# Black Loaded Columns--State of the Art Review
## 3 Numerical Modeling
It was shown that the column thickness, charge radius, and the ratio of standoff distance to charge radius play a significant role in the column response. They give an empirical formula based on the conducted simulations to predict the damage index of the column. Comparing the results obtained by formula and numerical simulations, the deviations are up to a maximum of 15% what is in an acceptable range. [PERSON] [54] modeled RC columns in Abaqus. The position of the spherical charge remained unchanged, but the charge weight, column height, longitudinal steel reinforcement, columns aspect ratio, and transverse steel ratio were varied. Fixed boundary conditions are provided at the top and bottom of the column. In addition to column damage, they measured acceleration and displacement concerning varied parameters. Four quantities of explosives were used (45.36, 226.80, 453.59, and 1016.05 kg) and placed at a distance of 4.87 m. The increase in the lateral reinforcement in the column had the effect of reducing the displacement in the middle of the column. It is recommended to examine the influence of the axial force during the blast load and to include additional parameters such as the variation in the standoff distance of the charge. In numerical simulations using Autodyn, [PERSON] and [PERSON] [55] tested three columns designed for different loads in accordance with the Canadian reinforced concrete design code [91]. The first type of column is designed only for gravity loads, and the distance between the transverse reinforcement is 300 mm, and the other two types of columns are designed for seismic loads, but in the second type, the distance between transverse reinforcement is 150 mm, and in the third 75 mm. Column damage is significantly less with denser reinforcement, especially at small-scaled distances. They have proven in research that regardless of the same scaled distance, in a situation where a larger amount of explosive is detonated, the column has a higher deflection. [PERSON] and [PERSON] [56] calibrated the numerical model for RC slab in LS-Dyna according to a previously performed experiment and then used that numerical model for RC column simulation. For good simulation of concrete spallation, the erosion criterion using principle tensile strain of 0.01 was defined. Through simulations, they concluded that denser reinforcement and greater column depth reduced spall damage, i.e., increase the confinement of concrete. The boundary conditions and column height do not play a significant role in the level of spall damage in close-in cases. [PERSON] and [PERSON] [57] analyzed a spatial and non-spatial simulation of the blast load on RC columns in LS-Dyna. They used three quantities of ANFO explosives, 50, 100, and 1000 kg, at distances from 0 to 30 m. The analysis is based on axial load-carrying capacity and concluded that the variability of the results in the spatial model is lower, and the probability of damage is significantly higher. They consider the spatial model more reliable and recommended it for future research with an additional assessment of the scale of fluctuation. [PERSON] et al. [50] used LS-Dyna for analyzing the behavior of the exterior building RC circular column and strengthened column with Carbon Fiber Reinforced Polymer (CFRP) sheets under blast load. Four different charge weights (100, 200, 500, and 1000 kg) of TNT at three different standoff distances (1, 4, and 15 m) and at 1 m height from the ground were analyzed. They modeled columns with different boundary conditions, first with both fixed ends and a second type with both hinged ends. For calculation of blast load parameters in all assumed scenarios, they used the software ConWep. The use of CFRP is increasing the shear capacity of the column and the strength of the column, which results in less lateral displacement, and more layers of CFRP can undergo more intense blast loads [50]. Moreover, at the scaled distance from 0.50 to 0.68 m/kg\({}^{1/3}\), columns with CFRP showed better behavior than RC columns.