Sustainability of Vibration Mitigation Methods Using Meta-Materials/Structures along Railway Corridors Exposed to Adverse Weather Conditions

Abstract

Noises and vibrations caused by operating transport systems can seriously affect people’s health and environmental ecosystems. Railway-induced vibrations in urban settings can cause disturbances and damages to surrounding buildings, infrastructures and residents. Over many decades, a number of mitigation methods have been proposed to attenuate vibrations at the source, in the transmission path, or at the receiver. In fact, low-frequency or ground-borne vibration is turned out to be more difficult to be mitigated at source, whilst some attenuation measures in propagation path can be applicable. To broaden the mitigating range at the low-frequency band, the applications of meta-materials/structures have been established. In railway systems, periodic structures or resonators can be installed near the protected buildings to isolate the vibrations. Despite a large number of proposed attenuation methods, the sustainability of those methods has not been determined. Based on rational engineering assumptions, the discounted cash flows in construction and maintenance processes are analysed in this study to evaluate lifecycle costs and the quantity of materials and fuels, as well as the amount of carbon emissions. This study is the world’s first to identify the efficacy and sustainability of some transmission path attenuation methods in both normal and adverse weather conditions. It reveals that geofoam trenches and wave impeding blocks are the most suitable methods. Although metamaterial applications can significantly mitigate a wider range of lower frequency vibrations, the total cost and carbon emissions are relatively high. It is necessary to significantly modify design parameters in order to enable low-cost and low-carbon meta-materials/structures in reality.

1. Introduction

Railway systems have been regarded as one of the most sustainable and safest public transport modes. Since railway systems have expanded rapidly in many countries, some railway lines have been built in urban areas and surrounded by buildings and infrastructures. The disturbances caused by railway vibrations to the surrounding residents and buildings have raised special public attention. Railway vibrations can affect passenger ride comfort, and low-frequency vibrations can cause structural damages to the buildings, tunnels, and buried infrastructures near the railway lines [1]. To attenuate ground vibrations along railway corridors, some mitigation methods have been proposed and implemented in the industry. However, it is difficult to identify and select an optimal method in real-life practical situations due to the lack of detailed assessments about cost efficiency, sustainable values, and environmental impacts throughout their lifecycle [2].

To compare the effectiveness and sustainability of the mitigation methods in terms of lifecycle cost and carbon emissions, the sources of railway vibration and the types of attenuation methods need to be identified first. The railway vibration is mostly generated at the wheel-rail contact surface and transmited from the track to subgrade, formation and bedrock. The dynamic loads from the rolling stock cause the waves to propagate into the ground, especially when the wheel-rail interface is irregular or when significant defects exist. When the railway vibration penetrates through the ground and causes secondary vibration generation (e.g., through ground amplifcation, from tunneling pipes, etc.), this vibration effect is often referred to as ground-borne vibration [3,4]. The amplitude and frequency of railway vibrations mainly depend on the condition of trains and tracks and the ability of the soil layers to transmit and absorb dynamic impacts. Based on dynamic amplification factors, geological condition, and the mitigating locations, the attenuation methods can be classified into three categories, including: (i) mitigating vibrations at the source, (ii) attenuating vibration intensity in the propagation path, and (iii) isolating the receiver such as surrounding structures from vibrations [5,6]. Compared with the other two types of mitigation methods (i.e., methods (i) and (ii)), it is rather difficult and often cost-consuming to build a vibration isolation system or to change the foundation condition under the existing buildings or infrastructures [7,8,9,10]. Therefore, the vibration mitigations at the source or at the transmission path are preferable to be applied in practice. In this study, some common mitigation methods are discussed, including trenches, sheet pile wall and subgrade stiffening methods.

Although many methods for vibration mitigation at source or propagation path have been tested and applied, lesser scale of research with respect to metamaterials applications in vibration abatements have been conducted [11,12,13]. Metamaterials are artificially constructed materials, which have repeated patterns in the configuration. One of the critical features of metamaterials is that the wave with specific frequencies can be prevented from propagating through metamaterials because of the periodic arrangement [14]. Actually, in a seismic design, metamaterials have been verified in a numerical model for protecting the buildings from structural damage in the earthquake due to this wave attenuation feature [15]. Considering the vibration mitigation mechanism is similar to seismic protection, the application of seismic metamaterials in railway systems can be proposed and analyzed. Two types of novel mitigation methods are discussed in this project, including clamped metamaterial stopbands and metamaterial resonators.

