In order to suppress and/or reduce the negative effects of ground-borne noise and vibration, different mitigation measures have been analysed and tested in the past years. These improvements can be applied to new infrastructure and/or existing ones, the different methodologies are to be compared both with their feasibility and the costs to be able to use them most conveniently. For the purpose of this research and to give a complete understanding of the state of the art of these improvements. In this section, the major available technologies will be illustrated and discussed exhaustively.
The mitigation systems can be applied in all three parts of the railway system, on the vehicle, on the track and on the transmission path (that is generally soil). It is also possible to make improvements directly at the receivers (i.e., buildings). Many of those have been tested in laboratories using full-scale and scaled models. But it comes out, due to the nature of the problem, that computer simulations after calibration using the experience from real projects are the right solution to proceed feasibly and competitively concerning physical models.
For simplicity, in this paper, the parts of the railway environment (where the mitigation measure are possible) are subdivided into four main subsystems: vehicle, track, transmission path, and receiver. Based on the different rail systems, the characteristics of the aforementioned components change from one to another. In literature are mainly subdivided in terms of new and retrofitting of existing lines, or in terms of surface and the underground lines.
Improvement in the vehicle
The vehicle dynamics play a crucial role in the generation of the ground-borne effects, principally when irregularities are present at the wheel-rail contact [87,88,89].
These days, rail vehicles are constructed using bogie system technology, with a single and double suspension, for the freight and passenger trains, respectively. Primary suspensions connecting the wheelsets to the bogie frame and are made with coil or rubber springs. Secondary suspension systems, located between the bogie and the car body, consist of elastomer elements, air spring or metal spring. Wilson et al.  demonstrated that a proper design of the bogie suspension can significantly reduce the levels of ground vibration. In general, vehicles with soft primary suspension produce lower levels of vibration than vehicles equipped with stiff suspensions [91,92,93]. It is also important to highlight that the way in which the vehicle affects the generation of the vibrations depends on the type of train and the technology that is used.
Despite the importance of the vehicle design parameters toward the generation of the ground-borne noise, the majority of efforts and research have been focusing on the other two sub-systems (track and ground) of the railway environment, which will be discussed later in Sects. 4.2 and 4.3. This is because the manufactures of trains focus on the car design within the ride comfort, stability and gauge in order to enhance the passengers’ pleasure (see Table 2).
Therefore, the different measures that can be applied to the means of transportation have to deal with the reduction of the effects of the rail passage but at the same time have to maintain the train passengers comfort at the highest standards. The importance of improvement of the vehicle is crucial for the ground-borne vibration since this effect is arising between the track and wheel contact, with the latter being a component of the train.
The principal measures to control and/or mitigate the ground-borne vibration coming from the vehicles will be presented in the sub-section and are the following:
Improving wheel roundness,
Reduction of the unsprung mass,
Reduction of speed,
When the main contributor in the vehicle is identified, it is possible to design the vehicle so as the dynamic forces acting on the track are reduced. It should be noted that wheel out of roundness and the unsprung mass of a single wheel are often the dominant excitation mechanisms .
Improving wheel roundness
Wheels out of roundness are one of the main causes of excessive vibration and are the result of the manufacturing process or repeated loading at high frequencies . The most common manifestation is the formation of wheel flats, caused primarily by train breaking/deceleration, and this results in high-frequency impact force whenever the corners of the wheel flat impact the rail during the rotation. Instead, Fig. 7 shows an example of wheel polygonalization in the first-, second- and third-order. The orders here are just taken as a reference. However, these can increase up to 23rd as reported by Wu et al.  or even more.
This can be achieved with good maintenance of the wheels, improvement of the sliding protection and steel quality. In particular, re-profiling, a high-quality wheel grinding program ensures the reduction of noise levels in the range of 5 to 10 dB.
Reduction of the unsprung mass
The unsprung mass is defined as the set of the loads generated by suspensions, wheels and bogies frames. This mass laying directly on the rail beams is the main cause of the damage to the tracks. Therefore, its reduction becomes relevant in terms of track and infrastructure damage and consequently with respect to the reduction of the vibrations level. However, the decrease of this mass is difficult to achieve due to safety criteria, wheels life and the vehicle dynamics design.
