# Black Loaded Columns--State of the Art Review
## 3 Numerical Modeling
[14] compared the numerical simulation with an already conducted experiment. The used explosive was Gelamon VF65 (65% TNT equivalence), 8 kg TNT equivalence at distances of 1 m and 0.60 m from the column, which is classified as a near-field range. Overpressure, impulse, deflection, acceleration, and visual damage to the column were measured and compared. For numerical modeling, the Ansys Autodyn program was used in which air and explosives were modeled through an Euler processor and the column through Lagrange. The optimal mesh size of concrete, steel, and the air was 10 mm. The authors made models with default RHT values and with the values proposed in [93] but concluded that the parameters that affect the strength degradation (damage factors \(D_{1}\) and \(D_{2}\), and \(e_{min}^{fail}\)) and the residual strength, \(Y^{\star}_{\text{fric}}\) (parameters \(B\) and \(M\)) should be changed in the model. For good prediction of spallation, the instantaneous geometric strain was used for erosion type with a value of 0.5. The obtained column damage with different RHT parameters is shown in Table 6. The parameters of the RHT material model (shown in Table 3) are validated for scaled distances (\(Z\)) from 0.5 to 0.3 m/kg\({}^{1/3}\). [PERSON] et al. [60] studied, using LS-Dyna numerical models, the influence of axial and blast load on the RC column of the bridge. For the concrete model, they used CSCM (Continuous Surface Cap Model) and for reinforcement MAT 24. Exact quantities of explosives and distances are not given, but scaled distances from 1.77 to 0.45 m/kg\({}^{1/3}\). They concluded that when an axial load ratio of 0.25 is applied, the displacement in the middle of the column decreases but the damage of the column increases. [PERSON] and [PERSON] [61] made a numerical model of the column, experimentally tested in [4] using LS-Dyna software. The influence of concrete strength, reinforcement ratio, axial load, and the column wrapping with SFRP (Steel Fiber Reinforced Polymer) was \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Autodyn (Default) [86] (b)** & **[PERSON] and [PERSON] [93]** & **[PERSON] et al. [14]** \\
**(a)** & **Autodyn (Default) [86] (b)** & **(c)** & **(d)** \\ \hline \(B\) & 1.6 & 0.7 & 0.35 \\ \(M\) & 0.61 & 0.8 & 0.55 \\ \hline \multicolumn{4}{c}{RHT damage model} \\ \hline \(D_{1}\) & 0.04 & 0.015 & 0.8 \\ \(D_{2}\) & 1 & 1 & 1 \\ \(e_{min}^{fail}\) & 0.01 & \(8.00\times 10^{-4}\) & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Column damage obtained: (a) experimentally and numerically using (b) default RHT model parameters; (c) parameters provided in [93]; (d) modified parameters by [14]. Figure 19: Failure mode of CFDST column with: (a) normal strength concrete and (b) UHPC [21]. Copyright permission obtained from authors. observed. The Johnson-Holmquist-Cook (JHC) model was used for concrete modeling and the elastic-plastic kinematic model for steel reinforcement. The impact of the blast load was determined in the ConWep software, and the detonation point was placed 5 cm above the ground, 40 cm from the column. SFRP proved to be an inexpensive and ductile retrofit. One layer has the largest contribution in blast capacity, while all additional layers have a small effect on increasing the capacity. They obtained a linear relationship between the concrete strength and the increase in the blast load capacity. [PERSON] et al. [62] performed numerical simulations of the RC column in LS-Dyna. The concrete was modeled using the CSCM concrete model (type 159 material) and reinforced using the plastic-kinematic model (type 3 material). They observed the influence of detonation of 10 kg of TNT at a distance of 1.2 m from the ground and 1 m from the column. They also concluded that the reinforcement ratio has a significant impact on the behavior of columns under the blast load and that the columns in the ground floor and bases need to be better reinforced due to their easy accessibility.