To enhance a detailed evaluation of cost efficiency and environmental impacts, it is necessary to carry out a lifecycle assessment of the above abatement methods in comparison with some existing approaches (such as geofoam, steel sheet piles, jet grouting columns, and stone columns). This study unprecedentedly conducts the lifecycle assessment of vibration abatement methods in both usual and adverse conditions. A tangent railway section of 100 m in length has been selected for comparative analyses in this study. In the lifecycle cost analysis, the net present costs in the processes of construction, maintenance and renewal for each method are determined after analysing the cash flow in the 50-year period. Allowing for the time value of money, the discount rate is applied in the cost estimation. For the environmental impacts analysis, the total carbon footprint, including the embedded emissions of the required quantity of materials and the emissions from devices used in the installation and maintenance period is estimated. This paper highlights two novel vibration attenuation measures with respect to metamaterials applications and then compares with conventional abatement methods proposed in the previous studies. The lifecycle cost and carbon emissions of each method are later determined to justify sustainable development criteria. These two aspects are the highlight of this study as they underpin the pillars of sustainable development [16,17]. Based on the lifecycle assessment results, the effectiveness of these methods can be compared in terms of economy and environmental protection in both normal and adverse weather conditions. This investigation is the world’s first to determine the sustainability of the vibration abatement methods when exposed to extreme weather conditions. The insight into lifecycle cost and carbon footprint will underpin the sustainable strategies and cleaner solutions for railway noise and vibration mitigation practices when exposed to extreme events due to climate change uncertainties and natural hazards.

2. Methods for Vibration Mitigations in Railway Corridors

Since railway lines are usually constructed to connect communities, cities and urban areas, rail neighborhoods have often experienced a variety of vibro-acoustic nuisances. As such, a number of vibration mitigation measures have been studied by many preeimnent scholars in relevant research fields. Suitability assessments of vibration mitigation methods are often needed when planning new railway lines or when new buildings are to be built close to railway lines. However, every technique and method for vibration mitigation and abatement requires supporting infrastructures and makes use of engineering assumptions; even though various uncertainties are often taken into account in the mitigation design. There are two groups of train-induced ground-borne vibration: (i) low-frequency vibration (2–80 Hz) is a kind of feelable vibration in which its waves have longer wavelengths and deeper penetration under the ground; and (ii) higher frequency vibration (30–250 Hz) can cause minor vibration of walls and floors and radiate ground-borne noise [3]. In this study, the track and soil conditions for suitability evaluation of each mitigation method are set identical. Compared with the mitigation methods for higher frequency vibrations, it is relatively more difficult to attenuate vibrations with a low frequency because of longer wavelengths, larger transmission depth, and greater ground conditions [18]. It is important to note that most previous studies of meta-structures/materials were aimed for seismic mitigation. In this study, the train-induced vibration is focused so the modifications of the meta-structures for railway applications have been engineered using similar track and foundation parameters (detailed in the Appendix A) on the basis of the guidelines and predictions from those previous studies [19]. Considering that conventional at-source attenuation methods can only mitigate the vibration in a limited range of frequency, some methods that can control low-frequency vibration in railway systems will also be discussed in the following section.

2.1. Seismic Metamaterial Applications

2.1.1. Clamped Metamaterial Stopbands

Based on previous studies, some researchers have proposed the application of periodic structure in the seismic protection of buildings. This idea came from the application of photonic crystals in light control technologies such as optical absorbers and invisibility cloaks. Photonic crystal is the periodic media, which have certain band-gaps so the optical waves in particular frequency ranges can be prevented from propagating through it. The band-gaps are actually hindered frequency ranges and would be formed if the wavelengths are much larger than the dimensions of structural elements forming the photonic crystal [20,21]. Given that seismic waves and optical waves have similar physical characteristics, band-gaps in periodic structures applied to suppress the light transmission can also be used to attenuate seismic waves.

Based on this theory, a clamped metamaterial stopband has been proposed to isolate buildings from seismic waves. This type of metamaterial is comprised of arrays of round columns clamped to the bedrock and aimed to form a zero-frequency stopband, which can hinder wave propagation [22]. For the application to seismic prevention, a protected building can be isolated from seismic waves by burying rows of columns in the bedrock around the building. Analogously, the clamped metamaterial can be utilized in railway systems to mitigate ground-borne vibrations. The vibration can be isolated completely in a low-frequency range from 1 to 30 Hz [23,24]. As Figure 1 shows, arrays of columns can be buried in the bedrock between the track and the surrounding building. In this way, vibration can be attenuated along the transmission path.

