Next Article in Journal
Assessing the Operation of a Multimodal Hub: A Traffic Impact Microsimulation Analysis
Next Article in Special Issue
Steel Slag Sub-Ballast for Sustainable Railway Track Infrastructure
Previous Article in Journal / Special Issue
Experimental and Computational Analyses of Sustainable Approaches in Railways
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Evaluating Different Track Sub-Ballast Solutions Considering Traffic Loads and Sustainability

1
Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano Gualberto, Trav. do Politécnico 380, São Paulo 05508-070, SP, Brazil
2
Laboratório Nacional de Engenharia Civil (LNEC), Av. do Brasil 101, 1700-066 Lisbon, Portugal
3
CONSTRUCT, Faculdade de Engenharia da Universidade do Porto (FEUP), R. Dr. Roberto Frias s/n, 4200-465 Porto, Portugal
4
Vale S.A., Av. Dante Michelini 5500, Parque Industrial, Vitória 22250-145, ES, Brazil
*
Author to whom correspondence should be addressed.
Infrastructures 2024, 9(3), 54; https://doi.org/10.3390/infrastructures9030054
Submission received: 2 February 2024 / Revised: 1 March 2024 / Accepted: 8 March 2024 / Published: 9 March 2024

Abstract

:
The railway industry is seeking high-performance and sustainable solutions for sub-ballast materials, particularly in light of increasing cargo transport demands and climate events. The meticulous design and construction of track bed geomaterials play a crucial role in ensuring an extended track service life. The global push for sustainability has prompted the evaluation of recycling ballast waste within the railway sector, aiming to mitigate environmental contamination, reduce the consumption of natural resources, and lower costs. This study explores materials for application and compaction using a formation rehabilitation machine equipped with an integrated ballast recycling system designed for heavy haul railways. Two recycled ballast-stabilised soil materials underwent investigation, meeting the necessary grain size distribution for the proper compaction and structural conditions. One utilised a low-bearing-capacity silty sand soil stabilised with recycled ballast fouled waste (RFBW) with iron ore at a 3:7 weight ratio, while the second was stabilised with 3% cement. Laboratory tests were conducted to assess their physical, chemical, and mechanical properties, and a non-linear elastic finite element numerical model was developed to evaluate the potential of these alternative solutions for railway sub-ballast. The findings indicate the significant potential of using soils stabilised with recycled fouled ballast as sub-ballast for heavy haul tracks, underscoring the advantages of adopting sustainable sub-ballast solutions through the reuse of crushed deteriorated ballast material.

1. Introduction

Railway track efficiency can be improved mainly by increasing the track’s service life, allowing it to resist additional loads over time and reducing maintenance cycles, track interruptions, and greenhouse gas emissions [1].
The sub-ballast layer plays a crucial role in a railway track’s life cycle. As outlined in [2], it serves to protect the subgrade from traffic loads and prevent mud from pumping into the ballast layer by providing separation and drainage for rainwater or groundwater. Numerous studies by researchers [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] have explored sustainable solutions related to geotechnical layers in railway tracks, such as ballast and sub-ballast, with their objectives including (i) enhancing the load-bearing capacity of the railway track, (ii) reducing strains from traffic loads, (iii) repurposing waste materials, (iv) proposing alternative materials, and (v) minimising ballast breakage.
Regarding the ballast layer, Indraratna and Salim [8] and Indraratna et al. [9] examined the stress–strain behaviour and the degradation of recycled ballast with geosynthetics, comparing it with clean ballast. Their aim was to reduce the amount of discarded ballast, maintenance costs, and environmental impact. The studies revealed that reinforced recycled ballast with geosynthetics showed promising potential to improve railway track resilience and reduce maintenance costs. Indraratna et al. [4] investigated the potential of using geogrids and recycled rubber in the ballast layer to enhance the track performance. Giunta [10] evaluated different recycled waste materials as potential solutions to improve the ballast behaviour.
Concerning the sub-ballast layer, Ebrahimi and Keene [5] investigated the possibility of rehabilitating the substructure and replacing the sub-ballast with alternative materials derived from a mixture of recycled ballast with recycled pavement materials (RPM), with or without industrial by-products (fly ash), to improve its mechanical behaviour (stabilised fouled ballast). They found that the use of fly ash mixed with RPM resulted in lower values in terms of permanent deformations, while the application of RPM alone provided behaviour similar that of conventional granular sub-ballast. Saborido Amate [11] assessed a novel alternative of recycled aggregates derived from blast furnace slag, known as SFS-Rail, for use in sub-ballast layers. The authors concluded that this type of recycled aggregate exhibits high quality in terms of durability, hardness, and resistance to abrasion, while also contributing to a reduction in environmental impacts. Giunta [10] also discussed various modern railway engineering sub-ballast sustainable solutions, including the use of alternative materials like cement-reinforced soils and asphalt binder for sub-ballast applications. Indraratna et al. [8] investigated the use of recycled rubber tires mixed with gravel as a sub-ballast layer. The authors found that this solution has the potential to reduce ballast degradation due to its damping characteristics, decrease the track’s modulus in the case of rigid substructures, and enhance lateral confinement and the track’s structural behaviour. Qi et al. [12] introduced two methods for stabilising railway substructure materials by blending waste materials such as blast furnace slag, washed coal, and rubber crumbs for use as sub-ballast materials. The authors showed that the proposed solutions can increase particle interlocking to provide proper shear strength as well as higher absorbing characteristics than traditional materials. In summary, the mentioned research focused mainly on improving the strength, load-bearing capacity, and durability of the sub-ballast layer by reusing recycled materials in a sustainable way.
However, limited research exists on recycled ballast fouled with iron ore, despite ongoing investigations into alternative and sustainable materials. Railways transporting iron ore often generate significant ballast waste, requiring extensive cleaning [18,19]. Ebrahimi and Keene [5] advocate for the cost-effective and sustainable practice of reusing materials obtained from ballast cleaning to construct a new sub-ballast layer, as opposed to disposal, which incurs additional expenses. The inclusion of iron ore as a fouling material may enhance the hydro-mechanical behaviour by improving interparticle contact, filling voids, and increasing stiffness, as observed in [19,20].
Schilder and Piereder [21], Auer et al. [22], and Mundrey [23] stated that the Rail-mounted Formation Rehabilitation Machine (RMFRM) can improve railway tracks’ structural behaviour by constructing and rehabilitating a new sub-ballast layer in recycling, reusing, and mixing the used ballast waste with different alternative materials, such as the subgrade soil itself. This process has higher productivity, less track disruption, and lower carbon emissions compared to conventional earthwork methods.
Nonetheless, the material originated from the integrated recycling process should satisfy the design specifications to be applied as sub-ballast to contribute to the proper mechanical behaviour. In recent decades, the analysis and design of railway components have been performed using various numerical modelling methods, notably the Finite Element Method (FEM). Many authors have studied complex railway problems through the development of 2D plane strain numerical models, applying the FEM due to its low computational effort requirements and computation times and greater simplicity in terms of the number of required parameters. Punetha et al. [24] developed a 2D numerical model to investigate the structural behaviour in bridge–track and track–bridge transition zones by considering the influence of a moving train, applying dynamic loads. The authors studied techniques that can increase the track stiffness and reduce track displacements at these critical zones. Indraratna and Nimbalkar [25] developed a 2D FEM numerical model to evaluate different scenarios and configurations of a cyclic triaxial chamber developed in the laboratory to simulate a railway multi-layer system stabilised using geosynthetics. The authors obtained important results regarding the stresses and deformations at the sleeper–ballast and ballast–sub-ballast interfaces. Jiang and Nimbalkar [26] developed a 2D FEM railway track model to predict the structural behaviour of the track’s substructure by simulating a geogrid reinforced ballast layer. The authors obtained relevant insights regarding vertical strains and tensile forces in geogrid and ballast settlement and justified that the method is convenient and economical for this purpose. Ramadan et al. [27] evaluated the influence of subgrade settlement on stresses for different loads and boundary condition scenarios. All of these mentioned works could reproduce different railway structural problems through the simplification of 2D plane strain FEM numerical models, as well as achieving important and accurate results.
The main objective of this paper is to evaluate the structural performance of alternative material solutions composed of recycled material from a ballast cleaning process and subgrade soil stabilised, or not, with cement for application as a sub-ballast layer using a RMFRM. This investigation aimed to analyse the structural conditions of the materials and their influence on the track performance in terms of displacements, strains, and stresses.

