Track Modulus Assessment of Engineered Interspersed Concrete Sleepers in Ballasted Track

applied sciences

Article Track Modulus Assessment of Engineered Interspersed Concrete Sleepers in Ballasted Track

Arthur de Oliveira Lima, Marcus S. Dersch, Jaeik Lee and J. Riley Edwards *

Rail Transportation and Engineering Center—RailTEC, Department of Civil and Environmental Engineering-CEE, University of Illinois at Urbana-Champaign—UIUC, 205 N. Mathews Ave., MC-250, Urbana, IL 61801, USA; [email protected] (A.d.O.L.); [email protected] (M.S.D.); [email protected] (J.L.) * Correspondence: [email protected]

Abstract: Ballasted railway track is typically constructed using sleepers that are manufactured from a common material type within a given length of track. Timber and concrete are the two most common sleeper materials used internationally. Evidence from historical installations of interspersed concrete sleepers in timber sleeper track in North America has indicated inadequate performance, due largely to the heterogeneity in stiffnesses among sleepers. Theoretical calculations reveal that interspersed installation, assuming rigid concrete sleepers and supports, can result in rail seat forces more than five times as large as the force supported by the adjacent timber sleepers. Recently, engineered interspersed concrete (EIC) sleepers were developed using an optimized design and additional layers of resiliency to replace timber sleepers that have reached the end of their service lives while maintaining sleeper-to-sleeper stiffness homogeneity. To confirm that the concrete sleepers can successfully replicate the stiffness properties of the timber sleepers installed in track, field instrumentation was installed under revenue-service train operations on a North American commuter rail transit agency to measure the wheel–rail vertical loads and track displacement. The results indicated that there are minimal differences in median track displacements between timber (2.26 mm, 0.089 in.) and

EIC sleepers (2.21 mm, 0.087 in). Using wheel-load data and the corresponding track displacements associated with each wheel load, track modulus values were calculated using the single-point load method based on beam on elastic foundation (BOEF) fundamentals. The calculated values for the Citation: Lima, A.d.O.; Dersch, M.S.; Lee, J.; Edwards, J.R. Track Modulus track modulus indicated similar performances between the two sleeper types, with median values of Assessment of Engineered Interspersed 12.95 N/mm/mm (1878 lbs./in./in.) and 12.79 N/mm/mm (1855 lbs./in./in.) for timber sleepers Concrete Sleepers in Ballasted Track. and EIC sleepers, respectively. The ﬁeld results conﬁrmed the suitability of the new EIC sleeper Appl. Sci. 2021, 11, 261. https:// design in maintaining a consistent track modulus for the location studied, thus evenly sharing loads doi.org/10.3390/app11010261 between and among sleepers manufactured from both concrete and timber.

Received: 28 November 2020 Keywords: track modulus; ballasted track; ﬁeld measurement; interspersed concrete sleeper; timber Accepted: 24 December 2020 sleeper; concrete sleeper; wheel–rail vertical load Published: 29 December 2020

Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional clai- 1. Introduction ms in published maps and institutional afﬁliations. More than 94% of the world’s railroad track infrastructure is ballasted [1], and 94% of the North American Class I rail network is ballasted track that is constructed with timber sleepers [2]. The current best practices for maintaining timber-sleeper track typically include either in-kind replacement with timber sleepers or out-of-face replacement Copyright: © 2020 by the authors. Li- with concrete sleepers. Each year, North American railroads undertake in-kind replace- censee MDPI, Basel, Switzerland. ment of more than 12 million timber sleepers that have reached the end of their service This article is an open access article lives [3]. The out-of-face replacement of timber sleepers with concrete sleepers is not regu- distributed under the terms and con- larly pursued because of the associated costs [4]. When properly manufactured, concrete ditions of the Creative Commons At- sleepers have an expected lifespan of up to 45 years, several times that of the average tribution (CC BY) license (https:// timber sleeper [5]. Longer lifespans reduce the number of sleepers replaced each year, thus creativecommons.org/licenses/by/ decreasing maintenance costs and delays due to track occupancy for maintenance activities. 4.0/).

Appl. Sci. 2021, 11, 261. https://doi.org/10.3390/app11010261 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 261 2 of 13

Despite the comparatively limited use of concrete sleepers in North America, they are often used in the most demanding service conditions for high-speed or heavy axle load (HAL) applications [6–8]. Additionally, as annual gross tonnages have increased on many routes that have been constructed with timber sleepers, there is a quantifiable benefit from the added strength of concrete sleepers. This is due in part to the properties of prestressed concrete, which is commonly used to withstand the demanding loading environment imparted by passing trains [9]. Prestressed concrete provides increased flexural strength, ductility, and resistance to cracking [10]. As timber sleepers in ballasted track are replaced in kind by interspersing, the age and health of sleepers varies throughout the length of any given track segment. Given the bene- fits of concrete-sleeper track, the North American rail industry has made several attempts to intersperse concrete sleepers with timber as an incremental step to improve the strength of timber-sleeper track and gradually transition to concrete-sleeper track [11]. However, interspersing concrete with timber leads to spatial variation (heterogeneity) of the track stiffness, which leads to increases in the maximum rail stress and accelerates the rail fatigue process, and the rail-seat load applied to a given sleeper, which accelerates the ballast and substructure deterioration rates, which can lead to decreased track quality index (TQI) and ride quality [12]. Therefore, any effort to intersperse sleepers of different materials should consider the stiffness of each component and its effect on the track modulus. In this study, we quantified the track modulus of engineered interspersed concrete (EIC) sleepers that were installed in track to replace timber sleepers that had reached the end of their service lives. These EIC sleepers were designed to replicate timber’s stiffness via an optimized structural design to reduce bending stiffness and construct an innovative engineered rail seat plate and pad system. The revenue-service vertical wheel loads and resulting sleeper vertical displacements were measured and used to determine the track modulus. The results provided an improved understanding of the ability of EIC sleepers in timber-sleeper track to provide consistent stiffness to the adjacent timber sleepers, and thus a consistent track modulus.

