## 2 FE Model Validation
### Numerical Model
#### 2.2.2 Material Model  
(1) Concrete  
The concrete material is simulated using the concrete damaged plasticity (CDP) model in the ABAQUS material library, in which the constitutive relation under the uniaxial state is set according to the Code for Design of Concrete Structure (GB50010-2010) ([PERSON] and [PERSON], 2017), as seen in Table 1. Meanwhile, since the paper simulates the impact load, instead of the long-term static load, the influence of the concrete aging ([PERSON] and [PERSON], 2017) was not considered. To consider the enhancement effect of the strain rate on concrete material, the calculation equations of the dynamic compressive and tensile strengths suggested by the Comite Euro-International du Beton (CEB) ([PERSON] and [PERSON], 2017) are utilized:  
\[\sigma_{\text{c, d}}/\sigma_{\text{c, s}}=\left\{ \begin{array}{ll}\left(\dot{ \varepsilon}/\dot{\varepsilon}_{\text{c, s}}\right)^{1.026\alpha}&\dot{ \varepsilon}\leq 30/\text{s}\\ \gamma(\dot{\varepsilon}/\dot{\varepsilon}_{\text{c, s}})^{1/3}&\dot{ \varepsilon}>30/\text{s}\end{array} \right. \tag{1}\]  
\[\sigma_{\text{t, d}}/\sigma_{\text{t, s}}=\left\{ \begin{array}{ll}\left(\dot{ \varepsilon}/\dot{\varepsilon}_{\text{t, s}}\right)^{1.016\alpha}&\dot{ \varepsilon}\leq 30/\text{s}\\ \lambda(\dot{\varepsilon}/\dot{\varepsilon}_{\text{t, s}})^{1/3}&\dot{ \varepsilon}>30/\text{s}\end{array} \right. \tag{2}\]  
where \(\dot{\varepsilon}\) is the strain rate; \(\sigma_{\text{c, d}}\) and \(\sigma_{\text{t, d}}\) are the dynamic compressive strength and dynamic tensile strength, respectively; and \(\sigma_{\text{c, s}}\) and \(\sigma_{\text{t, s}}\) are the compressive and tensile strengths under quasi-static conditions corresponding to the reference strain rates \(\dot{\varepsilon}_{\text{c, s}}=3.0\times 10^{-5}/\text{s}\) and \(\dot{\varepsilon}_{\text{t, s}}=3.0\times 10^{-6}/\text{s}\), respectively. Under compressive conditions, \(\lg\gamma=6.156\alpha\,-\,0.492\) and \(\alpha=1/(5+0.9f_{\text{cu}})\), in which \(f_{\text{cu}}\) is the compressive strength of the cube test block, while under tensile conditions, \(\lg\lambda=7\delta\,-\,0.5\) and \(\delta=1/(10+0.6f_{\text{tu}})\), in which \(f_{\text{tu}}\) is the tensile strength of the cube test block. (2) Rebar  
The constitutive relation of rebar is simulated using a bilinear elasto-plastic model with kinematic hardening, in which the yield strength and tensile strength are obtained according to the measured values in the tensile test of the material properties, and specific parameters are set as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(\rho\)/(\(\text{t/mm}^{3}\))} & \multirow{2}{*}{\(E\)/MPa} & \multirow{2}{*}{\(v\)} & \multirow{2}{*}{\(\varepsilon_{\text{u}}\)} & \multicolumn{2}{c}{\(f_{\text{y}}\)/(MPa)} & \multicolumn{2}{c}{\(f_{\text{u}}\)/(MPa)} \\ \cline{5-8}  & & & & \(\mathbf{\Phi}\)8 & \(\mathbf{\Phi}\)10 & \(\mathbf{\Phi}\)12 & \(\mathbf{\Phi}\)8 & \(\mathbf{\Phi}\)10 & \(\mathbf{\Phi}\)12 \\ \hline
7.8 \(\times\) 10\({}^{-9}\) & 2.1 \(\times\) 10\({}^{5}\) & 0.3 & 0.2 & 408.8 & 424.6 & 470.4 & 541.1 & 642.3 & 685.7 \\ \hlinePrevious studies have shown that the yield strength of steel shows a significant strain rate effect under impact [20; 21]. In this simulation analysis, the influence of the strain rate is considered using the classical Cowper-Symonds model [22], as seen in Formula (3):  
\[\sigma_{\text{y}}=\left[1+\left(\frac{\dot{\epsilon}}{C}\right)^{1/p}\right] \left(\sigma_{0}+\beta E_{p}e_{\text{eff}}^{p}\right) \tag{3}\]  
where \(\sigma_{0}\) is the yield strength of rebar under quasi-static loading; \(\dot{\epsilon}\) is the strain rate; \(C\) and \(p\) are the strain rate-related parameters in the Cowper-Symonds model, with their values set to 40 s\({}^{-1}\) and 5 [23], respectively; \(\beta\) is the strain hardening parameter, which takes the values of 0 and 1 to represent kinematic hardening and isotropic hardening, respectively.