2. Formation Rehabilitation

2.1. The Sub-Ballast Layer

The sub-ballast is located underneath the ballast layer and has as its main function providing a better load distribution from the ballast to the subgrade, protecting it against possible high stress magnitudes and strains, being an essential part of the track for heavy haul operational conditions [2,28,29].
Li et al. [30] emphasise that the grain size distribution of sub-ballast material is a critical parameter, as it significantly influences separation, filtration, drainage, and strength. It should ideally contain a specific percentage of fine material passing through a 0.075 mm sieve to prevent mud pumping from the subgrade soil [31,32]. However, this percentage should be balanced to avoid increasing the water susceptibility and plastic deformation and hindering drainage [2,33,34]. As a result, many researchers and technical specifications recommend a well-graded material for the sub-ballast layer to meet these criteria, including Mundrey [23] and AREMA [34].
Different materials can be employed as sub-ballasts, such as well-graded crushed rock [2,35], hot mix asphalt underlayment [36,37], and lateritic tropical soils from quarries [20,38]. Regarding the latter, Castro et al. [20] and Guimarães et al. [38] explain that these types of soils contribute to better railway track behaviour as sub-ballasts because their clay fraction contains minerals from the kaolinite group and hydrated iron and aluminium oxides, which are considered stable in the presence of water and can bind their particles. Studies on stabilising local soils with recycled ballast fouled with iron ore or binder, such as cement, to improve their strength and deformability characteristics are still scarce, so further exploration may be interesting from an environmental and economical point of view.

2.2. Ballast Recycling Using a Formation Rehabilitation Machine

According to Esveld [39] and Klotzinger [40], ballast cleaners are employed when ballast particles with dimensions smaller than 22 mm constitute more than 30% of the total ballast volume. Profillidis [41] also states that the equipment removes all ballast particles smaller than 35 mm to a depth of 0.25 m in a layer next to the sleeper.
A RMFRM has been developed to rehabilitate railway infrastructure by integrating different processes performed into a single machine, including ballast cleaning and subgrade rehabilitation through the construction of sub-ballast using different materials, such as the ballast waste from the cleaning process.
Some railways have employed the RMFRM in their rehabilitation processes, as reported by Schilder and Piereder [21], Auer et al. [22], Mundrey [23], and Fu et al. [42]. According to Schilder and Piereder [20] and Auer et al. [21], the RMFRM can save up to 50% of the amount of new material required. However, the excavated materials should meet the specifications, as previously mentioned.
Schilder and Piereder [21] and Auer et al. [22] stated that the compaction energy applied in studies conducted in Austria, regarding the RMFRM for passenger railway tracks, was the Standard Proctor, followed the European specification BS EN 13286-2 [43]. However, Brazilian specifications use a reference minimum compaction energy for sub-ballast layers of heavy haul tracks between the Standard and the Modified Proctor, named the Intermediate Proctor. Hence, chemical stabilisation materials may be necessary if material compaction in the field is ineffective or inefficient. However, the compaction efficiency of the RMFRM is not the focus of this work and will not be addressed.

3. Materials and Methods

3.1. Site Characteristics and Material Sampling

The methodology employed in this study aimed to investigate and propose different materials for compaction using a RMFRM by mixing recycled ballast with a low-bearing-capacity subgrade soil stabilised, or not, with cement for heavy haul tracks. The railway under investigation was the Carajás railway (EFC), located in Northern Brazil, which primarily transports iron ore using trains consisting of 330 wagons with 32.5 t/axle. The railway features the following main characteristics: (i) TR-68 (RE 136) rail; (ii) stiff rail pads; (iii) concrete sleepers averaging 2.80 m in length, 0.27 m in thickness, and 0.23 m in depth; (iv) a ballast layer with a depth of 0.30 m; (v) a sub-ballast layer initially 0.25 m thick, with plans to increase it to 0.30 m; (vi) a track gauge of 1.60 m; (vii) Pandrol fastenings; and (viii) sleepers spaced 0.61 m apart.
Firstly, the studied materials were collected from quarries and in the vicinity of the railway, where maintenance and rehabilitation works were being carried out: (i) Itapeti soil identified as a soft silty sand soil from Mogi das Cruzes city; (ii) São Pedro da Água Branca (SPAB) soil from km 650 + 560, characterised as a stiff subgrade soil; (iii) recycled fouled ballast waste 1 (RFBW 1) from km 554 + 000; and (iv) recycled fouled ballast waste 2 (RFBW 2) from km 15 + 000, in Bacabeira city. Some of the characteristics of these materials were obtained from the study conducted by Saico et al. [44]. Figure 1 depicts the piles of RFBW.

