Shock and Vibration

Volume 2017 (2017), Article ID 4813274, 11 pages

https://doi.org/10.1155/2017/4813274

## Numerical Modelling of Building Vibrations due to Railway Traffic: Analysis of the Mitigation Capacity of a Wave Barrier

University Institute for Multidisciplinary Mathematics, Polytechnic University of Valencia, 46022 Valencia, Spain

Correspondence should be addressed to Fran Ribes-Llario

Received 23 December 2016; Revised 15 March 2017; Accepted 2 April 2017; Published 18 April 2017

Academic Editor: Georges Kouroussis

Copyright © 2017 Fran Ribes-Llario 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

Transmission of train-induced vibrations to buildings located in the vicinity of the track is one of the main negative externalities of railway transport, since both human comfort and the adequate functioning of sensitive equipment may be compromised. In this paper, a 3D FEM model is presented and validated with data from a real track stretch near Barcelona, Spain. Furthermore, a case study is analyzed as an application of the model, in order to evaluate the propagation and transmission of vibrations induced by the passage of a suburban train to a nearby 3-storey building. As a main outcome, vertical vibrations in the foundation slab are found to be maximum in the corners, while horizontal vibrations keep constant along the edges. The propagation within the building structure is also studied, concluding that vibrations invariably increase in their propagation upwards the building. Moreover, the mitigation capacity of a wave barrier acting as a source isolation is assessed by comparing vibration levels registered in several points of the building structure with and without the barrier. In this regard, the wave barrier is found to effectively reduce vibration in both the soil and the structure.

#### 1. Introduction

The circulation of surface trains generates vibrations which are later propagated through the soil and transmitted to nearby buildings. This is becoming an issue of increasing relevance since it may cause nuisance to the people carrying out their activities there, as well as to originate the malfunctioning of sensitive equipment [1].

According to [2–4], vibrations propagate either as surface or as body waves. Among the first, compressional waves (or P-waves) induce particle motion parallel to the direction of propagation, while shear waves (or S-waves) generate perpendicular motion. Regarding surface waves, Rayleigh waves originate particle motion inside an elliptical vertical plane and decay more slowly with distance than body waves. The latter, together with the relevance of surface waves in the transmission process, as an order of magnitude, in the case of a vertical concentrated load, roughly 67% of the total excitation energy is transmitted through the soil by means of Rayleigh waves [4–6], making them a matter of major concern when assessing foundation isolation problems.

Moreover, high frequencies are particularly damped while propagating through the soil, which causes most part of the vibration spectrum arriving to a structure to be generally below 100 Hz. The soil thus shifts the track vibrations to a range more probable to resonate with structures, since natural frequencies of most buildings are located below 10 Hz [3, 4]. Nevertheless, vibrations transmitted into buildings are highly dependent on the coupling between soil and foundation. In this regard, if there is an impedance mismatch between them, a significant part of the energy may be reflected at the soil-structure interface [3, 7].

Vibration assessment is a key aspect when analyzing the environmental impact of railway projects, especially for the case of urban railways, due to its proximity to buildings and the large number of stakeholders potentially involved. It is thus essential to deeply understand how vibrations propagate from the track to the building through the soil as well as how to implement the adequate mitigation measures in order to reduce the railway negative affection to buildings.

Several authors have approached this problem in the last decades by means of field studies as well as analytical and numerical modelling of the processes involved. Among the first group, [1] performed ground-borne vibration measurements in several buildings in the Boston area (originated by the passing of urban and subway trains) in order to analyze the transmission process through the ground to the foundation slab and within the building. In addition, [8] registered ground vibration induced by the passing of high speed trains over different earthwork profiles in Belgium and studied vibrations in three directions. From the analysis of the recorded data, the authors concluded that horizontal vibration levels might be as significant as the vertical ones, especially as the distance from the track increases. This is of relevance to numerical studies, since they generally focus on the prediction of vertical vibrations. Finally, the field work in [9] should also be highly remarked, since it presents an extensive database of ground vibration measurements made out of over 1500 high speed train registers from 7 different European countries. Within the study, the datasets are statistically analyzed and major conclusions are drawn regarding the effect of train speed and soil material properties (low and high significance, resp.), as well as the influence of soil critical speed, which is found to be very strong on the quasi-static excitation mechanisms.

Concerning analytical approaches, [10] developed a simple impedance-based mathematical model for the study of the dynamic behaviour of the building and its interaction with the ground, which was experimentally validated using a scaled building model. Additionally, [11] presented a fully analytical approach for an accurate calculation of the soil critical velocity with a low demand of computing resources. The authors then applied the model to analyze the influence of several parameters (e.g., ballast height, slab track characteristics, and soil conditions) on critical velocity.

On the other hand, among numerical modelling of the ground-borne vibration problem in buildings, several recent approaches may be highlighted. In this regard, [12] proposed a methodology for the calculation of railway-induced ground vibration transmission into buildings; [13, 14] developed a 2D finite element model to analyze the efficacy of trenches and elastic foundations in building vibration reduction; Ju [15, 16] used a 3D finite element model with absorbing boundary conditions to study vibration transmission to buildings near high speed lines, as well as the mitigation effect of wave barriers and soil improvement; [17] employed a 2D FEM model to assess the wave screening efficiency of different trench types on buildings; [18] investigated the effectivity of open and infilled trenches in reducing building vibration by means of a 2D FE-BE model; and [19] validated a 3D FEM model with field experiments and used it to analyze the effect of trench geometry in its shielding performance.

