## 3 Results and Discussion  
In this study, in order to cover two different phases of prediction and simulation, GEP and MC techniques were proposed, respectively. A GEP model with R\({}^{2}\) values of 0.7283 and 0.6823 and RMSE values of 4.2814 and 4.0344 for training and testing, respectively, are able to provide a suitable accuracy level for PPV prediction.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Input** & **Minimum** & **Maximum** & **Distribution Function \({}^{*}\)** \\ \hline ST & 1.40 & 4 & Uniform \\ BS & 0.42 & 0.91 & MinExtreme \\ MC & 69.79 & 309.09 & Uniform \\ PF & 0.24 & 0.98 & Beta \\ D & 65 & 640 & Weibull \\ \hline \hline \end{tabular} \({}^{*}\) The distribution functions are considered by the Risk Solver Platform using the ‘best-fit’ function based on the given data.  
\end{table}
Table 4: Distribution function of the inputs used in MC simulation.  
Figure 6: Steps of application of Monte Carlo simulation in PPV risk analysis.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **BS** & **ST** & **PF** & **MC** & **D** \\ \hline BS & 1 & & & & \\ ST & \(-\)0.02196 & 1 & & & \\ PF & 0.01842 & 0.211813 & 1 & & \\ MC & \(-\)0.18773 & 0.628307 & 0.333094 & 1 & & \\ D & 0.267255 & 0.105316 & \(-\)0.08437 & 0.042226 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Correlation coefficient of model inputs.  
Then, the proposed GEP equation was used as an input for the MC technique for simulation purposes. The results of the MC simulation indicated that the minimum and maximum values of PPV are 1.13 mm/s and 34.58 mm/s, respectively, with a mean value of about 18.28 mm/s. According to the results, the distribution function of 10,000 outputs is 'logistic', which is illustrated in Figure 7. Based on the output values, with 90% confidence, the amount of PPV is less than 25.25 mm/s, and 99% of the results are less than 30.86 mm/s. In this study, the simulation of PPV was conducted after measurement on site and prediction using GEP. Because the means of PPV simulation and prediction are very close (18.28 mm/s and 16.23 mm/s, respectively), it can be stated that the accuracy of the MC model in the PPV simulation is acceptable. Figure 8 demonstrates the differences among the measured, predicted and simulated results of PPV. Furthermore, in order to have a better illustration regarding the contribution of the input values in the obtained output for each trial in MC simulation, Figure 9 plots the random amounts of all inputs, which have been taken by the MC simulator. This figure also shows their corresponding PPV results which were generated during MC simulation. It should be noted that Figure 9 was generated using the Risk Solver Platform, the MC simulator in our research, to show the involvement of each input in the PPV result. According to [PERSON] and [PERSON] (2007), as a main standard, PPV values of less than 50 mm/s can be considered as an acceptable value. In this paper, we can state with 100% confidence that the PPV for the blasting operations is in the allowable range.  
Figure 8: Measured PPV values together with their correspond predicted and simulated values.  
Figure 7: Obtained frequency of PPV results using Monte Carlo simulation.