The wheel-set mass is generally in the range of 700–3500 kg, from small-diameter wheels on freight wagons to large diameter locomotive wheels. Its reduction can be obtained by the optimization of the cross-section in its shape and/or material and is generally limited to 5%–10% of the nominal wheel mass, with which is possible to achieve a vibration reduction of 2–4 dB in the long-term . In addition, the reduction of the radial thickness would reduce wheel mass significantly but at the same time influence the number of re-profilings, wheel life and production costs.
Reduction of speed
A central role in the generation of ground-borne noise and vibration plays vehicle speed. Therefore, as its value changes the amount of ground-borne vibration and noise is affected. In particular, by reducing the train speed by a factor of two it is possible to reduce vibration levels approximately up to 6 dB .
For example at the beginning of the 1990s in the project of the high-speed trains (HST) at Ledsgard (Sweden) , different interventions were made in order to mitigate the generated vibrations. Traffic with HST started in spring 1997 with a speed of 200 km/h. Shortly afterwards, excessive vibrations were observed in some sites. These vibrations were in the order of ten times greater than those measured earlier from heavy train traffic in soft soil conditions and had been regarded as the worst case. Train speed was reduced to 160 km/h and later to 130 km/h. Thanks to these reductions of the operational speed of the HST line from 190 to 130 km/h it was possible to achieve an IL of 26 dB at 12 meters from the source, as reported in Fig. 8.
In general, when the train speed is approaching the Rayleigh wave speed of the transmission path it is possible to have considerable growth in the track vibration and consequently an increase in the ground-borne effects [98, 99] as in the case of the aforementioned Ledsgard project. Experimental demonstration of these effects has been redrawn for three sites located in Sweden, UK and Netherlands, by Connolly et al. [64, 100] as depicted in Fig. 9. It is straightforward that as the normalized speed (train velocity/Rayleigh wave speed) approaches unity, the track displacement increases exponentially.
In addition to the speed of the train, many other factors influence the vibration propagation, such as types of railway vehicles, transport type (passenger or freight), track type and others . In particular, this has been discussed by Thompson et al.  that presented a prediction of the wavefield generated by a point load of constant unit amplitude for three load speeds: 80, 168 and 250 m/s as depicted in Fig. 10.
Figure 10a shows the wave-field generated by the load moving at a speed that is below the wave phase velocities of the surface waves, here the wave speed is very low. Whereas, when the load speed is close to the Rayleigh wave speed of the upper layer, in Fig. 10b, the wave-field generated changes and the displacement amplitudes are significantly larger. If the velocity increase up to 250 m/s, as in Fig. 10c, the waves generated travel with significant amplitude away from the load.
Therefore, in order to get advantages from the reduction of the speed would be necessary to find the less impacting speed during the motion, depending on the type of train, type of transmission path (that will be discussed in Sect. 4.3), and other components. Even if vibration levels can be reduced up to 6 dB, the numerous factors involved in the process do not make speed reduction among favourite choices when developing mitigation systems. On the other hand, a disadvantage of this approach is that it has a high cost in a long time because the line capacity is reduced.
Resilient wheels are more effective in eliminating wheel squeal on tight turns where reductions of 10–20 dB . However, it is also possible to have a reduction in vibration in the range of 3–6 dB.
Figure 11 shows the positive effect of changing the stiffness of resilient wheel equipping trams in order to reduce the transmitted ground vibrations, in terms of IL, notice that the standard wheel have a stiffness of 145 MN/m decreased in the illustrated case to 13 and 18 MN/m. This also demonstrates the real interest of a compound vehicle-track-soil model in the design of this kind of wheel .
Improvement in the track
In urban areas where the railway effects are of more concern, it is quite logical and straightforward to understand that mitigation measures at the source (vehicle and wheel-track) are more convenient than the ones applied both in the path (ground) and in the receiver (surrounding resident and constructions). This is for the reason that by mitigating at sources all the surrounding receivers are protected, while with the protection at the receivers it is necessary to produce a system for each receiver. On the other hand, in areas where we have less neighbourhood might be convenient to intervene in the receiver.
