## 3 Model Validation and Numerical Examples
### Model Competition  
In order to profoundly investigate the accuracy of the modified K&C model and the modified HJC model, we decided to verify the applicability of the two modified material models to RPC materials according to the explosion experiment conducted by [PERSON] [33] in the recent report. The compressive strength of RPC is 135.1 MPa, and steel tube yield strength is 318.5 MPa. The top of the column limits the displacement in the \(x\), \(y\), and \(z\) directions, and the bottom end is a fixed-end constraint. Model parameters are shown in Table 7.  
The modified K&C model, HJC model, modified HJC model, and experiment comparison are shown in Figure 3. Among them, the material parameters of the HJC material model are determined according to [PERSON] [14]. It should be pointed out that the residual displacement results of the experiments are used for the verification. The results show that the modified K&C model parameters have better accuracy in calculating dynamic response than the modified HJC model parameters and parameters of the modified HJC model proposed by [PERSON] [14]. The displacement time history curve of the modified K&C model converges to the experimental value faster through vibration. The increase of RPC damage degree in RPC-FST under near-range explosion load is the main reason for the inaccurate numerical calculation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Mass density \(R\) (g/mm\({}^{3}\)) & 7.85 \(\times\) 10\({}^{-3}\) & [PERSON]’s modulus \(E\) (MPa) & 2.05 \(\times\) 10\({}^{5}\) \\ Poisson’s ratio \(PR\) & 0.3 & Yield stress \(SIGY\) (MPa) & 318.5 \\ Hardening parameter \(BETA\) & 0 & Strain rate parameter \(SRC\) & 6844 \\ Effective plastic strain \(FS\) & 0.25 & Strain rate parameter \(SRP\) & 3.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Material properties of steel tube. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen** & \begin{tabular}{c} **TNT Weight** \\ **(kg)** \\ \end{tabular} & \begin{tabular}{c} **TNT Height** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **TNT Distance** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **Steel Tube Thickness** \\ **(mm)** \\ \end{tabular} \\ \hline C-15 & 4 & 250 & 221 & 6 \\ C-16 & 4 & 950 & 221 & 6 \\ C-17 & 7 & 955 & 230 & 6 \\ C-18 & 10 & 945 & 275 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model parameters. Figure 3: Modified K&C model, HJC model, modified HJC model, and experiment comparison: (**a**) blast surface displacement of RPC-FST and (**b**) back blast surface displacement of RPC-FST. The structural response under explosion loading is influenced by the constitutive models of the material, which will bring uncertainty to structural protection. The result of residual displacement with the HJC model is obviously lower than the experimental value. This phenomenon is mainly because the parameters are modified for RPC containing coarse aggregate [14]. The porosity of RPC containing coarse aggregate is generally 10.5%, while the porosity of RPC without coarse aggregate is generally 5%, which leads to a certain deviation in the expression of the equation of state under this working condition. In addition, determining the parameters of the damage evolution equation based only on steel fiber content needs to be further discussed. Therefore, the dynamic response analysis of the modified HJC model is carried out. The results show that the modified HJC model has obvious advantages over the HJC model. This phenomenon is mainly because the modified HJC model considers the influence of porosity on the equation of state. Furthermore, the effects of the water/cement ratio, steel fiber content, and steel fiber length on the damage evolution equation are considered. However, the advantages of the modified K&C model are still obvious.