# A Review of Blast Loading in the Urban Environment
## 2 Current Knowledge  
### Basic Theory  
The detonation of an explosive mass causes a shock front to propagate outwards through a substance. A shock wave can be considered as a near-instantaneous change in pressure, density, and internal energy that travels through a medium faster than the medium's speed of sound--approximately 343 m/s in air at ambient conditions. The resultant pressure increase above atmospheric pressure from the shock wave is defined as the peak overpressure, denoted as \(p_{so,max}\) for incident shock waves and \(p_{r,max}\) for reflected shock waves. The parameter \(t_{a}\) corresponds to the time of arrival (the duration it takes a shock wave to travel a given stand-off distance), and \(t_{d}\) represents the positive phase duration (i.e., the duration over which above ambient pressures are acting). The impulse values, \(i_{so}\) and \(i_{r}\), are equal to the integral of their respective pressure curves with respect to time, \(t_{d}\). The negative phase has a similar set of respective parameters, as described by [PERSON] et al. [12], detailed in Figure 1 as an ideal far-field blast wave. Blast wave scaling is commonly used to compare geometrically similar explosive masses. Two geometrically similar shock waves will be produced upon the detonation of two geometrically similar explosive masses. The same scaled blast wave parameters will result from the two separate blasts, provided the scaled distances and control variables are identical [14]. The established scaling laws constitute cube-root scaling and were independently proposed by [PERSON] [15] and [PERSON] [16], and hence the term \"Hopkinson-Cranz\" scaling is often used. Figure 1: Pressure vs. time history curve that represents an ideal far-field blast wave, adapted from [PERSON] et al. [13]. Scaled distance, \(Z\), can be calculated via Equation (1). These scaling laws allow direct comparisons between explosive events at any reasonable scale, provided the differences in the explosive compounds are accounted for (e.g., shape effects [17; 18; 19; 20], secondary combustion [21], heat of detonation and/or reaction rates [22; 23; 24; 25], etc.). However, some have previously suggested a practical limit to the minimum reasonable scale for gathering experimental data [26]. [PERSON] et al. [27] analysed the effectiveness of Hopkinson-Cranz scaling within tunnel environment-based blast tests. The difference between the peak overpressures between full-scale and small-scale tests was 3%, reinforcing the validity of the Hopkinson-Cranz scaling method. \[Z=R/W^{1/3} \tag{1}\]  
* \(Z\) is the scaled distance (m/kg\({}^{1/3}\)). * \(R\) is the stand-off distance (m). * \(W\) is the explosive mass (kg, typically as an equivalent mass of TNT). Trinitrotoluene (TNT) equivalency is a widely agreed-upon concept within the field of blast engineering [28], where TNT equivalence is defined as the mass of TNT required to produce the same blast parameter(s) of a unit mass of the explosive in question, at the same stand-off distance. This enables the comparison and prediction of blast wave parameters caused by the detonation of fundamentally different explosive compounds. Additionally, TNT is the explosive compound utilised in commonly used empirical formulae and computational calculators such as ConWep [29], Blast-X [30], EMBlast [31], etc. Therefore, TNT equivalency is required to analyse blast parameters using these approaches. The TNT equivalence factor for a given explosive compound can be calculated as seen in Equation (2). \[TNT_{EQ}=W_{TNT}/W_{EC} \tag{2}\]  
* \(TNT_{EQ}\) is the TNT equivalence factor. * \(W_{TNT}\) is the mass of TNT that would create an \"equivalent energy\" blast compared to a mass of an explosive compound (kg). * \(W_{EC}\) is the mass of the explosive compound under investigation (kg). Generally, these approaches are accepted for use within simple geometric scenarios, such as unimpeded air blasts, to predict blast wave parameters.