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The effectiveness of heavy masses next to the track as a measure for the reduction of railway induced ground vibration is investigated by means of numerical simulations. It is assumed that the heavy masses are placed in a continuous row along the track forming a wall. Such a continuous wall could be built as a gabion wall and also used as a noise barrier. Since the performance of mitigation measures on the transmission path strongly depends on local ground conditions, a parametric study is performed for a range of possible designs in a set of different ground types. A two-and-a-half dimensional coupled finite element–boundary element methodology is used, assuming that the geometry of the problem is uniform in the direction along the track. It is found that the heavy masses start to be effective above the mass–spring resonance frequency which is determined by the dynamic stiffness of the soil and the mass of the wall. At frequencies above this resonance frequency, masses at the soil׳s surface hinder the propagation of surface waves. It is therefore beneficial to make the footprint of the masses as large and stiff as possible. For homogeneous soil conditions, the effectiveness is nearly independent of the distance behind the wall. In the case of a layered soil with a soft top layer, the vibration reduction strongly decreases with increasing distance from the wall.

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... It has been shown in [9] that bending waves in the stiff barrier are important. A row of heavy masses on the ground surface has also been shown to give attenuation of vibration at frequencies above the resonance frequency of the masses on the ground stiffness [11]. An open trench is commonly used to attenuate ground vibration from machinery [12]. ...

... The parameters from three sites are used at which field measurements were carried out during the RIVAS project [53]. The same sites have also been studied in [7,11] which allows comparison of the effectiveness of different mitigation measures. The dynamic soil characteristics (layer thickness h, shear wave velocity c s , compressional wave velocity c p , density ρ, and material damping loss factors η) [Hz] Insertion loss [dB] (a) One−third octave band centre frequency [Hz] Insertion loss [dB] h=1.5 m h=3 m h=6 m One−third octave band centre frequency [Hz] Insertion loss [dB] w=0.1 m w=0.2 m w=0.05 m [Hz] Insertion loss [dB] 100 m/s 150 m/s 200 m/s are shown in Table 6. ...

A trench can act as a barrier to ground vibration and is a potential mitigation measure for low frequency vibration induced by surface railways. However, to be effective at very low frequencies the depth required becomes impractical. Nevertheless, for soil with a layered structure in the top few metres, if a trench can be arranged to cut through the upper, soft layer of soil, it can be effective in reducing the most important components of vibration from the trains. This study considers the possibility of using such a realistically feasible solution. Barriers containing a soft fill material are also considered. The study uses coupled finite element / boundary element models expressed in terms of the axial wavenumber. It is found to be important to include the track in the model as this determines how the load is distributed at the soil's surface which significantly affects the insertion loss of the barrier. Calculations are presented for a range of typical layered grounds in which the depth of the upper soil layer is varied. Variations in the width and depth of the trench or barrier are also considered. The results show that, in all ground conditions considered, the notional rectangular open trench performs best. The depth is the most important parameter whereas the width has only a small influence on its performance. More practical arrangements are also considered in which the sides of the trench are angled. Barriers consisting of a soft fill material are shown to be much less effective than an open trench but still have some potential benefit. It is found that the stiffness of the barrier material and not its impedance is the most important material parameter.

... The last group of the remedial solutions, which is the main focus of this paper, is the installation of a wave barrier that intersects the path of the surface waves generated by the trains. Constructing wave barriers between the track and structures for scattering or filtering the traininduced surface waves has been the focus of many researches [5][6][7][8][9]. For example, Celebi and Göktepe [5], investigated the efficiency of wave impeding blocks (WIBs) under the track as the wave barriers and found that the most important parameters that control the efficiency of WIBs, is the position of the block with respect to the track and receiver and the material properties of the barrier. ...

... For example, Celebi and Göktepe [5], investigated the efficiency of wave impeding blocks (WIBs) under the track as the wave barriers and found that the most important parameters that control the efficiency of WIBs, is the position of the block with respect to the track and receiver and the material properties of the barrier. Dijckmans et al. [6] used heavy masses such as gabion walls beside the track in order to mitigate the vibrations; François et al. [7] focused on the design and efficiency of installing a composite isolating screen near the track and observed that a polystyrene-filled barrier has less mitigation efficacy when compared with an open trench. In addition, they found that adding two concrete panels to each side of the screen do not significantly increase the wave mitigation strategy. ...

Train-induced ground vibrations can cause major problems in structures that accommodate sensitive apparatus or located in densely populated districts. Wave barriers are used extensively in practice to mitigate the detrimental effects of these vibrations. Many factors have influence on the efficacy of the wave barriers, and a robust procedure is required for an appropriate design that can consider the effect of these factors. This paper describes a coupled genetic-algorithm/finite-element methodology for design of wave barriers. In this methodology, all of the important geometrical and material parameters associated with the performance of wave barriers are considered collectively. Therefore, the combined effect of all parameters and their interdependency is acknowledged. These parameters include the shape, dimensions, position, number, and material properties of the wave barriers. In addition, the uncertainties associated with the nature of transient train-induced loading are taken into account. The results of this study show that open trenches have much higher mitigation capacities when compared with the in-filled trenches, and importantly using double-trench barriers instead of single-trench, enhances the mitigation capacity by as much as 20%. However, such a great boost in the mitigation level is not observed for triple-trench barriers.

... Traditional measures in the transmission path are continuous soil barriers along the railway line. Table 2 lists relative research on continuous vibration mitigation measures along the propagation path, including open trench [14,40], soft-filled barriers [14,40], stiff wave barrier [41], hollow isolation wall [42], subgrade stiffening or WIB [9,[43][44][45][46], sheet pile wall [47], and heavy masses along the track [48]. In Table 2, almost all research considered the at-grand or elevated line, but not the underground line. ...

... However, whether periodic piles could mitigate building vibrations against traininduced vibrations, especially from an underground railway line, still needs to be investigated. Heavy masses along the track Dijkmans et al. [48] (a) Analogy of phononic crystal and piles with a periodic arrangement. ...

Laboratories with sensitive instruments need a low-vibration environment. It is a challenge to control the train-induced vibration impact on these instruments when a newly planned metro line is adjacent to a laboratory building. An alternative method of mitigating train-induced ground vibrations involves installing measures along the transmission path. Recent research has highlighted the potential of periodic pile barriers with specifically designed band gaps for controlling environmental vibrations. This study performed in-situ measurements of ambient vibrations inside and outside a laboratory containing various types of sensitive instruments and located adjacent to a newly designed metro line. The vibration transfer function of the laboratory was then obtained. To help design and optimize the band gaps of periodic piles, a novel band gap performance evaluation function was proposed. Finally, numerical analysis was conducted to validate the mitigation effect of the designed periodic piles. The results showed that the band gap performance evaluation function can be used to optimize the mitigation effect of periodic piles. The proposed periodic piles clearly attenuated vibrations between 52.4 and 74.3 Hz, especially those at 63 Hz. A comparison of general vibration criteria (VC) curves revealed that vibration attenuation of one level can be obtained by the designed periodic piles.

... In these analyses, these frequencies are 27 Hz, 18 Hz, and 10 Hz for the 1.5 m, 2 m, and 3 m concrete walls, respectively. Fig. 19 shows that these are approximately the frequencies in which the vertical insertion loss is maximum, which agrees with the results by Dijckmans et al. (2015) for the case of concrete walls under far-field external loads. The horizontal motion is also affected more significantly at the rocking frequency (Fig. 20). ...

This article presents a numerical study on the ground vibration attenuation performance of surface walls. A coupled IBEM–FEM model is derived for this analysis, in which long walls are modeled with classical finite elements, while the soil is modeled as a 2D, transversely isotropic half-space. The presented boundary element-based scheme yields accurate representation of energy propagation and scattering mechanisms through the soil, which are essential in this analysis. An extensive list of numerical results is presented on the attenuation performance of the wall for horizontal and vertical vibration of different target points of the soil surface, considering seismic and surface-load excitation, as well as various constitutive and geometric parameters of the wall and soil. The results show that wider, stiffer, heavier walls do not necessarily provide better attenuation. Optimal performances can be obtained for specified target points and excitation type and frequency by selecting walls with specific vibration modes and installation points.

... Open trenches [63] and barriers [64,65] can interrupt the wave propagation in soils, and thus decrease the building vibration. In addition, the application of heavy masses next to the track can also reduce the vibration induced by railway traffic [66]. More reviews on the vibration mitigation solutions for railway induced vibrations can be seen in the literature [1]. ...

This paper proposes a new efficient three-dimensional (3D) method to predict the vertical building vibration generated by trains running in tunnels in a multi-layered half-space. The tunnel-ground-building dynamic interaction involving in the proposed method is handled using the sub-structuring approach. The multi-story building is considered as rectangular floors supported by a distribution of columns. Each building floor is divided into several sub-plates. The dynamic stiffness matrix of a single sub-plate derived by the dynamic stiffness method is assembled to obtain the global one of each building floor. The free edge condition of the building floor is satisfied in this solution. The train-track-tunnel-ground dynamic interaction is modelled by a fully-coupled analytical method. The proposed method shows sufficient efficiency and accuracy, making it a suitable tool for predicting large-scale vibrations and performing parametric studies. The responses of a four-story building generated by the passage of trains in a tunnel are analyzed. The building vibrations are significantly affected by the dynamic properties of the building and the building-ground dynamic interaction. The dynamic interaction between the shallow foundations of buildings has a considerable influence on the building vibrations in the low-frequency range. The isolation effectiveness of the floating slab track and the base-isolation of buildings is highly dependent on the isolation frequency.

... The choice between measures applied at the source or at the receiver depends, for example, on whether a new building is to be constructed near an existing railway or a new or renewed railway is to be built close to existing buildings. Finally, attenuation in the transmission path can be achieved, for example, by using open trenches [11], in-filled trenches [12], rows of piles [13] or heavy masses [14]; each of these may be located close to the track or close to the buildings to be protected. The work presented in this paper explores the effects of subgrade stiffening on ground-borne vibration from surface railways. ...