2. Background and Theory Maintaining a consistent track modulus ensures that track performance meets the standard design and maintenance specifications (e.g., International Union of Railways (UIC) track performance evaluation criteria), and requires minimal maintenance interven- tions [13,14]. Fröhling [15] showed that vertical stiffness variations induce differential track settlements, resulting in accelerated deterioration of the railway track. Ensuring that sleeper support is consistent can also contribute to improved ride quality, and can minimize track and vehicle maintenance costs attributed to damage associated with variability in track stiffness. In this regard, stiffness transition zones are locations where abrupt changes in the track modulus occur due to a discontinuity in the track structure (e.g., between em- bankments and bridges or between different track configurations) [16], and a sizeable body of research has focused on providing a consistent track modulus to improve performance in these areas [17,18]. For example, Korea Code 14080 (KR C-14080) provides guidance on the maximum allowable change in the track modulus in a transition zone section [19]. In this guideline, the variance in the track modulus at the transition zone must be within the allowable range, which is commensurate with the maximum allowable train speed (Figure1) . This method considers the following factors: vibration acceleration of vehicle body, wheel load fluctuation, yield stress of rail fatigue, and uplifting force [19]. While the change in stiffness in typical transition zones is more abrupt and disruptive than sleeper- to-sleeper variation (approximately 42% between timber and concrete sleepers, and as much as 73% between regular track and an average bridge deck [20]), the comparison to interspersed concrete sleepers in timber sleeper track is still applicable. Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 13 Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 13

Appl. Sci. 2021, 11, 261 between regular track and an average bridge deck [20]), the comparison to interspersed3 of 13 between regular track and an average bridge deck [20]), the comparison to interspersed concrete sleepers in timber sleeper track is still applicable. concrete sleepers in timber sleeper track is still applicable.

Figure 1. The allowable ratio of the track modulus difference depending on train speed [19]. FigureFigure 1.1. TheThe allowableallowable ratioratio ofof thethe tracktrack modulusmodulus differencedifference dependingdepending onontrain trainspeed speed[ 19[19].]. Studies conducted on a Spanish high-speed line (HSL) indicate that maintenance at StudiesStudies conducted on a Spanish Spanish high-speed high-speed line line (HSL) (HSL) indicate indicate that that maintenance maintenance at transitions to bridges or box culverts can be up to three to six times more frequent attransitions transitions to tobridges bridges or or box box culverts culverts can can be be up up to to three three to six timestimes moremore frequentfrequent compared to open track [21]. This discontinuity at transitions can cause abnormal comparedcompared to to open open track track [21 ].[21]. This discontinuityThis discontinuity at transitions at transitions can cause can abnormal cause vibrationsabnormal vibrations in both the vehicle and the track, which compromise ride comfort and safety invibrations both the in vehicle both the and vehicle the track, and which the track, compromise which compromise ride comfort ride and comfort safety dueand tosafety the due to the difference in the track impact factor [22]. Low track-support stiffness can result differencedue to the indifference the track in impactthe track factor impact [22 fact]. Lowor [22]. track-support Low track-support stiffness stiffness can result can in result the in the development of adverse track geometry. Under these conditions, the track structure developmentin the development of adverse of adverse track track geometry. geometry Under. Under these these conditions, conditions, the the track track structure structure is is increasingly affected by vehicle loading, leading to loads that exceed the track strength increasinglyis increasingly affected affected by vehicleby vehicle loading, loading, leading leading to loads to loads that that exceed exceed the track the track strength strength and and accelerate track deterioration [8,23,24]. Building on earlier findings in track transition accelerateand accelerate track track deterioration deterioration [8,23, 24[8,23,24].]. Building Building on earlier on earlier ﬁndings findings in track in transitiontrack transition areas, areas, we investigated the difference in the track modulus due to the interspersed weareas, investigated we investigated the difference the difference in the track in modulus the track due modulus to the interspersed due to the installation interspersed of installation of EIC and timber sleepers. EICinstallation and timber of EIC sleepers. and timber sleepers. To mitigate the negative effects of train operation and maintenance, careful ToTo mitigatemitigate the the negative negative effects effects of train of operationtrain operation and maintenance, and maintenance, careful consid-careful consideration should be given when designing the track with different track materials. erationconsideration should should be given be when given designing when designin the trackg the with track different with different track materials. track materials. Various Various methods have been used to gradually change the track modulus (e.g., methodsVarious havemethods been usedhave tobeen gradually used changeto gradually the track change modulus the (e.g., track reinforcement modulus (e.g., rail, substructurereinforcement solidiﬁcation, rail, substructure reinforced solidification, roadbed reinforced layer, and changesroadbed tolayer, the timber-sleeperand changes to reinforcement rail, substructure solidification, reinforced roadbed layer, and changes to lengththe timber-sleeper and cross-sectional length and area) cross-sectional [25]. While the area) applications [25]. While are the quite applications different fromare quite the the timber-sleeper length and cross-sectional area) [25]. While the applications are quite currentdifferent practice from the of current interspersing practice concrete of inters andpersing timber concrete sleepers and (Figure timber2 ),sleepers the objective (Figure different from the current practice of interspersing concrete and timber sleepers (Figure is2), the the same—to objective maintain is the same—to a consistent maintain track modulus a consistent to minimize track modulus excessive to vehicle minimize and 2), the objective is the same—to maintain a consistent track modulus to minimize trackexcessive loads. vehicle and track loads. excessive vehicle and track loads.

Figure 2. Installation of timber and engineered interspersed concrete (EIC) sleepers. FigureFigure 2.2. InstallationInstallation ofof timbertimber andand engineeredengineered interspersedinterspersed concreteconcrete(EIC) (EIC)sleepers. sleepers. VariousVarious methodologiesmethodologies forfor estimating estimating a track’sa track’s structural structural behavior behavior have have been been de- Various methodologies for estimating a track’s structural behavior have been velopeddeveloped and and documented. documented. Pasternak’s Pasternak’s method method applies applies Winker’s Winker’s model model to to consider consider the the developed and documented. Pasternak’s method applies Winker’s model to consider the foundation based on the upper and lower spring layers and the shear layer [26]. Timo- shenko’s foundation model considers the effect of transverse shear deﬂection resulting from an error in shear force and moment distribution, which can become signiﬁcant in Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 13

foundation based on the upper and lower spring layers and the shear layer [26]. Appl. Sci. 2021, 11, 261 4 of 13 Timoshenko’s foundation model considers the effect of transverse shear deflection resulting from an error in shear force and moment distribution, which can become significant in foundation beams with a small length-to-depth ratio in closely spaced discretefoundation column beams loads with [27]. a smallA model length-to-depth developed by ratioKerr in[28], closely which spaced is based discrete on Pasternak’s column methodloads [27 and]. A employs model developed Reissner’s byfoundation Kerr [28], mo whichdel, has is based an advantage on Pasternak’s over other method models and becauseemploys in Reissner’s the upper foundation spring layer, model, no concentr has an advantageated reactions over or other infinite models reaction because pressure in the canupper appear spring [28]. layer, no concentrated reactions or inﬁnite reaction pressure can appear [28]. For this study’s comparative analysis of the effect of inserting EIC sleepers in continuous-welded rail timber-sleeper track, a beam on elastic foundation (BOEF) model developed by Kerr [[29]29] waswas employed.employed. This method, which is well-established in the international railway railway community, community, is known to be reasonablyreasonably representative,representative, andand allowsallows for determination of the track modulus (i.e., the stiffness of the spring k per unit length of track) [30]. [30]. In this this model, model, a a concrete concrete sleeper sleeper is is repres representedented by by a asingle single spring spring with with a constant a constant κ, whileκ, while the the timber timber sleepers sleepers are are represented represented by by a aWinkler Winkler base base with with a a track modulus k (Figure3 3)) [31].[31]. The The adjacent adjacent wheels wheels are are not cons consideredidered due to their negligible effect on the overall behavior of the system.