3.2. Laboratory Tests

3.2.1. Physical–Chemical Characterisation and Dosage

Initially, the studied materials underwent investigation to determine their grain size distribution and classification, assessing their suitability as sub-ballast materials according to ASTM D6913 [45]. The particle size distribution and characterisation of the fouled ballast waste material followed ASTM C136–06 [46] and ASTM C702 [47]. In addition, it was assumed that the particle size distribution curve of the sub-ballast material should meet the specifications of a well-graded material, satisfying the criteria for filtering, separation, drainage, compaction, and stiffness, outlined by AREMA [34], Mundrey [23], Selig and Waters [2], and Auer et al. [22].
The particle size distribution of the resulting coarse-grained material was evaluated based on the Brazilian specifications DERSA ET-DE-P006 [48] and DERSA ET-DE-P00/008 [49], which are applied to well-graded road pavement base materials and aggregate. Table 1 shows the characteristics and properties of the investigated soil materials.
The soils were further assessed in terms of their physical characteristics and properties. As the soft subgrade soil (Itapeti) did not meet the design requirements individually and faced the possibility of ineffective compaction using a RMFRM, the material was stabilised with RFBW and 3% cement. Previous studies have highlighted the positive potential of a low percentage of cement to improve the hydro-mechanical properties, compaction, and stabilisation of pavement materials [50,51,52,53,54]. On the other hand, the stiff subgrade soil SPAB, while suitable for subgrade applications, did not require stabilization.
Thus, the chosen soil–aggregate mixtures were (i) 30% soil and 70% RFBW 1, assuming a proportion that leads to higher load-bearing capacity values, in accordance with ABNT NBR 12053 [55], and (ii) a combination of 15% soil, 65% RFBW 2 passing through the 19 mm sieve, and 20% crushed ballast material (C–RFBW). The details about the RFBW 2 mixture have been well described by Saico et al. [44]. The chosen mixture dosages followed the maximum and minimum limits of Range C from DNIT 141 [56]. Figure 2 shows the grain size distribution and the mineralogical composition of the studied materials.
It was noticed that Itapeti soil requires granulometric stabilisation to increase its strength and resilient modulus (RM) and to meet sub-ballast specifications. In addition, the mineralogical composition data showed that it was not possible to determine the true quantity of clay minerals present in the Itapeti soil, which is why Itapeti data do not appear in Figure 2b. The XRD technique depends on the crystallinity of its compounds. Clays, in general, have low crystallinity, and when stabilised with highly crystalline minerals, the quantification method becomes less precise, potentially leading to significant errors in quantification.
Regarding the SPAB soil, it contains almost 30% kaolinite and 2% hematite, which can contribute to better mechanical behaviour compared to Itapeti soil. Furthermore, 40% hematite or iron ore and presence of kaolinite clay mineral could be observed in the fouled ballast waste materials, possibly originating from material falling off the wagon during transport and/or from existing sub-ballast/subgrade materials.

3.2.2. Mechanical Characterisation

For the mechanical behaviour assessment of the materials for the subgrade and sub-ballast layers, their resilient modulus (RM) values were determined following AASHTO T 307-99 [57]. The specimens were compacted in their optimal moisture content and maximum density conditions.
The RM of the ballast material was determined using a large-scale triaxial test, in accordance with the methodology outlined in detail by Costa et al. [58] and Merheb et al. [59] to prepare the specimen and to perform the test, which can be summarised as (i) fixing a latex membrane in a steel base; (ii) separating and inserting different homogenised portions of the material into the membrane; (iii) compacting the resulting material with a vibratory plate at a frequency of 20 Hz; and (iv) applying a pre-determined confining pressure with a deviatoric stress.
The laboratory test results underwent nonlinear regression analysis using nonlinear constitutive models for the different geotechnical materials (Equations (1) and (2)), in accordance with their prevailing response to confining and deviatoric stresses. This analysis, following the methodologies of Liu [60] and Delgado et al. [13], yielded regression parameters used as input in the numerical model. Table 2 and Table 3 present the regression coefficients and compaction conditions of the tested specimens, respectively.
M R = k 1 × σ d k 2
M R = k 1 × σ 3 k 2 × σ d k 3
k 1 = k 1 × 10 [ α 1 k 2 ]
where k 1 , k 2 , and k 3 are the material-specific nonlinear regression coefficients obtained in the RM test, and α = 6 was used to convert the regression parameter k 1 unit obtained in MPa into Pa.

3.3. Numerical Modelling of the Railway Track

3.3.1. Geometry, Meshing, Boundary Conditions, Load, and Materials

The mechanical response of the proposed materials was evaluated using the ABAQUS/CAE software using a 2D FEM numerical model developed for railway applications. A Fortran UMAT subroutine code, developed by Vargas [61] for road application, was employed in this research. In summary, the constitutive model is represented as a stress–strain relationship or Jacobian Matrix, in which the elastic modulus, or RM magnitude, depends on the stress state of the structure. More details regarding the UMAT processes and programming implementation can be found in Vargas [61].
To determine the most cost-efficient mesh that could provide accurate results while maintaining computational feasibility, a mesh convergence analysis was conducted. This involved varying the mesh settings to increase the number of elements and comparing the stress and displacement results for different configurations. The resulting mesh and geometry characteristics are depicted in Figure 3 and summarised in Table 4.
The boundary conditions were set with restrained vertical and free horizontal degrees of freedom (DOF) at the bottom of the model, while restrained horizontal and free vertical DOF were applied at the lateral edges. The operational conditions of the track under study, in terms of speed and rolling stock geometry, were simulated using a dynamic impact factor of 1.4558, corresponding to a wagon with a static load of 32.5 t/axle, a maximum allowable speed of 22.2 m/s, and a wheel diameter of 0.9144 m, resulting in an equivalent dynamic load of 23.6 t/wheel. The equation for calculating the impact factor was obtained from AREMA [34]. The interfaces between the track components were assumed to be completely bonded for simplification. The material characteristics of the geotechnical layers were assumed to be the RM constitutive models outlined in Table 5.
Considering a plane strain numerical model of this study, it was assumed that only 40% of the wheel load would be transferred to the single main sleeper, in accordance with Profillidis [41]. Additionally, a linear elastic 3D FEM numerical model developed by Castro et al. [62] was employed to validate this assumption, considering the same railway track characteristics. Therefore, the material properties outlined in Table 5 were applied in the analysis, including the rail, rail pad, and concrete sleeper mechanical characteristics. Figure 4 illustrates the stress distribution through the sleepers under a single wheel load of 23.5 t, as calculated in this study.

3.3.2. Validation and Calibration

In terms of the model calibration, the track structure was simulated using the linear elastic configuration within ABAQUS and compared to other simulations using the UMAT subroutine with the equivalent elastic properties. ABAQUS software requires the input of the elastic or Young’s modulus, density, and Poisson’s ratio, while the UMAT subroutine requires the constitutive equation, regression coefficients obtained through laboratory tests, and Poisson’s ratio. The displacement values obtained from both analyses were consistent. Table 6 presents a comparison of the different model scenarios for calibration.
Furthermore, additional numerical simulations were conducted using the data from Table 6 as the input parameters, employing the UMAT subroutine. These simulations were carried out to compare the results with field instrumentation and monitoring data obtained from various studies in the literature.