Railway-induced ground vibration is often associated with sites with soft ground. Stiffening of the subgrade beneath the railway track is one particular measure that has potential to reduce the vibration level at such sites. However, the mechanisms behind this reduction are not well understood. Here, the effects are examined in the context of two alternative approaches: (i) subgrade stiffening, where the soil directly under the track is stiffened, and (ii) stiff inclusions introduced at some depth beneath the track, sometimes known as 'wave impeding blocks'. The efficacy of the measures is considered for different ground types in a parametric study carried out using a 2.5D coupled finite-element/boundary-element methodology. The soil is considered to consist of a soft upper layer over a stiffer substratum; corresponding homogeneous grounds are also considered. With a 6. m wide, 1. m thick, concrete block directly under the track, the vibration between 16 and 50. Hz was found to be reduced by between 4 and 10. dB for ground with a 3. m deep soft upper layer. For a deeper soft layer the reductions were greater whereas, for a stiffer ground without the soft upper layer, the reductions in vibration from this block were negligible. Slightly smaller reductions in a similar frequency region were observed when the block was positioned 1. m below the surface, suggesting that, as with stiffening directly under the track, the reduction in vibration was primarily due to the increase of the effective stiffness of the soil beneath the track rather than the effective creation of a new, thinner soil layer. Jet grouting is considered as an alternative to concrete and, although it is found to be less effective due to its comparatively low stiffness, it may still be considered as a practical measure for existing tracks on soft soil sites. The reduction in vibration from this form of soil improvement with a depth of 3. m is similar to that for a 1. m thick concrete block. Finally, results are presented for three example sites with different soil properties which show similar trends.

... In addition, interventions on the propagation path between source and receiver have the advantage that no modifications of the track are required. These measures include open and in–filled trenches [6, 7], wave impeding blocks [8, 9] and heavy masses on the soil's surface [1, 10, 11]. The efficacy of open and in–filled trenches has been studied both by means of analytical models [12], finite element (FE) models [13], boundary element (BE) models [14, 15] and coupled FE-BE models [8, 16]. ...

This paper investigates the effectiveness of a sheet pile wall to reduce railway induced vibration transmission by means of field measurements and numerical simulations. At Furet, Sweden, a sheet pile wall has been installed in the soil near the track to reduce train induced vibrations in houses close to the track. The depth of the sheet piles is 12 m with every fourth pile extended to 18 m. The efficacy of the wall is determined from in situ measurements of free field vibrations during train passages before and after installation of the sheet pile wall. The field test shows that the sheet pile wall reduces vibrations from 4 Hz upwards. Up till 16-20 Hz, the performance generally increases with frequency and typically decreases with increasing distance behind the wall. The performance is further studied by means of two-and-a-hal--dimensional coupled finite element - boundary element models. The sheet pile wall is modeled as an orthotropic plate using finite elements, while the soil is modeled as a layered halfspace using boundary elements. The sheet pile wall acts as a stiff wave barrier and the efficacy is determined by the depth and the stiffness contrast with soil. The reduction of vibration levels is entirely due to the relatively high axial stiffness and plate bending stiffness with respect to the horizontal axis of the sheet pile wall; the plate bending stiffness with respect to the vertical axis is too low to affect the transmission of vibrations. Therefore, it is important to take into account the orthotropic behaviour of the sheet pile wall. It is concluded that a sheet pile wall can effectively act as a wave barrier in soft soil conditions provided that the wall is sufficiently deep.

... Several types of seismic barriers have been proposed in the past to protect buildings from traffic-induced ground vibrations, mainly from propagating Rayleigh surface waves. Among such barriers are trenches (both open and in- filled) [1][2][3][4], large concrete blocks embedded in the ground [5][6][7], rows of vertical piles [8, 9], periodic arrays of vertical holes [10], heavy masses placed on the ground surface [11, 12], etc. Theoretical predictions of Rayleigh wave propagation through such barriers are extremely difficult. Analytical solutions are possible only for a limited number of cases, for example for very shallow trenches [13]. ...

Several types of seismic barriers have been proposed in the past to protect buildings from traffic-induced ground vibrations, mainly from propagating Rayleigh surface waves. In many cases the developers are forced to use direct experimental measurements on real size seismic barriers at frequencies typical for traffic-induced ground vibrations, i.e. at 10-100 Hz. As an alternative and much less expensive approach, a reduced-scale experimental modelling using ultrasonic Rayleigh wave propagation over very small-scale replicas of real seismic barriers is considered in the present work. Rayleigh wave pulses with the central frequency of 1 MHz have been used, which corresponds to the value of scaling factor about 1:1000. Propagation over three types of seismic barriers was investigated: 1) arrays of periodic vertical holes, 2) Combinations of periodically positioned trenches, including a single trench, and 3) statistically rough surfaces. The results of the measurements of transmission and reflection coefficients are presented.

... Various numerical approaches have been explored for predicting the effectiveness of open and in-filled trenches, such as the finite element (FE) [17], the boundary element (BE) [18], or coupled FE-BE methods [9]. Other examples of vibration mitigation measures on the propagation path include buried wall barriers [19], wave impeding blocks [20], rows of piles [21], and heavy masses placed along a railway track for scattering the incident surface waves [22,23]. ...

... One of the earliest contributions was by Warburton et al.[2]who considered the interaction of two rigid circular foundations using a mixed integral equation approach, and Krylov[3]studied the effect of single blocking masses such as concrete blocks placed on a homogenous ground. More recently Alic and Persson[4]proposed form finding for ground vibration mitigation systems, and Dijckmans et al.[5]investigated the ground vibration mitigation effectiveness of an array of heavy masses placed along a railway track. The principle of the latter approach was to modify the wave propagation regime of the ground by introducing an inertial mass near the load. ...

To account for dynamic cross-coupling of structures via the soil, a computational model must be accurate enough to provide the correct overall behaviour of the scattered wave field. However, simplicity is also important when a model should be used for design purposes, especially in the early design stages and feasibility studies. The paper addresses the accuracy of simple models in which an array of structures is simplified into blocks placed on the ground surface or embedded within the soil. Comparisons are made between models that account or do not account, in a proper manner, for the inertia and embedment of the structures. Especially, the limitations of simplified models are discussed regarding their capability to quantify the insertion loss accurately.

... The fourth type is to set large mass objects. Dijckmans [25] studied the vibration isolation effect of heavy mass in the research of transmission path isolation under the European Union project RIVAS. ...

The environmental vibration induced by freight rail transport has become an important type of environmental pollution. The environmental vibration caused by a running freight train near a typical medium- to low-speed railway in China and in the surrounding residential area is measured and analyzed. The test result shows that in the region adjacent to the railway, the weighed vibration acceleration level as a function of time (VLz) in the vertical direction (VLz) is lower than 80 dB, which meets the requirements of the standard (GB10070-88); however, in the surrounding residential area, the VLz is in the range of 58-74 dB, which is 0-4 dB higher than the specified limit during the day and 0-2 dB higher than the specified limit at night. For the isolation of environmental vibration induced by the freight train, a dynamic model of the vehicle and track and a finite element model of the railway, stratum and building are constructed to analyze the feasibility of modifying the slope protection piles outside of the building to make them function as vibration isolating piles, and the vibration isolation effects of such piles in a single row and double rows are compared with the case without piles. The simulation result shows that vibration isolation piles can attenuate the vibration level in front of and behind the piles: compared with the case without piles, the VLz can be reduced by 2-4 dB within 5 m behind the piles in a single row, and can be reduced by 4-10dB behind the piles in double rows, so the double-row setup is recommended for vibration isolation. It is suggested that for residential buildings which are close to the existing medium- to low-speed freight railway lines and for which other vibration attenuation measures are impractical, satisfactory vibration isolation effects may be achieved by simply increasing the number of rows of slope protection piles.

... Open trenches provide a significant amount of mitigation due to its large impedance mismatch with soil; however, there are some practical limitations for constructing them because of the wall stability problems and overrun of surface waters and infiltration of groundwater into the barriers. Therefore, other types of barriers such as soft and hard in-filled trenches [5][6][7][8][9], periodic barriers such as rows of piles [10][11][12][13], vibration isolating screens [14,15], wave impeding blocks (WIBs) [16][17][18] and heavy masses installed next to the track (such as gabion and concrete walls) [19] have been used in various practical and theoretical projects. ...

Train-induced ground vibrations are one of the major disadvantages of the railway transportation particularly in urban areas. These vibrations can cause discomfort to the people, malfunctioning of sensitive instruments and structural problems. Open trenches can effectively mitigate the ground vibrations; however, the construction of open trenches is limited to shallow depths due to the stability issues and unavailability of space in densely populated regions. Therefore, in-filled soft and stiff trenches can be used as an alternative for impeding the train-induced surface waves. This paper discusses the effectiveness of overlapping jet-grouted columns as stiff wave barrier walls for scattering or better yet filtering the train-induced ground vibrations. These barriers are located on the wave propagation path between the railway and the receiving points, and their optimal layout is identified using a new coupled genetic-algorithm/finite-element topology optimization methodology. It is observed that this methodology can effectively find the optimal topology of the jet-grouted barriers within the design domain. The results show that the barriers with larger heights provide better mitigation. In addition, the barriers tend to be located either in the vicinity of the track or the receiving points. To provide better judgment, the efficacy of the jet-grouted wave barriers is compared to open and in-filled trenches.

... Ground-borne vibration could result in human distress (Fiala et al., 2008;Connolly et al., 2015), malfunctioning of sensitive equipment (Chik et al., 2015;Ulgen et al., 2016) and accelerating the fatigue of historic buildings (Ma et al., 2016;Alan and Caliskan, 2017). To address this issue, vibration mitigation measures can be implemented at the vibration source (Costa et al., 2012;Thompson et al., 2015;Vogiatzis and Kouroussis, 2015), on the propagation path (Coulier et al., 2013;Dijckmans et al., 2015), or at the receivers where vibration problems occur (Talbot and Hunt, 2003), among which source mitigation is believed to be the most cost-effective measure (Hemsworth, 2000). The source mitigation measures also include a variety of strategies: continuous welded rail (Eum et al., 2003); railpads (Wei et al., 2016(Wei et al., , 2017; special trackforms such as floating slab track (FST) (Lei and Jiang, 2014;Vogiatzis and Kouroussis, 2015;Dere, 2016) and ladder track (Xia et al., 2010); ballast mats (Auersch, 2006;Costa et al., 2012); and so on. ...