Figure 3. The analytical model of the interspersed concrete sleepersleeper in a continuous welded rail tracktrack [[29].29].

The corresponding governing equation for this model is:

IV EIw𝐸𝐼𝑤 + +kw 𝑘𝑤(𝑥)(x) = q0 = 𝑞 (1) where w is the vertical deflection of the rail axis at x; EI is the vertical flexural stiffness of where w is the vertical deﬂection of the rail axis at x; EI is the vertical ﬂexural stiffness one rail; k is the track modulus (for one rail), and uniformly distributed load; 𝑞 is the of one rail; k is the track modulus (for one rail), and uniformly distributed load; q is the general solution for w is as shown in Equation (2). 0 general solution for w is as shown in Equation (2). Based on the above model, the corresponding force that the rail exerts on the concrete Based on the above model, the corresponding force that the rail exerts on the concrete sleeper is: q κ 𝜅 q 4β3 F = κw(0) = κ 0𝑞 1 − 2EI = κ 0𝑞 4𝛽 , (2) c−t 3 +2𝐸𝐼κ 3 + κ 𝐹 =𝜅𝑤(0) =𝜅k 1 −4β 2EI𝜅 =𝜅k 4β 2EI𝜅 , (2) 𝑘 4𝛽 + 𝑘 4𝛽 + whereas the corresponding force that the rail exerts2𝐸𝐼 on the timber sleeper2𝐸𝐼 is: whereas the corresponding force that the rail exerts on the timber sleeper is: Fq0 = q0 × a (3) 𝐹 =𝑞 ×𝑎 (3) Therefore, the effect of the inserted concrete sleeper is: Therefore, the effect of the inserted concrete sleeper is: F − κ 1 c t = (4) Fq0 ak 1 + βκ/(2k) Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 13

𝐹 𝜅 1 = ( ) (4) 𝐹 𝑎𝑘 1+𝛽𝜅/(2𝑘) Based on the previous formulations and the common track property values listed in Appl. Sci. 2021, 11, 261 5 of 13 Table 1, the corresponding values of 𝐹/𝐹 can be determined for various values of κ (Table 2 and Figure 4).

Based on the previous formulations and the common track property values listed in Table 1. The values of various parameters for calculating the effect ratio [32]. Table1, the corresponding values of Fc−t/Fq0 can be determined for various values of κ (Table2 and Figure4). Modulus of Moment of Wood Timber Sleeper Concrete Sleeper Rail ElasticityTable 1. The values of variousInertia parameters for calculatingModulus, the effect ratio k [32]. spacing Modulus, 𝛋 Modulus of Moment of Wood Timber Sleeper Rail 210,000 MPa 36,700,000 mm 20.69 N/mm/mmConcrete Sleeper 508 mm Modulus, κ 132RE Elasticity Inertia Modulus, k Spacing Variable 30,000,000 psi 88.2 in. 3000 lbs./in./in. 20 in. 210,000 MPa 36,700,000 mm4 20.69 N/mm/mm 508 mm 132RE Variable 30,000,000 psi 88.2 in.4 3000 lbs./in./in. 20 in.

Table 2. The calculation result of 𝐹/𝐹 for various values of κ.

Table 2. The calculation result of Fc−t/Fq0 for various values of κ. 1.75 kN/mm 17.51 kN/mm 43.78 kN/mm 87.56 kN/mm 175.13 kN/mm 1.75 kN/mm 17.51 kN/mm 43.78 kN/mm 87.56 kN/mm 175.13 kN/mm 𝛋 κ 10 kips/in. 10 kips/in.100 kips/in.100 kips/in. 250250 kips/in. kips/in. 500 kips/in.500 kips/in.1000 kips/in. 1000 kips/in. F /F 0.160 1.204 2.124 2.851 3.440 𝐹/𝐹 c−t q0.1600 1.204 2.124 2.851 3.440

Figure 4. The result of Fc−t/Fq0 depending on the spring constant of the concrete sleeper (κ )[29]. Figure 4. The result of 𝐹/𝐹 depending on the spring constant of the concrete sleeper (κ) [29]. The above analysis reveals that when a concrete sleeper replaces a timber sleeper, the higherThe stiffness above of analysis the concrete reveals sleeper that will when result in a thatconcrete sleeper sleeper supporting replaces propor- a timber sleeper, the tionallyhigher higher stiffness rail-seat of the loads concrete due to the sleeper difference will in sleeper result stiffness. in that According sleeper supporting to this proportionally analysis, when a concrete sleeper is adjacent to a timber sleeper, the concrete sleeper can receivehigher as rail-seat much as ﬁve loads times due more to load the than difference the adjacent in timbersleeper sleepers stiffness. (Kerr’s According calcu- to this analysis, 2 lationswhen are a concrete as follows: sleeperlim Fc−t /isF qadjacent= = to5.076 a ).timber However, sleeper, Kerr’s analysisthe concrete assumes sleeper can receive as κ→∞ 0 βa thatmuch the concreteas five sleepertimes more and its load supporting than structurethe adjacent are rigid. timber The typical sleepers track (Kerr’s mod- calculations are as ulus value for mainline concrete-sleeper track is 41.38 N/mm/mm (6000 lbs./in./in.), follows: lim (𝐹/𝐹 )= = 5.076). However, Kerr’s analysis assumes that the concrete which is twice→ as stiff as the typical timber-sleeper track modulus of 20.69 N/mm/mm (3000sleeper lbs./in./in.) and its [32 ].supporting Considering this, structure and employing are therigid. same The analysis typical methodology track modulus value for by Kerr, the load supported by the concrete sleeper can be approximately 1.37 times higher thanmainline the load concrete-sleeper supported by the timber track sleepers. is 41.38 Regardless, N/mm/mm the concrete (6000 sleeperlbs./in./in.), will which is twice as acceptstiff as a greater the typical magnitude timber-sl verticaleeper load, and track will transfermodulus a higher of 20.69 pressure N/ tomm/mm the ballast. (3000 lbs./in./in.) [32]. TheseConsidering higher demands this, could and lead employing to localized sleeperthe same structural analysis damage, ballastmethodology crushing, by Kerr, the load and/or substructure damage that would result in an overall poor track condition after the accumulationsupported ofby tonnage. the concrete sleeper can be approximately 1.37 times higher than the load supported by the timber sleepers. Regardless, the concrete sleeper will accept a greater magnitude vertical load, and will transfer a higher pressure to the ballast. These higher demands could lead to localized sleeper structural damage, ballast crushing, and/or substructure damage that would result in an overall poor track condition after the accumulation of tonnage. The EIC sleeper used in this study attempts to reduce the differential stiffness between sleeper material types through an optimized structural design that reduces bending stiffness, and an innovative engineered rail seat plate and pad system. Appl. Sci. 2021, 11, 261 6 of 13

