## 4 Field Validation Tests and Global Vibration Intensity Prediction  
### Field Validation Tests  
Field validation tests were conducted on a construction site with ongoing vibratory sheet pile driving works. Figure 12(a) displays the photo of the selected construction site in Hong Kong. The ground investigation report indicated that the equivalent shear wave velocity was around 100 m/s. Figure 12(b) shows the steel sheet pile with a length of 6 m, and the pile head was driven by a commercial excavator-mounted vibratory hammer that operated at a frequency \(f_{0}\) = 20 Hz with an eccentric moment \(m_{e}\) = 7.5 kg\(\cdot\)m. Two sets of vibration data acquisition systems were used during the measurement. Figure 12(c) shows the first set of vibration data acquisition systems (model #: NI USB-6343 BNC), which comprised six uniaxial accelerometers (model #: KD 1000) to simultaneously collect vertical vibration signals at a sampling frequency of 1 kHz. The installation of one accelerometer on the ground surface is shown in Figure 12(d): a steel soil nail was first knocked into the soil at the selected monitoring point, and the accelerometer was then attached to the block surface of the soil nail by using strong magnets. Figure 12(e) shows the second set of vibration data acquisition systems, which is a portable three-channel C-series dynamic signal acquisition module (model #: NI 9230). By using the same installation method, triaxial accelerometers (model #: 356 B18), as shown in Figure 12(f), were used to measure vibration signals in three orthogonal directions. Figure 14 shows the layout of the ten selected monitoring points (six points with uniaxial accelerometers and four points with triaxial accelerometers) deployed on the ground surface. By using two sets of monitoring systems, the complete vibratory driving process (from the ground surface to 6 m depth) for one sheet pile was measured. The following particle vibration trajectories, vibration histories, and PPV values are presented based on the velocity signals, which were computed by using filters and performing one-time integration of the measured acceleration time histories. Using velocity can reduce the amplification of high frequencies compared with using acceleration and avoid the accumulated error of double integration when using displacement [32]. To investigate the wave type of measured vibration signals, particle vibration trajectories at a plan distance of \(d\) = 15 m measured by one triaxial accelerometer are plotted in Figure 15 by combining the vertical (i.e., V) and two horizontal (i.e., H1 (or Y) and H2 (or X)) time histories of motions. The particle motion occurs mainly in the radial vertical plane (H1-V) with an elliptical shape and the vertical magnitude of motion is greater than the horizontal one. These observations reflect the characteristics of R waves propagating near the ground surface. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Investigated Parameters**} & \multicolumn{3}{c}{**Mean**} & \multicolumn{3}{c}{**Max.**} \\ \cline{2-6}  & & **X (\%)** & **Y (\%)** & **X (\%)** & **Y (\%)** \\ \hline Shear wave velocity & \(v_{\text{s}}\) = 60 m/s & 2.52 & 0.08 & 4.17 & 0.25 \\ (when \(f_{0}\) = 20 Hz, & \(v_{\text{s}}\) = 120 m/s & 2.69 & 0.08 & 4.00 & 0.19 \\ \(\mu\) = 0.25) & \(v_{\text{s}}\) = 250 m/s & 3.56 & 0.07 & 4.78 & 0.25 \\ \hline Vibratory driving frequency & \(f_{0}\) = 20 Hz & 2.69 & 0.08 & 4.00 & 0.19 \\ (when \(v_{\text{s}}\) = 120 m/s, & \(f_{0}\) = 40 Hz & 2.71 & 0.06 & 3.68 & 0.17 \\ \(\mu\) = 0.25) & \(f_{0}\) = 60 Hz & 3.73 & 0.07 & 5.30 & 0.21 \\ \hline Pile–soil friction coefficient & \(\mu\) = 0.1 & 3.35 & 0.09 & 5.07 & 0.17 \\ (when \(v_{\text{s}}\) = 120 m/s, & \(\mu\) = 0.25 & 2.69 & 0.08 & 4.00 & 0.19 \\ \(f_{0}\) = 20 Hz) & \(\mu\) = 0.4 & 1.75 & 0.07 & 3.08 & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean and maximum relative errors of the estimated coordinates from sensitivity studies. Figure 14: The layout of monitoring points.