4. Results and Discussions

Figure 5, Figure 6, Figure 7 and Figure 8 show the results of the 2D model calibration and validation analyses.
Different analyses were performed to evaluate the structural potential of the sub-ballast solutions in protecting the subgrade soil foundation from the traffic loads. Figure 9, Figure 10 and Figure 11, along with Table 7, present the results on the displacements, strains, and stresses in the subgrade and rails when different sub-ballast alternative solutions with RFBW were applied over soft subgrade soil.
In terms of the results on the stresses and displacements obtained during the second calibration analysis, reasonable values were observed. Studies by Indraratna et al. [9] and Costa et al. [58] reported similar values, with vertical stresses around 280, 75, and 60 kPa at the sleeper–ballast, ballast–sub-ballast, and sub-ballast–subgrade interfaces, along with track vertical displacements of approximately 3 mm. The material characteristics and load conditions applied in the numerical model were also comparable with the field investigations and monitoring studies of Indraratna and Nimbalkar [25] and Wang and Markine [63]. The results on the stresses at the sleeper–ballast, ballast-sub–ballast and sub-ballast–subgrade interfaces and track displacements showed that the developed 2D modelling was effectively calibrated.
Regarding the peak subgrade vertical displacements, it was noticed that the scenarios without stabilisation with RFBW and/or cement resulted in approximately 5.9 mm. However, these values decreased to 5.1 and 4.9 mm when stabilised solely with RFBW1 or RFBW2, respectively. This difference may be attributed to the higher amount of hematite and quartz in the RFBW2 material. The incorporation of 3% cement further reduced the displacements to 4.5 mm and 4.6 mm for RFBW1 and RFBW2, respectively. This reduction may be attributed to the more homogeneous mixture achieved with cement stabilisation.
These values align with the peak rail displacements, which corresponded to 6.5, 6.1, 5.7, 5.1 and 5.2 mm, for the same scenarios, respectively. The high displacement values observed can be attributed to the heavy haul operational conditions simulated, characterised by heavy axle loads. These conditions differ from the typical conditions found in Western Europe, where the axle loads are generally lower. Additionally, the relatively high dynamic amplification factor assumed, under the assumption of well-maintained track and trains, further contributed to these elevated displacement values.
In terms of strains, it can be noted that the vertical strain at the top of the subgrade decreased from 0.199% to 0.155% with the application of the sub-ballast layer stabilised with RFBW and to 0.118% with chemical stabilisation using 3% cement. Stabilisation with the RFBWs also contributed to a decrease in the vertical stresses at the top of the subgrade from 72.2 kPa to 66.1 and 62.6 kPa for RFBW1 and RFBW2, respectively. Further stress reduction is achieved with 3% cement stabilisation, resulting in stresses of 57.8 and 59.1 kPa for RFBW1 and RFBW2, respectively. These values align with the findings from Trevizo [64], Li [65], and Xu et al. [66].
It Is important to note that the scenario under evaluation assumed soft (highly deformable) subgrade soil. The significant influence of the subgrade on track displacements is widely acknowledged. To verify this assertion, further numerical simulations were conducted, substituting the soft Itapeti subgrade soil with a stiff SPAB subgrade soil. Figure 12, Figure 13 and Figure 14, along with Table 8, illustrate the outcomes of the displacement, strain, and stress in the subgrade and rails when various sub-ballast alternative solutions with RFBW are applied over stiff subgrade soil.
The observed trends in the latter scenarios indicate lower track and subgrade displacements for all the investigated scenarios, as anticipated. The rail displacements reduced from 3.3 mm without a sub-ballast layer to 2.9 mm, with a sub-ballast stabilised using RFBWs and 3% cement. The difference between the values obtained for each material solution was also lower than in the last case. In other words, a higher load-bearing-capacity subgrade soil provides a stiffer foundation, which contributes to a better track mechanical performance, with or without sub-ballast gradation or chemical stabilisation. Consequently, the contribution of RFBW sub-ballast stabilisation proves more effective for soft track subgrade soils. In addition, the alternative RFBW solutions could decrease the strain values at the top of the subgrade from 0.074% to 0.070%.
The resulting mixture demonstrated potential for use as sub-ballast, especially when stabilised with a low percentage of cement (3%). The use of cement can be advantageous mainly when there are not local materials meeting the specifications for the construction of a new sub-ballast layer and when the maintenance is being performed with a RMFRM which may not compact the sub-ballast layer efficiently.
In other words, utilising a small amount of cement can still offer greater sustainability compared to transporting suitable soils over long distances from quarries or deposits to the construction site. Additionally, alternative binders like lime, bio-binders, or bio-asphalts, as well as binders from reclaimed asphalt mixtures, present lower carbon CO2 emissions during manufacturing and offer enhanced performance when applied in road and railway infrastructure [3,5,14,67].
The mixture potential is also attributed to the presence of stable minerals such as hematite, kaolinite, and goethite, which are relevant to sub-ballast layer applications, as reported by Castro et al. [20] and Guimarães et al. [38]. Additionally, the coarse grains contribute to a higher stability and stiffness and better interlocking within the material. The RFBW materials also demonstrated a potential to mitigate peak rail displacement, ensuring the limits of 6.35 mm set by AREMA [34] were not exceeded. The grain size distribution prescribed for the use of RMFR machinery ensured a better behaviour of the track structure as recommended and in agreement with the studies conducted by Schilder and Piereder [19], Auer et al. [22], Mundrey [23], and Fu et al. [42].
According to Mundrey [23], it is common to encounter poor subgrade conditions along railway tracks requiring extensive maintenance, such as replacing the sub-ballast material or constructing a new sub-ballast layer. However, soil deposits, aggregate stone crushing, or asphalt mixture plants are not always readily available to meet the demand in the field.
The results in this paper highlight the characteristics of alternative materials and the possibility of recycling and reusing degraded ballast from tracks mixed with local soils for subgrade rehabilitation. This can be accomplished using traditional earthwork machinery or advanced RMFRMs, thereby reducing environmental impacts and the costs for the railway operator. This alternative solution holds particular interest for heavy haul tracks transporting iron ore, as it has the potential to increase the load-bearing capacity of the track structure and influence the track modulus, thereby mitigating rail displacements. The developed modelling approach effectively captures the observed trends and results concerning stress, displacements, and strains, aligning with some studies found in the literature presenting track field monitoring, instrumentation data, and numerical modelling results, particularly on the stresses at the top of the subgrade and rail displacements [50].
Thus, despite the analysis being conducted in a plane strain state (2D), which neglected the stress and strain contributions from the components along the z-axis (the direction of the track), such as adjacent sleepers and the rail, the developed numerical model provided accurate insights into the mechanical behaviour of the railway track when applying a sub-ballast layer with RFBW alternative materials. These findings can assist in the design, construction, and maintenance of the track.

5. Conclusions

Mixtures incorporating RFBW material demonstrate significant potential for use as sub-ballast due to their mineralogical composition, including iron ore, kaolinite, and quartz. However, chemical stabilisation with 3% cement can further enhance the structural conditions of the track. However, the solutions proved to be more efficient for soft subgrade soil than on a stiffer soil foundation.
Despite the fact that the use of cement is not commonly sustainable, it may become more sustainable when there are no available materials near the construction site, which would otherwise demand higher carbon emissions from the dump trucks used to transport materials over long distances. In addition, cement may be replaced with different binders such as lime, bio-binders, bio-asphalts, or binders from reclaimed asphalt mixtures, considering the well-known lower carbon CO2 emissions in their manufacture and reuse and the acceptable behaviour they provide when applied in pavements and railways.
The physical and chemical analyses of the RFBW material revealed its pre-dominant composition of quartz, albite, and hematite. This not only signifies the presence of iron ore but also indicates the presence of fine material resulting from the breakdown and wear of ballast particles.
The developed 2D numerical model effectively assesses the non-linear behaviour of these materials by applying parameters derived from laboratory cyclic triaxial tests for the ballast, sub-ballast, and subgrade with a lower computational cost than a 3D numerical model. The stress, strain, and displacement trends aligned well with the characteristics of the materials evaluated. The magnitudes of the stresses and displacements were considered realistic, despite not considering the rail longitudinally and adjacent sleepers using this numerical approach.
This study contributes to proposing alternative sub-ballast materials through the recycling and reuse of fouled ballast waste, focusing on more productive and efficient rehabilitation methods such as the use of RMFRM equipment. It could be concluded that the combined application of both solutions has a high potential to enhance the sustainability of railway transportation.