Appl. Sci. 2021, 11, x FOR PEER REVIEW The EIC sleeper used in this study attempts to reduce the differential6 of 13 stiffness between sleeper material types through an optimized structural design that reduces bending stiffness, and an innovative engineered rail seat plate and pad system.

3. Field Experimentation3. Field Experimentation Methods Methods 3.1. Engineered3.1. EngineeredInterspersed Interspersed Concrete (EIC) Concrete Sleeper (EIC) Sleeper The EIC sleeperThe EIC installed sleeper at installed the commuter-rail at the commuter-rail field test site ﬁeld (Figure test site 5a) (Figure had a smaller5a) had a smaller cross-sectionalcross-sectional area, and consequently area, and consequently a smaller flexural a smaller rigidity, ﬂexural than rigidity, the two than typical the two typical concrete sleepersconcrete used sleepers for either used heavy for either axle heavy load (HAL) axle load freight (HAL) (Figure freight 5b) (Figure or light-rail5b) or light-rail transit (Figuretransit 5c) (Figureapplications5c) applications in North America. in North The America. EIC sleeper The featured EIC sleeper a ductile featured plate a ductile and resilientplate pad and positioned resilient pad in positionedthe vertical in load the verticalpath, which load path, reduced which the reduced sleeper’s the sleeper’s stiffness. Thisstiffness. reduced This stiffness reduced was stiffness engineered was to engineered be comparable to be tocomparable a timber sleeper, to a timberwith sleeper, the goal ofwith preventing the goal ofthe preventing various problems the various with problems stiffness with heterogeneity stiffness heterogeneity that were that were mentionedmentioned previously. previously.

(a)

(b)

(c)

Figure 5. A Figurecomparison 5. A comparisonof (a) an EIC of sleeper; (a) an EIC(b) a sleeper; typical North (b) a typical American North freight American HAL concrete freight HAL concrete sleeper; (c) a typical North American light rail transit concrete sleeper. sleeper; (c) a typical North American light rail transit concrete sleeper.

3.2. Field Site3.2. and Field Instrumentation Site and Instrumentation A field testA zone ﬁeld was test zoneselected was in selected a tangen int atrack tangent in which track the in whichtimber the sleepers timber had sleepers had recently beenrecently replaced been with replaced EIC sleepers. with EIC A sleepers. visual assessment A visual assessment showed evidence showed of evidence ballast of ballast fouling in thefouling test zone in the location, test zone although location, drainage although still drainage appeared still to appeared function to properly, function as properly, as there was nothere standing was no water, standing and water, appropriate and appropriate shoulders shoulders were still were present. still present.This selection This selection of of a singlea zone single limited zone limited the variability the variability in da inta data due due to tosubstructure substructure differences, differences, while while capturing capturing variousvarious installation installation conditions, conditions, including including different different permutations permutations of interspersed of timber interspersedand timber EIC sleepers and EIC (Figure sleepers6). The(Figure instrumentation 6). The instrumentation was deployed was to deployed quantify both to vertical quantify bothwheel–rail vertical input wheel–rail loads andinput vertical loads and track vertical displacements. track displacements. Vertical wheel–rail forces were quantiﬁed using strain-gauge-based industry-standard circuits as described by Edwards [33]. The installation of strain gauges on the rail required the welding of gauges to the rail using a portable strain-gauge welding unit. This process involved grinding the web and base of the rail to remove rust and expose pure metal, clamping a ground wire to the base of the rail, and placing the strain gauge and using the welding electrode to send current through the material, which welded the strain gauge to the rail. These gauges were subsequently calibrated using a loading frame with calibrated load cell, allowing strains to be used to quantify vertical wheel–rail loads. During the calibration, vertical loads of up to 200 kN (45,000 lbf) were applied to the rail while the voltage from the strain bridge was simultaneously recorded.

Figure 6. The test zone, with the timber and EIC sleepers shown with the instrumentation layout.

Vertical wheel–rail forces were quantified using strain-gauge-based industry- standard circuits as described by Edwards [33]. The installation of strain gauges on the rail required the welding of gauges to the rail using a portable strain-gauge welding unit. Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 13

3. Field Experimentation Methods 3.1. Engineered Interspersed Concrete (EIC) Sleeper The EIC sleeper installed at the commuter-rail field test site (Figure 5a) had a smaller cross-sectional area, and consequently a smaller flexural rigidity, than the two typical concrete sleepers used for either heavy axle load (HAL) freight (Figure 5b) or light-rail transit (Figure 5c) applications in North America. The EIC sleeper featured a ductile plate and resilient pad positioned in the vertical load path, which reduced the sleeper’s stiffness. This reduced stiffness was engineered to be comparable to a timber sleeper, with the goal of preventing the various problems with stiffness heterogeneity that were mentioned previously.

(a)

(b)

(c) Figure 5. A comparison of (a) an EIC sleeper; (b) a typical North American freight HAL concrete sleeper; (c) a typical North American light rail transit concrete sleeper.

