Mathematical Problems in Engineering

Volume 2019, Article ID 2751815, 15 pages

https://doi.org/10.1155/2019/2751815

## Experimental and Numerical Analysis and Prediction of Ground Vibrations Due to Heavy Haul Railway Viaduct

^{1}Hubei Key Laboratory of Roadway Bridge & Structure, Wuhan University of Technology, China^{2}School of Civil Engineering and Architecture, Wuhan University of Technology, China

Correspondence should be addressed to Yi Luo; nc.ude.tuhw@ouly

Received 12 September 2018; Revised 29 November 2018; Accepted 9 January 2019; Published 13 February 2019

Academic Editor: Gisella Tomasini

Copyright © 2019 Jingjing Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The ground vibration wave induced by the viaduct section of the heavy freight wagons is transformed into the ground vibration problem under the condition of point source excitation after it is transmitted to soil through pier. When the speed and axle load of wagon become larger and larger, the impact on the surrounding buildings will also increase. In this paper, the ground vibration around Shenshan Village in section of Shuo-Huang railway line is monitored and numerical analyzed; the 3D numerical model of the Bridge-Pier-Field-House system is established. The relationship between peak vibration velocity (PPV) and the distance to the pier caused by heavy freight wagons at different speeds and different type of wagons is analyzed. The power function relationship between the two when measuring line perpendicular to the centerline of railway is verified. Based on the modified Sodev’s equation, the relationship between PPV of ground points and wagon speed, axle load, and soil properties is proposed, and the value of every parameter in the formula is discussed in detail. The concept of energy index is put forward for the first time in the formula, and the relationship between energy index and wagon speed and wagon weight is analyzed by regression analysis. The accuracy of the calculation model and prediction formula is verified by comparing field test results; an analytical method is proposed to predict the ground vibration induced by viaduct.

#### 1. Introduction

Railway is one of the most efficient transport systems in recent years; railway transportation develops very fast in China and abroad. With the development of transportation, the vibration caused by railways has an increasing impact on the environment. The environmental vibration caused by traffic load has the characteristics of repeatability and long-term. When it exceeds a certain level, it will affect the daily life and work of people in nearby buildings. When the vibration reaches a larger level, it may also cause damage to the structure of the building, thus affecting the normal function of the building [1–3].

On the other hand, due to the influence of terrain, more and more sections are designed as railway viaducts to ensure the smoothness of the line [4]. For example, the total length of the Seoul-Busan high-speed railway in Korea is 412km, the highest running speed is 300km/h, and the viaduct proportion is 27.1%. The Madrid-Seville high-speed railway in Spain has 31 viaducts with a total length of 15 km; the bridge ratio is 3.2%. The Beijing-Shanghai railway line has a total length of 1318 km, with 244 main bridges and a total length of 1060km. The bridge length accounts for 80.7% of the total line. However, the study of railway viaduct mostly focuses on the deformation and stability of bridges, which is quite complex due to the vehicle-coupled-guideway vibration [5–7]. Due to the different ways of excitation, the ground vibration caused by viaducts should also be concerned [8, 9].

On the other hand, with heavy load, long marshalling, and fast running speed, the dynamic effect of heavy freight wagons is stronger than that of ordinary trains, and the dynamic influence of wagons on the railway structure and its surrounding structures is more serious [10, 11]. The environmental vibration problem caused by the railway viaduct system involves many complicated dynamic systems such as wagons, bridges, piers, and sites and buildings, involving a large number of nonlinear problems [1, 12, 13]. Usually the system is decomposed into several subsystems to study separately. The current theoretical research has not yet reached a high degree of precision or obtained a simplified analytical solution. Field measurements are the most common means of studying such problems [14–16].

However, railway line is usually long and the complexity of the problem is high, given the dynamic interaction between distinct domains, namely, the train, the viaduct, the ground, and the building. It is not realistic to detect each area nearby the line. As response to these needs, it is necessary to put forward the general law of ground vibration attenuation and to provide a method for evaluating the magnitude of train vibration in a viaduct area to be built.

Vibration assessment is a key element of the environmental impact assessment process for railway projects. For the propagation and attenuation law of ground vibration, many scholars have put forward different prediction formulas. They can be broadly classified into two categories: one is the amplitude representation and the other is the vibration level representation [17–19]. Among them, Bornitz [20] put forward the attenuation formula of ground vibration amplitude when disturbance force acts on the surface of half space of soil, considering the geometric attenuation of the vibration propagation and the medium absorption attenuation and the influence of propagation distance of the vibration. G. Volberg [21] based on tests at three different sites regressed the relationship between the vibration level and train speed. Chen Jianguo et al. [22] established an environmental vibration prediction formula based on the results of finite element vibration analysis. The formula reflects the logarithmic relationship between vibration acceleration level and distance and also considers the vibration level correction values of train speed, bridge span, and unit length and quality of the bridge by the additional function method. However, most of the above formulas can only reflect the attenuation relationship of vibration with distance or wagon speed and cannot clearly reflect the influence of geological conditions. More accurate prediction formulas should be put forward.

A large number of studies have shown that the vibration velocity and vibration frequency of the particle are closely related to the damage of the building [23–25]. It can directly reflect the vibration energy and play an important role in the evaluation of the vibration of building. Accurate prediction of the peak vibration velocity (PPV) of ground points under different site conditions is of great significance. In the field of traffic environment vibration, especially for the ground vibration caused by the heavy freight wagons, there are few studies using PPV as the evaluation index. Regarding the organization of the paper, firstly, a finite element model of track, box girder, pier, field, and building is established on the basis of field test. Numerical result of vibration response of ground and structure is studied by analyzing vibration velocity and spectra induced by trains of different weight and speed on a railway viaduct. Based on modified Sodev’s formula, the relationship between PPV and wagon speed, wagon weight, distance, and site is established. Finally, regression analysis is used to discuss the procedures of determining each parameter in the forecast formula.

#### 2. Field Test of Railway Viaduct in Shenshan Village

Shuo-Huang railway is an important part of the second largest channel of the “West-East Coal Transportation” in China. The total length of the railway is nearly 600 km, the transportation capacity exceeds 255 million tons, and the freight volume increases by tens of millions of tons every year. It is located in the connecting area between mountainous area and plain. The relative height difference is 200m-700m. The length of the bridge section accounts for more than 10% of the total length. In the northeast of Yuanping City, Shanxi Province, Shuo-Huang Heavy-Haul Line crosses Shenshan Village in the form of viaducts. The area is densely populated and there are a large number of residential buildings within 30 meters of the railway line, as shown in Figure 1.