The proposal of this clamped metamaterial is inspired by the clamped structured thin plate model in Kirchhoff–Love theory, which indicates that the range of zero-frequency stopband is affected by the plate thickness. Then, the large disparity between wavelengths and plate thickness can broaden the band-gaps [25]. Similarly, the role of the buried depth of columns in the bedrock is equivalent to the plate thickness. Apart from the buried depth, the stopband range is also related to the column radius. The research conducted by Achaoui et al. [22] has compared the stopband range of clamped steel columns in different radii and found that clamped metamaterials with smaller radius columns would have wider stopbands. The dispersion curves of two different radii clamped columns buried in the 15 m soil layer and 0.8 m bedrock are illustrated in Figure 2. The range of zero-frequency stopband of clamped columns with radius 0.3 m is around 0–26 Hz, while radius 0.6 m columns have the stopband range approximately 0–4.5 Hz. Thus, buried depth and columns radius need to be considered in the design of clamped structure to achieve broader band-gaps.

Actually, traditional periodic structures such as pile barriers have been applied in civil engineering to mitigate ground vibration before the proposal of the clamped metamaterial. As Huang and Shi [26] indicated, the stopbands produced in pile barriers are always in high-frequency range because it is affected by spatial configuration and pile diameter. To attenuate low-frequency vibrations, larger diameter piles need to be utilized. This measure is not preferable if the space between the railway line and surrounding buildings is limited. Besides, too large diameter of piles would increase the difficulty in construction and maintenance.

2.1.2. Metamaterial Resonators

Metamaterial resonators can be applied to attenuate the vibration by dissipating vibration energy in the process of local resonances before the waves arrive at the building. Resonators are commonly buried in the soil around the protected region and tuned to a particular frequency in accordance with the eigenfrequencies of the buildings. In this way, local resonances could be excited in the resonators when the frequency of propagating waves reaches the eigenfrequencies. The disturbance to the buildings caused by ground vibrations would be decreased due to local resonances [27]. Given that the mitigation mechanism of metamaterial resonators is not based on structural periodicity, the structural size of resonators would not be as large as the pile diameter in pile barriers discussed above in order to achieve low-frequency vibration abatements. This method could thus be more practical in construction. However, the complexity of metamaterial resonators components needs to be considered before employing this method. In general, this method can be designed to isolate vibrations in a low-frequency range of less than 10 Hz [19].

According to the wave attenuation mechanism of locally resonant metamaterials, the seismic metabarrier comprised of rows of cylinders with suspended inner resonator mass has been proposed by Palermo et al. [28]. This inner resonator is suspended by two elastic rubber bearings located at both ends of the outer hollow cylinder. In this buried resonant structure, the resonant frequency of the inner suspended mass is the key factor, which affects the band-gaps range. The structure and components of metabarrier are indicated in Figure 3. The local resonances can occur when the frequency of propagated elastic waves reaches the eigenfrequency of inner mass. Rayleigh waves can be converted into shear waves in this process and redirected into deeper soil to achieve the mitigation. As Liu et al. [29] pointed out, band-gaps in metamaterials resonators are in limited range and can just include some frequency values around the resonant frequency. To broaden the band-gaps’ range, resonators with different eigenfrequencies can be gathered in order and overlapped local resonance mode would be performed [30]. For the inner suspended resonator, the eigenfrequency is related to resonator mass and geometry characteristics of the bearings, so these parameters can be changed to achieve wider band-gaps. In this regard, it is feasible to apply this seismic metabarrier for the railway vibration abatement since the configuration is not complex and the band-gaps broadening is achievable. Besides, Palermo et al. [28] have built the scaled experimental model and found that this metamaterials resonator can well mitigate the seismic waves in frequency range below 10 Hz. Considering it is difficult to abate low-frequency vibrations using traditional measures, this novel method provides an alternative, effective solution.

Apart from the suspended resonator, Kim and Das [31] proposed another metamaterial resonator system, which consists of several groups of hollow cylinders with side holes; these cylinders are combined and buried around the protected area. The shielding zone of seismic waves is formed because of the negative shear modulus of metamaterials in resonators, which results in the dissipation of the velocity and energy of the waves. Although the configuration of this resonator system is not complex, the spacing between two cylinders is short, which may influence stress distribution on the buried cylinder. Hence, this resonator structure is not generally recommended in practical applications.

2.2. Trenches and Sheet Pile Wall

2.2.1. Geofoam Filled Trenches

The application of trenches is one of the common measures to provide vibration scattering. The waves can be diffracted at the trench so that the vibration abatement can be achieved. The effectiveness of waves impediment at trenches is related to geometric parameters, distance between the trench and the protected building, and in-filled materials property. In a previous study, a numerical model using various influence factors have been built and analyzed by many researchers. As Adam and Estorff [32] proved and compared with broadening the trench width, it is more effective to improve the screening performance by increasing the depth of trenches. The waves isolation performance can be enhanced by excavating the trench in a shorter distance from protected region. Besides, Thompson et al. [33] found that low stiffness in-filled material is beneficial to vibration isolation. These findings can be applied in the design of trenches to improve the performance. However, increased depth would affect the stability of open trenches. For deeper trenches, a supporting structure or in-filled materials need to be applied. Mizutani et al. [34] conducted real experiments, which have shown that this method can suppress up to 35dB of ground vibrations (in a frequency range of 1 to 30 Hz).