3.2. Field Site and Instrumentation A field test zone was selected in a tangent track in which the timber sleepers had recently been replaced with EIC sleepers. A visual assessment showed evidence of ballast fouling in the test zone location, although drainage still appeared to function properly, as there was no standing water, and appropriate shoulders were still present. This selection of a single zone limited the variability in data due to substructure differences, while

Appl. Sci. 2021, 11, 261 capturing various installation conditions, including different permutations7 ofof 13 interspersed timber and EIC sleepers (Figure 6). The instrumentation was deployed to quantify both vertical wheel–rail input loads and vertical track displacements.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 13

This process involved grinding the web and base of the rail to remove rust and expose pure metal, clamping a ground wire to the base of the rail, and placing the strain gauge and using the welding electrode to send current through the material, which welded the strain gauge to the rail. These gauges were subsequently calibrated using a loading frame with calibrated load cell, allowing strains to be used to quantify vertical wheel–rail loads. During the calibration, vertical loads of up to 200 kN (45,000 lbf) were applied to the rail FigureFigure 6. 6. TheThe test test zone, zone, with with the the timber timber and and EIC EIC sleepers sleepers shown shown with with the the instrumentation instrumentation layout. layout. while the voltage from the strain bridge was simultaneously recorded. VerticalVertical tracktrack displacementsdisplacements were were measured measured to to quantify quantify the the track track modulus modulus on bothon both EIC Vertical wheel–rail forces were quantified using strain-gauge-based industry- EICsleepers sleepers and timber and sleepers.timber sleepers. Displacement Displa transducers,cement transducers, which are linear which potentiometers are linear standard circuits as described by Edwards [33]. The installation of strain gauges on the potentiometers(Figure7), were (Figure used to 7), measure were used the trackto measure displacement the track at displacement the rail base at relative the rail to base the rail required the welding of gauges to the rail using a portable strain-gauge welding unit. relativeground. to This the wasground. accomplished This was accomplished by driving support by driving rods support 40 mm (5/8rods in.)40 mm in diameter (5/8 in.) toin diameterrefusal in to the refusal ﬁeld-side in the crib field-side between crib the between sleepers. the The sleepers. potentiometers The potentiometers had a maximum had a − maximumstroke length stroke of 25 length mm (1of in.),25 mm and (1 were in.), and accurate were toaccurate±0.002 to mm ±0.002 (7.9 mm×10 (7.95 in.). ×10 The in.). cali- Thebration calibration factors werefactors provided were provided by the manufacturer by the manufacturer and further and checked further before checked installation before installationusing a calibration using a heightcalibration gauge. height gauge.

FigureFigure 7. 7. TheThe linear potentiometer and rod system used to measure the vertical track displacement.

AllAll data data were were recorded recorded using a National National Instruments Instruments (NI) Compact Data Acquisition SystemSystem (cDAQ) (cDAQ) via via a a LabVIEW LabVIEW virtual virtual instrume instrumentnt (VI) developed developed for the instrumentation instrumentation usedused in in this experiment. The The data data were were collected collected at at a a sampling rate of 2.5 kHz to ensure thethe maximum maximum wheel–rail wheel–rail load load was was captured.

3.3.3.3. Single-Point Single-Point Load Load Method Method for for Track Track Modulus Calculation TheThe track track modulus modulus values values were were calculated calculated using the single-point single-point load method, which was developeddeveloped and and documented documented by Seligby Selig and Waters and Waters [34]. This [34]. method This requires method knowledge requires knowledgeof the rail’s sectionalof the rail’s properties, sectional the properties wheel load,, the and wheel the track load, deﬂection. and the Using track these deflection. inputs, Usingand based these on inputs, the BOEF and fundamentals, based on the the BOEF track fundamentals, modulus was computed.the track modulus The equation was computed.used to calculate The equation track modulus used to iscalc shownulate below:track modulus is shown below: 4/3 P𝑃 / (wm ) k = 𝑤 (5) 𝑘=( )1/3 64(64𝐸𝐼)EI /

where 𝑘 is the track modulus (kN/mm, lb./in./in. ); 𝑤 is the maximum track deflection (mm, in); 𝑃 is the wheel load (kN, lb.); 𝐸 is the modulus of elasticity of steel (MPa, psi) = 210,000 MPa, 30 × 106 psi; 𝐼 is the moment of inertia of rail (mm,in) = 36,700,000 mm, 88.2 in (132RE Rail); 𝐸𝐼 is the flexural rigidity of the rail. Other methods to calculate the track modulus require additional knowledge of the entire deflection basin and its area, which is more complicated to quantify analytically. For this study, the single-point load method was deemed appropriate. This study required a deviation from the traditional single-point load method for determining the track Appl. Sci. 2021, 11, 261 8 of 13

where k is the track modulus (kN/mm, lb./in./in.); wm is the maximum track deflection (mm, in); P is the wheel load (kN, lb.); E is the modulus of elasticity of steel (MPa, psi) = 210, 000 MPa, 30 × 106 psi; I is the moment of inertia of rail (mm4, in4) = 36,700,000 mm4, 88.2 in4 (132RE Rail); EI is the flexural rigidity of the rail. Other methods to calculate the track modulus require additional knowledge of the Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 13 entire deflection basin and its area, which is more complicated to quantify analytically. For this study, the single-point load method was deemed appropriate. This study required a deviation from the traditional single-point load method for determining the track modulus because of themodulus interaction because between of the the interaction wheels applying between loads the wheels adjacent applying to the loads point adjacent in to the which the peakspoint were in extracted,which the peaks so there were was extracted, no true so single there point was no that true applied single point the load. that applied the For the rollingload. stock For used, the rolling this interaction stock used, effect this interaction of the adjacent effect of wheels the adjacent was negligible wheels was negligible (approximately(approximately 0.8% based on the0.8% BOEF based analysis). on the Additionally, BOEF analysis). the interaction Additionally, influenced the interaction both the EIC sleepersinfluenced and timberboth the sleepers EIC sleepers in the and same timber manner, sleepers which inmitigated the same manner, its potential which mitigated negative impactits on potential the results, negative which impact were on largely the results, comparative which were in nature. largely comparative in nature. For the single-pointFor the load single-point method, thereload method, is typically there no is adjustment typically no for adjustment potential for slack potential slack in the system duein the to system gaps beneath due to gaps the sleepers.beneath the While sleepers. this couldWhile leadthis could to errors lead basedto errors based on on visual deflectionvisual observationsdeflection observations that appeared that to appeared indicate gapsto indicate were present,gaps were the present, large the large number of sleepersnumber for whichof sleepers data werefor which collected data (23were total) collected increased (23 ourtotal) confidence increased inour the confidence in data, and quantifiedthe data, the and representative quantified the behavior representative of each sleeperbehavior type of each while sleeper mitigating type while the mitigating presence of gapsthe below presence any of given gaps crosstie. below any given crosstie.

