# Ground-Borne Vibration Model in the near Field of Tunnel Blasting
## 4 Vibration near Blasting Area
### Comparison of Prediction Results between Sadovsky Formula and New Approach  
Under the same conditions, the near-field vibration velocity of blasting was predicted by using the fitted Sadovsky formula and the new approach and compared with the actual monitoring results. For different directions of the tunnel face and different types of blast holes, when the Sadovsky formula is used to predict blasting vibration, the data should be distinguished to improve the prediction accuracy, as shown in Equations (16)-(27) above. However, in order to use the same data set for comparison, the Sadovsky formula and the new approach were used to predict the vibration law in three different directions of \(X\), \(Y\), and \(Z\), respectively. In addition, the data were not processed. Different densities were brought in when the tunnel face direction was different, and different numbers of free surfaces were brought in when the types of blast holes were different, so as to obtain the vibration law in three directions. The analysis of variance (ANOVA) and Akaike information criterion (AIC) results for the Sadovsky formula and new approach are presented in Table 3.  
Comparing models in the same direction, the sum of squares, mean squares, F values, and AIC values of models 1, 2, and 3 are relatively smaller. It is clear that models 1, 2, and 3 are the best-fit linear regression models for the available field data in three directions. In order to intuitively understand the prediction effect of the new approach, the synthetic PVS \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **df** & **Sum of Squares (SS)** & **Mean Squares (MS)** & **F** & **Significance F** & **AIC** \\ \hline Model 1: Equation (28) & & & & & & \(-\)863.187 \\ \hline Regression & 2 & 78.309 & 29.154 & 263.505 & 0 & \\ Residuals & 375 & 19.768 & 0.056 & & & \\ Corrected total & 377 & 118.077 & & & & \\ \hline Model 2: Equation (29) & & & & & & \\ \hline Regression & 2 & 105.052 & 42.526 & 464.299 & 0 & \\ Residuals & 467 & 23.955 & 0.044 & & & \\ Corrected total & 469 & 149.007 & & & & \\ \hline Model 3: Equation (30) & & & & & & \\ \hline Regression & 2 & 96.905 & 38.452 & 388.194 & 0 & \\ Residuals & 457 & 25.415 & 0.049 & & & \\ Corrected total & 459 & 142.319 & & & & \\ \hline Model 4: Sadovsky formula in X direction & & & & & \\ \hline Regression & 1 & 95.829 & 95.829 & 852.859 & 0 & \\ Residuals & 376 & 42.248 & 0.112 & & & \\ Corrected total & 377 & 138.077 & & & & \\ \hline Model 5: Sadovsky formula in Y direction & & & & & \\ \hline Regression & 1 & 120.651 & 120.651 & 1167.679 & 0 & \\ Residuals & 468 & 48.356 & 0.103 & & & \\ Corrected total & 469 & 169.007 & & & & \\ \hline Model 6: Sadovsky formula in Z direction & & & & & \\ \hline Regression & 1 & 115.612 & 115.612 & 1133.649 & 0 & \\ Residuals & 458 & 46.708 & 0.102 & & & \\ Corrected total & 459 & 162.319 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The ANOVA and AIC results for six models. (PVS = \(\sqrt{V_{X}{}^{2}+V_{Y}{}^{2}+V_{Z}{}^{2}}\)) in three directions was used to compare with the measured results. Figure 7 presents the predicted values versus observed values of PVS. As shown in the above comparison, when the vibration velocity value is small (<10 cm/s), the predicted results of the Sadovsky formula and the new method show good convergence. When the vibration velocity value gradually increases (>10 cm/s), the deviation of the Sadovsky formula prediction results increases rapidly, reaching a maximum of 6 times, while more than 90% of the prediction deviation of the new method remains within 1.3 times. Figure 8 shows the variation in the average absolute error of the two prediction methods at different monitoring distances. It can be seen that although the prediction errors of the two methods are similar at a long distance, the prediction effect of the new method is significantly improved compared with that of the Sadovsky formula in the near field of blasting.