Geofoam is a polymeric material, which contains air-filled spherical particles and it is also called expanded polystyrene (EPS). This material has numerous applications in geotechnical engineering due to techanical performances such as compressible inclusion, vibration damping and lightweight fill [35,36]. Although geofoam is the lightweight material, it has high strength-to-weight ratio. In this regard, it is recommended to apply geofoam as an in-filled material in deep trenches so that trenches could bear larger compressive stress from surrounding soil. To investigate the effectiveness of geofoam-filled trenches in vibration screening, Murillo et al. [37] proposed centrifuge modelling in which the railway vibration was simulated. The results illustrated that the trench depth is the main factor, which determines the screening effect and the increase of depth-to-wavelength ratio would accelerate the decrease of waves amplitude in geofoam trenches, which can be employed to improve the trench performance.

2.2.2. Sheet Pile Wall

Sheet pile walls can be applied as a stiff wave barrier to isolate vibrations. Compared to trenches, the lateral stability of this structure is better. According to Dijckmans et al. [18], the performance of the sheet pile walls depends on the depth, stiffness and elastic modulus contrast to the soil. The depth of the sheet pile needs to be sufficiently larger than the wavelength of incident waves so that vibration screening effect can be achieved. Besides, the sheet pile wall is equivalent to orthotropic plate. The bending stiffness in the horizontal direction is much larger than that in the vertical direction so the former would have larger effects on the isolation efficacy. Actually, the sheet pile wall can be employed as the supplementary measure to reduce vibration after applying at-source abatement methods. In this way, low-frequency vibrations can be further reduced. However, based on Dijckmans et al. [18], the vibration can be suppressed up to 12 dB in the frequency range between 30 to 40 Hz, and up to 5 dB in other frequency ranges lesser than 100 Hz.

2.3. Subgrade Stiffening

Subgrade stiffening is the method of improving the stiffness of the soil and subgrade under the track to achieve waves impediment. As Skipp [38] mentioned, the location of stiffened soil is always directly below the track or at certain depth under the ground and the depth of stiffened soil layer would influence the stiffening effects. Given that stiffening the soil close to the track might result in track uplifting, it is preferable to select the methods, which can stiffen soil at a certain depth below the track for subgrade stiffening of the existing railway. Some alternative techniques of subgrade stiffening have been proposed in the past research, including jet grouting, vibro-replacement, and wave impeding blocks. Coulier et al. [39] observed that the vibration suppression using this technique can be up to 6 dB along a traditional rail corridor (48 m away from a vibration source) in the frequency range between 30 and 40 Hz.

2.3.1. Jet Grouting Columns

Jet grouting is a mechanical method that can mix subgrade soil with the grout and form stiff mass underground. The high pressure of jet fluid can erode the soil and accelerate the mixture of soil particles and cement. This mixture would produce columns, which can decrease the permeability and compressibility of the original subgrade soil. Also, the stiffness of the subgrade would increase in this process, so differential settlement can be prevented and railway induced vibration would be mitigated [40,41]. The main jet fluid applied in this method is cement slurry. To form columns with different diameters and strengths that can be used in different soil conditions, air and water can also be introduced into the grout. As the types of jet fluid increase, the friction between the grout and soil at the nozzle would reduce. In this way, the grout stream would become more concentrated and the quality of the columns would be improved [42]. Considering the stiffening mechanism of jet grouting is based on grout erosion, this method can be employed in wider range of soil types from clays to gravels. However, it is notable that the jet pressure would be affected by treatment depth. This technique can reduce ground vibration up to 3 dB in a low-frequency range lesser than 10 Hz [19].

2.3.2. Vibro-Replacement with Stone Columns

Vibro-replacement is another subgrade stiffening method, which can densify the soil and replace soft soil with coarse material such as crushed stones or gravels. This replacement process is actually the installation process of stone columns in subsoil by a special depth vibrator [43]. The stone columns and the surrounding densified soil constitute an integrated support system with low compressibility and improved strength, so the subsoil would be stiffened. The stiffening effect of vibro-replacement is influenced less by the treatment depth, which is different from jet grouting. As Black et al. [44] pointed out, the vibratory compaction process may result in excessive settlement of the track. Thus, additional ballast materials may need to be prepared to level up the track before construction. The ground vibration can be suppressed using this method up to 3 dB in a low-frequency range lesser than 10 Hz [19].

