**4. Fragmentation simulation model**

The basic questions that are asked in the simulation model of fragmentation are related to the assessment of fragmentation density and sector angle. Fragmentation density refers to the number of fragments whose range will correspond to an area. The sector angle refers to the most common angle in the horizontal plane at which the fragments will burst due to the explosion of the tank. The simulation model of fragmentation is based on the research given in Sections 2 and 3.

#### **4.1 Assessment of fragmentation density**

The density of fragments is estimated based on the results of fragmentation mechanics for different trajectories, masses and shapes of fragments. Assessment of fragment density requires the definition of appropriate distribution functions depending on the mass, the initial launch angle of the fragment and the limit values of the coefficients *kL* i *kD*. The considered masses of fragments are in the range from 200 *kg* to 200 *kg*, while the initial angles take values from 5<sup>0</sup> to 350 . The characteristic density functions for the defined parameters are given in **Table 5**.

*Simulation Model of Fragmentation Risk DOI: http://dx.doi.org/10.5772/intechopen.98955*


**Table 5.**

*Fragmentation densities for characteristic fragments.*

#### **4.2 Sector angle assessment**

The sector angle is the angle in the horizontal plane under which the fragment is launched. The explosion of the cylindrical tanks is accompanied by the generation of fragments from segments 1, 2 and 3 according to **Figure 1**. If the fragments belong only to segment 1, then their bursting is done exclusively in the axial direction. If the fragments belong only to segments 2 and 3, then the scattering of the fragments takes place in the action direction. In practice, the most common cases are when we have the generation of fragments from segments 1 and 2 or 1 and 3. Therefore, the first step in assessment the sector angle is to define the fragmentation probabilities by tank segments. For this purpose, the results on fracture and conditional fracture probabilities presented in Section 2 are used. Limit values of fragmentation probabilities by the number of generated fragments are given in **Table 6**.

The sector angles *α* and *β* are determined on the basis of the following formula:

$$p\_f \left( 1 - \frac{\Re^0 - \beta}{a} \right) = \frac{11}{2\mathsf{6}} \tag{16}$$

The condition should be added to the previous formula: *α* + *β* = *π*/2, where *pf* is the fragmentation probability of the tank corresponding to the first segment (S1).


#### **Table 6.**

*Fragmentation probabilities by number of generated fragments.*


**Table 7.**

*Sector angles by number of fragments generated.*

**Figure 7.** *Burst simulation with risk matrix.*

Sector area 2*α* covers fragmentation zones in which fragments generated predominantly from the cylindrical part of the tank are located (S1). Sector angle 2*β* covers the area corresponding to the fragments generated from segments 2 and 3 (S2 i S3). Sector angles by number of generated fragments are given in **Table 7**.
