## 2 Simulation of Blast Events
### State of the Art on Blast Load Analyses of Tank Structures  
Due to some severe explosion events in tank farms with sometimes far-reaching negative effects, a blast load analysis should be part of the design of tanks, especially for tanks as part of critical infrastructure or for hazardous fills. However, because tanks have long been designed based on simplified rules and many years of experience, and because finite-element analysis has only been the state of the art for more complex tank analysis problems in the last two decades, blast load analyses of tank structures are still challenging and part of the current research. A large proportion of the analyzed literature uses the simplified dynamic method based on the shockwave propagation described in Section 2.2, which can be applied in LS-DYNA [18] by means of the already mentioned feature \"LOAD_blast_ENHANCED, for instance [24; 26; 41]. In contrast, there are several works that adopt a different approach. The most relevant sources are discussed in the following. In [23], a very simple approach is proposed. Although initially suited to structures in chemical plants, it can be applied in general: in determining overpressures, the closest point of the structure to the blast source can be used as a reference for the determination of the scaled distance and corresponding blast parameter. The resulting peak overpressure can be used for the entire structure, which is quite conservative especially for blast loads in closer distances to structures and/or larger structures since the distance-related decay behavior of the overpressure is neglected. For larger structures, considering the average overpressure on the surface or the overpressure at the centroid of the surface can be less conservative. The advantage of this method lies in the user-friendliness of the application, as the same load is applied to each structural element in a simplified manner. However, the propagation velocity of the blast wave is neglected. Here, the TNO Green Book [16] proposes a procedure that considers the time span required for a blast wave to reach the back face of a building. Furthermore, the decrease in the pressure amplitude acting on the back face of a building is considered. The procedure primarily applies to buildings. Especially for industrial buildings, values for the blast load are specified: the walls subjected to possible reflection must be designed for a reflected overpressure of 30 kPa and the roof must withstand 20 kPa with a positive phase duration equal to 100 ms each. Additionally, control buildings shall be designed for a shock wave with a reflected peak overpressure of 300 kPa for walls and 100 kPa for the roof with a positive phase duration of 15 ms. It must be mentioned that the proposal of [16] applies to buildings. It is stated that data for industrial installations other than buildings are scarce and insufficient. An application to tank structures is therefore questionable. The work of [PERSON] et al. [31] considers the blast pressure time history applied to a cylindrical tank depending on scaled distance (Equation (1)) using a modified Friedlander equation. The resulting shock wave time history is applied normally and uniformly to one half of the cylindrical tank surface as shown in Figure 3.  
The tank side facing away from the blast source is not loaded. With this type of load application, maximum overturning loads can be determined for the tank. However, the one-sided load only on the side facing the blast source seems rather conservative. The inherent advantage of the shell load-bearing capacity of a cylindrical tank, even with non-uniform loads, is completely neglected by taking one half of the shell unloaded. Furthermore, the decay behavior of the peak overpressure with increasing scaled distance to the blast source is not considered. The tank studied is not provided with a roof and the pressure distribution acting on the free liquid surface is not discussed. [PERSON] et al.