Author Contributions

Conceptualisation, E.d.M. and R.M.; data collection, G.C. and J.S.; data analysis, G.C. and J.S.; writing—original draft preparation, G.C.; writing—review and editing, R.M., A.P. and E.F.; project administration, R.M.; funding acquisition, R.M., L.O. and L.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by VALE S.A—Cátedra Under Rail and by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.

Data Availability Statement

Some of the data used in this study may be available from the authors upon reasonable request.

Acknowledgments

The authors acknowledge VALE S.A.—Cátedra Under Rail for the technical support.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Plano Nacional de Logística. Available online: https://www.gov.br/participamaisbrasil/blob/baixar/3499 (accessed on 10 January 2024).
  2. Selig, E.; Waters, J. Track Geotechnology and Substructure Management; Thomas Telford: London, UK, 1994. [Google Scholar]
  3. Celauro, C.; Cardella, A.; Guerrieri, M. LCA of different construction choices for a double-track railway line for sustainability evaluations. Sustainability 2023, 15, 5066. [Google Scholar] [CrossRef]
  4. Indraratna, B.; Qi, Y.; Ngo, T.; Rujikiatkamjorn, C.; Neville, T.; Ferreira, F.; Shahkolahi, A. Use of geogrids and recycled rubber in railroad infrastructure for enhanced performance. Geosciences 2019, 9, 30. [Google Scholar] [CrossRef]
  5. Ebrahimi, A.; Keene, A. Reconstruction of Railroad Beds with Industrial Byproducts and In Situ Reclamation Material; Student Project Report; University of Wisconsin: Madison, WI, USA, 2010. [Google Scholar]
  6. Ho, C.; Humphrey, D.; Hyslip, J.; Moorhead, W. Use of recycled tire rubber to modify track-substructure interaction. Transp. Res. Rec. 2013, 2374, 119–125. [Google Scholar] [CrossRef]
  7. Indraratna, B.; Salim, W. Deformation and degradation mechanics of recycled ballast stabilized with geosynthetics. Soils Found. 2003, 43, 35–46. [Google Scholar] [CrossRef]
  8. Indraratna, B.; Sun, Q.; Heitor, A.; Grant, J. Performance of rubber tire-confined capping layer under cyclic loading for railroad conditions. J. Mater. Civ. Eng. 2017, 30, 06017021. [Google Scholar] [CrossRef]
  9. Indraratna, B.; Nimbalkar, S.; Christie, D.; Rujikiatkamjorn, C.; Vinod, J.S. Field assessment of the performance of a ballasted rail track with and without geosynthetics. J. Geotech. Geoenvironmental Eng. ASCE 2010, 136, 907–917. [Google Scholar] [CrossRef]
  10. Giunta, M. Trends and challenges in railway sustainability: The state of the art regarding measures, strategies, and assessment tools. Sustainability 2023, 15, 16632. [Google Scholar] [CrossRef]
  11. Saborido Amate, C. New recycled aggregates with enhanced performance for railway track bed and form layers. In Proceedings of the 2nd International Conference on Railway Technology: Research, Development, and Maintenance, Ajaccio, France, 8–11 April 2014; Civil Comp-Press: Scotland, UK, 2014. [Google Scholar]
  12. Qi, Y.; Indraratna, B.; Tawk, M. Use of recycled rubber elements in track stabilization. In Proceedings of the Geo-Congress 2020: Geo-Systems, Sustainability, Geoenvironmental Engineering, and Unsaturated Soil Mechanics (GSP 319), Minneapolis, MI, USA, 25–28 February 2020. [Google Scholar]
  13. Delgado, B.; Fonseca, A.; Fortunato, E.; Paixão, A.; Alves, R. Geomechanical assessment of an inert steel slag aggregate as an alternative ballast material for heavy haul rail tracks. Constr. Build. Mater. 2021, 279, 122–438. [Google Scholar] [CrossRef]
  14. Bressi, S.; Santos, J.; Giunta, M.; Pistonesi, L.; Lo Presti, D. A comparative life-cycle assessment of asphalt mixtures for railway sub-ballast containing alternative materials. Resour. Conserv. Recycl. 2018, 137, 76–88. [Google Scholar] [CrossRef]
  15. Navaratnarajah, S.; Mayuranga, H.; Venuja, S. Influence of type of sleeper–ballast interface on the shear behaviour of railway ballast: An experimental and numerical study. Sustainability 2022, 14, 16384. [Google Scholar] [CrossRef]
  16. Hashemian, S.; Nejad, F.; Esmaeili, M. Laboratory and numerical investigation on the behavior of reclaimed asphalt pavement (RAP) as railway track subballast layer. Constr. Build. Mater. 2023, 384, 131442. [Google Scholar] [CrossRef]
  17. Arulrajah, A.; Naeini, M.; Mohammadinia, A.; Horpibulsuk, S.; Leong, M. Recovered plastic and demolition waste blends as railway capping materials. Transp. Geotech. 2020, 22, 100320. [Google Scholar] [CrossRef]
  18. Costa, R.; Motta, R.; Bernucci, L.; Moura, E.; Alves, A.; Sgaviolli, F. Avaliação da contaminação do lastro ferroviário. In Proceedings of the 28° Congresso de Pesquisa e Ensino em Transportes, ANPET, Curitiba, PR, Brazil, 24–28 November 2014. [Google Scholar]
  19. Pires, J. Integrated Maintenance Model for Heavy Haul Tracks. Ph.D. Thesis, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 2015. [Google Scholar]
  20. Castro, G.; Pires, J.; Motta, R.; Costa, R.; Moura, E.; Bernucci, L.; Oliveira, L. Numerical and experimental study of the unsaturated hydraulic behavior of a railroad track profile considering fouled ballast subjected to tropical climate condition. In Advances in Transportation Geotechnics IV 2022, LNCS; Tutumluer, E., Nazarian, S., Al-Qadi, I., Qamhia, I., Eds.; Springer Nature Switzerland AG: Cham, Switzerland, 2022; Volume 166. [Google Scholar]
  21. Schilder, R.; Piereder, F. Formation rehabilitation on Austrian Federal Railways—Five years of operating experience with the AHM 800-R. Rail Eng. Int. 2000, 4, 11. [Google Scholar]
  22. Auer, F.; Schilder, R.; Zuzic, M.; Breymann, H. 13 years of experience with rail-mounted formation rehabilitation on the Austrian network. Railw. Technol. (RTR) 2008, 1, 29–36. Available online: https://www.plasser.com.br/pt/media-library/publicacoes.html (accessed on 10 January 2024).
  23. Mundrey, J. Railway Track Engineering, 4th ed.; McGraw-Hill: New York, NY, USA, 2009. [Google Scholar]