To effectively reduce the railway vibration and its environmental impact, vibration mitigation measures are increasingly used. The vibration reduction effect of railway tracks is described quantitatively by insertion loss (IL). ILs obtained from in situ measurements under moving train loads and laboratory tests under artificial excitation differ significantly due to the different track loading state between these two methods. The differences of track loading state are induced by the moving effect of train passages and the preloads effect of vehicle masses, the latter of which is a significant factor to discuss in this paper. In order to study the static preload by vehicle masses influence on the vibration reduction effect in isolated tracks, the steel spring floating slab track and regular slab track, as a reference case, were compared. First, a theoretical simplified model was constructed, following which a finite–infinite element coupled model was built, which was calibrated by experimental test results. Impact loads were applied to both tracks with preloads using unsprung wheelsets or sprung vehicle-body masses, with the total mass varying from 0 t to 30 t. The results demonstrate that the increase in preload of unsprung mass makes the natural frequencies further reduced, and the peak IL value increased from 39 dB to 48 dB. The increase in preload has a significant effect on vibration responses below 5 Hz, and the application of the preload has different effects on the reduction effect in different frequency ranges.

... erefore, vibration reduction is required in sensitive areas along subway lines. Vibration reduction measures can be divided into three types based on vibration source, propagation mode, and effectiveness: (i) active isolation of vibration source; (ii) termination of vibration propagation [4][5][6][7][8][9]; (iii) passive vibration isolation of vibrating object. First used for active vibration source isolation in Germany in 1965, floating slab tracks have good vibration reduction properties, and their use in controlling vibration from subways has since become more widespread [10,11]. ...

At present, steel-spring floating slabs have been widely used in urban rail transit to reduce the influence of ground vibration caused by vehicle operation on the surrounding environment. As a core part of vibration reduction for floating slab track, the steel-spring vibration isolator may fail in different forms during operation. In order to study the influence of vibration isolator failure on vehicle operation performance and floating slab track structure vibration reduction effectiveness, a rigid-flexible coupling dynamic model of vehicle-rail-floating slab track is established by multibody dynamics and finite element simulation, and the rationality of the model and its parameters is verified by comparing the theoretical calculation results with the measured data. Based on the model, the failure conditions of steel spring are simulated, considering the failure position and number of steel springs. The results show that the failures of steel-spring vibration isolators have a significant impact on operating safety and stability of vehicle, and the failure at end is more dangerous than that at midspan. In addition, it also changes the local restraint state of floating slab, resulting in the local vibration mode, which reduces the floating slab track structure vibration reduction effectiveness, mainly within 10 Hz. The different numbers of steel-spring failures will change the natural modal frequency of floating slab to varying degrees, which may cause the resonance of a certain frequency of the vehicle-track coupling system, leading to other track structure diseases.

... Alternative mitigation techniques are short soil-binder [31], jetgrouted overlapping columns [32], grouting consolidation or deep subsoil mixing [33]. In addition, the construction of heavy gabion walls next to the HSR in order to minimize the HST vibrations has been studied by Dijckmans et al. [34]. Furthermore, the implementation of concrete or stone blocks on the subsoil surface near to HSR has been investigated by several researchers [35][36][37]. ...

The main aim of this work is to present an efficient mitigation measure of ground vibrations induced by high-speed trains (HST). It is very important to propose such mitigation measures against soil vibrations due to various negative impacts to the population, structures, as well as railway infrastructure. This study examines the application of expanded polystyrene (EPS) blocks as an efficient mitigation measure against the ground vibrations induced by HST’s passage. EPS is a high-performance geosynthetic fill material, which is widely used due to its low weight and great compressibility. In the present numerical study, an three-dimensional (3D) model was used, utilizing the finite element software ABAQUS in conjunction with a user-developed subroutine in order to accurately simulate the complex dynamic phenomenon of soil response during the passage of HST. For this purpose, field data of a typical soil embankment from Paris– Brussels Thalys line were used to validate the adopted numerical approach. Subsequently, the use of different types of EPS schemes was investigated and compared in order to obtain an optimal geometrical configuration of EPS blocks that significantly reduces train-induced vibrations.

... Mitigation of ground vibration is important and researchers have suggested different approaches. Use of ground barriers to interrupt wave propagation is a popular method and studies have been carried out using open trenches (Ahmad et al., 1996, Saikia and Das, 2014, Tsai and Chang, 2009, in-filled trenches (Pu et al., 2018, Jayawardana et al., 2018, Saikia, 2016, Thompson et al., 2016, Jayawardana W.A.P.D. et al., 2016, Ekanayake et al., 2014, Bo et al., 2014, appropriately shaped landscapes (Persson, 2013), sheet piles (Barkan et al., 1962) and heavy masses (Dijckmans et al., 2015). Trenches or ground barriers can affect wave propagation and it is important to identify the degree of influence of their geometry and in-fill material. ...

Development activities in a city often generate ground vibration that can cause discomfort to the occupants in nearby buildings, disturbances to the activities undertaken in the buildings and possible damage to nearby structures. This ground vibration is caused by construction activities such as pile driving, ground compaction etc., and road and rail traffic. The use of trenches has been an effective way to mitigate the adverse effects of such ground vibration. The effectiveness of the trench depends on many parameters including the properties of the vibration source, soil medium and trench in-fill material, trench dimensions and the requirements of the receiver. The process of selecting an effective trench for vibration mitigation can therefore become complex due to the influence of a number of parameters and their wide range of values. This paper investigates the use of artificial neural network (ANN) as a smart and efficient tool to predict the effectiveness of geofoam-filled trenches to mitigate ground vibration. Towards this end, a database is developed from an extensive study on the effects of the controlling parameters through numerical simulations with a validated finite element (FE) model. At a certain distance from the vibration source, a geofoam-filled trench is introduced to evaluate the efficiency of vibration mitigation with changes in key parameters such as excitation frequency, amplitude of load, trench configuration (i.e. depth and width), soil shear wave velocity, soil density and damping ratio. These were selected as the input parameters for the ANN while amplitude reduction ratio and peak particle velocity (PPV) were considered as outputs. A multilayer feed forward network was used and trained with the Levenberg-Marquardt algorithm. Neural networks with different configurations were evaluated by comparing coefficient of determination (R ² ) and mean square error (MSE). The optimum architecture was then used to predict previous results, which revealed the accuracy and the effectiveness of the ANN approach. The findings of this study will provide useful information for vibration mitigation using geofoam-filed trenches.

... Apart from open and in-filled trenches, several other wave barriers have been proposed. For instance, the placement of a heavy mass such as a gabion wall across the track was proposed by Dijckmans et al. (2015). Furthermore, wave impeding blocks (WIBs) have been used to reduce the developed vibrations (Gao et al., 2015). ...

The vibrations induced by the passage of high-speed trains (HSTs) are considered a crucial issue in the field of environmental and geotechnical engineering. Several wave barriers have been investigated to reduce the detrimental effects of HST-induced vibrations. This study is focused on the potential implementation of an innovative mitigation technique to alleviate the developed vibrations. In particular, the use of expanded polystyrene (EPS) blocks as partial fill material of embankment slopes was examined. The efficiency of the proposed mitigation technique was numerically investigated. More specifically, a 3D soil-track model was developed to study the cross-section of a railway track, embankment, and the underlying soil layers. The passage of the HST, Thalys, was simulated using a moving load method, and the soil response was calculated at several distances from the track. Several parameters influenced the effectiveness of the examined mitigation measure. Therefore, to ensure an optimal design, a robust procedure is necessary which considers the impact of these factors. Hence, the implementation of EPS blocks on several embankments with different geometry, in terms of height and slope angle, was investigated.

... However, these they still have some potential benefits. The stiffness of the filling material and not its impedance is the most important material parameter [16,17]. ...

Due to the expansion of cities through megaprojects and the increase in populations in large cities, many buildings are constructed beside train tracks. Trains passing nearby buildings cause ground vibrations that may affect the structures and their foundations. In this research, a detailed 3-D finite element analysis is conducted on a ten-story reinforced concrete framed structure resting on a raft foundation using ABAQUS. The soil profile consists of silty clay for 10 m followed by dense sand for 40 m. The soil block considered in the analysis has plan dimensions of 100 m x 100 m. The train loads are modeled using moving point loads. The train track is considered at different distances from the building. The effect of the train speed and its track distance from the building on the response of the structure with its foundations are investigated. Mitigation techniques including open trenches and in-filled foam trenches are considered in order to mitigate the effect of vibrations induced by trains on the adjacent building. The results showed that these techniques are efficient in reducing the train-induced vibrations transmitted to the soil and the adjacent building. The average reduction percentage in acceleration was 61.29 % and 57.39 % when using in-filled foam trench and open trench mitigation techniques, respectively.

... Finally, heavy mass (see Fig. 16d) have been proposed to reduce ground-borne vibration coming from the railway traffic. By placing a gabion wall composed of stone or concrete on the ground surface next to the track [142], it is possible to have an attenuation of vibration at frequencies above the resonance frequency of the masses on the ground stiffness [143]. Two-dimensional (2D) calculations indicate insertion loss values up to 10 dB in a frequency range from about 20% below to about 20% above the natural frequency [144]. ...

Vibration and noise aspects play a relevant role in the lifetime and comfort of urban areas and their residents. Among the different sources, the one coming from the rail transit system will play a central concern in the following years due to its sustainability. Ground-borne vibration and noise assessment as well as techniques to mitigate them become key elements of the environmental impact and the global enlargement planned for the railway industry. This paper aims to describe and compare the different mitigation systems existing and reported in literature through a comprehensive state of the art analysis providing the performance of each measure. First, an introduction to the ground-borne vibration and noise generated from the wheel-rail contact and its propagation through the transmission path is presented. Then, the impact and the different ways of evaluating and assessing these effects are presented, and the insertion loss indicator is introduced. Next, the different mitigation measures at different levels (vehicle, track, transmission path and receiver) are discussed by describing their possible application and their efficiency in terms of insertion loss. Finally, a summary with inputs of how it is possible to address the future of mitigation systems is reported.

... Therefore, ditch opening and ditch filling can be combined in practical engineering. Other vibration reduction methods for cutting propagation paths include column [26,27], heavy mass [28,29], sheet pile wall [30], rigid baffle [31], and expanded polystyrene blocks [32]. ...

