## 3 A Simulation Model and Verification of Its Rationality
### A Simulation Model of Civil Buildings  
The selected vacant civil building in Hangzhou City, China, is rectangular (32.8 m \(\times\) 27.8 m \(\times\) 57.2 m), and the horizontal and vertical layouts of the building are shown in Figure 7, in which the cross-section dimensions of frame columns of the 1 st-2 nd floors, the 3 rd-6 th floors, the 7 th-9 th floors, and the 10 th-15 th floors are 0.75 m \(\times\) 0.75 m, 0.7 m \(\times\) 0.7 m, 0.65 m \(\times\) 0.65 m, and 0.6 m \(\times\) 0.6 m, respectively. The cross-section dimensions of the girders and beams are 0.35 m \(\times\) 0.7 m and 0.25 m \(\times\) 0.6 m, respectively. The thickness of the floor is 0.12 m.  
In the vibration measurement using the hammering method, a metallic sphere (0.15 m in diameter and 13.77 kg in weight), which can produce a large excitation force and excite various vibration modes of the structure, was chosen as the impact source. It was dropped freely from a height of 0.6 m above the first floor and hit the floor. As shown in Figure 7, the impact point (C1) was located at the central point of an area enclosed by a red dashed line. The vibration measurement points C2-C8 were set on the second, fourth, sixth, eighth, tenth, twelfth, and fourteenth floors directly above the impact point (see Figure 7). An acceleration sensor (PCB 356B07) with a sampling frequency of 24 kHz was used to collect the vibration acceleration data at each measurement point.  
A finite element model was established according to the actual structure and dimensions of the vacant civil building. All nodes at the bottom of building were completely fixed in the model. The beams, columns, and floors in the building were made of C40 concrete, while the infill walls were made of standard brick [20]. The parameters of each material are shown in Table 1. An impulsive vibration whose vertical vibration acceleration values were taken from the sampled data at C1 under the impact of the metal ball was loaded at C1 in the simulation model. The results of the vibration measurement at point C1 are shown in Figure 8. The grid size of building in the simulation model was set to 0.5 m. The step size of time integration in the simulation calculation was taken as 0.002 s.  
A comparison of the measured results and simulated results of \(VL_{\text{Zmax}}\) and 0-250 Hz vertical vibration acceleration level, _VAL_, at each measurement point of the vacant civil building is shown in Table 3. Table 3 indicates that the error between the simulated values and measured values of \(VL_{\text{Zmax}}\) at each measurement point was \(-\)1.5-1.2 dB, and the relative error was less than 2.0%. Similarly, the error between simulated values and  
Figure 7: Layouts of the civil building and measurement points: (**a**) horizontal layout; (**b**) vertical layout.  
measured values of _VAL_ at each measurement point was \(-0.9\)-\(1.6\) dB, and the relative error was less than \(2.0\%\).  
Overall, the simulated results of measured points on the over-track platform of a metro depot and on different floors in a civil building were close to the measured results, which could indicate that the simulation method and parameter settings were reasonable.  
The Influence of the Over-Track Platform and Over-Track Building Parameters on Indoor Vibration Caused by a Train