  24. Punetha, P.; Maharkan, K.; Nimbalkar, S. Finite Element Modeling of the Dynamic Response of Critical Zones in a Ballasted Railway Track. Front. Built Environ. 2021, 7, 660292. [Google Scholar] [CrossRef]
  25. Indraratna, B.; Nimbalkar, S. Stress-strain degradation response of railway ballast stabilized with geosynthetics. J. Geotech. Geoenviron. Eng. ASCE 2013, 139, 684–700. [Google Scholar] [CrossRef]
  26. Jiang, Y.; Nimbalkar, S. Finite Element Modeling of Ballasted Rail Track Capturing Effects of Geosynthetic Inclusions. Front. Built Environ. 2019, 5, 69. [Google Scholar] [CrossRef]
  27. Ramadan, A.N.; Jing, P.; Zhang, J.; Zohny, H.N.E.-D. Numerical Analysis of Additional Stresses in Railway Track Elements Due to Subgrade Settlement Using FEM Simulation. Appl. Sci. 2021, 11, 8501. [Google Scholar] [CrossRef]
  28. Selig, E.; Cantrell, D. Track substructure maintenance–from theory to practice. In Proceedings of the Annual Conference, American Railway Engineering and Maintenance of Way Association, Chicago, IL, USA, 9–12 September 2001; pp. 9–12. [Google Scholar]
  29. Li, D.; Rose, J.; Lopresti, J. Test of hot-mix asphalt trackbed over soft subgrade under heavy axle loads. Association of American Railroads. Technol. Digest. 2001, 1, 4. [Google Scholar]
  30. Ghataora, G.; Burns, B.; Burrow, M.; Evdorides, H. Development of an index test for assessing anti-pumping materials in railway track foundations. In Proceedings of the 1st International Conference on Railway Foundations, Birmingham, UK, 11–13 September 2006; pp. 355–366. [Google Scholar]
  31. Duong, T.; Cui, Y.; Tang, A.; Dupla, J.; Canou, J.; Calon, N.; Robinet, A. Investigating the mud pumping and interlayer creation phenomena in railway sub-structure. Eng. Geol. 2014, 171, 45–58. [Google Scholar] [CrossRef]
  32. Cui, Y. Unsaturated railway track-bed materials. Web Conf. 2016, 9, 01001. [Google Scholar] [CrossRef]
  33. Rushton, K.; Ghataora, G. Design for efficient drainage of railway track foundations. Proc. Inst. Civ. Eng. Transp. 2012, 167, 3–14. [Google Scholar]
  34. AREMA: Manual for Railway Engineering; American Railway Engineering and Maintenance-of-Way Association: Lanham, MD, USA, 2020.
  35. Teixeira, P.F.; López-Pita, A.; Casas, C.; Bachiller, A.; Robusté, F. Improvements in high-speed ballasted track design: Benefits of bituminous subballast layers. Transp. Res. Rec. 2006, 1943, 43–49. [Google Scholar] [CrossRef]
  36. Anderson, J.; Rose, J. In-situ test measurement techniques within railway track structures. In Proceedings of the Joint Rail Conference, Wilmington, DE, USA, 22–24 April 2008; pp. 187–207. [Google Scholar]
  37. Alves, T.; Pereira, P.; Motta, R.; Vasconcelos, K.; Teixeira, J.; Bernucci, L. Three-dimensional numerical modelling of railway track with varying air voids content bituminous subballast. Road Mater. Pavement Des. 2020, 23, 414–432. [Google Scholar] [CrossRef]
  38. Guimarães, A.; Silva Filho, J.; Castro, C. Contribution to the Use of Alternative Material in Sub-Ballast Layer of Heavy Haul Railroad; Transportation Geotechnics; Elsevier: Amsterdam, The Netherlands, 2021. [Google Scholar]
  39. Esveld, C. Modern Railway Track, 2nd ed.; Delft University of Technology: Delft, The Netherlands, 2001. [Google Scholar]
  40. Klotzinger, E. Further development of mechanized ballast cleaning. Railw. Technol. (RTR) 2002, 2, 21–28. Available online: https://www.plasserindia.com/fileadmin/user_upload/Media_Library/Publications/rtr_0202.pdf (accessed on 10 January 2024).
  41. Profillidis, V. Railway Management and Engineering, 3rd ed.; Burlington: Burlington, NJ, USA, 2006. [Google Scholar]
  42. Fu, L.; Xiao, J.; Zhou, S.; Zhang, D.; Wang, Y.; Liu, W.; Jiang, L. Roadbed improvement of an existing railway line located in cold region by reusing crushed deteriorated ballast. In Proceedings of the 10th International Conference on the Bearing Capacity of Roads, Railways and Airfields 2017, BCRRA, Athens, Greece, 28–30 June 2017; Loizos, A., Al-Qadi, I., Scarpas, T., Eds.; Taylor & Francis: Abingdon, UK, 2017; pp. 1845–1850. [Google Scholar]
  43. CEN European Standard EN: EN 13286-2:2010; Unbound and Hydraulically Bound Mixtures—Part 2: Test Methods for Laboratory Reference Density and Water Content—Proctor Compaction. Comité Européen de Normalisation: Brussels, Belgium, 2010.
  44. Saico, J.; Castro, G.; Motta, R.; Moura, E.; Bernucci, L.; Oliveira, L. Evaluation of the behavior of recycled ballast waste applied in subballast railway track layer rehabilitation. In Proceedings of the Anais do 37° Congresso de Pesquisa e Ensino em Transportes, Galoá, Santos, SP, Brazil, 6–10 November 2023. [Google Scholar]
  45. ASTM D6913–04; Standard Test Methods for Particle-Size Distribution (Gradation) of Soils Using Sieve Analysis. American Society for Testing and Materials: West Conshohocken, PA, USA, 2009.
  46. ASTM C136; Standard Test Methods for Sieve Analysis of Fine and Coarse Aggregates. ASTM International: West Conshohocken, PA, USA, 2006.
  47. ASTM C702; Reducing Samples of Aggregate to Testing Size. ASTM International: West Conshohocken, PA, USA, 2011.
  48. DERSA—ET-DE-P00/006; Sub-Base ou Base de Solo Brita. DERSA Desenvolvimento Rodoviário S/A: São Paulo, SP, Brazil, 2006.
  49. DERSA—ET-DE-P00/008; Sub-Base ou Base de Brita Graduada. DERSA Desenvolvimento Rodoviário S/A: São Paulo, SP, Brazil, 2005.
  50. Abu-Farsakh, M.; Dhakal, S.; Chen, Q. Laboratory characterization of cementitiously treated/stabilized very weak subgrade soil under cyclic loading. Soils Found. 2015, 55, 504–516. [Google Scholar] [CrossRef]
  51. Beja, I.; Motta, R.; Bernucci, L. Application of recycled aggregates from construction and demolition waste with portland cement and hydrated lime as pavement subbase in Brazil. Constr. Build. Mater. 2020, 258, 119520. [Google Scholar] [CrossRef]
  52. Amhadi, T.; Assaf, G. Improvement of pavement subgrade by adding cement and fly ash to natural desert sand. Infrastructures 2021, 6, 151. [Google Scholar] [CrossRef]
