## 3 Field Measurements and Model Verification
### Outline of Measurements  
The detection point was at a surface location 36 m from the centreline of the metro line, whose tunnel was a double-track double-hole shield straight tunnel with a buried depth of 15 m, diameter of 6 m and segment thickness of 0.3 m. The ground at the layout of the measuring point is flat and free from potholes, and motor vehicles and pedestrians are rare here, so had little interference with the testing. Two accelerometers were installed at the detection point in both the vertical and horizontal directions. Lance AS0130 series vibration acceleration sensors with a test range of 0.12 g and frequency range of 0.5-1000 Hz, and a 3160-A-042 multi-channel data acquisition instrument from Danish B&K company, were used to record the ground vibration accelerations induced by subway trains running on ordinary tracks at 54 km/h. The sampling frequency of the field test was set as 1024 Hz, which could obtain the ground acceleration below 512 Hz in the frequency domain according to the Nyquist rule. Due to the focus of this paper being on train-induced environmental vibration issues, focusing on the frequency range of 1-100 Hz and considering the efficiency of subsequent FE calculations, the results shown in this paper are only below 100 Hz. The tested data was processed by Coinv Dasp V11 software. Because of the possibility of signal leakage caused by time-domain signal truncation, the Hanning window, which is suitable for processing non-periodic continuous signals, was  
Figure 4: 3D track bed–tunnel–stratum FE analysis model. Figure 5: Location of measurement points and metro line direction map. used when we transformed the tested time-history signal into the frequency domain, which could be directly selected in the software to eliminate high-frequency interference and energy leakage. The Hanning window function \(Hanning(n)\) is shown below. \[Hanning(n)=\left\{ \begin{matrix}0.5-0.5\cos(\frac{2\pi n}{N-1}),0\leq n\leq N-1\\ 0,\text{else}\end{matrix} \right. \tag{19}\]  
where \(n=1,2,\ldots,N-1\) is the serial number of the window function; \(N\) is the total length of the window  
The testing equipment and on-site layout are shown in Figure 6. The tested metro train, similar to the model, consisted of six carriages, and the parameters of the metro train and ordinary track are listed in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  
Figure 6: Diagram of test equipment and on-site layout. The established prediction model was used to numerically calculate the surface vibration response under the test conditions. The steel spring stiffness under the slab in the train-FST model was set to the maximum value (10\({}^{6}\) MN/m) to determine the fastener reaction force of all fasteners within the range of the FE model. The action of the moving train results in a certain time difference in the support reaction of each fastener as the train passes through the sequence of fasteners. After calculating the support reaction force of each corresponding fastener within the range of the FE model via the established train-FST model, the reaction forces were then applied in the actual spatial order in the form of point loads to certain positions of the corresponding fasteners on the track bed in the FE model. A subsequent analysis and calculation could be carried out. A typical fastener reaction force calculated using the vehicle rail model is shown in Figure 7. Subsequently, the calculated reaction force of the entire set of fasteners was applied as the excitation load in the actual spatial sequence to the track bed-tunnel-soil FE model, and the vibration acceleration of the ground detection points was computed. The Rayleigh damping assumption was adopted for the soil, and the damping ratio was set to \(\xi\) = 0.03. Because the focus of this study was on frequencies ranging from 1 to 100 Hz, the Rayleigh damping constants could be calculated using \(\alpha\) = 0.373 and \(\beta\) = 9.454 \(\times\) 10\({}^{-5}\).