# Numerical Simulation of Piles in a Liquefied Slope Using a Modified Soil-Pile Interface Model
## 3 Validation of Numerical Modeling  
The applicability of the numerical model proposed in Section 2 was verified by comparing the results with the centrifuge model experiments. Figures 6 and 7 show the excess pore pressure in the ground and the settlement of the crest, respectively. Figure 5: Reduction of the interfacial normal spring force according to the excess pore pressure ratio. The numerical analyses conducted in this study demonstrated an overall agreement with the experimental results. However, the estimated excess pore pressure in the deep soil was found to underestimate the experimental results. The limited excess pore pressure observed in the deep soil was attributed to the numerical modeling of the soil container. A cork was attached to the rigid soil container to minimize the boundary effect and allow for free deformation of the soil adjacent to the boundary in the experiment conducted by [PERSON] et al. [33]. However, in the numerical simulation, the cork was not individually simulated; only the rigid soil container was considered. Consequently, limited deformation constrained the increase in excess pore pressure of deep soil in the numerical simulation. The simulation results using the flexible soil container successfully captured the increase in excess pore pressure in the deep layer. However, due to the complete exclusion of the restraining effect of the rigid container, it was challenging to simulate the excess pore pressure response throughout the entire ground. Therefore, in this study, the soil container was simulated under rigid conditions to align with the experimental setup. The simulation results of the crest settlement closely replicated the experimental results with an acceptable margin of error. The final settlements were 1.19 m and 1.25 m in the simulation and experiment, respectively, achieving an accuracy of approximately 95%. Furthermore, the model successfully captured the time-dependent behavior, accurately predicting an increase in settlement rate after approximately 10 s, coinciding with the  
Figure 6: Comparison of the excess pore pressure between the numerical and experimental results (case 3). Figure 7: Comparison of the crest settlement between the numerical and experimental results (case 3). sufficient increase in excess pore pressure in the soil. The average settlement velocities of the crest were 0.085 m/s and 0.088 m/s in the simulation and experiment, respectively, resulting in an error of 3%. Modeling the interface between the liquefied soil and piles is crucial because existing interface models have limitations in simulating the soil-pile dynamic behavior within liquefied soil. Figure 8 compares the pile-bending moments of applying constant interface friction angles of 60 degrees and 7.8 degrees, and applying the proposed model, which linearly decreased the interface friction angle from the initial value of 60 degrees according to the increase in excess pore pressure ratio. The constant 60 degrees model overestimated the bending moments from approximately 15 s, which was when the excess pore pressure ratio of the deep layer started to increase. The constant value of the interface friction angle led to an overestimation of the lateral soil load caused by the liquefaction-induced slope failure. In addition, the analysis results revealed that using the pile-pushing analysis to determine the initial friction angle of the normal spring was incompatible with the PM4 Sand model. The constant 7.8 degrees model predicted that the bending moment would decrease after approximately 20 s when the deep soil became fully liquefied. On the other hand, the proposed interface model accurately predicted the time history of the pile-bending moments in comparison with the experimental results. In particular, the proposed model predicted that the bending moment would be maintained with the quick recovery of the normal force, reflecting the effect of the development and the dissipation of the excess pore pressure.