1. Introduction
By 2020, China’s railway mileage in operation has reached 146,300 km, including 38,000 km of high-speed railways [
1]. In this sense, developing over-track buildings in the region of the urban railway can utilize land resources economically and intensively, which can alleviate the contradiction of urban land resource scarcity. However, railway vibration can be transmitted to over-track buildings through tracks and soil layers and produce indoor vibration pollution. Therefore, vibration impact from the railway is an environmental constraint in the development of over-track buildings [
2,
3,
4]. Many studies on railway vibration source strength and its environmental impact have been conducted. Train speed, track type, etc. are the main factors that affect railway vibration source strength [
5]. The degradation of railway sleepers due to dynamic loading action will also influence railway vibration source strength [
6]. In the field of railway vibration impact on the surrounding environment, many pieces of research have focused on predicting the vibration impact of railways on neighboring and over-track buildings.
It is worth mentioning that the existing models for predicting the railway vibration effects on neighboring buildings can be divided into two categories. One category is only suitable for predicting the influence of vibration on the first floor of neighboring buildings, the other category is suitable for predicting the influence of vibration on different floors.
China’s railway industry presented an empirical model (See Equations (1) and (2)) [
7] for the prediction of railway vibration based on vibration data from high-speed railway acquired by field test in 2010. The model applies only to the prediction of environmental vibration impact from railways on the first floor of neighboring buildings.
where
is the environmental vibration caused by railways;
is the vibration source strength;
Ci is the vibration correction term of train
i;
n is the number of pass-by trains;
,
,
,
,
,
,
,
are the correction terms of speed, axle weight, line type, track type, bridge height, geology, distance, and building type, respectively. To predict the influence of railway vibration on the first floor of adjacent buildings, Silva et al. [
8] proposed a multiple linear regression model whose parameters include train speed, track type, geological condition, building type, and the distance between building and track. Similarly, Colaco et al. [
9] studied the entire propagation path from vibration source (vehicle and track) to the receiver (building) and established a 2.5D finite element prediction model concerning the track, soil, and buildings. The model is simple in calculation but it can only predict the vibration response at the first floor of neighboring buildings.
In order to predict the vibration effect caused by trains on different floors of buildings near the railway, Madshus et al. [
10] proposed a semi-empirical prediction model predicting vibration propagation. This model includes many parameters, train type, train speed, line quality, embankment design, and the distance from track to a building, as well as foundation, building structure, and the story number of the building. The Federal Railroad Administration of the U.S. Department of Transportation [
5] published an empirical model predicting the influence of railway vibration on different floors of buildings near the railway. In this model, many correction terms relating to train speed, type of track structure, propagation distance, geologic conditions, building foundation, and the number of the story were considered, but its prediction accuracy is low relatively [
11]. Using springs and viscous dampers to simulate a soil body, Auersch [
12] built a simplified soil-wall-floor model to predict environmental vibration at each floor of buildings near railway based on an empirical transfer function. In China, Wang et al. [
13] took the Wuhan-Guangzhou high-speed railway (265 km/h) as a research object and established a 3D finite element model of train-track-foundation-building to analyze the vibration response at the different floors of buildings based on measured data.
However, these models above predicting the influence of railway vibration on buildings near railway are not suitable for over-track buildings. In view of this point, Sanayei and other researchers [
14,
15] presented an impedance-based model to predict environmental vibration caused by trains and verified the reasonability of the model by analyzing the response of over-track buildings to railway vibration. Zheng et al. [
16] established a finite element model of a multifunctional railway hub and analyzed the vibration impact of the Shanghai-Hangzhou high-speed railway passing the hub at the speed of 130 km/h on over-track buildings.
