## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Explosive**} & **Density (g/cm\({}^{3}\))** & \multicolumn{6}{c}{**EME Equivalent (\%)**} \\ \cline{3-6}  & **Equation (4)** & **Equation (5)** & **Equation (6)** & **Equation (7)** & **Equation (8)** \\ \hline Emulsion explosive (EME) & 1.175 & 100.00 & 100.00 & 100.00 & 100.00 & 100.00 \\ EMM/EPS (50/50) & 0.627 & 95.17 & 98.46 & 96.98 & 26.87 & 61.39 \\ EMM/EPS (40/60) & 0.437 & 88.83 & 92.95 & 91.94 & 13.19 & 50.10 \\ EMM/EPS (30/70) & 0.302 & 82.20 & 87.24 & 85.89 & 7.33 & 43.16 \\ EMM/EPS (20/80) & 0.218 & 71.04 & 76.61 & 75.83 & 4.44 & 38.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculated EME equivalents for tested explosives. where n is the number of points, x\({}_{i}\) and y\({}_{i}\) are the ith variable in the set i = 1 to n, and x and y are the means of each of the variables in the given set [40]. Based on the experimental data given in Table 4, the fitting constants a and b (Equation (10)) for EME are derived using the Instantel Blastware application. The application works by importing data directly from records and by manually entering the values of the actual charge weight per delay (W) and the distance of the monitoring points from the explosion (R) for each MO into the application. The values of PPV are recorded by the instruments at the monitoring points, based on which the application calculates the fitting constants (best-fit line) and additionally calculates and presents a 95% confidence line with equation (upper limit). The output results for monitoring points in Line 1 for EME are shown in Figure 2.  
Since the Instantel Blastware application does not give the fitting constants a and b for the best-fit line, the same is calculated by CurveExpert--curve fitting and data analysis code. The constants H and \(\beta\) in Equation (9), calculated from constants a (a = log(H)) and b (b = \(\beta\)), and final equations for the best-fit line and 95% confidence lines are:  
Best-fit line:  
\[PPV_{EME}=395.64\cdot SD^{-1.161}\quad(\sigma\ =\ 7.306\ \mathrm{mm}\ /s,\ r\ =\ 0. 8357) \tag{15}\]  
95% confidence line, upper limit:  
\[PPV_{EME}=852.7\cdot SD^{-1.161} \tag{16}\]  
95% confidence line, lower limit:  
\[PPV_{EME}=183.7\cdot SD^{-1.161} \tag{17}\]  
Once the fitting constants for the reference explosive EME are determined, the equivalence principle can be applied to predict the blast effect, i.e., PPV value at a specified distance and charge weight, for any explosive, provided its EMEe is known. For illustration, let us assume we want to predict the PPV, which will be generated by the detonation of 15.5 g of an explosive X at a distance of 6 m. The EMEe of explosive X equals 38.5%. The equivalent weight of EME (\(W_{e}\)), which gives the same effect as 15.5 g of explosive X, can be obtained by Equation (3) (\(W_{e}=W\cdot EME_{e}/100=5.97\) g). The scaled distance for EME equals \(SD(W_{e},R)=R/\sqrt{W_{e}}=6/\sqrt{5.97/1000}=77.7\ \mathrm{m/kg^{0.5}}\). By substituting the value of \(SD\) (\(W_{e}\), \(R\)) in Equation (15), we obtain PPV = 2.53 mm/s. Therefore, 15.5 g  
Figure 2: The best-fit line and corresponding 95% confidence line for EME. of explosive X will produce PPV = 2.53 mm/s at a distance of 6 m, the same as 5.97 g of EME at the same distance. Similarly, we can predict a mass of mixture X that will give the same value of PPV, at 6 m distance, as 72 g of reference explosive EME. In this case \(W_{e}=72\) g, \(SD(W_{e,}R)=22.3\) m/kg\({}^{0.5}\), and the calculated PPV for that SD (Equation (15)) will be 10.7 mm/s. The mass of mixture X, which will produce PPV = 10.7 mm/s at R = 6 m, equals \(W=W_{e}/(EME_{e}/100)=187\) g.  
To validate the above-described equivalency approach to predict blast-induced seismic effects, we used the experimentally measured PPV vs. charge weight and distance data from [PERSON] et al. [30] for four mixtures based on an emulsion matrix (EMM) and expanded polystyrene (EPS).