## 4 Conclusions  
To study the seismic performance of a wide PSW with a gentle soil slope, our research suggested an FA method that considers both inertial and kinematic forces based on the PSW damping coefficient. The main conclusions of this study are as follows:  
1. FA provides the fastest and most reliable calculation tools for assessing the seismic performance of PSWs and it is effective for considering the effect of kinematic forces. It is also able to produce bending moments that are comparable to those calculated using FEA.
2. The typical damping coefficient employed in PSW seismic design is 0.05. Our research indicates that a wide PSW has a more significant damping coefficient than a typical smaller-width PSW. We provide an equation for calculating the PSW damping coefficient based on its width and natural periods.
3. The bending moment of a PSW pile is generated by a combination of inertial and kinematic forces. The bending moment produced by the inertial force is only about half of the FEA bending moment. Adding kinematic force into the analysis could demonstrate the impact of soil displacement and the impedance contrast between the soil layers, thus producing a comparable result with FEA, considering only inertial forces for PSWs on a slope could lead to the underestimation of the bending moment. Even in the case of a PSW on a gentle slope, the effect of kinematic force is still significant.
4. Seismic evaluations that consider only the inertial force or the kinematic force using the JRA equation are inappropriate, while seismic evaluations using the proposed method are highly applicable. The inability of the JRA method to estimate kinematic force was found in the bending moment distribution of the piles. At some depth, the bending moment became too large because of the triangular distribution of the kinematic force. The JRA method is unsuitable for calculating kinematic force caused by ground deformation because it produces a constant kinematic force regardless of the amount of ground deformation.
5. The kinematic force in FA can be computed using ground displacement and soil spring characteristics. In conjunction with ground displacement (as determined by the FEA), soil reaction value can be used as a kinematic force with satisfactory results. A technique to estimate ground displacement without referring to FEA results will be developed in a future study.  
Conceptualization, C.B. and T.N.; methodology, C.B. and T.N.; software, C.B.; validation, C.B. and T.N.; formal analysis, C.B. and T.N.; investigation, C.B. and T.N.; resources, C.B. and T.N.; data curation, C.B.; writing--original draft preparation, C.B.; writing--review and editing, T.N.; visualization, C.B.; supervision, T.N.; project administration, C.B.; funding acquisition, C.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the PT. ITSC, grant number: 036/ADM.ITSC/VIII/2019 and the APC were funded by the PT. ITSC.  
Not applicable.  
The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.  
**Acknowledgments:** The authors would like to express their gratitude to the PT. Inti Teknik Solusi Cemerlang (PT. ITSC) for providing the PLAXIS 2D software and SAP 2000.  
**Conflicts of Interest:** The authors declare no conflict of interest.