## 2 Simulation of Blast Events
### State of the Art on Blast Load Analyses of Tank Structures
Research on the effects of long-duration blast loadings induced by the explosion of flammable vapor clouds on tank structures is rare. [PERSON] and [PERSON] [47] provide a static calculation approach considering the dynamic characteristics of the deflagration blast load due to vapor cloud explosion by means of an increasing factor, the dynamic load factor (DLF). The use of the DLF concept, also described in the TNO Green Book, Chapter 2, Section 4.3 [16], allows the estimation of the structural response for a dynamic blast case simply by performing a static analysis. The DLF reflects the increase in response to the dynamic load with respect to an equivalent static load. It depends on the positive phase duration t\({}_{d}\) of the blast loading in relation to the natural period T\({}_{n}\) of the tank structure. The ratio t\({}_{d}\)/T\({}_{n}\) can be taken from diagrams, e.g., in [16; 47], and indicates whether the loading can be treated as impulsive (t\({}_{d}\)/T\({}_{n}\) < 0.4), dynamic (0.4 \(\leq\) t\({}_{d}\)/T\({}_{n}\) < 2) or quasi-static (t\({}_{d}\)/T\({}_{n}\) > 2). [PERSON] and [PERSON] [47] use the DLF concept to estimate the value of the peak overpressure. The corresponding blast load distribution around the tank circumference is shown in Figure 4. This pressure distribution shows a peak at an angle of circumference of 60\({}^{\circ}\), while the tank side facing away from the blast source experiences reduced but still positive overpressure. [PERSON] et al. [25] provide gas blast experiments as well as numerical and theoretical models to investigate the response and energy absorption mechanism of steel tanks. The experimental equipment, however, only offers the possibility of applying blast pressure to a small area of the tank. Similarly, in the numerical model, only a small circular area is subjected to uniform time-dependent blast pressure. The blast pressure distribution around the tank or on the roof is not analyzed. The most comprehensive research so far on the blast load distribution around circular cylinders was conducted by [PERSON] et al. [48]. A small-scale gas explosion test was developed by [PERSON] et al. [48]. The pressure distribution around the tank was calculated by [PERSON] et al. oped: a rigid PVC cylinder fitted with a flat cover at the top was equipped with pressure sensors around its height, circumference, and top cover to evaluate the reflected pressure field around the whole cylinder. The pressure sensor distribution consists of three sensors along the height of the cylinder and radius of the top side, which are installed every 15\({}^{\circ}\) along the circumference. The pressure distribution showed the following characteristics: the peak pressure reaches a maximum at the point with a circumferential angle of 0\({}^{\circ}\) (directly perpendicular to the pressure source) and decreases with an increase in the circumferential angle. The time at which the peak pressure occurs at any position of the cylinder shifts backwards in time as the circumferential angle increases. The positive load phase increases as the circumferential angle increases. The negative pressure phase decreases and approaches approximately zero as the circumferential angle increases. Unfortunately, the exact explosion characteristic for pressure distribution is not provided. Although pressure gauges on the roof are applied, no information about the resulting pressure distribution is available. However, the investigations confirm that a distance-related pressure distribution occurs along the cylinder. Furthermore, in [48], a numerical simulation was performed to evaluate the different responses of flexible or rigid cylinder walls under blast loading. These analyses were performed using LS-DYNA software with a weakly coupled approach: the blast wave of a solid explosive (TNT)--since gaseous detonation is not supported in LS-DYNA--is mapped on a coupled 3D Euler-Lagrange mesh under some simplifying assumptions.