# Construction of a Dimensional Damage Model of Reinforced Concrete Columns under Explosion Loading
## 3 Numerical Simulations to Obtain the Undetermined Coefficient
### Numerical Simulation Results and Analysis  
Due to the explosive loading, the concrete on the blasting surface of reinforced concrete easily fails, but the stirrup does not easily fail. Therefore, the average displacement of the two observation points on the stirrup at the center is used to characterize the disturbance in the column. The two observation points are recorded as observation point 1 and observation point 2 (see Figure 1). The coordinate system is established by taking an end point at the bottom of the column as a dot and the coordinates of observation point 1 and observation point 2 are (20, \(-\)2, 185) and (20, \(-\)2, 205). The numerical simulation results are shown in Table 7. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Simulation of** & **Explusive Equivalent** & **Initiation Distance** & **Simulation of** & **Explusive Equivalent** & **Initiation Distance** \\
**Condition** & **m (kg)** & **L (m)** & **Condition** & **m (kg)** & **L (m)** \\ \hline Z1-1 & & & 0.1 & Z4-1 & & 0.1 \\ Z1-2 & & 0.2 & Z4-2 & & 0.2 \\ Z1-3 & 1 & 0.3 & Z4-3 & 4 & 0.3 \\ Z1-4 & & 0.4 & Z4-4 & & 0.4 \\ Z1-5 & & 0.5 & Z4-5 & & 0.5 \\ \hline Z2-1 & & & 0.1 & Z5-1 & & 0.1 \\ Z2-2 & & 0.2 & Z5-2 & & 0.2 \\ Z2-3 & 2 & 0.3 & Z5-3 & 5 & 0.3 \\ Z2-4 & & 0.4 & Z5-4 & & 0.4 \\ Z2-5 & & 0.5 & Z5-5 & & 0.5 \\ \hline Z3-1 & & & 0.1 & & \\ Z3-2 & & 0.2 & & & \\ Z3-3 & 3 & 0.3 & & & \\ Z3-4 & & 0.4 & & & \\ Z3-5 & & 0.5 & & & \\ \hline \end{tabular}
\end{table} 
Table 6: Numerical simulation conditions. Figure 4: Mesh model of the reinforced concrete column. (**a**) is a 45 \({}^{\circ}\) view of the cylinder; (**b**) is the side view of the cylinder. When the explosion distance is 0.1 m, when the 4 kg and 5 kg explosion equivalents are detonated, the large-area failure of the concrete at the center of the blasting surface column disappears, and the stirrup breaks and disperses (its damage diagram is shown in Figure 5). This time, the column is seriously damaged and it is difficult to use the disturbance in the column to study the damage to reinforced concrete columns. Therefore, when using software to analyze the numerical simulation data, Z4-1 and Z5-1 conditions were not considered. Using Origin software to fit and analyze the simulation results under the same explosion equivalent and the same explosion distance, Figures 6 and 7 were obtained. Figure 6 shows the relationship between the disturbance \(\xi\) in the column and the explosion distance and the explosion equivalent under different explosion equivalents. Figure 7 shows the relationship between the disturbance \(\xi\) in the column and the explosion distance and explosion equivalent under different explosion distances. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Simulation**} & \multicolumn{3}{c}{**Maximum Displacement in Column (cm)**} & \multicolumn{3}{c}{**Maximum Displacement in Column (cm)**} \\ \cline{2-9}  & **Observation** & **Observation** & **Square** & **Position** & **Observation** & **Observation** & **Average** \\  & **Point 1** & **Point 2** & **Value** & & **Point 1** & **Point 2** & **Value** \\ \hline Z1-1 & 0.645 & 0.673 & 0.659 & Z3-4 & 0.423 & 0.452 & 0.4375 \\ Z1-2 & 0.278 & 0.285 & 0.2815 & Z3-5 & 0.249 & 0.259 & 0.254 \\ Z1-3 & 0.139 & 0.145 & 0.142 & Z4-1 & & Stirrup fracture scattered \\ Z1-4 & 0.068 & 0.069 & 0.0685 & Z4-2 & 2.010 & 2.370 & 2.190 \\ Z1-5 & 0.021 & 0.022 & 0.0215 & Z4-3 & 1.230 & 1.280 & 1.255 \\ Z2-1 & 0.149 & 1.92 & 1.0345 & Z4-4 & 0.733 & 0.775 & 0.754 \\ Z2-2 & 0.628 & 0.651 & 0.6395 & Z4-5 & 0.433 & 0.458 & 0.4455 \\ Z2-3 & 0.423 & 0.441 & 0.432 & Z5-1 & & Stirrup fracture scattered \\ Z2-4 & 0.198 & 0.203 & 0.2005 & Z5-2 & 3.070 & 3.660 & 3.365 \\ Z2-5 & 0.120 & 0.126 & 0.123 & Z5-3 & 1.740 & 1.790 & 1.765 \\ Z3-1 & 3.550 & 4.320 & 3.935 & Z5-4 & 1.060 & 1.100 & 1.080 \\ Z3-2 & 1.400 & 1.510 & 1.455 & Z5-5 & 0.658 & 0.689 & 0.6735 \\ Z3-3 & 0.814 & 0.838 & 0.826 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Numerical simulation results table.