## 1 Introduction
Numerous studies have discussed the pile-soil interaction modeling method and its application for the dynamic analysis of structures [22; 23; 24; 25; 26]. Frame analysis (FA) is a simplified approach to the seismic analysis of PSWs [27] and corroded reinforced concrete (RC) structures [28; 29] that offers a reasonable compromise between accuracy and computational time. Nonlinear behavior can be modeled in FA by applying hinge properties (e.g., force-deformation or moment-rotation relationships) to one or more points along the frame element [30]. Nonlinear procedures for FA have been introduced in the design codes for buildings [31; 32] by providing recommended force-deformation or moment-rotation relationships for RC members. However, the moment-rotation relationship specified in building design codes is unsuitable for the nonlinear seismic response analysis of corroded PSWs due to differences in inelastic behavior and cross-sectional configuration, which have also not been considered for corrosion-induced material property degradation. Therefore, the moment-rotation relationship of corroded spun piles should be developed first in the nonlinear seismic response analysis of corroded PSWs using FA. Corrosion is known to degrade the material properties of RC members, including spun piles. Therefore, the nonlinear seismic response analysis of PSWs with corroded spun piles should consider the deterioration of material properties due to corrosion. [PERSON] and [PERSON] [33] demonstrated the prediction of the material properties of corroded spun pile materials, including the cover and core concrete compressive strength, prestressed concrete steel bar (PC bar) yield strength, and concrete-PC bar bond strength. These predictions are expected to provide more accurate nonlinear seismic response analysis results for corroded PSWs than analyses based on material deterioration predictions from non-spun pile studies [34; 35]. Since little research has been conducted on the nonlinear seismic response analysis of PSWs with corroded spun piles, this study aims to develop a novel FA method to investigate the nonlinear seismic response of PSWs with corroded spun piles. According to Indonesian government regulations [36], buildings and infrastructure (including port facilities) must remain operational for at least 50 years. Therefore, in this study, the nonlinear seismic response of corroded PSWs was observed for 75 years. The nonlinear seismic response of corroded PSWs was determined by performing pushover analysis using three methods: FA using the method of the previous study (FA-1), the proposed FA method (FA-2), and FB-FEA. This study also considered vertical pile and batter pile configurations as variations of PSW foundations. The pushover analysis results for the corroded PSWs using FA-1, FA-2, and FB-FEA were compared in terms of several parameters, such as natural period, plastic hinge formation, and load capacity of the corroded PSW. The material responses of the spun pile in terms of stress-strain curves for corroded PC bars, cover concrete, and core concrete, along with the reduction of the corroded PC bar area, were considered in FB-FEA. Furthermore, FA-1 and FA-2 considered several characteristics (i.e., PC bar area reduction, deteriorated concrete compressive strength, PC bar yield strength reduction, spun pile bending stiffness reduction factor, and spun pile moment-curvature relationship).