Keeping the conflicts that the design of the vehicle could have in terms of internal comfort, and the generation vibration the improvements in the track achieves a crucial role in the quest to mitigate negative effects coming from the rail traffic. Additionally, as it can be seen in Fig. 12, among the numerous dynamic excitations that contribute to railway vibrations, the excitation due to the vehicle are found at low frequencies, and the excitation associated with the wheel, rail and track is found at higher frequencies.
Before introducing the improvements that can be applied to the track, it is worth to briefly present the track system and its component :
Rail is the main part of railway track, acts as two parallel lines.
Rail pad is designed between the sleeper plate and foot of the rail, generally made by an elastic polyurethane mat. Together with spikes and the fasteners joining the steel rails to the sleepers.
Sleepers is laid perpendicular to steel rail. Railway sleeper can be properly deformed to trimmer pressure when the train passes through and are generally of three types (wooden, steel and concrete sleeper).
Ballast bed is a layer of free-draining coarse aggregate used as a bed elastic support for sleepers.
An important factor for the ground-borne effects is the overall track stiffness. Indeed if too low there is an increase in the deformation of the soil and ballast, while on the contrary when the stiffness is too high a corrugation is easier to be generated . Additionally, if the stiffness has radical fluctuations over the track section then also in this case track deterioration and vibration are increased . The values of stiffness change from country to country based on types of traffic that are expected (e.g., freight or passenger transport), consequently it is difficult to fix an ideal value of the stiffness since generally, the lines host various types of trains. Therefore, track imperfection and degradation (not only due to track stiffness) are crucial to the track vibrations.
Therefore, a correct selection of these elements (rail, fastening, sleepers, ballast) plays a central role in diminishing the formation and propagation of vibration. Increasing the flexibility of the superstructure components raises their ability to damp (dissipate) vibration generated at wheel-rail interface .
The irregularity in the track and the ballast can be an important source of vibration. Indeed, a good track alignment can provide a 10 dB reduction for the ground-borne noise for speeds at 320 km/h, therefore, maintenance to the rail plays an important role in the vibration mitigation.
Embedded rail systems are also an alternative (Fig. 14d), typically used in urban tram lines. In these systems, the rail is embedded in a concrete slab which is then either filled by pouring out elastic embedding material (at the bridges steel moulds are applied) or by the installation of prefabricated rubber parts around the rail web, with a wedge on either side to keep the rail in place. Eszter et al.  showed that the elimination of metal-to-metal contact contributes to a reduction up to 8 dB in the frequency range 5–200 Hz; Whereas, Lakušić et al.  showed a vibration reduction between 12.9 and 18.6 dB in a tram line after implementation of continuously embedded rails depending on the tram vehicle type.
Rail dampers can also be used for vibration mitigation. These are prefabricated passive elements in steel material, which are fixed to both sides of the rail web serve to reduce the vibration of the rails. Rail dampers are usually installed between every sleeper in problematic areas of the track. Studies conducted by German (DB) and French (SNCF) Railways, at the rail track sections with rail dampers installed, showed an in vibration up to 9 dB .
Rail fasteners are used mostly, even if several improvements have been made over the years are the one presented a long time ago, named resilient rail fasteners. However, with the recent application of new designs where the rail is supported by resilient blocks such as in the Thameslink project in London, it has been possible to have a reduction of 13 dB in ground-borne noise .
Additional studies have demonstrated that high resilience fastening systems (Fig. 13a), in which elastic elements supporting the rail at the web prevent direct contact between the rail foot and sleeper, allows significantly greater vertical deflection of the rails under operation, gaining a low vertical stiffness of the entire system that reduces vibrations by 5–10 dB at frequencies above Hz . Instead of rail fasteners with a highly resilient under base-plate pad (Fig. 13b), where the resilient pad is pre-compressed with a load equivalent to 80% the normal static load on the fastener during vehicle passage , vibration isolation of 20 dB is ensured with range frequency between 25 and 20 Hz , to notice that in this last case the spring is unloaded during the train passage and as a result, there is no vibration transmission to the lower parts of the track.