To reduce the disturbance of train vibration to adjacent tunnels during the operation of near-distance twin tunnels, three reduction methods are proposed. In this paper, the vibration mitigation effects of steel plate (SP), concrete zone (CZ), and double liner (DL) on their tunnels and adjacent tunnels during train vibration are compared by scale model and discrete element method (DEM). The distance between twin tunnels is 0.25 D, where D (6.2 m) is the diameter of the tunnel. The results show that CZ can produce a good vibration isolation effect on the first tunnel (T1) and second tunnel (T2). At the same time, SP has a good vibration isolation effect on the liner and surroundings of T2 but has the potential to increase the dynamic characteristics of T1 surroundings. The vibration mitigation effect of the DL on T1 and T2 is the same, and the ratio of weakening effect is about 30%–50%. In summary, the most recommended vibration isolation method in practical engineering is CZ. This study provides a reference for studying the vibration mitigation effect on adjacent tunnels during operation.

... Various numerical approaches have been explored for predicting the effectiveness of open and in–filled trenches, such as the finite element (FE) [18], the boundary element (BE) [19], or coupled FE–BE methods [9]. Other examples of vibration mitigation measures on the propagation path include buried wall barriers [20], wave impeding blocks [21], rows of piles [22, 23], and heavy masses placed along a railway track for scattering the incident surface waves [24, 25]. Although numerical simulations are indispensable for understanding and designing efficient wave barriers , there remains a strong need to validate the outcome of these simulations by means of in situ tests. ...

This paper discusses the design, the installation, and the experimental and numerical evaluation of the effectiveness of a stiff wave barrier in the soil as a mitigation measure for railway induced vibrations. A full scale in situ experiment has been conducted at a site in El Realengo (Spain), where a barrier consisting of overlapping jet grout columns has been installed along a railway track. This barrier is stiff compared to the soil and has a depth of 7.5 m, a width of 1 m, and a length of 55 m. Geophysical tests have been performed prior to the installation of the barrier for the determination of the dynamic soil characteristics. Extensive measurements have been carried out before and after installation of the barrier, including free field vibrations during train passages, transfer functions between the track and the free field, and the track receptance. Measurements have also been performed at a reference section adjacent to the test section in order to verify the effect of changing train, track, and soil conditions over time. The in situ measurements show that the barrier is very effective: during train passages, a reduction of vibration levels by 5 dB is already obtained from 8 Hz upwards, while a peak reduction of about 12 dB is observed near 30 Hz immediately behind the barrier. The performance decreases further away from the jet grouting wall, but remains significant. The experimental results are also compared to numerical simulations based on a coupled finite element–boundary element methodology. A reasonable agreement between experiments and predictions is found, largely confirming the initially predicted reduction. This in situ test hence serves as a ‘proof of concept׳, demonstrating that stiff wave barriers are capable of significantly reducing vibration levels, provided that they are properly designed.

... In those cases, the position of the loading point keeps changing over time, thus leading to the change of the wave incident directions over time. Investigations on isolating such vibrations induced by different moving loads have been conducted by many researchers (Karlström and Boström, 2007;Lu et al., 2009a;Coulier et al., 2013;Dijckmans et al., 2015;Dijckmans et al., 2016;Kaewunruen et al., 2017;Lyratzakis et al., 2020), and various designs have been suggested, such as open or in-filled trenches (Karlström and Boström, 2007;Cao et al. 2012;Zoccali et al., 2015;Thompson et al., 2016;Yang et al., 2018;Yarmohammadi et al., 2018Yarmohammadi et al., , 2019Guo et al., 2020) and pile groups (Lu et al., 2009ab;Xu and Xu, 2012;Pajouh et al., 2017;Pinto et al., 2018;Gao et al., 2020;Li et al., 2020ab). Overall, those designs exhibit good vibration attenuation performance. ...

The attenuation property of periodic pile barriers for elastic-wave propagation in certain direction induced by stationary loading sources has been extensively investigated. However, the corresponding studies under moving-load excitations are rather limited due to the complexity caused by the time-varying feature of the induced wave-propagation directions. To address this issue, this paper investigates the vibration isolation performance of periodic pile barriers under moving loads. Using the periodic structure theory, a novel method for deriving the attenuation zones of periodic pile barriers under harmonic moving loads is proposed, which allows calculation of the directional attenuation zones (DAZs) for waves propagating in different directions. This is realized by combining the moving-load speed line with the dispersion properties of periodic pile barriers. A simplified numerical model is also developed to analyze the dynamic responses of the periodic pile barriers in frequency domain. The responses of periodic pile barriers under different moving loads are also conducted in time domain to validate the theoretical predictions. The two-dimensional (2D) Fourier transform in both time and space domain is used to study the filtering property of periodic pile barriers under harmonic moving loads and to reveal their vibration isolation mechanism. It is found that different from the stationary loading situation, for which the induced elastic waves mostly propagate in one certain direction, the filtering property of periodic pile barriers under moving loads is related to its dispersion properties along each possible wave-propagation direction. Besides, the attenuation zones for the moving loads are dependent not only on the dispersion properties of the periodic pile barriers, but also on the loading itself, namely the velocity and excitation frequency of the moving load.

Barrier is an effective vibration isolation measure to reduce railway-induced vibrations. However, the full-scale model test is seldom conducted. In this paper, the ceramsite or the ceramsite-sand mix is first introduced as an in-filled material for wave barriers in mitigating railway-induced vibrations. A full-scale model test and a 3D finite element model with a perfectly matched layer as the absorbing boundary are used for studying the vibration isolation effects of the wave barriers in a continuous or non-continuous form. Before the test, the dynamic parameters of soil in the test site are obtained by the MASW test. The transfer function and the insertion loss due to the barriers at the fixed observation points have been experimentally investigated. Subsequently, the contour map of the wavefield, the Arias intensity, the influence of different depths, and the different ceramic ratios on the vibration isolation effect are examined by the numerical model. Results show the promising screening effectiveness of the ceramsite-sand mix barrier.

Erschütterungen und sekundärer Luftschall aus dem Schienenverkehr stellen ein immer stärker wahrgenommenes Problem dar und müssen daher bei der Planung von Neu- und Umbauprojekten sorgfältig berücksichtigt werden. Das vorliegende Kapitel liefert hierfür die Grundlage für den Ingenieur. Neben den Entstehungsmechanismen und der Minderung von Erschütterungen und sekundärem Luftschall aus dem Schienenverkehr wird daher auch auf deren Bewertung sowie auf Prognoseverfahren eingegangen. Das Kapitel baut dabei auch auf Erkenntnissen aus dem Kap. Luftschall aus dem Schienenverkehr auf.

Comparing with the straight track, the curved track accounts for a large proportion with the rapid development of metro networks. The train-induced horizontal vibrations, which can’t be ignored, are close to the vertical vibrations. The residents and the service of building structures adjacent to the curved subway lines are greatly affected by the train-induced horizontal vibrations and vertical vibrations. Meanwhile, subway lines inevitably pass through the sensitive areas which have the requirements for vibration control, and the effect of soil-structure interaction on vibration propagation from the ground to upper building structures are not clear so far. Thus, this paper presents a numerical method to study the vibration propagation laws in the ground soil and the effect of soil-structure interactions on building vibrations along a curved subway segment. The method consists of a train-track coupled model and a finite-infinite model. The train-track coupled model could obtain both vertical and horizontal forces of inner and outer wheel-rail, and they are the dynamic loads applying at the finite-infinite numerical model. Then, the numerical method is verified by comparing with the situ measurements, which have been performed along a curved track of Guangzhou metro. Finally, building with pile, raft, or strip foundations was modeled to study the impact of soil-structure interactions. The numerical results show that the horizontal and vertical vibrations along the curved track are larger than the corresponding vibrations induced by train operation on the straight track. The soil-structure interaction has a significant effect on vibration propagation both in the ground soil and from the ground soil into the upper building. A building with a pile foundation can alleviate the vibration of the upper structure, especially in high-frequency band.

Concrete material can reduce the disturbance of train vibration to adjacent tunnels during the operation of near-distance twin tunnels. This paper adopts the discrete element method (DEM) and experimental model (scaled by 1:20) to study the influence of the train vibration at the speed of 120 km/h on the static and dynamic characteristics of the adjacent tunnel's liner and sleeper. The region between the twin tunnels was set as the concrete zone (CZ) to explore the effect of train vibration waves. The distance between twin tunnels is set to 0.25 D, where D (6.2 m) is the diameter of the tunnel. Foam brick (FB) is the similar materials of CZ in similar experiment. The DEM and similar experiments obtained similar results. The CZ (FB) can effectively block the propagation of the train vibration waves in T1, thus reducing the disturbance to the T2 liner and sleeper. Next, the CZ with four thicknesses and six heights are discussed with DEM, and it is found that thickness and height have a significant influence on the isolation effect of CZs, so the size should be selected according to actual engineering needs. This study provides a reference for studying the vibration reduction effect of CZs on adjacent tunnels during train operation.

Excessive vibrations inside buildings in the Lihu New Village caused by the Shenzhen Metro Line 2 underground railway were investigated by conducting analyses of the tunnel, the track irregularities, the stiffness of the fastening system, and the vibrations of the track system and the building at different speeds. A numerical simulation based on the dynamic coupling theory of the vehicle-track system was used to verify the experimental results. Suitable countermeasures were investigated. The results show that rail corrugation is the primary reason for the excessive vibration, and an increase in the stiffness of the vertical fastening system is the secondary reason. The solution was to eliminate the rail corrugation using rail grinding and decrease the vertical stiffness by changing the fastening system. The results of this study provide references for solving vibration problems caused by rail lines.

Railway-induced vibrations can cause significant environmental issues. This paper proposes an efficient analytical method to investigate the mitigation of railway-induced vibrations by using periodic barriers in a layered half-space. The general solutions for layered ground and multiple inclusions are derived by using the potential decomposition and multiple scattering theory. The conversion equation between cylindrical and exponential functions and the addition theorem are introduced to achieve the transformation between plane and cylindrical wave functions and the translation between cylindrical wave functions. Combined with the transfer matrix method, the fundamental solution for the soil-inclusion dynamic interaction in a layered half-space is derived. The railway train and track are subsequently coupled to the ground-inclusion system. Numerical studies demonstrate that the phononic crystal effect induced by the periodic distribution of barriers improves the mitigation efficiency at high frequencies. The increase in the number, size, and stiffness of barriers can give a higher mitigation efficiency in a wider frequency range. The mitigation efficiency of periodic barriers can be guaranteed when their depth is shorter than half the Rayleigh wavelength in the considered frequency range. Owing to the scattering of waves at layer interfaces, the periodic barriers beneath the track have a higher efficiency than those located next to the track, which does not appear in the homogeneous half-space. The performance of periodic barriers is significantly affected by the soil stiffness of the upper shallow layer, while it is less affected by the soil stiffness of the bottom stiffer layer.