4. Results and4. Discussion Results and Discussion The data were collectedThe data from were a total collected of 10 revenue-service from a total trainof 10 passes revenue-service at approximately train passes at 64 km/h (40 mph).approximately The trains 64 includedkm/h (40 amph). combined The trains 12 locomotives included a combined and 116 passenger12 locomotives and 116 coaches, totalingpassenger 512 axle coaches, passes. totaling A total 512 of axle 23 rail-basepasses. A displacementtotal of 23 rail-base channels displacement were channels recorded (the sensorwere recorded placed on(the sleeper sensor 11 placed malfunctioned), on sleeper 11 and malfunctioned), the corresponding and the data corresponding (11,236 data points)data (11,236 were used data to points) generate were the used ﬁgures to genera below.te Thethe figures data were below. found The to data have were found to high signal-to-noisehave high ratios signal-to-noise and were considered ratios and clean were (Figure considered8). As clean expected, (Figure the 8). peaks As expected, the in the two datapeaks streams in the were two generated data streams when were a wheel generated was directly when a abovewheel eachwas sleeperdirectly above each (in the case of displacements)sleeper (in the case and of in displacements) the center of theand cribin th (ine center the case of the of crib the wheel-load(in the case of the wheel- bridge). The peaksload frombridge). the The load peaks anddisplacement from the load channelsand displacement were extracted channels from were the extracted data from the primarily throughdata manual primarily peak through selection, manual with somepeak assistanceselection, providedwith some using assistance developed provided using MATLAB algorithms.developed MATLAB algorithms.

Figure 8. An exampleFigure of 8. track An example displacement of track and displacement wheel load and data. wheel load data.

Wheel Load and4.1. Displacement Wheel Load Comparison and Displacement Results Comparison Results The distributionThe of distribution wheel loads of measured wheel loads at the measured ﬁeld site at for the both field passenger site for both coaches passenger coaches and locomotivesand matched locomotives the expected matched loads the expected based on loads the nominalbased on static the nominal load ratings static thatload ratings that were acquired previouslywere acquired (Figure previously9). (Figure 9). Appl.Appl. Sci. 20212021,, 1111,, 261xx FORFOR PEERPEER REVIEWREVIEW 9 of of 13 13

FigureFigure 9.9. The distribution ofof thethe wheelwheel loadsloads measuredmeasured atat site.site.

TheThe datadata showed showed a minimala minimal difference difference in track in tracktrack displacements displacementsdisplacements between betweenbetween the two thethe sleeper twotwo typessleeper (Figure types (Figure10) independent 10) independent of load of source load source (passenger (passenger coach coach or locomotive). or locomotive). The The ob- servedobserved median median displacement displacement values values under unde ther the passenger passenger coaches coaches were were 2.26 2.26 mm mm (0.089 (0.089 in.) andin.)in.) 2.21andand mm2.212.21 (0.087 mmmm (0.087 in.)(0.087 for in.)in.) timber forfor andtimbertimber EIC sleepers,anand EIC respectively.sleepers, respectively. The observed The median observed dis- placementmedian displacement values under values the locomotives under the werelocomotives 2.70 mm were (0.1062 2.70 in.) mm and (0.1062 2.74 mm in.) (0.1078 and 2.74 in.) formm timber (0.1078 and in.) EIC for sleepers,timber and respectively. EIC sleepers, The re locomotivespectively. The data locomotive were also usefuldata were because also theyuseful provided because a they proxy provided for the expected a proxy behaviorfor the expected of these sleeperbehavior types of these under sleeper loaded types HAL freight-trainunder loaded loads. HAL freight-train loads.

FigureFigure 10.10. ComparisonComparison ofof thethe tracktrack displacementdisplacement betweenbetween thethe timbertimber andand EICEIC sleepers.sleepers.

TheThe fieldfield resultsresults (Figure(Figure 1111)) showedshowed thatthat thethe sleepers’sleepers’ positionalpositional variabilityvariability exceededexceeded thatthat ofofof thethethe observedobservedobserved variabilityvariabilityvariability betweenbetweenbetween sleeperslsleeper types.types. ForFor example,example, thethe displacementdisplacement resultsresults ofof thethe firstfirst tenten sleeperssleepers rangedranged fromfrom 1.221.22 mmmm (0.048(0.048 in.)in.) to 3.02 mm (0.119 in.). WithinWithin thisthis range, range, both both the the minimum minimum and and maximum maximum peak peak values values were recordedwere recorded for timber for sleepers.timbertimber sleepers.sleepers. The highest TheThe highesthighest median medianmedian values valuesvalues weremeasured wewere measured in sleepers in sleepers 21 to 24,21 to ranging 24, ranging from 3.81from mm 3.81 (0.150mm (0.150 in.) toin.) 4.32 to 4.32 mm mm (0.170 (0.170 in.), in and.),.), andand included includedincluded both bothboth sleeper sleepersleeper types. types.types.When WhenWhen wewewe comparedcompared sleeper-displacementsleeper-displacement results alone,alone, itit waswas difficultdifficult toto distinguishdistinguish variabilityvariability betweenbetween timbertimber andand EIC EIC sleepers, sleepers, a a finding finding that that was was also also documented documented in priorin prior research research [9]. [9]. Using both the loading data and the corresponding track displacements, the track- modulus values for all axles were determined using the single-point load method (Figure 12). As discussed in Section3, any potential contribution for slack in the system was mitigated by capturing many replicate sleepers (23 in total). The timber-sleeper and EIC- sleeper median track-modulus values were 12.95 N/mm/mm (1878 lbs./in./in.) and 12.79 N/mm/mm (1855 lbs./in./in.), respectively. The five-sleeper moving-average track Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 13

Appl. Sci. 2021, 11, 261 10 of 13

modulus result showed a minimal difference in track response to load when the rail was supported by either a timber sleeper or an EIC sleeper (Figure 13). The calculated results are not independent measurements; they are dependent on the speciﬁc site conditions and interspersed arrangement, so the modulus of the EIC sleepers was dependent on the adjacent Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 13 sleepers, and vice versa. Nevertheless, the obtained results indicated that the EIC sleepers provided a similar stiffness response to the timber sleepers in this interspersed installation.

Figure 11. The displacement results for each individual sleeper (passenger coaches only).

Using both the loading data and the corresponding track displacements, the track- modulus values for all axles were determined using the single-point load method (Figure 12). As discussed in Section 3, any potential contribution for slack in the system was mitigated by capturing many replicate sleepers (23 in total). The timber-sleeper and EIC- sleeper median track-modulus values were 12.95 N/mm/mm (1878 lbs./in./in.) and 12.79 N/mm/mm (1855 lbs./in./in.), respectively. The five-sleeper moving-average track modulus result showed a minimal difference in track response to load when the rail was supported by either a timber sleeper or an EIC sleeper (Figure 13). The calculated results are not independent measurements; they are dependent on the specific site conditions and interspersed arrangement, so the modulus of the EIC sleepers was dependent on the adjacent sleepers, and vice versa. Nevertheless, the obtained results indicated that the EIC sleepers provided a similar stiffness response to the timber sleepers in this interspersed installation. FigureFigure 11. 11.The Thedisplacement displacement results results for for each each individual individual sleeper sleeper (passenger (passenger coaches coaches only). only).

