# Vibration Analysis and Empirical Law Definition for Different Equipment in a Civil Construction
## 3 Results and Discussion  
### Analysis of the Equipment  
The vibration level is characterized by the maximum velocity or peak particle velocity (PPV) in the vertical direction because it is less influenced by the alignment of the geophone than the longitudinal or transversal components. Table 2, Table 3, Table 4, gather the peak particle velocities at different distances, recorded in situ for the equipment working directly in shale rock mass and backfill material. \begin{table}
\begin{tabular}{c c} \hline \hline
**Source** & **Threshold Value (mm/s)** \\ \hline Studer and Suestrunk [45] & 1.8–3 \\ Forsblad [46] & 2 \\ Swiss Standard & 3 \\ Standard DIN 4150 & 2.5–10 \\ Schiappa de Azevedo and Patricio [37] & 1.75–10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values stablished by different sources/authors. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Distance (m)** & **Velocity (mm/s)** & **Distance (m)** & **Velocity (mm/s)** \\ \hline
2.5 & 1.36 & 4 & 1.36 \\
5 & 1.33 & 10 & 0.38 \\
6 & 0.66 & 10 & 0.25 \\
6.6 & 0.38 & 11 & 0.095 \\
6.6 & 0.51 & 11 & 0.183 \\
9.5 & 0.23 & 30 & 0.009 \\
10 & 0.215 & 30 & 0.019 \\
40 & 0.008 & & \\
40 & 0.009 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Velocities at different distances for the excavation equipment. It can be seen that the behavior of three types of equipment (excavator, ripper and breaker hammer) working on the shale bed rock is quite similar, achieving very low velocity values from 30 m and further, being much lower than the threshold values established by the legal requirements and international standards. The rock mass behavior to the vibration transmission is almost the same in the three types of equipment, varying only in the vibration intensity, especially in the case of the hydraulic hammer. On the other hand, a few differences have also been detected. The excavation using the bucket has a more uniform evolution regarding the distance of measurement, while the ripper operation has a higher value close to the source and, then, the velocity decreases faster. A plot of the actual data, taking into account the distance from the vibration source, is included in Figure 4, showing an almost linear trend with a negative slope. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Bulldozer**} & \multicolumn{2}{c}{**Vibrating Roller**} \\ \hline
**Distance (m)** & **Velocity (mm/s)** & **Distance (m)** & **Velocity (mm/s)** \\ \hline
1 & 5.1 & 1.5 & 3.33 \\
3 & 2.5 & 3 & 15.76 \\
3 & 1.14 & 3.5 & 4.99 \\
4.5 & 2.5 & 5 & 4.54 \\
5 & 1.77 & 5 & 6.12 \\
7 & 1.58 & 5 & 3.99 \\
7 & 0.51 & 6.5 & 3.85 \\
8.5 & 0.45 & 7 & 5.44 \\
9 & 1.33 & 7 & 5.33 \\
11 & 1.4 & 8.5 & 4.31 \\
11 & 1.36 & 9 & 6.6 \\
12.5 & 0.66 & 10.5 & 1.27 \\
30 & 0.044 & 30 & 0.27 \\
30 & 0.035 & 30 & 0.27 \\
30 & 0.039 & 30 & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Backfill operations with different equipment. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Vibrating Ripper**} & \multicolumn{2}{c}{**Hydraulic Hammer**} \\ \hline
**Distance (m)** & **Velocity (mm/s)** & **Distance (m)** & **Velocity (mm/s)** \\ \hline
2 & 4.31 & 2 & 3.33 \\
2 & 3.63 & 3.5 & 1.99 \\
10 & 1.85 & 3.5 & 2.72 \\
15 & 1.39 & 5 & 1.36 \\
18 & 1.16 & 8 & 0.88 \\
18 & 1.39 & 8.5 & 0.90 \\
27 & 1.38 & 9.5 & 0.51 \\
27 & 0.46 & 10 & 0.40 \\
35 & 0.92 It has to be pointed out that the vibrating ripper generates vibration levels of about one order of magnitude bigger than the other equipment (Figure 5). This vibrating ripper will be considered, from a ground vibration point of view, equivalent to the vibrating roller which is analyzed henceforward. In the case of compacted granular material, the velocity achieves a value lower than 0.1 mm/s at a distance around 25 m for the bulldozer and 50 m for the vibrating roller, with the usage of the last one having a much higher impact (Table 4).