Erschütterungen und sekundärer Luftschall aus dem Schienenverkehr stellen ein immer stärker wahrgenommenes Problem dar und müssen daher bei der Planung von Neu- und Umbauprojekten sorgfältig berücksichtigt werden. Das vorliegende Kapitel liefert hierfür die Grundlage für den Ingenieur. Neben den Entstehungsmechanismen und der Minderung von Erschütterungen und sekundärem Luftschall aus dem Schienenverkehr wird daher auch auf deren Bewertung sowie auf Prognoseverfahren eingegangen. Das Kapitel baut dabei auch auf Erkenntnissen aus dem Kap. Luftschall aus dem Schienenverkehr auf.

Stiff wall barriers can be effective in reducing the transmission of environmental ground vibration. Up to now, single wall barriers have mostly been studied. In building acoustics, however, double walls are used in order to realize a high level of sound insulation. In this paper, the potential of using double walls in reducing ground vibration transmission is investigated by means of numerical simulations. Two cases are studied: jet-grout walls and concrete walls in a homogeneous soil with elastic properties representative of a sandy soil. For both cases, the three-dimensional free field response due to a point load is computed using a 2.5D finite element methodology. Subsequently, the free field response is computed for a simplified train load. Double jet-grout wall barriers are found to be slightly more effective than single wall barriers, in particular when the thickness of the walls and the intermediate soil matches a quarter Rayleigh wavelength. The largest increase in vibration reduction is found for the area closest to the vibration source, where the vibration levels have the highest values. The performance of concrete wall barriers, however, is mainly determined by the stiffness of the walls, and almost no difference in performance is found for single and double walls.

Stiff wall barriers can be effective in reducing the transmission of environmental ground vibration. As double walls are used in building acoustics in order to realize a high level of sound insulation, the potential of using double jet-grout walls in reducing ground vibration transmission is investigated in this paper. The three-dimensional free field response due to a point load and a simplified train passage is computed using a two-and-a-half dimensional finite element methodology. In some cases, double jet-grout wall barriers are found to be slightly more effective than single wall barriers, in particular when the thickness of the walls and the intermediate soil matches a quarter Rayleigh wavelength. If there is a large difference between the soil and barrier stiffness, the performance is dominated by the stiffness effect and is similar for single and double wall barriers.

Stiff wall barriers can be effective in reducing the transmission of environmental ground vibration. Up to now, single wall barriers have mostly been studied. In building acoustics, however, double walls are used in order to realize a high level of sound insulation. In this paper, the potential of using double jet-grout walls in reducing ground vibration transmission is investigated. The three-dimensional free field response due to a point load and a simplified train load is computed using a two-and-a-half dimensional finite element methodology. Double jet-grout wall barriers are found to be slightly more effective than single wall barriers, in particular when the thickness of the walls and the intermediate soil matches a quarter Rayleigh wavelength. The largest increase in vibration reduction is found for the area closest to the vibration source, where the vibration levels have the highest values.

Over the last years, a rapid growth of high-speed railways (HSR) has been observed in many countries. Due to the increased operational speed, a major side-effect of this growth is the high levels of imposed traffic-induced vibrations by high-speed trains (HST). Hence, when HSR are cited or planned to be constructed near to “sensitive” structures (e.g., hospitals, schools, etc.), the users / residents of these buildings will probably be affected by these vibrations, as well as the noise of continuously passing HST. For this reason, during the design and construction of new HSR or the upgrading of existing ones, the vibration levels should be minimized. In this study, the mitigation of the low-frequency vibrations induced by the HST passage in the case of HSR cuttings is studied. A new mitigation approach, i.e., the application of expanded polystyrene (EPS) blocks at the cutting slopes, has been investigated in order to reduce the levels of vibrations. The efficiency of this measure has been investigated via advanced three-dimensional numerical simulations. The retrofitted models have been compared with a typical cutting without any mitigation measures in Paris-Brussels line in Belgium. For this site, pre-available field measurements have been used to validate the developed computational models. The presented results illustrate that EPS consists an efficient solution for the mitigation of HST-ground vibrations in HSR cuttings.

There is a great need to develop rail networks over long distances and within cities as more sustainable transport options. However, noise and vibration are seen as a negative environmental consequence. Compared with airborne noise, the related problem of ground vibration is much more complex. The properties of the ground vary significantly from one location to another. There is no common assessment criterion or measurement quantity and no equivalent to the noise maps. Ground-borne vibration is transmitted into buildings and perceived either as feelable whole-body vibration or as low frequency noise; it can also affect sensitive equipment but it is generally at a level that is too low to cause structural or cosmetic damage to buildings. A review is given of evaluation criteria for both feelable vibration and ground-borne noise, empirical and numerical prediction methods, the main vehicle and track parameters that can affect the vibration levels and a range of possible mitigation methods.

In recent decades, High-Speed Railway (HSR) lines have become one of the most extended and environmental-friendly ways to plan new mass transport networks. These systems are directly influenced by its operational speed generated dynamic effects and the areas where it runs through. This necessarily requires to predict ground-borne vibrations generated by trains passing-by populated areas and its influence zone.
Trends in ground-borne measurements, prediction models, and isolation systems are usually performed for maximum operation speed. This method implies the maximum dynamic forces which are suitable for structural calculations (generally developed in time domain) but not necessary for vibration related issues (emission and/or transmission). Additionally, these studies are mainly focused on urban areas where maximum operational speed are frequently far from railways service’s top speeds.
Related to frequency domain, it is known that upper frequencies are not the most disturbing ones. In fact, European structural standards usually cut frequencies off at 30 Hz, so much relevant information for vibrational prediction is ignored due to it does not influence structural issues.
Moreover, current common predictive numerical models usually apply punctual loads (birth & death) that are disposed to run in certain speed conditions. This method, which is considered valid for time domain analysis, are identified to be incomplete for frequency domain components due to its discontinuous application of loads.
The implementation of contact theories in the wheel-rail interface implies a continuous load application, refining the obtained results but increasing computational cost.
In this study, different scenarios are compared varying inner and boundary conditions of a model, with the aim of validate results and optimize resources by obtaining a parametrical influence study that will show how different assumptions and cases could condition ground-borne vibrational studies results.

Ground-borne vibrations due to high-speed trains passage strongly depend, apart from the speed of the train, on the geometry of the railways as well as the properties of the underlying soil layer(s). The main aim of this study is to investigate the effectiveness of expanded polystyrene (EPS) blocks in mitigating soil vibrations induced on railway embankments for different subsoil and railway embankment material conditions. The EPS blocks are placed in suitable locations, either as embankment's side fill material, or trench filling material, or combination of the above. An efficient three-dimensional numerical model has been developed -in conjunction with a user-developed subroutine for applying the moving loads-to accurately calculate the dynamic response of the coupled embankment-soil model. Four typical soil types - categorized as rock, dense sand with gravels, stiff and soft clay - are investigated. In addition, the mechanical properties of the embankment material have been altered to assess to what extend they can affect the HST vibrations.

In this paper, the effectiveness of elastic anti-vibration mats in reducing ground-borne vibrations from rail viaducts is investigated by means of theoretical analysis and is validated by the results of field tests. A two-step procedure is adopted for analyzing the vehicle-track-bridge-soil coupling system. In the first step, the train-track-bridge-pier subsystem is considered, and the bridge-bearing reaction force is solved. In the second step, the pier-pile-soil subsystem is considered, and the ground vibration solution is obtained by applying the negative bridge-bearing reaction force to the pier top on a pier-pile-soil model. The accuracy of the presented model is then verified in comparison with in-situ measurement results. On the basis of this comparison, a parametric study on the impact of anti-vibration mats on ground-borne vibrations was investigated theoretically, and the effectiveness of elastic anti-vibration mats with the suggested optimal parameters was further validated by field tests. The results show that when the stiffness of the elastic anti-vibration mats is 1.5 MPa/m, ground vibration decreases significantly and the vertical rail displacement agrees with high-speed railway regulations.

This paper set up a test section of Shuohuang heavy-haul railway in China to investigate the influence of cement–soil pile reinforcement subgrade on surroundings vibration. The X-, Y-, and Z-direction accelerations of the surrounding environment for the reinforced section and unreinforced section were collected. The study found that in the near-field area, the accelerations of the reinforced subgrade section were smaller than those of the unreinforced section. In addition, the vibration response caused by heavy-haul trains running in parallel after meeting was significantly higher. As the subgrade was reinforced with cement–soil piles, the overall stiffness increased, which had the blocking effect on the high-frequency acceleration of the near-field region. Besides reinforced cement–soil piles have the effect on the peak dominant frequencies of vibration accelerations in near-field area, resulting in a decrease in the peak dominant frequency. The cement–soil piles not only could inhibit the settlement deformation of the subgrade but also had a certain blocking effect on the vibration of the near-field region.

To study heavy train-related vibration, this paper examines the world's largest heavy-freight railway – the Daqin Railway – to study the impacts of the seasonally frozen soil layer on vibrational acceleration. With increasing axle weight, the peak and mean values of the acceleration increased. Vibration acceleration attenuated the most from the shoulder to the embankment footing (51%–71%), while the vibrations at 70 m were attenuated by more than 90%. Certain measures must be taken by those living within 70 m of the railway shoulder. In addition, the acceleration peak caused by trains running in parallel after meeting amplified the vibration by 10%–39%. Moreover, the overall vibrations attenuate with increasing distance, whereas the local vibrations fluctuate. During the freezing period, the acceleration is 13%–26% greater than that of the unfrozen period. The vibration acceleration spectrum is comparatively wider, and is dominated by high-frequency components. Finally, using a three-dimensional model verified by field measurements, the vibrational features were analyzed at different embankment and foundation depths.

