# Vulnerability Analysis of Column-Supported Reinforced Concrete Silo Structures
## 5 Conclusions  
In this study, through a numerical analysis, the damage states of column-supported reinforced concrete silos were defined by means of an IDA, and the seismic vulnerability of the silos was analyzed. First, the EDPs, IMs, and limit states of the different damage indices of the silo were defined and incorporated into the fragility analysis. Second, fragility curves of the silo under a series of seismic excitations, such as in the empty-, half-, and full-silo states, were obtained and used to evaluate the damage states. Finally, the IDA method was applied to calculate the exceedance probability and evaluate the seismic performance of the silo structure. The results and conclusions of this study are summarized below:  
1. The displacement at the top of the column can be used as a damage index to assess the seismic fragility of column-supported reinforced concrete silos. Notably, four limit states were defined for the first time so as to better determine the damage states of column-supported reinforced concrete silos in the event of earthquakes. 2. According to the time history analysis of the seismic effects on the column-supported reinforced concrete silo with the empty-, half-, and full-silo, the top position of the silo support column is first damaged and is the weak part of the structure, which has nothing to do with the storage condition and PGA. 3. The existence and volume of the stored grain were directly related to the damage behavior of the silo. With the increase in the storage mass, the supporting column of the silo structure will enter the nonlinear state earlier. In the nonlinear stage, the degradation effect of damage stiffness under full-silo is significantly higher than that of half-silo and empty-silo, and the size of storage mass is an important factor that determines the damage stiffness degradation of the column-supported reinforced concrete silo. Special attention should be paid to the impact of storage mass during the assessment of seismic performance and seismic risk. 4. The full-silo state was the most dangerous working state of the column-supported reinforced concrete silo. The maximum probability of collapse under a seven-degree rare earthquake was 0.12%, and the 50-year collapse risk was 0.38%. Thus, it could be concluded that the seismic performance and collapse resistance of the column-supported reinforced concrete silo are both favorable and that there is a high degree of structural safety redundancy. Based on the results of this research, it is suggested that the appropriate limit states should be taken into account before the seismic safety assessment for column-supported reinforced concrete silos. Meanwhile, the results of the damage pattern lend insights into the vulnerable areas of a silo structure under seismic effects. The vulnerability analysis of the silo structure can guide the engineering design quantitatively. **Author Contributions:** All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication. Collection of Data: J.L. Writing--Original Draft: G.W., Q.X. and Y.D. Visualization: G.W. and Q.X. Writing-Reviewing and Editing: G.W., Q.X. and Y.D. Resources: Q.X. Supervision: Q.L. All authors have read and agreed to the published version of the manuscript. **Funding:** This study was supported by the Key Technologies R & D Program of Henan Provincial Department of Science and Technology (Grant number: 212102310955), the Natural Science Program of Henan Provincial Department of Science and Technology (Grant number: 2321023201864) and the Natural Science Program of Henan Provincial Department of Science and Technology (Grant number: 232102320186). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.