## 2 Simulation of Blast Events
### Discussion of State of the Art on Blast Load Analyses of Tank Structures  
The literature review in Section 2.4 shows that there are no specific rules for load distribution around the cylindrical shell and on the roof, nor general rules for evaluating adequate design criteria. Although many tank explosion studies can be found in the literature, a general design approach is not yet available. There is widespread consensus that the position of the tank wall directly perpendicular to the blast source experiences the greatest peak overpressure, while, toward the tank sides, the overpressure decreases. Additionally, the application of overpressure (no suction or zero-overpressure) on the tank side facing away from the explosion source seems to be common. The experimental study presented in [48] shows that the time at which the peak pressure occurs shifts backwards in time as the circumferential angle increases and, furthermore, the positive load phase increases as the circumferential angle increases. This load approach is congruent with the load distribution as a function of both the scaled distance and the angle of incidence presented in Section 2.2, which applies for shock waves resulting from high explosives. Here, the minimal pressure applied to the tank would be the incident pressure at the tank's backside with the longest load duration consistent with the largest scaled distance. There is no similarly simple method for the propagation of slow deflagration pressure waves that depends only on the scaled distance (see Section 2.3), but the general propagation behavior is comparable. Therefore, in the present study, a simple approach is developed to consider the following: the combination of a distance-related pressure distribution with a distribution depending on the angle of incidence corresponds to a pressure load being applied on the overall tank structure, with varying amplitudes over the tank height and circumference and roof. This method allows the relevant correlations to be put into a formula-based context and, thus, prepared for systematic application. Section 3.4 introduces the approach in detail. The approaches of [31], displayed in Figure 3, and [47], given in Figure 4, are also examined in the present research in order to investigate the advantages and disadvantages of the individual methods for comparative analysis. Special attention is paid to the load direction of the blast load acting on the roof surface. The approach presented in Section 2.2 and in Figure 2 states that the ordinate of the pressure load depends on the angle of incidence. When applying this approach, it results in a compression load for the entire roof surface. A non-uniform compression load can severely damage the thin-walled roof membrane. In addition, the explosion load acting as a compression load on the roof is transferred to the tank shell as axial compression load and increases the already existing axial compression load. Since thin-walled shells are typically susceptible to buckling, which can lead to critical shell loads. However, as discussed in [46], a roof suction load introduced by blast wave propagation can occasionally damage tanks due to roof uplift. The roof to shell joint may tear and peel away the roof plate, or the roof structure may be dislodged by distortion of the shell. Additionally, the anchorage of the tank is heavily stressed due to the uplift load. There are now two completely contradictory recommendations for load application on the roof. Following the general application of wind loads on dome roof structures according to Eurocode's approach [50], the sign of the pressure coefficient (compression or suction) is determined depending on the relation of the tank height to diameter or roof height to diameter. For the usual dimensions of storage tanks with dome roofs, wind load is always applied as the suction load to the total roof. At this point, reference is made to DIN EN 1991-1-4, Figure 7.12 [50].