Zusammenfassung
Dieser Beitrag präsentiert eine Berechnungsmethode für die Wellenausbreitung infolge einer dynamischen Belastung in einem elastischen Halbraum mit zylinderförmigem oder sphärischem Hohlraum, Graben oder kugelförmigem Einschnitt. Durch die Superposition der Grundlösungen der Integraltransformationsmethode (Halbraum, Vollraum mit zylinderförmigem Hohlraum und Vollraum mit sphärischem Hohlraum) erhält man für diese Systeme eine semianalytische Lösung im Wellenzahl-Frequenzraum. Daraus resultieren schließlich die wellenzahlabhängigen Nachgiebigkeiten an der Oberfläche des Halbraums sowie des zylindrischen oder sphärischen Einschlusses. Diese Nachgiebigkeiten können dann mit der Finiten-Elemente-Methode gekoppelt werden, so dass beliebige komplexe Strukturen in das Bodenmodell eingebettet werden können.

Dieses Kapitel spricht über Wellenarten in homogenen, inhomogenen und geschichteten Medien, Lage der Schwingungsquelle und weitere Einflüsse. Bei der Fortpflanzung von elastischen Wellen wird nur Energie transportiert, aber keine Masse. Die einfachste Wellenart ist die so genannte eindimensionale, harmonische Welle. Bei einer dreidimensionalen Wellenausbreitung ist die mathematische Darstellung komplizierter, da die eindimensionale Koordinate x in Gleichung durch einen dreidimensionalen Ortsvektor zu ersetzen ist. Der natürliche Boden weist neben seinen elastischen Eigenschaften immer auch Materialdämpfung auf. Daher nehmen die Amplituden bei der Wellenausbreitung neben der Abminderung infolge Abstrahlungsdämpfung auch aufgrund von Energiedissipation im Material (Materialdämpfung) ab. Treffen elastische Scher‐ oder Kompressionswellen im Baugrund auf eine Schichtgrenze zwischen Böden mit unterschiedlichen Ausbreitungsgeschwindigkeiten, so werden sie – außer in Sonderfällen – zurückgeworfen (Reflexion) sowie in die andere Schicht hineingebrochen (Refraktion). Infolge einer Bodeninhomogenität (Änderung der Scherwellengeschwindigkeit über die Tiefe) oder einer Bodenschichtung ist die Ausbreitungsgeschwindigkeit der Oberflächenwellen nicht mehr konstant, sondern von der jeweiligen Anregungsfrequenz abhängig. Dieses Phänomen wird als Dispersion bezeichnet.

In the development of a high-speed railway system, controlling the vibration and noise caused by the system plays an important issue, since the vibration and noise have an influence on the surrounding environment. This study describes the field experiment conducted in September 2015 on the Chengdu–Dujiangyan high-speed railway system where elastic rubber mats – the only countermeasure that is currently applied to reduce vibration and noise in high-speed elevated railway systems in China – were installed in September 2010. The effects of mats under the tracks on noise and vibration were evaluated and analyzed systematically compared to the tracks without mats in the following three aspects: vertical wheel–rail forces; vibration characteristics of the track system, bridge, and ground in combination with the environmental noise characteristics in several frequency domains; and the ride comfort and the interior noise of the vehicle. The results indicate that mats have a negligible effect on the vertical wheel–rail forces, ride comfort, and the interior noise of the vehicle. However, even though they significantly reduce the vibration of the base slab, bridge, and the ground below the mats, vibration of the rails and track slabs above the mats is increased, especially at low frequencies. Mats can also effectively reduce the bridge-borne noise but have little influence on the far-field noise. Furthermore, their control effect on environmental noise and vibration was evaluated in September 2010 and September 2015, showing that mats could effectively minimize the environmental vibration and bridge-borne noise after five years of practical operation, although their control effect declined as their stiffness increased.

A new Swiss ordinance, planned to come into force in autumn 2008, will demand
mitigation measures for groundborne vibration over the whole existing Swiss railway
network. Swiss Federal Railways (SBB) tested several mitigation measures on open
lines and in tunnels.
Under ballast mats: For open lines the tracks with under ballast mats need enhanced
lateral support of the ballast to stabilize the ballast. The under ballast mats on
open lines show some reduced insulation efficiency especially for dam situations in
contrast to tunnels.
Under sleeper pads: First results in Switzerland show that insulation efficiency of
under sleeper pads is very similar for open lines and tunnels and comparable to under
ballast mats on open lines.
Mitigation measures for switches: Measurements of SBB demonstrate that so far a
movable frog for switches is not a satisfying solution for vibration control. Two recent
Swiss studies adjacent to a switch illustrate that the insulation efficiency of trenches is
effective with about 6 dB over a large frequency domain (20/25 Hz to 250 Hz).
Finally SBB proposes a simple cost-benefit-method for vibration and ground-borne
noise similar to a method used in Swiss noise abatement.

This paper studies the efficiency of subgrade stiffening next to the track as a mitigation measure for railway induced vibrations by means of a two-and-a-half-dimensional coupled finite element–boundary element methodology. An analysis in the frequency–wavenumber domain for a homogeneous halfspace reveals that the block of stiffened soil next to the track can act as a wave impeding barrier. It is demonstrated that the wave impeding effect depends on the relation between the Rayleigh wavelength in the soil and the free bending wavelength in the block of stiffened soil, as the transmission of plane waves in the soil with a longitudinal wavelength smaller than the bending wavelength is hindered. This leads to a critical frequency from which this mitigation measure starts to be effective, depending on the stiffness contrast between the soil and the block of stiffened soil. The existence of a critical angle delimiting an area where vibration levels are reduced in case of harmonic excitation on the rail is also demonstrated. Two applications involving a layered halfspace are finally discussed to demonstrate that the performance of this mitigation measure critically depends on the soil characteristics.

This research work aims at evaluating the acoustic performance of conventional and low height gabions noise barriers. On one hand, in situ as well as scale model measurements at a scale of 1:10 have been carried out to assess the intrinsic acoustic properties of a 3 m high gabions barrier. Single number ratings of transmission and reflection indices reached 20 dB and 5 dB, respectively. On the other hand, numerical simulations using a 2D boundary element method (BEM) and scale model measurements are carried out to study the effectiveness of low height gabions noise barriers when they are inserted in dense urban areas. The agreement between numerical and scale model measurements results is satisfactory. The effectiveness of low height gabions noise barriers is significant for receivers of limited height and the insertion loss values can reach 8 dB(A) behind the barrier. This confirms that gabions noise barriers are possible candidates as useful devices for environmental noise reduction.

A mathematical model is presented for ground vibration induced by trains, which uses wavenumber finite- and boundary-element methods. The track, tunnel and ground are assumed homogeneous and infinitely long in the track direction (x-direction). The models are formulated in terms of the wavenumber in the x-direction and discretization in the yz-plane. The effect of load motion in the x-direction is included. Compared with a conventional, three-dimensional finite- or boundary-element model, this is computationally faster and requires far less memory, even though calculations must be performed for a series of discrete wavenumbers. Thus it becomes practicable to carry out investigative study of train-induced ground vibration. The boundary-element implementation uses a variable transformation to solve the well-known problem of strongly singular integrals in the formulation. A `boundary truncation element' greatly improves accuracy where the infinite surface of the ground is truncated in the boundary-element discretization. Predictions of vibration response on the ground surface due to a unit force applied at the track are performed for two railway tunnels. The results show a substantial difference in the environmental vibration that could be expected from the alternative designs. The effect of a moving load is demonstrated in a surface vibration example in which vibration propagates from an embankment into layered ground.

To reduce railway induced low frequency vibration, two mitigation measures - open trenches and buried soft wall barriers have been studied in this paper by using coupled finite element-boundary element models. These models were developed at KU Leuven and ISVR, and have been cross-validated within the EU FP7 project RIVAS (Railway Induced Vibration Abatement Solutions). Variations in the width, depth, location of trench and properties of soft barrier material are considered under various soil conditions. Results show that in all ground conditions, the notional rectangular open trench performs better than the other constructions. The width of an open trench has little influence on its performance, whereas increasing the width of a filled trench reduces the stiffness of the barrier, improving the performance of the trench. Likewise, fill materials with lower Young’s modulus give higher insertion losses.

This paper studies the efficiency of stiff wave barriers for the mitigation of railway induced vibrations. Coupled finite element–boundary element models developed at KU Leuven and ISVR are employed; these models have been cross–validated within the EU FP7 project RIVAS (Railway Induced Vibration Abatement Solutions). A first mitigation measure consists of a block of stiffened soil embedded in a halfspace that acts as a wave impeding barrier. The existence of a critical frequency from which this mitigation measure starts to be effective, as well as a critical angle delimiting the area where the vibration levels are reduced, is demonstrated. Next, a sheet piling wall is considered, accounting for the orthotropic behaviour of this wall. Calculations show that the reduction of vibration levels is entirely due to the relatively high axial and bending stiffness in the vertical direction (along the profiles), while the bending stiffness for bending waves traveling in the longitudinal direction (perpendicular to the profiles) is too low to affect the transmission of vibrations. Field tests are being carried out in Spain and Sweden to confirm the conclusions of these numerical computations.

This paper is aimed at studying the effectiveness of different vibration countermeasures in isolating the ground vibrations induced by trains moving at sub- and supercritical speeds, with respect to the Rayleigh wave speed of the supporting soils. The vibration countermeasures considered herein include the installation of open trenches, in-filled trenches, and wave impeding blocks. The 2.5D finite/infinite element approach developed previously by the authors is employed in this study. This approach allows us to consider the load-moving effect of the train in the direction normal to the two-dimensional profile considered, and therefore to obtain three-dimensional results using only two-dimensional elements. The moving train is simulated as a sequence of moving wheel loads that may vibrate at some specific frequencies. The performance of the three types of wave barriers in isolating soil vibrations for trains moving at sub- and supercritical speeds with various excitation frequencies is evaluated with respect to some key parameters, along with suggestions made for enhancing the isolation efficiency.

The transmission and reduction of vibrations in the far-field of the surface of the ground due to a surface load is investigated theoretically and validated with given field measurement data. The performance of a given stabilization column, located directly underneath the load, at a number of receiver positions is studied and measured in terms of insertion loss. A numerical model is presented, which enables the wave-field in the region of the column to be determined, based on an integral equation formulation of the problem which is solved using a boundary element approach. It is shown that the column has a beneficial effect at low frequencies especially in certain frequency bandwidths and is validated with field data. However, when the Rayleigh wavelength becomes short compared with the depth and width of the column adverse effects occur at some frequencies which are also observed in the far-field. Various depths of columns and material properties of the surrounding soil medium are studied and results presented so that some preliminary physical conclusions may be derived.

