofac_ & Factor of anisotropic plastic response & 1.0 & 1.00 & 1.00 \\ \hline \(C_{\rm h}\) & Cyclic hardening & \(8.33\times(D_{\rm r})^{2}-5.0\times D_{\rm r}+2.2292\) & 1.89 & 2.22 \\ \hline \multicolumn{4}{l}{Note: \(\sigma^{\prime}_{\rm ov}\) = initial vertical effective stress, and \(P_{\rm atm}\) = atmospheric pressure (=100 kPa). (\(\tau\)) = the numerator is the value at \(\sigma^{\prime}_{\rm ov}\) = 100 kPa when the denominator presents the values at \(\sigma^{\prime}_{\rm ov}\) = 200 kPa.} \\ \end{tabular}
\end{table} 
Table 1: Input parameters of the UBCSAND2 model for Pohang sand by CDSS tests. Figure 5: Comparison of the UBCSAND2 model for loose Pohang sand and laboratory CDSS test at \(CSR=0.14\), \(\sigma^{\prime}_{\rm ov}\) = 100 kPa, and \(\alpha=0.0\) in the variations of (**a**) stress path, (**b**) shear stress–strain curve, (**c**) excess pore water pressure generation, (**d**) shear strain and number of cycles to liquefaction. The typical comparisons between the undrained CDSS test results and calibrated UBCSAND2 model considering the initial static shear stress bias (i.e., \(\alpha=\tau_{\text{sta}}/\sigma^{\prime}y_{0}>0\)) are shown in Figures 7 and 8. The level of the initial static shear stress ratio \(\alpha\) is defined as the ratio of the driving initial static shear stress, \(\tau_{\text{sta}}\), to the initial vertical effective stress, \(\sigma^{\prime}y_{0}\) (i.e., \(\alpha=\tau_{\text{sta}}/\sigma^{\prime}y_{0}\)). This kind of effect is varied in the soil elements beneath the slope. The predictions generally give a reasonable representation for stress reversal patterns, including an accumulating pattern of shear strain.