2.3.3. Wave Impeding Blocks

Wave impending block (WIB) can also be utilized in vibration reduction by introducing the artificial stiffened inclusion at a certain depth in the subgrade. Compared to other subgrade stiffening methods, which stiffen the soil close to the track, WIB would cause smaller disturbance to the track. As Peplow et al. [45] indicated, the installation of WIB could change the cut-off frequency of the upper layer, so the waves below this frequency are stopped from propagating. This modified wave propagation regime results in the reduction of low-frequency vibration in the transmission path. Besides, Jiang et al. [46] found that WIB could achieve better performance in layered ground but the increased depth of stiffened block has little effect on the improvement of the performance, which should be considered in the design period. It was found that WIB can suppress the ground vibrations between 6 and 8 dB in a low-frequency range (<30 Hz) [47,48].

2.4. Impacts of Extreme Temperature

Climate change has always been a focus issue that is being investigated by many researchers. The influence of global warming on the operation and maintenance of infrastructures has been considered in the construction industry. As Binti et al. [49,50,51] mentioned, extreme weather would result in the increase of renewal cost and the acceleration of wear and degradation in railway components. Kim et al. [52] found that concrete would have lower later-age strength after curing in high temperature (40 °C). Given that most of the mitigation methods discussed in this project consist of concrete materials, the effects of extreme temperature on the lifespan and performance of each method need to be considered.

3. Methodology

Lifecycle assessment is a systematic method, which can evaluate the mitigation measures in the areas of economic effect and environmental impact. In this study, lifecycle cost and carbon emissions in different measures are calculated and compared. Considering the quantity of materials needed in each abatement method [53,54,55,56,57,58,59,60] is the main factor (which influences the overall cost and carbon footprint), rational engineering assumptions are made before conducting the lifecycle assessments.

3.1. Engineering Assumptions

The engineering assumptions provide the same baseline for estimating material demand, which would be consistent in different periods. The assumptions of the structure size and materials demand are based on previous literature and industry reports. The relevant parameters, which affect the efficacy of abatement methods, should be considered when selecting the size of vibration isolation structure. The materials quantities in a 100-metre railway line can be estimated and the assumptions in the control case of each method are identical as illustrated in the following.

(1)

Clamped metamaterial stopbands:

The number of cylinders in the periodic structure can be estimated according to the widths of the seismic barrier. As Kim [53] proposed, the width of the barrier can be calculated by Equation (1). Although this equation was initially based on a seismic waveform, Kim [53] and Achaoui et al. [22] found that it could also be used to estimate the size of meta-barriers for similar waveform vibrations, such as the train-induced ground-borne vibration. The uncertainty of soil conditions can be taken into account by the factor of safety in design process.

$$\Delta \mathrm{x}=\frac{\ln 10}{2\pi }\frac{\lambda \Delta M}{\mid n\mid }=\frac{0.366\lambda }{\mid n\mid }\Delta M$$

(1)

where $\lambda$ is the wavelength of the incident wave, n is the refractive index of wave barrier and $\Delta M$ is the seismic magnitude of Richter scale needed to reduce, which is the expected reduction of seismic magnitude after the waves transmit through the protected zone. To apply seismic metamaterial in attenuating railway induced vibrations, it is assumed using simplication approaches in [22] that λ = 100 m and n = 1.5, then the width of metamaterial periodic structure $\Delta \mathrm{x}=25\mathrm{m}$ for $\Delta M=1$. In this study, the steel pipes (diameter d = 1200 mm; thickness t = 30 mm; unit weight = 866 kg/m) are selected to form periodic structure [22]). The configuration of the pipes is shown in Figure 4. The length of the pipe is related to the soil layer thickness and buried depth in the bedrock. The reasonable pipe spacing is selected (a = 3600 mm) to avoid the effects of surrounding pipes in the groups. Thus, the total number pipes can be calculated based on the pipes diameter and the clamped structure width. The justifications and details of the pipes’ parameters and the quantities are shown in Appendix A.

(2)

Metamaterial resonators:

According to the scaled experimental setup related to metamaterial resonators [54], the parameters of each component can be estimated. Considering that the train-induced ground-borne vibration could be an elastic surface wave, the design by Krödel et al. [54] and Palermo et al. [28] can be modified for railway applications. Note that uncertainties in soil conditions are not within the scope of this study. As shown in Figure 5, each resonator consists of an outer concrete pipe (r_c = 600 mm; thickness t = 30 mm; ρ_c = 2500 kg/m³; h_c = 8 m); an inner suspended steel mass (r_r = 225 mm; ρ_r = 7800 kg/m³; h_r = 5 m) suspended by two rubber bearings or soft springs (ρ_eff = 1225 kg/m³; h = 1 m). Considering the broadening of band-gaps range does not depend on the periodic arrangement but the density of resonators arrangement. The triangular lattice is selected to achieve a high-density arrangement.