Sleepers and ballast enhancements
The sleeper can be installed in concrete or wood. Concrete sleepers are the most used type because of different economical advantages (simpler installation, greater durability, lower maintenance and operation costs), but wooden sleepers present a higher vibration damping capacity [113, 114]. The studies made by FTA  showed a vibration reduction by 5 dB when using wooden sleepers.
At the same time, there are also other important improvements that can be done just under the track in order to achieve vibration attenuation, such as by placing the elastomeric pads between the sleepers and the ballast bed. This elastomeric pad is usually composed of two layers of different material, the upper made by viscoelastic rubber with high vibration damping ability and the lower layer is a coarse geotextile that serves to prevent possible upper layer damage from impressing of crushed ballast material .
UIC stated in  that for pads under the sleepers a reduction of 8–20 dB can be archived. These pads have the advantage that they are easy to install during a sleeper renewal operation since they are delivered already fixed to the bottom of the sleeper . Whereas, for the ballast mats (that can be applied to both the surface and underground systems) the reduction ranges from 3 to 15 dB. However, if a ballast mat is too soft there is a risk that the ballast layer becomes more feeble when solicited to the vibration produced by the passing train. Therefore, this could compromise the ride quality unless rigorous maintenance is performed (increasing in costs) .
Alternative track technologies
In the track improvements, the technology of the track itself plays a crucial role and, in addition to the classical ballasted track, there are other approaches with different track design concepts projected in order to mitigate the ground-borne noise and vibration.
The most common measures to mitigate the ground-borne effects in ballasted track presented above and some possible alternatives (which will be presented further down) are depicted in the order of cost upwards from top to bottom, in Fig. 14.
In reference to vibration damping, track structures with ballast bed are better than the track structures on special reinforced concrete slabs the commonly named slab tracks (where the ballast is replaced by a rigid concrete track slab which transfers the load and provides track stability), with up to 3–5 dB of enhancement . The main disadvantage of this type of track construction, compared with tracks laid in ballast bed, is its greater rigidity, which results in increased vibrations. Further reduction of the vibration propagation can be achieved by increasing the height of the ballast bed, the German Railways (DB)  showed that an increase in the ballast bed height from the usual 30 to 75 cm can reduce the vibrations by 6 dB at frequencies lower than 10 Hz.
Another alternative to ballasted tracks is the floating-slab tracks. These are special types of slab tracks with the so-called mass-spring systems principle, here the track is mounted on a thick concretes lab that rests on rubber bearings, glass fibre or steel springs. With such designs, the highest possible mass is added above the track spring to form a system with a very low resonance frequency.
Floating-slab tracks are typically used to manage the vibration and ground-borne noise from underground trains where a large reduction is required . As well as the greater construction cost of the track form itself, the great expense can come from any increase in the diameter of the tunnel that has to be made to accommodate sufficient mass for the floating lab. The slab may be cast in-situ, resulting in a continuous piece of concrete, or maybe constructed in discrete precast sections laid end to end. Continuous slab designs usually have a lower deflection for a given resonance frequency and make maximum use of the tunnel space but have the disadvantage that they are harder to design in such a way that the slab mounts can be replaced .
Studies have shown that the natural frequency of such structures lies between 8 and 12 Hz, depending on the material used and the total weight of the structure. The application of floating slaps and other mass-spring systems allows the vibration reduction by 10 dB with frequencies above 16 Hz or by 25 dB with frequencies of 125 Hz . Whereas vibration measurements performed on a floating track with ballast bed and spacing of the springs in 3,7 m showed that the system has 90% vibration isolation efficiency, and the transmission loss was about 40 dB between 10 and 100 Hz frequency .
This measure of allocating the rail line in tunnels has the greatest reduction of noise and vibration and can achieve up to 40 dB as aforementioned [107, 119]. However, this technology can present some limitations due to the high costs of construction, service and maintenance of the tunnel.
