## 5 A Model Predicting the Impact of Vibration from Trains on Over-Track Buildings  
On the basis of the simulation results above, a model predicting the impact of train vibration on over-track buildings in the throat area of a metro depot could be developed (see Equation (9)). \[VL_{\text{Zmax,OB}}=VL_{\text{Zmax,FL}}+C_{\text{P}}+C_{\text{D}}+C_{\text{F}}+C_ {\text{M}}+C_{\text{S}} \tag{9}\]  
where \(VL_{\text{Zmax,OB}}\) is the maximal value among \(VL_{\text{Zmax}}\)s at the centre on all floors of an over-track building, \(VL_{\text{Zmax,FL}}\) is the \(VL_{\text{Zmax}}\) on the ground right under the over-track building, \(C_{\text{P}}\) is the correction item of the over-track platform, \(C_{\text{D}}\) is the correction item of the horizontal distance between the center of the over-track building and the central line of track, \(C_{\text{F}}\) is the correction item of the total amount of storeys of the over-track building, \(C_{\text{M}}\) is the correction item of the dimensions of the floor of the over-track building, and \(C_{\text{S}}\) is the correction item of the structure type of the over-track building. \(VL_{\text{Zmax,FL}}\) can be calculated according to Equations (10) and (11), which were given in HJ 453-2018, the standard issued by the Ministry of Ecology and Environment of the People's Republic of China and titled Technical Guidelines for Environmental Impact Assessment-Urban Rail Transit [25]. \[VL_{\text{Zmax,FL}}=VL_{\text{Z0 max}}+C_{\text{VB}} \tag{10}\]  
\[C_{\text{VB}}=C_{\text{V}}+C_{\text{W}}+C_{\text{R}}+C_{\text{T}}+C_{\text{D} }+C_{\text{B}}+C_{\text{TD}} \tag{11}\]  
where \(VL_{\text{Z0 max}}\) is the vibration source strength of the reference train, \(C_{\text{VB}}\) is the vibration correction, \(C_{\text{V}}\) is the correction item of the speed of the train, \(C_{\text{W}}\) is the correction item of axle weight and unsprung mass, \(C_{\text{R}}\) is the correction item of wheel-rail condition, \(C_{\text{T}}\) is the correction item of tunnel type, \(C_{\text{D}}\) is the correction item of distance attenuation, \(C_{\text{B}}\) is the correction item of building type, and \(C_{\text{TD}}\) is the correction item of traffic density [25]. The Correction Item of the \(VL_{\text{Zmax}}\) Caused by the Over-Track Platform, \(C_{\text{P}}\)  
To predict the influence of train vibration on over-track buildings in the throat area of a metro depot, \(C_{\text{P}}\) was introduced. According to fitting results given in Figures 17-19, \(C_{\text{P}}\) can be calculated by Equation (12). \[ \begin{array}{l}C_{\text{P}}=a+\text{k}_{\text{T}}(T-0.25)+\text{k}_{\text{ S}}(S-1.0)+\text{k}_{H}(H-7.5)\\ =-11.5-22.1(T-0.25)-2.1(S-1.0)-0.86(H-7.5)\end{array}  \tag{12}\]  
where the constant term, a, is the difference between the \(VL_{\text{Zmax}}\) of the first floor of a 12-storey frame building and the \(VL_{\text{Zmax,FL}}\) of the ground right under it. \(\text{k}_{H}\), \(\text{k}_{T}\), and \(\text{k}_{\text{S}}\) are the variations of \(VL_{\text{Zmax}}\) at the first floor of the over-track building when the height of the transfer storey, the thickness of the over-track platform, and the side length of the cross-section of the over-track platform column increase by one unit, respectively. According to Equations (10) and (11), the \(VL_{\text{Zmax,FL}}\) can be calculated and is 78.8 dB. The \(VL_{\text{Zmax}}\) of the first floor of a 12-storey frame building given in Figure 9 is 67.3 dB. Consequently, the calculated constant term, a, is -11.5 dB. By introducing \(C_{\text{P}}\), the \(VL_{\text{Zmax}}\) of the first floor of an over-track building can be predicted. The Correction Item of Horizontal Distance between the Centre of the Over-Track Building and the Central Line of Track, \(C_{\text{D}}\)  
To predict the influence of train vibration on over-track buildings at different \(D\), \(C_{\text{D}}\) was introduced.