Using both the loading data and the corresponding track displacements, the track- modulus values for all axles were determined using the single-point load method (Figure 12). As discussed in Section 3, any potential contribution for slack in the system was mitigated by capturing many replicate sleepers (23 in total). The timber-sleeper and EIC- sleeper median track-modulus values were 12.95 N/mm/mm (1878 lbs./in./in.) and 12.79 N/mm/mm (1855 lbs./in./in.), respectively. The five-sleeper moving-average track modulus result showed a minimal difference in track response to load when the rail was supported by either a timber sleeper or an EIC sleeper (Figure 13). The calculated results are not independent measurements; they are dependent on the specific site conditions and interspersed arrangement, so the modulus of the EIC sleepers was dependent on the adjacent sleepers, and vice versa. Nevertheless, the obtained results indicated that the EIC sleepers provided a similar stiffness response to the timber sleepers in this interspersed Figureinstallation. 12. Comparison of the track modulus between th thee timber timber and and EIC EIC sleepers, sleepers, considering considering all all measured locomotivelocomotive andand passengerpassenger coachcoach ﬁeldfield data.data.

Figure 12. Comparison of the track modulus between the timber and EIC sleepers, considering all measured locomotive and passenger coach field data. Appl. Sci. 2021, 11, 261 11 of 13 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 13

FigureFigure 13.13. TheThe tracktrack modulusmodulus resultsresults for for each each individual individual sleeper sleeper instrumented instrumented in in the the field field test test zone. zone. 5. Conclusions 5. ConclusionsThis study assessed a section of track with interspersed timber sleepers and EIC sleepersThis that study were assessed designed a tosection replicate of track timber-sleeper with interspersed stiffness, timber and provided sleepers an and analyt- EIC icalsleepers evaluation that were of the designed expected stiffnessto replicate variation timber-sleeper between traditionalstiffness, concreteand provided sleepers, an whichanalytical can leadevaluation to an acceleratedof the expected deterioration stiffness of variation the railway between track andtraditional its components. concrete Basedsleepers, on Kerr’swhich structural-analysiscan lead to an accelerated method, thedeterioration conducted of theoretical the railway analysis track demon-and its stratedcomponents. that the Based expected on variation Kerr’s structural-analysis in the track-modulus method, value between the conducted sleeper types theoretical caused aanalysis difference demonstrated in the load-support that the distribution.expected variation A field in investigation the track-modulus was used value to evaluatebetween thesleeper performance types caused of an intersperseda difference sleeperin the load structure-support composed distribution. of EIC A and field timber investigation sleepers. Basedwas used on thisto evaluate background, the performance the field experimentation of an interspersed results, sleeper and thestructure evaluation composed of each of rail-seatEIC and performance,timber sleepers. the Based findings on andthis background, conclusions were: the field experimentation results, and •the evaluationThe theoretical of each analysis rail-seat showed performa thatnce, interspersed the findings standard and conclusions concrete sleepers were: placed • withinThe theoretical a timber-sleeper analysis track showed can that experience interspersed a load standard up to five concrete times greater sleepers than placed the loadwithin supported a timber-sleeper by the adjacent track can timber experience sleepers. a load up to five times greater than the • Based on measurements of sleeper displacement, both timber sleepers and EIC sleepers load supported by the adjacent timber sleepers. presented a similar track response. For timber sleepers, the median displacement • Based on measurements of sleeper displacement, both timber sleepers and EIC value was 2.26 mm (0.089 in.), and for EIC sleepers, it was 2.21 mm (0.087 in.). sleepers presented a similar track response. For timber sleepers, the median • The track-displacement results from the field instrumentation ranged from 1.22 mm displacement value was 2.26 mm (0.089 in.), and for EIC sleepers, it was 2.21 mm (0.048 in.) to 4.32 mm (0.170 in.) for all timber sleepers. (0.087 in.). • The track-modulus results indicated a median modulus of 12.95 N/mm/mm • The track-displacement results from the field instrumentation ranged from 1.22 mm (1878 lbs./in./in.) for the timber sleepers, and 12.79 N/mm/mm (1855 lbs./in./in.) (0.048 in.) to 4.32 mm (0.170 in.) for all timber sleepers. for the EIC sleepers. • The track-modulus results indicated a median modulus of 12.95 N/mm/mm (1878 • The variance in performance for the two sleeper types cannot be clearly distinguished lbs./in./in.) for the timber sleepers, and 12.79 N/mm/mm (1855 lbs./in./in.) for the EIC with track-displacement or modulus results, which provides a favorable indication for sleepers. future field performance. • The variance in performance for the two sleeper types cannot be clearly distinguished Basedwith track-displacement on the results, the or desired modulus performance results, which of the provides EIC sleepers a favorable in maintaining indication consistent track modulus was demonstrated for this application and set of track conditions. for future field performance. This homogeneity in modulus is crucial to ensure a smooth ride quality and minimize trackBased maintenance on the dueresults, to geometry the desired deviations. performance The principalof the EIC design sleepers characteristics in maintaining that contributedconsistent track to the modulus EIC sleeper’s was performancedemonstrated were for the this reduced application cross-sectional and set areaof track and resultingconditions. reduction This homogeneity in flexural rigidity, in modulus and the is resilientcrucial to rail-seat ensure plate a smooth system, ride with quality the latter and providingminimize mosttrack of maintenance the stiffness reduction.due to geometry This study deviations. showed that The properly principal engineered design concretecharacteristics sleepers that can contributed be interspersed to the EIC in timber-sleeper sleeper’s performance track to were achieve the a reduced similar cross- track response.sectional area Nevertheless, and resulting the exact reduction results in for flexural the track rigidity, modulus and obtainedthe resilient in thisrail-seat study plate are notsystem, entirely with independent, the latter providing and should most not of bethe extrapolated stiffness reduction. to other This applications/locations study showed that withoutproperly further engineered study. Futureconcrete work sleepers should can include be interspersed field experimentation in timber-sleeper in locations track with to aachieve higher overalla similar track track modulus response. and Neverthele different arrangementsss, the exact ofresults the sleeper for the installation. track modulus obtained in this study are not entirely independent, and should not be extrapolated to Appl. Sci. 2021, 11, 261 12 of 13