An additional measure, that plays an important role when dealing with ground-borne vibration and noise mitigation, is the dynamic vibration absorber (DVAs) [27, 120,121,122]. DVA is a vibration system that combines dampers and springs, to absorb and dissipate the vibration energy, the rubber layers bonded with the rail waist are mainly used to perform as the distributing elastic components of the DVA; the steel plates are used as the quality layer and the constraints layer to form the distributing power quality of DVA, together with the rubber damping layer. Then the distributing elastic components and distributing power quality can jointly constitute a set of distribution parameters of the dynamic vibration absorber. The DVA can absorb the vibration and prevent the noise radiation when the rail waist is vibrating . The DVA system can be an effective measure to address the ground-borne effects and can reduce between 5.3 and 6.6 dB depending on the type of soil and the train speed .
Improvement along the path
Another important part of the rail environment, where it is possible to intervene in order to mitigate the effects of rail traffic, is the transmission path. Here, the elastic waves travel from the source to the receiver (see Sect. 2.2). In most cases, when referring to the transmission path we have soil and/or rock materials.
Measures in the transmission path are typically applied in the surface train, where surface waves are the main contributor for the ground-borne effects, because for the P- and S-waves and the parts of the buildings that are below the ground level these measures would not be worthwhile. The aim of the measures insert between the track and the adjacent building is to act as a barrier, diverter or damper of the vibration waves that travel from the source with the scope of minimizing and/or cancel their effects at the receiver.
In literature, there are different methods/technologies that can be applied between the source and the receiver, here to follow an introduction of the most common.
Increasing the distance
An obvious and effective way to reduce ground-borne noise and vibration is by augmenting the distance between the track and the receiver. However, this measure is applicable only in some cases when urbanization permits it, and the cost of the free land is cheaper than other mitigation measures. At a distance of 500 m from the rail track, people no longer perceive the rail traffic vibrations [124, 125]. The Federal Transit Administration  gives some guidelines on how to calculate the velocity levels according to the distance from the source.
Embankments are constructions that allow railway lines to pass at an acceptable level and gradient over low lying ground. Their principal and the original role was to keep track horizontally. However, their use is showing good behavior in the mitigation of ground-borne effects coming from the railway traffic. A prediction model was presented by Connolly et al.  and Ju et al. .
Studies such as the one did by the FRA  showed that by situating rail tracks on an embankment, a reduction of noise at the point of emission for up to 5 dB(A) can be achieved if the height of the embankment is at least 3 m . Whereas, Olivier et al.  demonstrated how the subgrade configuration affects the transmission path: embankment with specific material stiffness can play the role of a waveguide by trapping energy within it (Fig. 15). The latter was confirmed by other studies that demonstrated similar results [126, 130, 131].
The barrier is generally an introduction of material or geometry without material as in the case open trench in the soil between the source and the receiver that thanks to its characteristics such as density, stiffness, weight, etc., are able to deviate/damp the waves. Different barriers are available with different shapes and materials.
The use of open trenches (cuts in the soil filed with air as depicted in Fig. 16a), to moderate the effects of ground vibration is a methodology that is commonly used , that acts by diffracting below the barrier the vibration waves as the acoustic barrier with air-borne sound. Studies have shown that the reduction in vibration at a frequency of 30 Hz requires a minimum trench depth of 4.5 m . Good results are obtained when the depth of the trench is at least half the Rayleigh wavelength; for example, Thompson et. al  obtained a reduction of 12 dB with a trench depth of 0.6 times the wavelength of Rayleigh waves.
Open trenches are limited to a certain depth due to stability reasons and the presence of water that can compromise their operation. Therefore, it can be useful to use soft or stiff material (see Fig. 16b) to fill the trench. The material used to feel the trench should be as low as possible in order to limit the transmission of the vibration.
For soft wave barriers among the ones that are available in the literature:
Gas cushions, reduction around 6–10 dB when the depth is equivalent to the wave length ,
Rubber chips, express a high reduction that exceeds 12 dB ,
Polystyrene, at 20 Hz reduction of 12 dB and at 40 Hz reduction of 6 dB ,
Water, named also ditches not deeper than 2–5 m have an effectiveness of up 3 dB .
For the stiff wave barriers, the stability is not anymore a problem as in the previous type of barriers . For these categories of barriers, the following materials are used:
Steel and concrete piles (as in Fig. 16e), depending on the number of pile and cross-section, the reduction is around 80%–90% of the open trench .