(3)

Geofoam filled trenches:

The geofoam density is around 1–2% to the soil and ranges from 10–30 kg/m³ [55]. In this study, the 16 kg/m³ geofoam is selected for the cost and carbon emission calculations. The trench depth is the main factor, which determines the efficacy of vibration scattering. Some design criterion indicated that the minimum depth should be 0.6 times Rayleigh wavelength to achieve an effective vibration isolation [33]. Based on parameters in previous research, a 6-m depth and 8-m width geofoam trench is analyzed.

(4)

Sheet pile wall:

Compared with the uniform depth wall, the alternating depth wall is more effective to scatter low-frequency vibration and costs less [18]. Thus, cost efficiency of the wall consisting of the 12 m depth sheet piles with every fourth pile alternating to 18 m depth is evaluated.

(5)

Jet grouting columns:

The stiffening width of jet grouting is related to the width of ballast and formation above the subgrade. The arrangement and design parameters of the cement columns are indicated in Figure 6; the total number of columns can be calculate based on the stiffening width, the diameter and the spacing of columns [56].

(6)

Vibro-replacement with stone columns:

The arrangement of stone columns is similar to jet grouting columns as shown in Figure 6. The design parameters (column diameter d = 1000 mm, spacing s = 2000 mm; stiffening width w = 10 m) are assumed based on the previous practical application [44]. Other details of the design parameters are illustrated in Appendix A.

(7)

Wave impeding blocks:

The inserted block (with a width of 6 m; thickness of 1 m; and depth of 1 m) has been adopted for analyses. The assumption is based on the previous parametric analysis [60], which compares the influence of depth, width, and depth on impeding effectiveness.

3.2. Lifecycle Cost Analysis

Lifecycle analysis can be applied to estimate the costs of vibration attenuation methods over the lifespan of the employed methods and materials. Considering the time value of money is changeable, the Net Present Value (NPV) of lifecycle cost is used to compare the cost efficiency of each vibration reduction method [61]. The cost and carbon footprint are key life cycle perspectives for a project’s decision making in compliance with ISO 14,040 [62]. In this study, the 50-year period lifecycle is selected for analysis and the base financial year is assumed to be 2018. The discount rate of 6% is adopted in accordance with the recommendation value for governmental projects [63]. The discounted cash flow, which includes initial cost, maintenance cost and renewal cost, are then analyzed. The initial costs of materials are illustrated in

Table 1. Assumptions of initial cost of mitigation methods.

Mitigation Method	Lifespan (Years)	Quantity of Material (Unit)	Initial Cost (£/Unit)	References
Clamped metamaterial stopbands	50	224 pipes	3272	[53]
Metamaterial resonators	50	78 resonators	5632	[54]
Geofoam filled trenches	25	480 m3	77	[55]
Sheet pile wall	50	153.23 ton	470	[18]
Jet grouting columns	50	7560 m	21	[56]
Vibro-replacement (stone columns)	50	3060 m	35	[44]
Wave impeding blocks	50	600 m3	90	[60]

, which is estimated based on the costing and price data from industry reports and former research. The principles of assessment are based on ISO 14,040 [62]. In this study, the function of the meta-structures is to provide the abatement to railway ground vibrations stemming from the movements of trains. Its performance characteristics are based on the suppression (i.e., insertion losses) of groundborne vibrations. The overarching functional unit of the meta-structures and their components is to assure that insertion losses occur in a low-frequency range (0–40 Hz). The specific functional unit is set as the insertion loss more than 3–6 dB of ground-borne vibrations in an urban setting. This implies that the track corridor is the system boundary, which can be modified to assure the construction of each type of vibration abatement techniques.

As for maintenance costs, no direct maintenance cost is considered in the analysis because the vibration attenuation methods discussed above are all applied underground and can avoid large disturbance caused by the operation of railway. As

Table 2. Maintenance cost and renewal cost (NPVs) in control case.

Mitigation Method	Lifespan (Years)	Initial Cost (£)	Maintenance Interval (Months)	Maintenance Cost (£/Time)	Renewal Cost (£/Unit)
Clamped metamaterial stopbands	50	733,152	36	4200	3273
Metamaterial resonators	50	439,296	36	4200	5632
Geofoam filled trenches	25	36,960	24	4200	77
Sheet pile wall	50	72,015	24	4200	470
Jet grouting columns	50	158,760	12	4200	21
Vibro-replacement (stone columns)	50	107,100	12	4200	35
Wave impeding blocks	50	54,000	24	4200	180

indicates, the maintenance cost (based on net present value, NPV at 6% expected rate of return) is estimated from the costs of rail and ballast maintenance [64].

