## 3 Simulation Model for Numerical Analyses
### Blast Load  
In the present study, an idealized equivalent time-dependent pressure wave according to Figure 8 representing a high pressure and long duration over pressure is considered. The maximal peak reflected pressure acting on the tank is set to 30 kPa. The overpressure function is set as a linear function with the same gradient in increasing and decreasing parts. As already mentioned in the introduction, the load scenario was selected based on its inclusion as a requirement for safe tank design in both the Belgian and Dutch guidelines [13; 14]. Figure 7: Material plastic kinematic: 1 and \(l_{0}\) are the undeformed and deformed lengths of uniaxial tension specimen while the tangent modulus \(\text{E}_{t}\) is the slope of the bilinear stress strain curve. The adopted values are reported in Tables 1 and 2. In contrast to shock waves for a triangular pressure wave according to Figure 8, rules to determine the blast parameter like the ratio of reflected to incident pressure, pressure wave velocity and time of arrival of the pressure wave depending on the scaled distance Z are not available. The pressure wave velocity could be determined using appropriate formulas that would also allow determining the time of arrival. However, the ratio of reflected to incident pressure remains unknown. The current state of knowledge precludes the determination of the distance- and time-dependent pressure distribution along both the tank circumference and height without having specific information about the source of the blast pressure. In [30], it is proposed to adopt the blast parameter of a shock wave in order to transfer their distance-related behavior to the triangle pressure shape. With impulse equality, a pressure wave can be transferred to a shock wave and vice versa. That means that each ideal pressure wave can be converted to a corresponding shock wave with congruent impulse and peak pressure [23; 30], as depicted in Figure 9. This method is inspired by the TNT equivalence method of blast prediction for vapor cloud explosions. As already mentioned in Section 2.3, this method is considered inaccurate [33]. However, the points of criticism relate to the fact that the conversion of the explosion source of highly flammable substances into the corresponding TNT equivalent is difficult to capture and prone to error. However, since the resulting pressure has already been determined in the present research (Figure 8) and only the missing blast parameters are to be determined, the points of concern regarding TNT equivalence appear negligible. With the maximal peak reflective pressure specified in Figure 8, a fictive scaled distance can be determined, for example, by using the Kingery-Bulmash [35] or similar equations. From the impulse equality, it is possible to derive the scaled distance, then an equivalent TNT mass and a distance according to Equation (1). Furthermore, the blast equations allow the determination of blast parameters like the shock wave velocity and time of arrival, which can be adapted for the impulse-equal pressure wave. Since the Kingery-Bulmash equations [35] are quite advanced for practical application, in this study, the modified blast equations proposed by [PERSON] et al. [56] are used. The following procedure to determine the resulting distance-related, time-dependent pressure load acting on the tank is developed:  
1. The maximal peak reflected pressure is set to 30 kPa; the positive phase duration of the pressure wave is defined with 300 ms. The impulse amounts to 4500 kPa ms.
2. With the maximal peak reflected pressure of 30 kPa, the scaled distance is calculated as Z = 8.365 m/kg\({}^{1/3}\) according to [PERSON] et al. [56]. 3. With impulse equality (I\({}_{\text{ref}}\) = 4500 kPa ms), the blast equation of [56] and Equation (1), a distance R and equivalent TNT-mass W can be determined: R = 785 m, W = 826.44 to. 4. An explosion scenario is therefore established. In this contribution, the blast source is set to a point in the positive x-direction as seen from the center of the tank (Figure 10).