## 2 Simulation of Blast Events
### State of the Art on Blast Load Analyses of Tank Structures
The selected case is performed on a real scale and refers to the explosion of 1 ton of TNT at a 40 m distance from the tank [48]. The numerical analysis provides the following characteristics of the pressure distribution along the circumference of the tank (rigid and flexible): the maximum peak pressure is located at the position with a circumferential angle of 0\({}^{\circ}\) (directly perpendicular to the pressure source) and decreases as the circumferential angle increases. The same applies to the negative peak pressure, which is in fact a plateau rather than a peak, as the circumferential angle increases. The time at which the positive peak pressure occurs shifts backwards in time as the circumferential angle increases. The positive load phase decreases as the circumferential angle increases. The last aspect is notably in contradiction with the phenomena observed in the experiment and may be due to the simplifications in the blast load application. In [48], numerical analysis is primarily used to show that neglecting fluid-structure interaction leads to an error in the evaluation of the maximum reflected positive overpressure that is lower than 5% around the tank until the separation angle and lower than 1% in the most solicited region. Therefore, this simplification might be considered a valid assumption. Design criteria for tank structures exposed to explosion pressure are not discussed in the literature. Recognized normative verification methods such as the methods of DIN EN 1993-1-6 [49] for steel shell structures only apply to static load conditions or dynamic loads that are considered quasi-statically. In [23], it is stated that in conventional design, stresses are limited to the elastic range. In blast design, however, yielding should be acceptable and in fact desirable for economic reasons. Therefore, the adequacy of a blast-loaded component hinges on the maximum deformation rather than stress level [23]. In [23], Annex 5, deformation limits are proposed for structural members in industrial facilities. Although cylindrical shells are not particularly mentioned, the relevant criteria are mentioned here due to the lack of appropriate values for tank structures. First, a distinction is made between three damage levels--low, medium, and high. A low damage ratio comprises localized component damage with the building being usable, although repairs are required to restore the overall integrity. The description corresponds to general buildings but offers the possibility to be adopted to tank structures whose integrity should be ensured after a blast event. Next, for each damage level, a limit ductility ratio \(\mu\) is specified. For steel components, low-damage-level ductility values of 1 to 5 are specified depending on the structural type [23], with the ductility ratio \(\mu\) being defined as  
\[\mu=(\epsilon_{\text{elast}}+\epsilon_{\text{plast}})/\epsilon_{\text{elast}}, \tag{4}\]  
\[\epsilon_{\text{elast}}=\text{f}_{\text{yk}}/\text{E}, \tag{5}\]where \(\epsilon_{\text{elast}}\) is the elastic strain, \(\epsilon_{\text{plast}}\) is the plastic strain, \(f_{\text{yk}}\) is the characteristic yield strength, and E is the modulus of elasticity.