  53. Peng, L.; Ge, D.; Lv, S.; Xue, Y.; Chen, J.; Sun, H.; Wang, J. Use of waste rubber particles in cement-stabilized aggregate for the eco-friendly pavement base layer construction: Laboratory performance and field application. Constr. Build. Mater. 2023, 402, 133023. [Google Scholar] [CrossRef]
  54. Hoy, M.; Tran, N.; Suddeepong, A.; Horpibulsuk, S.; Mobkrathok, M.; Chinkulkijniwat, A.; Arulrajah, A. Improved fatigue properties of cement-stabilized recycled materials—Lateritic soil using natural rubber latex for sustainable pavement applications. Transp. Geotech. 2023, 40, 100959. [Google Scholar] [CrossRef]
  55. ABNT NBR 12053; Solo-Brita—Determinação da Dosagem—Método de Ensaio. Associação Brasileira de Normas Técnicas: São Paulo, Brazil, 1994.
  56. DNIT 141–ES; Pavimentação—Base Estabilizada Granulometricamente. Instituto de Pesquisas em Transportes, Departamento Nacional de Infraestrutura de Transportes: Brasilia, Brazil, 2022.
  57. AASHTO T 307–99; Standard Method of Test for Determining the Resilient Modulus of Soils and Aggregate Materials. American Association of State and Highway Transportation Officials: Washington, DC, USA, 2021.
  58. Costa, R.; Pires, J.; Moura, E.; Motta, R.; Castro, G.; Bernucci, L.; Oliveira, L. Proposition for in situ evaluation of geotechnical and structural aspects of a heavy haul track. In Advances in Transportation Geotechnics IV 2021; Tutumluer, E., Nazarian, S., Al-Qadi, I., Qamhia, I., Eds.; Springer Nature Switzerland AG: Cham, Switzerland, 2021; Volume 165. [Google Scholar]
  59. Merheb, A.; Motta, R.; Bernucci, L.; Moura, E.; Costa, R.; Vieira, T.; Sgavioli, F. Equipamento triaxial cíclico de grande escala para análise mecânica de lastro ferroviário. Transportes 2014, 22, 53–63. [Google Scholar] [CrossRef]
  60. Liu, S. Kentrack 4.0: A Railway Trackbed Structural Design Program. Master’s Thesis, University of Kentucky, Lexington, KY, USA, 2013. [Google Scholar]
  61. Vargas, G. Simulação Numérica do Comportamento Mecânico de um Pavimento Asfáltico Instrumentado Submetido a Diferentes Condições de Saturação. PhD. Thesis, Universidade Federal do Rio de Janeiro, URFJ/COPPE, Rio de Janeiro, RJ, Brazil, 2020. [Google Scholar]
  62. Castro, G.; Moura, E.; Costa, R.; Motta, R.; Bernucci, L.; Fortunato, E.; Paixão, A.; Oliveira, L. Numerical evaluation of a full-scale laboratory test facility for heavy-haul railroad tracks. In Proceedings of the 12th International Heavy Haul Association Conference, Rio de Janeiro, Brazil, 27–31 August 2023. [Google Scholar]
  63. Wang, H.; Markine, V. Corrective countermeasure for track transition zones in railways: Adjustable fastener. Eng. Struct. 2018, 169, 1–14. [Google Scholar] [CrossRef]
  64. Trevizo, M. FAST/HAL Ballast and Subgrade Experiments. Association of American Railroads, Report R-788 FRA ORD-91/10, 1991. 1991. Available online: https://railroads.dot.gov/elibrary/fasthal-ballast-and-subgrade-experiments (accessed on 15 January 2024).
  65. Li, D. 25 years of heavy axle load railway subgrade research at the Facility for Accelerated Service Testing (FAST). Transp. Geotech. 2018, 17, 51–60. [Google Scholar] [CrossRef]
  66. Xu, F.; Yang, Q.; Liu, W.; Leng, W.; Nie, R.; Mei, H. Dynamic stress of subgrade bed layers subjected to train vehicles with large axle loads. Shock. Vib. 2018, 2018, 2916096. [Google Scholar] [CrossRef]
  67. Zhang, Z.; Fang, Y.; Yang, J.; Li, X. A comprehensive review of bio-oil, bio-binder, and bio-asphalt materials: Their source, composition, preparation, and performance. J. Traffic Transp. Eng. (Engl. Ed.) 2022, 9, 151–166. [Google Scholar] [CrossRef]
Figure 1. Photos of piles of fouled ballast in EFC Carajás. (a) Pile 1, reference code: RFBW 1; (b) pile 2, reference code: RFBW 2.
Figure 1. Photos of piles of fouled ballast in EFC Carajás. (a) Pile 1, reference code: RFBW 1; (b) pile 2, reference code: RFBW 2.
Infrastructures 09 00054 g001
Figure 2. (a) Grain size distribution; (b) mineral composition of the materials.
Figure 2. (a) Grain size distribution; (b) mineral composition of the materials.
Infrastructures 09 00054 g002
Figure 3. Mesh configuration and geometric characteristics of the developed 2D model.
Figure 3. Mesh configuration and geometric characteristics of the developed 2D model.
Infrastructures 09 00054 g003
Figure 4. Mesh configuration and geometric characteristics of the 3D model developed by Castro et al. [62]: (a) general configuration of the model; (b) vertical stress contours, S22 (in Pa); (c) vertical stress at the sleeper-ballast interface.
Figure 4. Mesh configuration and geometric characteristics of the 3D model developed by Castro et al. [62]: (a) general configuration of the model; (b) vertical stress contours, S22 (in Pa); (c) vertical stress at the sleeper-ballast interface.
Infrastructures 09 00054 g004
Figure 5. Vertical stresses, denoted as S22 [Pa], within the ballast layer, in a transverse cross-section (X-Y) aligned with the axle load.
Figure 5. Vertical stresses, denoted as S22 [Pa], within the ballast layer, in a transverse cross-section (X-Y) aligned with the axle load.
Infrastructures 09 00054 g005
Figure 6. Vertical stresses, denoted as S22 [Pa], within the sub-ballast layer, in a transverse cross-section (X-Y) aligned with the axle load.
Figure 6. Vertical stresses, denoted as S22 [Pa], within the sub-ballast layer, in a transverse cross-section (X-Y) aligned with the axle load.
Infrastructures 09 00054 g006
Figure 7. Vertical stresses, denoted as S22 [Pa], within the subgrade, in a transverse cross-section (X-Y) aligned with the axle load.
Figure 7. Vertical stresses, denoted as S22 [Pa], within the subgrade, in a transverse cross-section (X-Y) aligned with the axle load.
Infrastructures 09 00054 g007
Figure 8. Vertical displacements, denoted as U2 [m], in the track structure, in a transverse cross-section (X-Y) aligned with the axle load.
Figure 8. Vertical displacements, denoted as U2 [m], in the track structure, in a transverse cross-section (X-Y) aligned with the axle load.
Infrastructures 09 00054 g008