The maintenance cost in high temperature and low temperature (exceeding the 95th percentile) is shown in

Table 3. Maintenance cost and renewal cost (NPVs) in extreme temperature.

Mitigation Method	Lifespan (Years)	Initial Cost (£)	Maintenance Interval (Months)		Maintenance Cost (£/Time)	Renewal Cost (£/Unit)
			High Temp.	Low Temp.
Clamped metamaterial stopbands	50	733,152	24	36	4200	3273
Metamaterial resonators	50	439,296	24	24	4200	5632
Geofoam-filled trenches	25	36,960	24	24	4200	77
Sheet pile wall	50	72,015	12	12	4200	470
Jet grouting columns	50	158,760	6	12	4200	21
Vibro-replacement (stone columns)	50	107,100	12	12	4200	35
Wave impeding blocks	50	54,000	24	24	4200	180

. The lifespan of materials used in each method is assumed to be not affected by the extreme temperature. The maintenance interval is considered to be shorter because the infrastructure of vibration isolation is built using concrete, rubber and steel; the performance of some materials can be vulnerable to and influenced by extreme temperature. Also, more frequent inspection should be carried out in adverse situations.

3.3. Carbon Emissions Analysis

The estimation of carbon emissions from railway systems mainly focuses on the construction and maintenance period. To compare carbon emissions caused by different vibration abatement methods, the carbon footprint of the required materials and machine utilized in the maintenance processes are estimated. Krezo et al. [65] proposed the carbon emissions from maintenance machines in railway systems and found it is related to the fuel type and fuel quantity. Thus, the emission in maintenance can be estimated by the fuel emission factor. Similarly, the carbon footprint is related to embedded emission factor EF of material type and the amount material QM. As shown in

Table 4. Carbon emissions from mitigation methods in control case.

Mitigation Method	EF (kg/kg)	QM (kg)	Emissions from Materials (kg)	Lifespan (Years)	Maintenance Interval (Months)	Emissions in Maintenance (kg)	Total Emissions (kg)
Clamped metamaterials stopbands	1.37	2,094,700	2,869,328	50	36	50,000	2,919,328
Metamaterial resonators	Concrete-0.15 Steel-2.59 Ribber-1.63	1,759,907 580,571 130,015	1,979,589	50	36	50,000	2,029,589
Geofoam filled trenches	3.07	15,360	47,155	25	24	80,000	127,155
Sheet pile wall	1.55	173,710	269,250	50	24	80,000	349,250
Jet grouting columns	0.084	4,107,806	345,055	50	12	130,000	475,055
Vibro-replacement (stone columns)	0.058	5,309,312	307,940	50	12	130,000	437,940
Wave impeding blocks	0.15	960,000	144,000	50	24	80,000	224,000

, the different EF of any selected material is collected from past research [66,67,68,69,70,71,72]. The embedded emission from materials can be estimated by multiply EF and QM. The QM has been calculated based on the engineering assumptions discussed before.

As indicated in

Table 5. Carbon emissions of mitigation methods at high temperatures i.

Mitigation Method	EF (kg/kg)	QM (kg)	Emission from Materials (kg)	Lifespan (Years)	Maintenance Interval (Months)	Emission During Maintenance (kg)	Total Emissions (kg)
Clamped metamaterial stopbands	2.78	2,094,400	2,869,323	50	24	80,000	2,949,328
Metamaterial resonators	Concrete 0.15; Steel 2.59; Rubber 1.63	1,759,907 580,571 130,015	1,979,589	50	24	80,000	2,059,589
Geofoam filled trenches	3.07	15,360	47,155	25	24	80,000	127,155
Sheet pile wall	1.55	173,710	269,250	50	12	130,000	399,250
Jet grouting columns	0.084	4,107,806	345,055	50	6	180,000	525,055
Vibro-replacement (stone columns)	0.058	5,309,312	307,940	50	12	130,000	437,940
Wave impeding blocks	0.15	960,000	144,000	50	24	80,000	224,000

, carbon emissions stemmed from materials exposed to high temperature are relatively the same as that in control case, but the increase in total emissions is related to maintenance frequency.

In low temperature, the total emissions can be estimated based on the shortened maintenance interval and the increased emissions in maintenance. The changes in the maintenance interval due to low temperature is shown in

Table 6. Carbon emissions of mitigation methods at low temperatures.

