# Black Loaded Columns--State of the Art Review
## 3 Numerical Modeling
[PERSON] and [PERSON] [92] modeled a bridge column in the Ansys Autodyn software to analyze the impact of concrete grade and spacing of ties under the blast load. They observed total deformation and principal stress for concrete grades M40 and M50 and ties spacings of 10 and 20 cm in the near and far-field. In the near field, the explosive is placed at the same standoff distance of 2 m, and the charge weight varies from 250 to 1500 kg. The influence of the concrete grade on the maximum deformation is visible only at the weight of explosives greater than 750 kg. With concrete M50, the principal stress is higher, but there is no big difference in it when increasing the weight of explosives. In the far-field, the explosive was placed at a standoff distance of 10 m, and the weight also varied from 250 to 1500 kg. There is a slight difference in total deformation concerning the grade of concrete. The principal stress exceeds the strength of concrete, and the difference in stress is visible for the grade of concrete. The effect of tie spacing is visible in the near field only in the increase in the maximum principal stress, while in the far-field, there is no effect on either deformation or principal stress. [PERSON] et al. [58] modeled the bridge column and bent it in the LS-Dyna for three design categories provided in [35]. They determined six damage mechanisms in the models, four of the column and two of bent. In all three design categories (A, B, C), spalling of concrete and crushing of the bent concrete were observed. Plastic joints in the column and shear of bent occur only in B and C categories. The shear or flexure failure of the column is most probable in category C, i.e., at the highest blast load. They found that increasing the transverse reinforcement reduces damage. In LS-Dyna, they received underestimated blast load, and therefore they used the ConWep program to calculate pressure-time diagrams. [PERSON] et al. [59] concluded through numerical simulations of columns in LS-Dyna that a larger cross-section and reinforcement ratio, smaller spacing between the stirrups, and a thinner concrete cover for columns exposed to close-in explosions give less damage. [PERSON] et al. [12] analyzed circular and square CFST (Concrete Filled-Steel Tube) columns with tube thicknesses of 2.8 and 3.8 mm. The Emulsion explosive was used, with TNT equivalences of (0.7) 17.5, 25, and 35 kg. A numerical simulation of the columns was performed in LS-Dyna, see Figure 18, but to reduce the computation time and model congestion, an air blast model was made in the ConWep program and then imported into LS-Dyna. By comparing the obtained periods of oscillation and maximum displacements, a good match between the numerical model and the experiment was obtained. Differences are found only in residual deflections but are not considered crucial to the accuracy of the model. [PERSON] et al. [21] numerically modeled CFDST columns with steel-fiber reinforced concrete using LS-Dyna and compared them with experimentally obtained results. For concrete, the KC model was used, and for the steel tube, the Material model 24 was used. The parameters for the concrete model were modified (\(f\)--tensile strength, \(B_{1}\)--parameter for residual strength, \(w_{2}\)--strain softening, \(\omega\)--confinement effect, \(\lambda\), and \(\eta\)--damage parameters) because UHPC was used. Column erosion occurs when the maximum shear strain value reaches 0.045. Numerical research concluded that the axial load up to a certain limit has a favorable effect on the deflection in the middle of the column. It is  
Figure 18: The numerical model of the blast test [12]. Copyright permission obtained from authors. not recommended to use columns with a hollow section ratio greater than 0.5. Increasing the thickness of the outer steel tube affects the decrease in deflection in the middle of the column. Columns filled with UHPC have less plastic deformation than columns filled with normal strength concrete, shown in Figure 19.  
[PERSON] et al.