# Assessment of Pohang Earthquake-Induced Liquefaction at Youngil-Man Port Using the UBCSAND2 Model
## 3 Results and Discussion
### Shear Stress-Strain and Acceleration  
Figure 22 illustrates the maximum shear strain contours at the end of the earthquake. Two shear bands are localized near the quay wall and the far field of the model. Near the quay wall, the shear band would be extended to the top of the quay wall due to the significant displacements of the caisson. Due to the free-field boundary conditions, the right side of the model was not constrained nor tied with a rigid body to fix the horizontal displacement. Therefore, many significant shear bands are localized in this region.  
Figure 21: (**a**) Horizontal displacement (positive values are to the right side, and negative values are to the left side), and (**b**) settlement of the observed nodes in the analysis.  
Figure 22: Maximum shear strain at the end of shaking contours (scale up to 10%, dimension unit in meters).  
Figure 23 depicts the shear stress-strain response during the earthquake of the observed elements in Figure 15. When maximum shear strain produced by the Mohr-Coulomb model is approximately 0.03% in element E4, the significantly higher ones generated by the UBCSAND2 model in elements E1, E2, and E3 are 0.35%, 0.2%, and 0.5%, respectively. Additionally, the effect of initial static shear stress (i.e., \(\alpha>0\)) can be addressed in the stress-strain responses of elements E1, E2, and E3 as shown in Figure 23a-c. This initial shear stress produced a constant bias in the cyclic shear load of the soil elements assigned by the UBCSAND2 model. In the regions behind the steel pipe piles represented by element E3, in which the \(\alpha\) value is approximately zero, the symmetrical response of shear stress is in a range of (\(-30,30\)) kPa. Whereas, the non-symmetrically mobilized shear stress of elements E1 with \(\alpha\approx 0.075\) and E2 with \(\alpha\approx 0.05\), are in the range of (\(-15,25\)) and (\(-10,15\)) kPa, respectively.  
Figure 24 shows the comparison between the input ground motions and transmission motions in the analysis. The observed nodes were set in Figure 15. In this study, the recorded acceleration-time history of the Pohang earthquake was extracted to 40 s, filtered to 20 Hz, and baseline drifted. Then, a transformation of the corrected velocity motion to shear stress motion was made to be applicable to the quiet boundary condition in FLAC, as in Equation (19). Therefore, it is essential to check the wave transmission during shaking. At the bottom of the observed nodes, there are slight differences in the acceleration-time histories comparing the input ground motion. It can be said that the transformation from velocity history to shear stress history was successfully implemented. In dynamic analysis, it is important to consider the effect of velocity doubling at the model base and at the top of the model. If elastic materials are defined for the model and run in an un-damped analysis, the velocity-doubling effect would occur in the free surface [30]. In other words, the velocity at the top is double the velocity at the base for un-damped elastic materials. In this study, Rayleigh damping was used for the dynamic analysis, in which there is a small amplification of the velocity wave at the  
Figure 23: Shear stress–strain relationship of the observed elements in the analysis: (**a**) element E1, (**b**) element E2, (**c**) element E3, and (**d**) element E4.  
free surface compared to the base, indicating that the base is within the range of velocity. The trend of this effect is depicted in Figure 24b-d. It is interesting that the velocities at the top of the model for nodes N3 and N4 are approximately 25% higher than those at the base, when only 5% of the difference is presented for node N2. This may be due to the very high stiffness of the gravel preventing wave transmission from the base to the top surface of node N2.