# Vulnerability Analysis of Column-Supported Reinforced Concrete Silo Structures
## 3 Determination of Silo Damage Index and Seismic Demand Parameters
### IDA Results  
With the application of the IDA to the silo structure, the dynamic load-carrying curve (IDA curve) and the absolute maximum values of the base shear (V) of the silo in the most dangerous state, i.e., the full-silo state, were extracted, along with the top displacement of the supporting column, as shown in Figure 7a. In view of the randomness of ground motion, the V- value is not always outputted at the same time when plotting IDA curves. Therefore, using the maximum absolute value can provide a safety upper limit for the structural response so as to ensure a safety upper limit for the division of damage states [32]. Correspondingly, the 12 seismic actions selected in Section 3.1 were modulated from 0.025 g according to the PGA value, and the step was 0.025 g when the PGA was less than 0.2 g. Otherwise, the step was 0.1 g. If necessary, additional steps can be applied to ensure the accuracy of the seismic response calculation of the silo in the entire IDA. The acceleration-time histories were inversed following the response spectra.  
Subsequently, 12 IDA curves were obtained by performing 216 dynamic time-history analyses and using the ABAQUS software (Figure 7a). Evidently, when the ground motion is small, the initial pure elastic region of the IDA curve can be clearly detected until the occurrence of the first yield; after the elastic stage, the IDA curve reaches the second hardening stage, which ends in the final yield zone, and then the silo structure enters the nonlinear deformation stage, and the IDA curve reaches the plateau region after the final  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Earthquake Event** & **Time** & **Recording Station** & **Magnitude** & **Epicenter** & **Site** \\ \hline
1 & San\_Fernando & 1971 & Maricopa\_Array\_\#1 & 6.6 & 193.9 & MA1220 \\
2 & Imperial\_Valley-06 & 1979 & El\_Centro\_Array\_\#3 & 6.5 & 12.8 & E03140 \\
3 & Northridge-01 & 1994 & Rinaldi\_Receiving\_Sta & 6.7 & 6.5 & RRS318 \\
4 & San\_Fernando & 1971 & Maricopa\_Array\_\#2 & 6.6 & 109.7 & MA2130 \\
5 & Landers & 1992 & Barstow & 7.3 & 34.9 & BRS090 \\
6 & Northridge-01 & 1994 & LA\_Dam & 6.7 & 5.9 & LDM334 \\
6 & Chi-Chi-Taiwan-06 & 1999 & TCU49 & 6.3 & 32 & TCU49 \\
7 & Northridge-01 & 1994 & Lawndale-Osage\_Ave & 6.7 & 39.9 & LOA092 \\
8 & San\_Fernando & 1971 & Borrego\_Springs\_Fire\_Sta & 6.6 & 214.3 & BSF135 \\
9 & Loma\_Prieta & 1989 & Bear\_Valley\_\#5-Callens\_Ranch & 6.9 & 53.6 & BVC220 \\
10 & Imperial\_Valley-06 & 1979 & Brawley\_Airport & 6.5 & 10.4 & BRA315 \\
11 & Loma\_Prieta & 1989 & So\_San\_Francisco-Sierra\_Pt. & 6.9 & 63.1 & SSF115 \\
12 & Coalinga-01 & 1983 & Parkfield-Fault\_Zone\_15 & 6.4 & 29.4 & Z15090 \\ \hline \end{tabular}
\end{table}
Table 2: Seismic waves for IDA.  
Figure 6: Response and target spectra of seismic records.  
yield region. In practice, a structure begins to exhibit a nonlinear behavior after the initial linear elastic region; however, the behavior changes randomly depending on the type of seismic wave; this is largely due to the nature of the specific acceleration profiles inherent in the IDA [33]. In summary, the same structure had a different dynamic response under the action of seismic waves with the same intensity but of different types.