Mitigation Method	EF (kg/kg)	QM (kg)	Emission from Materials (kg)	Lifespan (Years)	Maintenance Interval (Months)	Emission During Maintenance (kg)	Total Emissions (kg)
Clamped metamaterial stopbands	2.78	2,094,400	2,869,323	50	36	50,000	2,919,328
Metamaterial resonators	Concrete 0.15; Steel 2.59; Rubber 1.63	1,759,907 580,571 130,015	1,979,589	50	24	80,000	2,059,589
Geofoam filled trenches	3.07	15,360	47,155	25	24	80,000	127,155
Sheet pile wall	1.55	173,710	269,250	50	12	130,000	399,250
Jet grouting columns	0.084	4,107,806	345,055	50	12	130,000	475,055
Vibro-replacement (stone columns)	0.058	5,309,312	307,940	50	12	130,000	437,940
Wave impeding blocks	0.15	960,000	144,000	50	24	80,000	224,000

.

4. Results and Discussion

The life cycle costs of different vibration abatement methods are indicated in Figure 7. The clamped metamaterial stopband is the most expensive because large amounts of steel piles are required to be arranged periodically underground to form a low-frequency stopband. The cost of this method is 10 times more than that of the geofoam trenches. Another method, which adopts metamaterial resonators, is also more costly than other common measures due to the complexity of the structure of the resonators. Although the metamaterial application could achieve wia der range of stopbands for low-frequency vibrations, it is not recommended to use this method unless the cost reduction design is proposed. Geofoam filled trenches and wave impeding blocks are the most economical solution whilst the extreme temperature condition has small effects on them. It is important to note that WIB is more suitable for new construction sites (i.e., greenfield projects) since the cost of soil removal and replacement could be relatively expensive in existing railway sites (i.e., brownfield projects). The cost of jet grouting columns is still more expensive than other conventional methods because small spacing and large quantity of soilcrete columns need to be constructed on site.

The comparison of wholelife carbon emissions caused by different attenuation methods is illustrated in Figure 8. The application of the clamped metamaterial stopband can result in the highest carbon footprint, which is around 1.5 times more than the emissions from the metamaterial resonator. The large proportion of carbon footprint in these two methods is from the material consumption. In comparison with metamaterials, the weight of geofoam is much lighter and the required quantity is lesser. Thus, geofoam trenches are the least contributor to the carbon footprint. Besides, the geofoam has excellent thermal insulation performance; and extreme temperature conditions have an insignificant influence on its effectiveness. The carbon emissions from its maintenance are also insignificantly increased. A similar amount of carbon footprint is produced by jet grouting columns and vibro-replacement techniques in the control case, but the emissions from maintenance activites for the jet grouting can increase in a high-temperature condition because more frequent maintenance is required. In this situation, carbon footprint from the jet grouting columns is 1.2 times more than that from the vibro-compaction method.

5. Conclusions

According to World Green Building Council [58], the activities related to building and construction are responsible for 39% of all carbon emissions in the world, with operational emissions (from energy used to heat, cool and light buildings) accounting for 28%. The remaining 11% stems from embodied carbon emissions, or ‘upfront’ carbon that is directly related to materials, construction, and maintenace processes throughout the whole building lifecycle. This has led to the drastic concern for better, greener, and more sustainable development (including building, construction and maintenance stages) of critical infrastructures, including railway infrastructures and their assets along the railway corridor. In reality, noise, vibration and carbon emissions derived from operations of transport sectors can seriously affect people’s health and environmental ecosystems requiring the implementation of mitigation measures to achieve a higher reduction in all transport modes, especially at construction and maintenance stages. The railway vibration mitigation measures, which can suppress low-frequency vibrations along the transmission path, have been thus highlighted in this study taking into account the systems-thinking approach. Lifecycle cost and carbon emission have been analyzed to assess the effectiveness and sustainability of each measure. According to the results, WIB and geofoam trenches are the most economical and sustainable methods to abate groundborne vibrations. These two techniques are the greenest approaches for the vibration suppression. Notably, WIB is more applicable to new construction sites. Although meta-material applications have been proven to an effective method to completely isolate wider range of low-frequency waves, they indeed yield relatively high costs and carbon emissions. Therefore, more research into the revised design and modification of metamaterials need to be conducted to achieve lower cost and carbon footprint. The new insight from this study will result in the more sustainable development of harmonized methodologies, as well as embedded systems and infrastructures to detect and suppress railway noises and vibrations. The additional insight into vulnerability and resilience of the vibration mitigation implementations to adverse weather conditions will help engineers and managers select an optimal approach and better plan risk-based inspections and maintenance of railway assets along network corridors.