Figure 9. Displacements with depth in the subgrade (over 5 m depth).
Figure 9. Displacements with depth in the subgrade (over 5 m depth).
Infrastructures 09 00054 g009
Figure 10. Peak strains with depth in the subgrade (over 5 m depth).
Figure 10. Peak strains with depth in the subgrade (over 5 m depth).
Infrastructures 09 00054 g010
Figure 11. Peak stresses in the subgrade top at 5 m from the bottom vs. transversal distance.
Figure 11. Peak stresses in the subgrade top at 5 m from the bottom vs. transversal distance.
Infrastructures 09 00054 g011
Figure 12. Displacements with depth in the subgrade (over 5 m depth).
Figure 12. Displacements with depth in the subgrade (over 5 m depth).
Infrastructures 09 00054 g012
Figure 13. Peak strains with depth in the subgrade.
Figure 13. Peak strains with depth in the subgrade.
Infrastructures 09 00054 g013
Figure 14. Peak stresses in the subgrade top at 5 m from the bottom vs. transversal distance.
Figure 14. Peak stresses in the subgrade top at 5 m from the bottom vs. transversal distance.
Infrastructures 09 00054 g014
Table 1. Characteristics and properties of the investigated soil materials.
Table 1. Characteristics and properties of the investigated soil materials.
Characteristics and PropertiesSoil Materials
Itapeti (Soft Soil)SPAB (Stiff Soil)
Sand fraction (%)57.256.3
Silt and clay fraction (%)38.339.4
Gs2.7902.720
LL (%)4134
PL (%)2919
PI (%)1215
γdmax (kg/m3)17301950
wopt (%)16.912.2
HRB soil classificationA-7-5A-6
MCT tropical soil classificationNS′-NG′LA′-LG′
Table 2. RM constitutive model and regression coefficients of the materials.
Table 2. RM constitutive model and regression coefficients of the materials.
MaterialRM Non-Linear Constitutive Modelk1′k2k3R2
Pa
Ballast M R = k 1 σ d k 2 6,096,87760.1-0.94
Itapeti soil M R = k 1 σ 3 k 2 σ d k 3 8,727,4940.48241−0.297360.84
SPAB soil33,728,6340.3969−0.28140.74
RFBW 1 + ITA + CEM76,445,9290.27569−0.005030.97
RFBW 2 + ITA + CEM224,523,3180.21365−0.081930.91
RFBW 1 + ITA2,229,3170.43700−0.044010.94
RFBW 2 + ITA52,787,3630.068710.027790.20
Table 3. Compacted conditions of the studied materials.
Table 3. Compacted conditions of the studied materials.
MaterialγdmaxγdwoptwDegree of Compaction (DPr)
(kg/m3)(%)(%)
ITAPETI soil1730172016.216.999
SPAB soil1950197312.012.2101
RBFW 1 + ITA + CEM211021439.49.1102
RBFW 2 + ITA + CEM229322936.56.7100
RBFW 1 + ITA211021819.48.0103
RBFW 2 + ITA224022188.78.199
Table 4. Meshing characteristics of the developed numerical model.
Table 4. Meshing characteristics of the developed numerical model.
Railway Track ComponentNumber of ElementsElement TypeElement ShapeTechnique
Rail4CPE8RQuad-dominatedStructured
Rail pad2
Concrete sleeper16
Ballast41
Sub-ballast51
Subgrade119
Table 5. Constitutive model and input parameters of the materials applied in the numerical model.
Table 5. Constitutive model and input parameters of the materials applied in the numerical model.
Track ComponentMaterial TypeConstitutive ModelModel TypeYoung’s Modulus (MPa)Poisson’s Ratio (ʋ)k1′k2k3
RailSteel M R = E Linear elastic210,0000.30Table 2
Rail padElastomer135.50.01
SleeperReinforced concrete32,0000.20
BallastCrushed rock M R = k 1 σ d k 2 Non-linear elastic-
Sub-ballastRFBW 1/ITA/CEM M R = k 1 σ 3 k 2 σ d k 3 -0.30
RFBW 2/ITA/CEM-0.30
RFBW 1 + ITA-0.30
RFBW 2 + ITA-0.30
SubgradeItapeti soil-0.35
SPAB soil-0.35
Table 6. Model scenarios for the UMAT subroutine calibration and application to railway tracks.
Table 6. Model scenarios for the UMAT subroutine calibration and application to railway tracks.
Model ScenarioRailway Track ComponentABAQUS Built-In Linear ModelUMAT SubroutinePoisson’s Ratio
Young’s ModulusConstitutive Modelk1k2k3
(MPa)(Mpa)
ABAQUS built-in linear modelRail210,000 M R = E ---0.20
Rail pad135.5---0.25
Concrete sleeper32,000---0.01
Ballast- M R = k 1 σ d k 2 2080-0.20
Sub-ballast- M R = k 1 σ 3 k 2 σ d k 3 300000.30
Subgrade-70000.35
UMAT subroutine Rail210,000 ---0.20
Rail pad135.5---0.25
Concrete sleeper32,000---0.01
Ballast208 ---0.20
Sub-ballast300 ---0.30
Subgrade70---0.35
Table 7. Summary of the vertical displacements (U2), strains (ε22), and stresses (S22) for the Itapeti subgrade scenario.
Table 7. Summary of the vertical displacements (U2), strains (ε22), and stresses (S22) for the Itapeti subgrade scenario.
Subgrade ScenarioSub-Ballast SolutionTop of the Subgrade
(Depth = 0 m)
Rail
U2ε22S22U2
mm%kPamm
Itapeti soilItapeti soil without sub-ballast5.90.19972.26.5
RFBW 1 + ITA5.10.16866.16.1
RFBW 2 + ITA4.90.15562.65.7
RFBW 1/ITA/CEM4.50.11857.85.1
RFBW 2/ITA/CEM4.60.12459.15.2
Table 8. Summary of the vertical displacements (U2), strains (ε22), and stresses (S22) for the SPAB subgrade scenario.
Table 8. Summary of the vertical displacements (U2), strains (ε22), and stresses (S22) for the SPAB subgrade scenario.
Subgrade ScenarioSub-Ballast SolutionTop of the SubgradeRail
U2ε22S22U2
mm%kPamm
SPAB soilSPAB soil without sub-ballast2.70.07475.03.3
RFBW 1 + ITA2.50.07970.53.4
RFBW 2 + ITA2.40.08067.63.2
RFBW 1/ITA/CEM2.30.06763.82.9
RFBW 2/ITA/CEM2.30.07064.83.0
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Castro, G.; Saico, J.; de Moura, E.; Motta, R.; Bernucci, L.; Paixão, A.; Fortunato, E.; Oliveira, L. Evaluating Different Track Sub-Ballast Solutions Considering Traffic Loads and Sustainability. Infrastructures 2024, 9, 54. https://doi.org/10.3390/infrastructures9030054

AMA Style

Castro G, Saico J, de Moura E, Motta R, Bernucci L, Paixão A, Fortunato E, Oliveira L. Evaluating Different Track Sub-Ballast Solutions Considering Traffic Loads and Sustainability. Infrastructures. 2024; 9(3):54. https://doi.org/10.3390/infrastructures9030054

Chicago/Turabian Style

Castro, Guilherme, Jonathan Saico, Edson de Moura, Rosangela Motta, Liedi Bernucci, André Paixão, Eduardo Fortunato, and Luciano Oliveira. 2024. "Evaluating Different Track Sub-Ballast Solutions Considering Traffic Loads and Sustainability" Infrastructures 9, no. 3: 54. https://doi.org/10.3390/infrastructures9030054

Article Metrics

Back to TopTop