Sheet pile wall, at 25 Hz the insertion loss values around 3 dB .
Jet grouting wall, vertical vibration up to 45% were achieved at distances up to 60 metres from the track .
An alternative solution to limit the propagation of vibration waves in urban areas where it is not possible to develop trenches is underground barriers near the rail track. These barriers are generally obtained by mixing live lime or cement into the existing soil.
In a similar way, phononic crystal barriers represent a promising innovative anti-vibration method . Those are also well-developed for the acoustic barriers (air-borne noise), but their use to contrast the ground-borne effect is coming out in recent times. Generally, the barriers consist of a periodic buried structure, made of stiff inclusion (e.g., concrete), this organization produces the so-called crystal effect that manipulates the vibration waves. Albino et al.  for example have demonstrated that attenuation up to 18 dB can be reached that is next to the values that can be achieved by using a wall (that on the contrary is much more expensive). Castanheire-Pinto et al.  played with the orientation of the inclusions, and they proved that is less effective to arrange the inclusion vertically since doing so the wavefront hits all the inclusions at the same time not allowing the sonic crystal effect to be triggered.
In addition to these, other mitigation measures can be inserted in this section, even if some differences are present. The wave impeding blocks (represented in Fig. 16c) are stiff inclusions placed under the railway track horizontally to modify the wave propagation in the soil [140, 141].
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 , it is possible to have an attenuation of vibration at frequencies above the resonance frequency of the masses on the ground stiffness . 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 .
It is also possible to mitigate the ground vibration intervening in the geotechnical proprieties of the soil around the track, either under the track, by stiffening the sub-grade as depicted in Fig. 16f, in order to improve the bearing capacity and therefore reducing ground vibration  (but they are not practical since need interruption of railway operation), or between the source and the receiver by performing various methods of soil stiffening (lime modification, lime injection and jet grouting) it is possible to get improve the soil absorption capacity. Research has shown that reducing the coherence of the soil allows reducing vibration by 14 dB within the frequency of 4–32 Hz .
In addition to all the mitigation measures that can be applied within the transmission path, one should consider the exact soil characteristics since these have a direct relationship with the propagation of the waves. Degrande investigated through in situ measurements and numerical calculations , the relationship among the soil characteristic, waves velocity and their frequencies at a different distance.
Improvement at the receiver
The last element part of the railway environment affected by the effects is the receiver, generally buildings where vibration is perceived. Generally, in construction, mitigation measures are applied for vibration waves much more severe than the ones coming from the rail, such as anti-seismic devices . In railway, precedence is given to the mitigation measures at source and in the transmission path (presented previously), in view of the fact that these are more effective and economical .
However, the relevance and advantages of applying the measures before reaching the receiver. Sometimes, for example with a new building near an existing railway and/or insensitive spaces (such as theatres, concert halls, historical buildings), it is necessary to introduce base isolation within the building itself .
There are different factors that influence levels of ground-borne vibration and noise at the receiver level. Such as the foundation type and the building construction, where generally applies rule-of-thumb i.e., the more massive the foundation (or building), the lower the levels of ground-borne vibration; and the amount of acoustical absorption in the receiver room that affects the levels of the ground-borne noise .
The measures that can be applied are different. At the foundation level, it is possible for example to introduce a vertical elastic layer around the foundation in order to create protection around it and protect it from vibration waves, a reduction between 2 and 6 dB for ground-borne noise can be obtained. At the same level for new sensitive buildings, a resilient bearing, which generally consists of steel coil springs or elastomeric bearings, can be introduced in the foundation (generally for underground lines), in this case, the reduction can reach 20–26 dB both for vibration and ground-borne noise. Whereas at the construction level for one-storey buildings. it is possible to stiff the ground floor by using piles (reduction up to 2 dB), or in addition in case of wooden floors, the stiffness of the floor can be improved by inserting additional beams to support the floor (reduction up to 20 dB) .
The improvements mentioned above have generally a considerable interaction with surrounding existing construction, and their cost in some cases increases exponentially especially when the proposal is to apply them to the existing building. This is an additional reason that makes them the last choice in the available mitigation techniques.