# A Review of Blast Loading in the Urban Environment
## 2 Current Knowledge
### Degree of Confinement
Cylindrical and spherical charges of the same mass were used, and the average scaled impulse measured across multiple sensors was plotted against the degree of confinement. A reasonable logarithmic relationship was apparent between the variables; see Figure 4, adapted from [PERSON] et al. [47]. The results in Figure 4 suggest that blasts within more confined urban settings will produce greater loading more often than not. [PERSON] et al. [49] found a similar characteristic, where the peak impulse was shown to increase along a \"quarter symmetry wall\" when [PERSON] were present, compared to a no-obstacle scenario. Likewise, a similar behaviour was observed by [PERSON] et al. [50], where overpressure increased with confinement, although this confinement is not quantified, but visually shown instead. This could also agree with what is seen in [PERSON] et al. [37], where larger areal densities increased the average impulse measured on a target wall, but this is only relevant for a small sample and range of areal densities with a direct line from the blast to the target wall. Furthermore, the findings by [PERSON] et al. [47] also contradict what is reported by [PERSON] et al. [42], where the scaled impulse decreases slightly within a confining array. A direct comparison cannot be made as the input metrics are not the same, but it can be said with reasonable confidence that there exists a gap in the knowledge, which requires further investigation. The degree of confinement metric has since been explored further using a largely numerical basis [51]. It was acknowledged that the first iteration of the degree of confinement was limited in that _\"it becomes very difficult to compute for more complex, real-world urban environments\"_. Likewise, in its previous form, the method did not _\"[PERSON] itself to incorporation into automated software\"_. For these reasons, a refined approach was determined. The geometry is first discretised into a 3D mesh, with a mesh resolution size of 0.1 m/kg\({}^{1/3}\). A confinement region extends outwards from the charge position until it reaches a structure or a \(Z_{\text{cutoff}}\) of 6 m/kg\({}^{1/3}\). This region can \"wrap\" around structures to points outside the line of sight relevant to the charge. The weighted \"open\" and \"closed\" areas, \(A\), are then calculated based on the cut-cell areas between the structural elements and the mesh. The inverse distance of each cut cell to the charge is also accounted for, \(D^{-1}\). The revised calculation for the degree of confinement is shown in Equation (6). Figure 4: Plot of the degree of confinement vs. average scaled impulse for multiple urban street tests, adapted from [PERSON] et al. [47]. \[DC=\frac{\sum_{i}^{closedcells}(AD^{-1})_{i}}{\sum_{i}^{allcells}(AD^{-1})_{i}} \tag{6}\]
* \(A\) is the cut cell area. * \(D\) is the inverse distance of each cut cell from the charge. To incorporate a range of charge masses for the relationship between the degree of confinement and blast loading, a [PERSON] termed the urban blast load (UBL) was used[PERSON] The UBL is a function of the charge mass and the total walled area loaded from the blast, which falls inside \(Z_{\text{cutoff}}\). The UBL is defined in Equation (7), where \(I_{\text{total}}\) is defined in Equation (8). \(I_{\text{total}}\) is described as the sum of the max impulse values for any given cell at a structural boundary, divided by the total area of the structural boundary. The UBL displays an improved correlation (see Figure 5) between blast loading and the degree of confinement compared to that found in [47]. Although a relationship is not quantified, visually, it is evident that a nonlinear fit is appropriate. \[UBL=\frac{I_{\text{total}}A_{\text{wall}}}{W_{\text{TNT}}} \tag{7}\]  
* \(A_{\text{wall}}\) is the total wall area loaded by the blast (within \(Z_{\text{cutoff}}\)). * \(W_{\text{TNT}}\) is the TNT equivalent charge mass. * \(I_{\text{total}}\) is the average maximum specific impulse across all cells at a structural boundary (Equation (8)).