The present paper deals with the multiple scattering by randomly distributed elastodynamic systems at the surface of a horizontally layered elastic halfspace due to an incident plane wave. Instead of solving this problem for a particular configuration of the system, multiple scattering theory is used to compute the ensemble response statistics. The Dyson equation is used to calculate the mean field, while the nonstationary second order statistics are obtained by means of the Bethe-Salpeter equation. This allows for the determination of the mean square response of the system in the time and frequency domains. This model is used to study multiple scattering between buildings under seismic excitation. The influence of multiple scattering on the seismic site response is verified. Furthermore, the influence of the footprint and the damping of the buildings are investigated. The results are compared to results of a coupled finite element/boundary element solution for a group of buildings.

Railways are an environmentally friendly means of transport well suited to modern society. However, noise and vibration are key obstacles to further development of the railway networks for high-speed intercity traffic, for freight and for suburban metros and light-rail. All too often noise problems are dealt with inefficiently due to lack of understanding of the problem. This book brings together coverage of the theory of railway noise and vibration with practical applications of noise control technology at source to solve noise and vibration problems from railways. The author has wide experience of dealing with these issues, having developed a wide range of theoretical models as well as dealing with practical problems. It will be found useful by all who have to deal with noise and vibration from railways, whether working in the industry or in consultancy or academic research. * Discusses fully the theoretical background and practical workings of railway noise * Includes the latest research findings, brought together in one place * Forms an extended case study in the application of noise control techniques.

Although the main mechanisms of generating ground vibrations at source, e.g. by rail and road traffic, are now well understood, there are still very few investigations aimed to protect the affected buildings by influencing the propagation of ground vibrations, mainly Rayleigh surface waves, from a source to a receiver. A promising and cost effective method of screening the affected properties can be using heavy masses placed on the ground surface near the roads (e.g. concrete or stone blocks, specially designed brick walls, etc). The principle of operation of such masses is based on the fact that their natural frequencies of vibration, which depend on the mass value and on the local ground stiffness, can be chosen within the frequency range of railway-or road-generated ground vibrations (normally from 5 to 50 Hz). When the mass is shaken under the impact of incident Rayleigh surface waves, it scatters the incident waves into the depth of the ground and at different directions on the surface, thus resulting in noticeable resonant attenuation of transmitted ground vibrations. Using suitable combinations of such mass scatterers, one can expect to achieve efficient vibro-isolation of affected buildings. While some initial efforts have been made in the past to investigate the above-mentioned mass scatterers, largely by means of numerical calculations, very little progress in understanding their behaviour has been made so far. The aim of the present paper is to give a brief introduction to the theory of resonant mass scatterers and to discuss some problems that still need to be considered to achieve a fuller understanding of their operation as means of control of low frequency ground vibrations.

The main motivation of this work is to analyze whether or not the presence of buildings is able to modify the seismic field significantly. We first present a numerical method able to account for a three-dimensional building distribution resting on a layered elastic-half-space. The proposed method is based on a variational coupling between Boundary Elements and modal representation for the buildings. Provided with the hypothesis of a stochastic homogeneous distribution of these buildings or a deterministic periodic one, a realistic model of an entire city may be accounted for. This method is applied to practical situations and it is shown that modifications of the incident field occur mainly for soft layered soils. However from an engineering point of view, it appears that the amplification levels are not significantly modified even in these extreme cases. Nevertheless, a strong scattering of the response inside the city depends on the nearby buildings can be observed.

Vibrations induced by traffic and construction activities cause serious environmental problems. The reduction of the impact of these vibrations on the nearby environment constitutes an important challenge, mainly in urban area. This paper presents both experimental investigation and 3D numerical modeling of the performance of heavy masses technology for scattering the ground vibrations. The efficiency of this method is compared to that of the trench barriers, largely studied in the literature. Analyses show that the heavy mass constitutes an efficient technology for the attenuation of the traffic induced vibrations. The performance of this method depends mainly on the mass weight. An amplitude reduction ratio up to 70% can be reached using this technology.

This paper presents a numerical study developed in order to understand the dynamic behavior of ballasted tracks with mats including the train–track–ground interaction. In order to achieve that goal, a case study is modeled by a 2.5D FEM–BEM formulation. A comprehensive approach is presented and the effects of the mat stiffness and location in depth are discussed. The comparison between isolated and non-isolated scenarios allowed concluding that the ballast mat has a dual effect, focusing on the train–track dynamic behavior and on the reduction of high-frequency vibrations that are transmitted to the ground. Furthermore, it was found that global efficiency can be reached by placing the mat beneath the subballast instead of below the ballast layer.

The main motivation of this work is to analyze whether or not the presence of buildings is able to modify the seismic field significantly. We first present a numerical method able to account for a three-dimensional building distribution resting on a layered elastic-half-space. The proposed method is based on a variational coupling between Boundary Elements and modal representation for the buildings. Provided with the hypothesis of a stochastic homogeneous distribution of these buildings or a deterministic periodic one, a realistic model of an entire city may be accounted for. This method is applied to practical situations and it is shown that modifications of the incident field occur mainly for soft layered soils. However from an engineering point of view, it appears that the amplification levels are not significantly modified even in these extreme cases. Nevertheless, a strong scattering of the response inside the city depends on the nearby buildings can be observed.

Vibration from trains can cause annoyance and also concern about possible damage to property. It is a major issue in the environmental impact assessment of new railways and where new traffic is to be added on existing railways. Track designed to control vibration has been implemented on a number of railways. These designs are effective for vibration at frequencies at the low end of the audible range. Such vibration causes re-radiated noise in buildings and is especially associated with trains in tunnels. However, at present there are no proven, effective solutions for vibration from heavy freight trains. This occurs at lower frequencies (down to about 4 Hz) and can be felt. In an attempt to deal with low-frequency vibration, experimental track has been built containing continuous slabs of concrete. This has shown encouraging results in tests but it is not clear how generally applicable these improvements would be, or even whether the test results were valid. To clarify these matters it is necessary to develop theoretical models. To date, a number of two- and three-dimensional models have been developed at British Rail Research. These are used to investigate the expected performance of different track constructions covering the cases of both re-radiated noise and low-frequency vibration. Experimental work is being carried out in parallel to validate the theoretical approach and to provide data on appropriate material parameters for the ground.

The problem of vibration isolation by a row of piles is numerically solved in a three-dimensional context by an advanced frequency domain boundary element method (BEM). Both the piles and the soil are modelled by boundary elements and coupled together through equilibrium and compatibility at their interfaces. Linear elastic or viscoelastic material behaviour is assumed for both the piles and the soil. The piles can be tubular or solid and have circular or square cross-section. The vibration source is a vertical harmonically varying with time force and the row of piles acts as a wave barrier in a passive way. The boundary element method is first validated for accuracy by solving two three-dimensional wave diffraction problems dealing with spheres and trenches as scatterers for which there are analytical and highly accurate numerical solutions available in the literature. Numerical examples dealing with passive vibration isolation by a row of piles are then solved and the screening effectiveness of these wave barriers is assessed and compared against that of trenches. Copyright © 1999 John Wiley & Sons, Ltd.

Although the main mechanisms of generating ground vibrations at source, e.g. by rail and road traffic, are now well understood, there are still very few investigations aimed to protect the affected buildings by influencing the propagation of ground vibrations, mainly Rayleigh surface waves, from a source to a receiver. A promising and cost effective method of screening the affected properties can be using heavy masses placed on the ground surface near the roads (e.g. concrete or stone blocks, specially designed brick walls, etc). The principle of operation of such masses is based on the fact that their natural frequencies of vibration, which depend on the mass value and on the local ground stiffness, can be chosen within the frequency range of railway- or road-generated ground vibrations (normally from 5 to 50 Hz). When the mass is shaken under the impact of incident Rayleigh surface waves, it scatters the incident waves into the depth of the ground and at different directions on the surface, thus resulting in noticeable resonant attenuation of transmitted ground vibrations. Using suitable combinations of such mass scatterers, one can expect to achieve efficient vibro-isolation of affected buildings. While some initial efforts have been made in the past to investigate the above-mentioned mass scatterers, largely by means of numerical calculations, very little progress in understanding their behaviour has been made so far. The aim of the present paper is to give a brief introduction to the theory of resonant mass scatterers and to discuss some problems that still need to be considered to achieve a fuller understanding of their operation as means of control of low frequency ground vibrations.

When a seismic wavefield impinges on the foundation of a building, the building vibrates and generates waves in the subsoil. In a city, different buildings interact with each other through the scattered waves. The detailed description of the wave propagation in this coupled city–soil system is a complex problem. Instead of solving this problem for a particular city configuration, a statistical description of the city is applied and the limit of a city of infinite size is considered. This leads to a model of the coupled city–soil system, where the buildings are modelled as resonant scatterers that are uniformly distributed at the surface of a deterministic, horizontally layered elastic half-space that represents the soil. The equations that govern the interaction between the city and the soil now become a set of stochastic equations. Based on these equations, the Dyson and Bethe–Salpeter for the configurationally averaged field and field correlation are formulated. The solution of the single scatterer problem is used to obtain an approximate solution of these equations that allows us to quantify the change of the mean site response through the presence of the city and the ratio of the coherent and incoherent response. Furthermore, the influence of the city on the duration of the seismic records is estimated by the approximate solution of the non-stationary Bethe–Salpeter equation. The results obtained for the configurationally averaged field quantities are validated by means of results for the seismic response of a deterministic model of a city quarter of Mexico City.

The project RENVIB has been sponsored by the Union of International Railways to further the knowledge on train-induced ground vibration. The long-term aim is to develop a general model that will predict the vibration caused by trains operating in tunnels and on the surface. A State-of-the-Art survey was carried out during Phase 1 of the project and that is summarized in this paper. This highlighted the lack of standards in the assessment of groundborne noise and inconsistencies in the treatment of low-frequency vibration in other standards. Phase 2 is current and is concentrating on some preliminary validation of existing models using measurement data from national vibration mitigation projects.

Vibration control provisions available to the transit designer include (among others) precision straightened rail, ballast mats, floating slabs and very soft direct fixation fasteners, in addition to rail grinding, wheel truing, and continuous welded rail. Recently, the Los Angeles Metro has developed specifications for a soft resilient direct fixation fastener to fit the same base dimensions as the standard direct fixation fastener. In San Francisco, low resonance frequency (8 Hz) floating slabs have been constructed to mitigate predicted ground vibration impacts at nearby residential structures. In Atlanta, low resonance frequency loading slabs have been constructed to maintain a low vibration environment in a medical building planned to be built over the subway structure. In Portland and Pasadena, ballast mats have been recommended to control light rail transit ground vibration impacts on housing located at typically 35 feet from the alignment. Each of these provisions are briefly described in view of recent applications at U.S. transit systems.