Other authors, such as [20], divide the noise and vibration problem into three weakly coupled subproblems (emission, transmission, and immission) and develop a specific model for each stage. First, the generation of vibrations at the rail-wheel interface is studied, assuming a large distance between track and building. Second, the previously obtained wave field is used as an excitation of a coupled soil-structure model. Structural vibrations are then calculated assuming that the acoustic field inside the building rooms does not influence wall vibrations. Lastly, the computed structural displacements are used as vibration input for the calculation of ground-borne noise in the building enclosures.

In a similar way, Kouroussis et al. [5, 21] presented and validated a numerical model dividing the process in two decoupled subsystems: (i) the vehicle-track-foundation interaction is analyzed by means of a 2D, 2-layer multibody model accounting for track irregularities; and (ii) the vibration propagation on the ground is reproduced on a 3D FEM model. To this aim, the reaction forces of the ballast obtained in the previous step are introduced as input loads acting at the ground surface. Such approach allows benefitting from the advantages of both techniques, namely, the short computation times of the 2D multibody model, the accuracy of 3D FEM modelling, and its ability to reproduce nonperiodic complex geometries. This model was successfully employed in [22] for studying simplified mathematical models of local irregularities (e.g., turnout, foundation transition, wheel flat, and rail joint).

Finally, the work of [23] shall be mentioned, which proposed a simplified numerical model consisting of three different submodels separately addressing each phase of the problem. Such approach was later validated in [24] by comparing the results with detailed numerical modelling (BEM + FEM formulation) and constitutes a simple, fast, and user-friendly tool providing reasonably accurate results for engineering purposes.

This paper analyzes the generation and transmission of train-induced vibrations to a nearby building, due to the passage of an urban railway. To this aim, a numerical 3D finite element model has been developed and validated, which is presented in Section 2. Then, the vibration transmission to a nearby building is studied in Section 3 and the efficiency of an infilled wave barrier as a mitigation measure is assessed in Section 4. Conclusions are drawn in Section 5.

#### 2. Description of the Model

A 3D finite element model has been developed using the commercial software ANSYS LS-DYNA V17. It consists of two submodels that will be described separately within the section: the multibody system reproducing the vehicle and the track-soil-building model. It should be noted that this technique has been widely used for the numerical modelling of railway-induced building vibrations in the last years. In this regard, although they require a considerable computational effort, 3D FEM models are a very convenient and versatile technique, since they can easily and accurately reproduce complex and nonperiodical geometries [6, 21, 22]. The calibration and validation processes carried out with field data of a real train are also described in the final part of this section.

##### 2.1. Multibody Vehicle Model

When studying railway-induced vibrations both the vehicle and the track-soil-structure modelling should have a similar degree of complexity (i.e., the model should be globally simple or complex) [25]. Therefore, the vehicle has been reduced to a car body, two bogies, and four axles, which have been modelled as a three-dimensional multibody system. In this sense, although this technique requires a higher computational time, it also offers the highest accuracy [6]. According to [26], the vehicle’s equation of motion can be reduced towhere , , and represent the acceleration, velocities, and displacements of the element denoted by the subscript (car body), (bogie), or (unsprung mass, i.e., wheelset); , , and are the total masses of each component (with ); and are the stiffness and damping of the primary () and secondary () suspension; is the gravity acceleration; represents the wheel-rail contact force; and is the rail displacement vector.

For the modelling of the different parts of the vehicle, 8-node hexahedral elements were selected for both car body and bogies; point elements were chosen for the wheels; and springs and dampers were selected for reproducing the primary and secondary suspension. The wheel/rail contact is modelled simulating a Hertzian spring [26, 27] and its interaction as a node-to-beam contact (allowing for sliding and loss of contact by means of the penalty algorithm). The track has been assumed to be in excellent conditions and therefore no roughness spectrum has been added to the rail. The latter shall not reduce significantly the accuracy of the model, since a short distance between track and building is considered and dynamic excitation (i.e., that caused by the rail unevenness) dominates the vibration levels in areas far from the track [9]. A full Newton-Raphson method has been employed for solving the nonlinear equations, while the transient dynamic equilibrium has been solved by means of a Newmark implicit time integration.

##### 2.2. Track-Soil-Building Model

The track, soil, building, and their components are represented as a mesh of hexahedral elements, whose maximum dimensions depend on the maximum wavelength, while the minimum size is set according to [28]. In every node of the mesh, (2) is solved:where , , and are the mass, damping, and stiffness matrixes, respectively; , , and are the acceleration, velocity, and displacement vectors; and is the vector of external forces, which introduces in this submodel the influence of the vehicle on the track.

In order to reduce the model complexity, it is commonly assumed that the effect of the train does not induce large strains in the soil (which is assumed to be nonlayered homogenous), and thus the displacements are limited to the elastic range in the stress-strain diagram. Such simplification is realistic, as shown in [8] for field measurements, and, therefore, material behaviour in this model has been assumed to be linear and elastic. The mechanical properties of the main elements of the model have been measured from the real track materials and are summarized in Table 1. For the modelling of the sleeper-ballast contact zone, bonded DOF’s technique was used [29], which requires the introduction of duplicated nodes at the contact surface, one for each material. Between these nodes, the movement perpendicular to the contact plane is linked and therefore must move equivalently in such direction, while the movements parallel to the contact plane are not restricted.