The vibration response at each floor of an over-track building increases with the rise of trains speed [
17,
18]. Accordingly, to reduce the investment of vibration pollution prevention in the development of over-track buildings in the region of urban railway, it is better that over-track buildings are constructed above railways with a low pass-by speed of trains. In this study, on the basis of the planning project of over-track buildings development in the region of high-speed railways with a pass-by speed of 105 km/h in Hangzhou, a finite element model was established. The reasonability of the model was verified by measurement results. Furthermore, this study quantitatively explored the influence of the thickness of the concrete floor of the over-track platform (as a transformation layer), the height of the over-track platform away from the ground, the structural type, and the number of stories of buildings on an over-track platform on indoor environmental vibration. Finally, a model predicting the vibration impact from railways on each floor of over-track buildings was proposed by improving an existing model released by the railway industry of China. Compared with the existing model only being suitable for predicting environmental vibration on the first floor of buildings, the improved model can predict the vertical maximum Z-weighted vibration acceleration level at different floors of over-track buildings. Research results can provide a theoretical and technical basis for the prediction and prevention of environmental vibration effects from the railway on over-track buildings.
3. An Finite Element Model and Its Verification of Reasonability
A finite element model (see
Figure 3) being composed of track and soil was established on the basis of geological condition, track lines distribution, and parameters of trains in the urban area where a project of over-track buildings is planned. The relevant parameters in this model were set as follows. The distance between the center lines of railways is 5 m, the distance between two rails of a railway is 1.4 m, the sleeper spacing is 0.6 m and the width at the bottom of the track-bed is 4 m. According to the geological condition of the land, the soil was simplified into three layers including an artificial fill layer with a thickness of 5 m, a cohesive soil layer with a thickness of 25 m, and a mucky soil layer with a thickness of 15 m. In addition, as shown in
Figure 3, several viscoelastic solid units with a thickness of 1 m were set as an artificial boundary at the bottom of three layers of soil and around the soil in the model. The material parameters of rail, sleeper, track-bed, and three layers of soil are shown in
Table 1 [
19,
20,
21].
The vertical vibration line load caused by the high-speed train of 105 km/h was acted on one railway track. The step of line load in the time domain is 0.002 s. Verification point 1 and point 2 were set on the sleepers of this railway track and its adjacent railway track, respectively (see
Figure 4). The maximum vertical Z-weighted vibration acceleration level (
) at each verification point by simulation and measurement is shown in
Table 2. It can be seen from
Table 2 that the difference between the simulated
and the measured
at verification point 1 is 4.0 dB and the relative error is 3.54%. The difference at verification point 2 is 4.0 dB and the relative error is 4.50%. The relative error between the simulated
and the measured
at each verification point is less than 5%, which indicates that this simulation model is accurate relatively and the parameter setting in the model is reasonable.
6. Conclusions
To study the influence of environmental vibration from a high-speed railway on over-track buildings, a finite element model including track, soil, and buildings was set up. Based on the vertical vibration accelerations sampled on the rail, the equivalent line load acting on rails vertically is obtained by a simplified model. On the basis of the verification of the simulation model, the vertical vibration induced by high-speed railway in over-track buildings was studied quantitatively through a computer simulation. The main conclusions are as follows.
(1) The s at the center of different floors in frame buildings and shear wall buildings both increase with the increase of story number. The s at the center of different floors in multi-story, sub-high-rise, and high-rise frame buildings are 0.1~4.4 dB, 0~3.8 dB, and 0.1~5.1 dB higher than that in three types of shear wall buildings, respectively.
(2) Increasing the thickness of the over-track platform can reduce the indoor environmental vibration from railways effectively. When the thickness of the over-track platform increases 0.5 m, the at the center of different floor of multi-storey, sub high-rise, and high-rise frame buildings will decrease 0.4~3.0 dB, 1.3~3.3 dB, and 0.1~3.4 dB, respectively.
(3) The s at the center of different floors will increase 0.1~0.5 dB, 0.1~0.9 dB, and 0.3~0.9 dB in multi-story, sub-high-rise, and high-rise frame buildings, respectively, when the height of over-track platform away from ground increases 4 m.
(4) By introducing correction terms relating to the thickness of the over-track platform and its height away from the ground, the story of the over-track building and the structure of the over-track building, the existing model of railway vibration prediction released by the Ministry of Railways of the People’s Republic of China was improved. The improved model can predict the vertical maximum Z-weighted vibration acceleration level at different floors of over-track buildings.
Based on the model improved by this study, researchers can determine the amount of indoor environment vibration exceeding relative standards in over-track buildings. The corresponding prevention measures of environmental vibration effects from the railway on over-track buildings can be selected, which can provide a guideline for the design of over-track buildings.