This paper outlines a test program in southern Sweden for measurement of the vibration induced in the ground and railway embankment by high-speed trains, together with a rigorous numerical model developed for the prediction of embankment/ground response. In this formulation the ground is modeled as a layered viscoelastic half-space, and the railway embankment is modeled as a viscoelastic beam excited by the moving loads of the train. The model uses the Kausel-Roeesset Green's functions to calculate the soil stiffness matrix at the ground-embankment interface and assembles it with the dynamic stiffness matrix of the embankment. The solution is carried out in the frequency domain, and the time histories of the motions are derived through a Fourier synthesis of the frequency components. Numerous simulations of train-induced vibration are presented for the ground conditions and embankment parameters at the test site and compared with measured records. The simulations agree well with the measurements, both in qualitative and quantitative terms. In particular, the large ground deformations registered for train speeds exceeding 140 km/h are reproduced by the simulations. With the help of the prediction model, the effectiveness of a remediation measure for the mitigation of ground vibration is explored.

Ground-borne vibration has existed ever since the development of urban road and rail networks. Vibration generated by the moving traffic propagates through the ground and into buildings, resulting in unacceptable levels of internal noise and vibration. A common solution to this increasingly significant problem is the base-isolation of buildings by incorporating vibration isolation bearings between the buildings and their foundations. This technique has been employed for over forty years but the exact performance of base isolation remains uncertain.
This paper describes a generic computational model; generic in that it accounts for the essential dynamic behaviour of a typical base-isolated building in order to make predictions of isolation performance. The model is a linear one, formulated in the frequency domain, and consists of a two-dimensional portal-frame model of a building coupled to a three-dimensional boundary-element model of a piled-foundation. Both components of the model achieve computational efficiency by assuming they are infinitely long and using periodic structure theory.
Following an overview of the model, a virtual case study is presented to illustrate its practical application. Along with some initial observations, the case of a point-load surface excitation of the foundation is used to investigate the isolation performance of typical isolation bearings.

The ElastoDynamics Toolbox (EDT) version 2.1 offers an extensive set of MATLAB functions to model elastodynamic wave propagation in horizontally layered media. The toolbox is based on the direct stiffness method and the thin layer method. These methods provide stiffness matrices for a homogeneous layer and a homogeneous halfspace, which are formulated in the frequency-wavenumber domain. EDT 2.1 can be used to solve a variety of problems governed by wave propagation in the soil, such as (1) site amplification, (2) the computation of dispersive wave modes in layered soils, and (3) the calculation of the forced response of the soil due to harmonic and transient loading. The toolbox serves as an electronic learning environment for the simulation and processing of seismic wave propagation in layered media. It has also been used by various authors to model wave propagation in layered soils

The attenuation of Rayleigh waves due to their interaction with resonating structures randomly distributed on the surface of a semi-infinite elastic medium is calculated along with the Rayleigh wave frequency. The resonating structures are modeled by single oscillators coupled to the displacement field at the surface of the elastic medium. Using the coherent potential approximation, the dependence of the frequency and damping constant of the Rayleigh waves on wave vectors are determined for various values of the concentration of oscillators on the surface.

The problem of vibration isolation by a row of piles is numerically solved in a three-dimensional context by an advanced frequency domain boundary element method (BEM). Both the piles and the soil are modelled by boundary elements and coupled together through equilibrium and compatibility at their interfaces. Linear elastic or viscoelastic material behaviour is assumed for both the piles and the soil. The piles can be tubular or solid and have circular or square cross-section. The vibration source is a vertical harmonically varying with time force and the row of piles acts as a wave barrier in a passive way. The boundary element method is first validated for accuracy by solving two three-dimensional wave diffraction problems dealing with spheres and trenches as scatterers for which there are analytical and highly accurate numerical solutions available in the literature. Numerical examples dealing with passive vibration isolation by a row of piles are then solved and the screening effectiveness of these wave barriers is assessed and compared against that of trenches. Copyright © 1999 John Wiley & Sons, Ltd.

Although railway-generated ground vibrations usually have greater energy levels at lower frequencies, vibrations in the audible range above 20 Hz can nevertheless be relevant for secondary noise problems in buildings. One countermeasure is soil stabilization under the track embankment. While effective at low frequencies, a potential side effect is amplification in some audible bands. Presented here are both experimental and theoretical assessments of the countermeasure in the audible bands. The main innovation is the treatment of an infinite periodic track–ground system, using a transfer matrix approach with a repeating element including the rail, pad, sleeper, and an underlying half-space (ballast and soil). Excitation in this band is attributed to rail and wheel roughness. The model makes successful predictions when the half-space properties are allowed to be frequency-dependent such that the dispersion of the surface wave matches that in the actual layered earth (including ballast and underlying soil layers). The field measurements are also unique in that both before and after evaluation of the countermeasure was possible.

Trains running in built-up areas are a source to ground-borne noise. A careful design of the track may be one way of minimizing the vibrations in the surroundings. For example, open or infilled trenches may be constructed along the track, or the soil underneath the track may be improved. In this work, the influence of the track design and properties on the level of ground vibration due to a vehicle moving with subsonic speed is examined. A coupled finite element-boundary element model of the track and subsoil is employed, adopting a formulation in the moving frame of reference following the vehicle. The computations are carried out in the frequency domain for various combinations of the vehicle speed and the excitation frequency. The analyses indicate that open trenches are more efficient than infilled trenches or soil stiffening–even at low frequencies. However, the direction of the load is of paramount importance. For example, the response outside a shallow open trench may change dramatically when horizontal load is applied instead of vertical load.

This paper presents a general 2.5D coupled finite element–boundary element methodology for the computation of the dynamic interaction between a layered soil and structures with a longitudinally invariant geometry, such as railway tracks, roads, tunnels, dams, and pipelines. The classical 2.5D finite element method is combined with a novel 2.5D boundary element method. A regularized 2.5D boundary integral equation is derived that avoids the evaluation of singular traction integrals. The 2.5D Green’s functions of a layered halfspace, computed with the direct stiffness method, are used in a boundary element method formulation. This avoids meshing of the free surface and the layer interfaces with boundary elements and effectively reduces the computational efforts and storage requirements. The proposed technique is applied to four examples: a road on the surface of a halfspace, a tunnel embedded in a layered halfspace, a dike on a halfspace and a vibration isolating screen in the soil.

This paper presents the experimental validation of a numerical model for the prediction of train induced vibrations. The model fully accounts for the dynamic interaction between the train, the track and the soil. The track geometry is assumed to be invariant with respect to the longitudinal direction, which allows for an efficient solution of the dynamic track–soil interaction problem in the frequency–wavenumber domain. The model is validated by means of several experiments that have been performed at the occasion of the homologation tests of the new HST track on the line L2 between Brussels and Köln. A first set of experiments is used to determine the dynamic soil and track characteristics. In a second set of experiments, the soil transfer functions, the track–soil transfer functions and the track and free field vibrations during the passage of a Thalys high speed train have been measured. These results are used for a step-wise validation of the numerical model that is based on the identified model parameters and allows to study the propagation of errors in the prediction model.

A full 3D analytical approach is adopted to account for trenches on one or both sides close to a railroad. Low-frequency ground vibrations are investigated due to the passing of trains, and open trenches are used as wave barriers. The modelling technique is based on Fourier transforms and Fourier series. The ground is modelled as a layered semi-infinite domain and the embankment with finite layers. The trenches are obtained by simulating the upper surface layer with two or three finite rectangular regions with appropriate widths. A particular boundary condition is adopted at the vertical sides of all finite regions to enable the solution procedure. Rails and sleepers are accounted for with Euler–Bernoulli beams and an anisotropic Kirchhoff plate with transversal isotropy. The wheel loads from the boogie wheel pairs of the train are simulated as moving forces. Hence, no irregularities in rails or wheels are accounted for.

Ground vibration is an important aspect of the environmental impact of rail traffic. Vibration from about 2–200 Hz is caused by trains moving on the ground surface or in tunnels. The wave field thus created must be modelled in three dimensions because of the excitation under each axle and the movement of the train. For arbitrary geometry of structures and ground surface to be allowed in the analysis, numerical models are required. In most practical situations, the ground and built structures, such as tunnels and tracks, can be considered to be homogeneous in the track direction and may be modelled using the wavenumber finite/boundary element method which is formulated in terms of the wavenumber in that direction. Compared with a conventional, three-dimensional finite/boundary element model, this model is more computationally efficient and requires far less memory since discretization is only made over the vertical–transverse section of the ground and/or built structures. With this model it is possible to predict complete vibration spectra. In this paper, the wavenumber-based modelling approach is outlined and then the applicability of the method to surface vibration and tunnel vibration analyses is demonstrated.

Vibrations induced by the passage of trains are a major environmental concern in urban areas. In practice, vibrations are often predicted using empirical methods such as the detailed vibration assessment procedure of the Federal Railroad Administration (FRA) of the U.S. Department of Transportation. This procedure allows predicting ground surface vibrations and re-radiated noise in buildings. Ground vibrations are calculated based on force densities, measured when a vehicle is running over a track, and line source transfer mobilities, measured on site to account for the effect of the local geology on wave propagation. Compared to parametric models, the advantage of this approach is that it inherently takes into account all important parameters. It can only be used, however, when an appropriate estimation of the force density is available. In this paper, analytical expressions are derived for the force density and the line source transfer mobility of the FRA procedure. The derivation of these expressions is verified using a coupled finite element–boundary element method.

Use of numerical models to determine the effectiveness of anti-vibration systems for railways

- C J C Jones

C.J.C. Jones. Use of numerical models to determine the effectiveness of
anti-vibration systems for railways. Proceedings of the Institution of
Civil Engineers-Transport, 105(1):43-51, 1994.

Theory manual for WANDS 2.1. ISVR Technical Memorandum 975

- C.-M Nilsson
- C J C Jones

C.-M. Nilsson and C.J.C. Jones. Theory manual for WANDS 2.1. ISVR
Technical Memorandum 975, University of Southampton, 2007.