## 3 Results and Discussion
### Results of the First Tests and Attenuation Law for the Air Overpressure Due to Common Blasts
Due to the fact that the aim of the research is safety, a coefficient can be used to assure that any predicted value is higher than the actual one with a given confidence level, i.e., 90% (the predicted value is higher than the actual one in more than 90% of the cases). By using the coefficient of 1.35, the predicted air overpressure fulfils this requirement. The expression deduced in this way is known as the attenuation law:  
\[S_{b}=417.59\cdot Z^{-1.216} \tag{5}\]  
Equation (4) corresponds to the lower line of the graph, while Equation (5) corresponds to the upper one. With the values given by Formula (5), we have a predictive model that allows us to characterize the aerial wave generated by the detonation of Riodin-type gelatinous dynamite charges as a function of the distance to the detonation focus. It allows us to assess the overpressure generated by the detonation of a charge of this specific explosive and the possible effects on people or buildings that it will produce. Thus, protection and attenuation mechanisms are established and designed to greatly reduce the consequences of this detonation. However, the reality is that explosive substances can be of a different nature and composition, not just gelatinous dynamites. For example, a typical blasting work, which produces high air overpressure, is the demolition of metallic structures with shaped charges (Figure 5). It is due to the fact that the explosive is not confined in a blast hole, but it detonates in the open air. In this case, the explosive is pentolite (Riocut), different from dynamite (Riodin), and then the deduced Formula (5) cannot be used directly. So, in order to be able to characterize the wave generated by any explosive substance and to be able to compare them with each other to assess their harmful effects after a detonation in the open air, the equivalent TNT mass is used. To apply this calculation method, it is necessary to know the heat of explosion, both of the TNT and of the explosive to be compared. The heat of explosion for TNT is 4520 kJ/kg, and from Table 3, there is a heat of explosion for this Riodin dynamite of 4090 kJ/kg. So, 1 kg of Riodin is equivalent to \(1\times 4090/4520=0.905\) kg of TNT. With these explosion heat values, the TNT equivalent of each charge used in the 90 detonations is determined, as well as the reduced distance for each of them with this resulting TNT-equivalent charge (Table 7). The resulting values from Table 7 are shown in Figure 6 in which the measured overpressure is plotted against the TNT-equivalent scaled distance. Due to the proportionality between the Riodin and TNT explosion heats used, the expression deduced in this case by linear regression is similar to the previous one:  
\[S_{b}=322.13\cdot Z^{-1.216} \tag{6}\]  
where \(S_{b}\) is the overpressure generated by the wave in kPa, and \(Z\) is the reduced distance in m/kg\({}^{1/3}\). The correlation coefficient for this prediction model is also 96.06%. By using the coefficient of 1.35, the predicted air overpressure will be higher than the actual one in more than 90% of the cases, and the formula represents the attenuation law of the air wave in the case of TNT explosive:  
\[S_{b}=434.87\cdot Z^{-1.216} \tag{7}\]  
Equation (6) corresponds to the lower line of the graph, while Equation (7) corresponds to the upper one. Figure 2:0 Demolition of metallic structures with shaped charges (**(left)** metallic silo; **(right)** large mining stacker). Figure 2:1 Overpressure measured as a function of scaled distance using the equivalent mass of TNT (dots are actual values while lower and upper lines correspond to Equations (6) and (7)). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**N**} & \multirow{2}{*}{**Distance (ns)**} & \multirow{2}{*}{**Edge (ns)**} & \multirow{2}{*}{**Edge (ns)**} & \multirow{2}{*}{**Edge (ns)**} & \multirow{2}{*}{**N**} & \multirow{2}{*}{**Distance (ns)**} & \multirow{2}{*}{**Edge (ns)**} & \multirow{2