# Black Loaded Columns--State of the Art Review
## 3 Numerical Modeling
[PERSON] and [PERSON] [63] modeled three RC columns in LS-Dyna, which differ in the distance between the transverse reinforcement. They designed the columns according to the instructions for the level of seismicity in the Canadian concrete design code [91]. Concrete was modeled using the Continuous Surface Cap Model (MAT_CSCM_159), and for reinforcement, they used Material Piecewise Linear Plasticity (MAT_024) model, while blast load was calculated in ConWep and then imported with Load Blast Enhanced (LBE) in LS-Dyna. They performed simulations with mesh sizes from 5 to 100 mm, and with 15 mm, they obtained a good ratio of the time spent for the calculation and the accuracy of the results compared with the experiment in [94]. The used explosive was ANFO (100, 250, 500, and 1000 kg) at scaled distances of 0.8, 1.0, and 1.5 m/kg\({}^{1/3}\). In near-field explosions, the distance between the transverse reinforcement has a significant effect on the reduction in displacement, while in far-field explosions, this effect is negligible. At a high axial load ratio (0.35), the seismically designed columns showed better behavior at scaled distances than the standard ones. [PERSON] et al. [23] performed numerical simulations in LS-Dyna of the circular and square columns of the bridge, exposed to the contact explosion of 1 kg of TNT. To reduce the computation time, at the height of 1 m, in the area of the contact explosion, they placed a denser mesh (8 mm), while on the rest of the column, the mesh size was courser (20 mm), shown in Figure 20. The principal strain of 0.5 was used as the erosion criterion. Numerical simulations well described the damage on the front sides of the column, while on the back, there are differences. They concluded that the damage was greater on the square column due to the flat surface and the higher stress concentration than on the circular column. The damage of the columns is shown in Figure 21.  
Figure 20: Detailed views of a mesh of 3D column models [23]. Copyright permission obtained from authors. [PERSON] et al. [77] investigated the effect of axial load on RC bridge columns subjected to far-field, close-in, and contact explosion. Columns in the far-field have mainly a flexure response, and the axial load affects the reduction in the maximum displacement in the middle of the column. In the case of a close-in detonation, a shear failure is expected, and the axial load affects the increase in the damage of the column and should not be neglected. In contact detonation, the concrete covers at the front and backside of the column spall off. The axial load reduces the damage of the concrete but increases the stress in the reinforcement and must be considered. [PERSON] et al. [65] conducted numerical investigations on CFDST columns under contact explosion in LS-Dyna. CFDST columns have proven to be good for two reasons: the first is that the confinement of concrete by steel tube allows better energy absorption, and the second is the prevention of the spallation of the concrete cover. In work [73], the researchers concluded that increasing the cross-sectional area and the ratio of reinforcement plays a significant role in the post-blast residual capacity of CFDST columns under contact explosion. In [67], the behavior of CFDST columns subjected to close-in blast loading was studied. They concluded that the influence of the charge shape significantly affects the response and behavior of the column at scaled distances from 0.079 m/kg\({}^{1/3}\) to 0.175 m/kg\({}^{1/3}\). [PERSON] et al. [66] performed a dynamic and static analysis of the bridge columns in LS-Dyna. Dynamic analysis is based on the comparison of accelerations and static analysis on the determination of damage through the ratio of the residual to the ultimate axial bearing capacity. They examined the damage to the column concerning the position of the explosives, at the bottom, in the middle, and at the top, shown in Figure 22. In all three cases, bending deformation occurs at the column, but the position of the crack formation differs.