# Black Loaded Columns--State of the Art Review
## 3 Numerical Modeling
Figure 21: Comparison of damages of circular and square RC columns after the detonation of 1 kg of TNT: (**a**) front side and (**b**) back side [23]. Copyright permission obtained from authors. Figure 22: Shock wave propagation depending on the position of the explosive [66]. [PERSON] et al. [68] performed a parametric analysis in LS-Dyna to determine the influence of longitudinal and transverse reinforcement ratios, longitudinal force, and boundary conditions. They concluded that at smaller-scaled distances, the increase in transverse and longitudinal reinforcement reduces the displacement in the middle of the column. It is recommended that the percentage of longitudinal reinforcement does not exceed 6% of the cross-sectional area of the column because too much reinforcement can lead to brittle failure. Analyzing the influence of the axial compressive load, they found that in an amount of up to 40%, it reduces the maximum displacement in the mid-span of the column due to the increase in moment capacity. The conclusions are based on close-in blast loading; a recommendation for future research is to conduct a parametric analysis for near and far filed scenarios. [PERSON] et al. [69] made numerical models of RC columns strengthened with CFRP in LS-Dyna. The size of the mesh elements for all materials was 10 mm, and for air, 20 mm. The 1 kg and 2 kg TNT charges were placed in contact with the column at the height of 30 cm. The numerical results show that the dragging force of the blast load separates the CFRP from the concrete, but despite this, CFRP protects the column from contact explosion. Column damage is shown in Figure 23.  
[PERSON] et al. [70] modeled in LS-Dyna RC steel jacked columns (25 cm \(\times\) 25 cm \(\times\) 360 cm) and observed the influence of steel thickness, scaled distance, and longitudinal compressive force on the behavior of the columns under the blast load. The columns are designed according to Eurocode 2. A 10 mm mesh was used for the column, while 5 mm elements were used for the explosive. Placing 8 kg of TNT in the middle of the column causes less global damage to the column, while placing the same amount at a distance of 32 cm from the ground causes significant local damage. The scaled distance was varied from 0.10 to 0.40 m/kg\({}^{1/3}\). Increasing the steel thickness from 3 mm to 6 mm did not result in less damage. [PERSON] et al. [33] investigated numerically in LS-Dyna the influence of charge and scaled distance on the level of column damage and influence of column width, concrete strength, and reinforcement ratio on the residual axial load capacity. [PERSON] et al. [72] performed a parametric analysis in LS-Dyna on the RC columns exposed to the contact explosion. They used from 115 g to 1000 g TNT, varied the compressive strength of concrete from 20 to 55 MPa, and reduced the distance of the transverse reinforcement from 200 to 50 mm. Increasing the transverse reinforcement reduces the damage to the concrete core, and higher compressive strength of concrete contributes to the reduction in cracks and peeling. The columns under contact explosion have local damage, while the global damage is negligible. [PERSON] et al. [28] investigated in LS-Dyna the influence of the column cross-sectional width under the contact explosion. They concluded that a larger cross-sectional width (greater by two or more times from the depth) has a favorable effect on the behavior and damage of the column. Figure 23: Column damages after detonation of 1 kg TNT: (**a**) RC and (**b**) RC + CFRP column [69]. Copyright permission obtained from authors. [PERSON] et al. [74] examined 45 numerical models of reinforced concrete columns in scale 1:4 (85 mm \(\times\) 85 mm \(\times\) 900 mm) in LS-Dyna. In the models, the behavior of four different cross-sections (circular, octagonal, hexagonal and square) on the blast load was examined. The circular column retains the lowest peak pressures and has the smallest deflection in the middle, while the square has the highest pressures and the largest deflection.