Author Contributions: Conceptualization, A.d.O.L. and J.R.E.; methodology, A.d.O.L. and M.S.D.; data collection, A.d.O.L., J.R.E. and M.S.D.; data processing, A.d.O.L. and J.L.; writing—original draft preparation, A.d.O.L., J.R.E., J.L.; writing—review and editing, A.d.O.L., J.R.E. and M.S.D.; super- vision, J.R.E.; project administration, A.d.O.L.; funding acquisition, J.R.E. and A.d.O.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was primarily supported through funding from the National University Rail Center (NURail). The positions presented within this paper represent those of the authors and not necessarily those of the US Department of Transportation. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Restrictions apply to the availability of these data. Data are owned by a sponsoring agency but may be available from the authors with permission of the sponsoring agency. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Matias, S.R.; Ferreira, P.A. Railway slab track systems: Review and research potentials. Struct. Infrastruct. Eng. 2020, 16, 1635–1653. [CrossRef] 2. Railway Tie Association (RTA). Available online: https://www.rta.org/faq (accessed on 12 November 2020). 3. Qiao, P.; Davalos, J.F.; Zipfel, M.G. Modeling and optimal design of composite-reinforced wood railroad crosstie. Compos. Struct. 1998, 41, 87–96. [CrossRef] 4. McCombe, E.; Ryan, M. Development of sleeper strategies focusing on timber sleeper replacement. In Proceedings of the AusRAIL PLUS 2003, Investing in Australian Rail-Strategies and Solutions, Sydney, Australia, 17–19 November 2003. 5. Alexander, H.L. Railroad Decision Support Tools for Track Maintenance. Ph.D. Thesis, University of Illinois at Urbana-Champaign, Champaign, IL, USA, 2017. 6. Bastos, J.C.; Dersch, M.S.; Edwards, J.R. Statistical Prediction of Center Negative Bending Capacity of Pretensioned Concrete Crossties. J. Transp. Eng. Part A Syst. 2020, 146, 04019074. [CrossRef] 7. Alvaro, E.C.R.; Qian, Y.; Edwards, J.R.; Dersch, M.S. Analysis of the Temperature Effect on Concrete Crosstie Flexural Behavior. Constr. Build. Mater. 2019, 196, 362–374. 8. Bastos, J.C.; Alejandro, Á.R.; Dersch, M.S.; Edwards, J.R.; Barkan, C.P.L. Laboratory Characterization of Structural Capacity of North American Heavy Haul Concrete Crossties. Transp. Res. Rec. J. Transp. Res. Board 2018, 2672, 116–124. [CrossRef] 9. Edwards, J.R.; Canga, R.A.E.; Cook, A.A.; Dersch, M.S.; Qian, Y. Quantifying bending moments in rail-transit concrete sleepers. J. Transp. Eng. Part A Syst. 2018, 144, 04018003. [CrossRef] 10. Naaman, A.E. Prestressed Concrete Analysis and Design: Fundamentals, 2nd ed.; Techno Press: Ann Arbor, MI, USA, 2004. 11. Ngamkhanong, C.; Chuah, M.W.; Sakdirat, K. Buckling Analysis of Interspersed Railway Tracks. Appl. Sci. 2020, 10, 3091. [CrossRef] 12. Celestin, N. Inﬂuence of Spatial Variations of Railroad Track Stiffness and Material Inclusions of Fatigue Life. Ph.D. Thesis, University of Nebraska, Lincoln, NE, USA, 2015. 13. Cai, Z.; Raymond, G.P.; Bathurst, R.J. Estimate of static track modulus using elastic foundation models. J. Transp. Res. Board 1994, 1470, 65–72. 14. Arnold, R.; Lu, S.; Hogan, C.; Farritor, S.; Fateh, M.; El-Sibaie, M. Measurement of vertical track modulus from a moving railcar. In Proceedings of the American Railway Engineering and Maintenance-of-Way Association Annual Conference, Louisville, KY, USA, 17–20 September 2006. 15. Fröhling, R.D. Deterioration of Railway Track Due to Dynamic Vehicle Loading and Spatially Varying Track Stiff-Ness. Ph.D. Thesis, University of Pretoria, Pretoria, South Africa, 1997. 16. Fortunato, E.; Paixão, A.; Calçada, R. Railway Track Transition Zones: Design, Construction, Monitoring and Numerical Modelling. Int. J. Railw. Technol. 2013, 2, 33–58. [CrossRef] 17. Buddhima, I.; Muhammad, B.S.; Trung, N.; Antonio, G.C.; Richard, K. Improved performance of ballasted tracks at transition zones: A review of experimental and modelling approaches. Transp. Geotech. 2019, 21, 100260. 18. Wang, H. Measurement, Assessment, Analysis and Improvement of Transition Zones in Railway Track. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 2019. 19. Korea Rail Network Authority (KR). KR C-14080: Interaction Between Track, Vehicle, Signal, Structure, Electricity; KR: Daejeon, Korea, 2012. 20. Plotkin, D.; Davis, D. Bridge Approaches and Track Stiffness; Federal Railroad Administration: Washington, DC, USA, 2008. 21. López Pita, A.; Teixeira, P.F.; Casas-Esplugas, C.; Ubalde, L. Deterioration in geometric track quality on high speed lines: The experience of the Madrid-Seville high speed line (1992–2002). In Proceedings of the TRB 85th Annual Meeting, Washington, DC, USA, 22–26 January 2006. Appl. Sci. 2021, 11, 261 13 of 13

22. Sanudo, R.; Dell’Oli, L.; Casado, J.A.; Carrascal, I.A.; Diego, S. Track transitions in railways: A review. Constr. Build. Mater. 2016, 112, 140–157. [CrossRef] 23. Priest, J.A.; Powrie, W. Determination of Dynamic Track Modulus from Measurement of Track Velocity during Train Passage. J. Geotech. Geoenviron. Eng. 2009, 135, 1732–1740. [CrossRef] 24. American Railway Engineering and Maintenance-of-Way Association (AREMA). Manual for Railway Enginnering; AREMA: Lanham, MD, USA, 2017. 25. Lee, K.Y. A Study Improvement the Transition Area of Bridge and Embankment Using Reinforced Rail and Ballast Stabilizer. Master’s Thesis, Seoul National University of Science and Technology, Seoul, Korea, 2014. 26. Rade¸s,M. Dynamic analysis of an inertial foundation model. Int. J. Solids Struct. 1972, 8, 1353–1372. [CrossRef] 27. Avramidis, I.E.; Morﬁdis, K. Bending of beams on three-parameter elastic foundation. Int. J. Solids Struct. 2006, 43, 357–375. [CrossRef] 28. Kerr, A.D. A study of a new foundation model. Acta Mech. 1962, 1, 135–147. [CrossRef] 29. Kerr, A.D. The determination of the track modulus k for the standard track analysis. In Proceedings of the American Railway Engineering and Maintenance-of-Way Association Annual Conference, Washington, DC, USA, 24 September 2002. 30. Tzanakakis, K. The Railway Track and Its Long Term Behaviour: A Handbook for a Railway Track of High Quality; Springer: Berlin/Heidelberg, Germany, 2013. 31. Winkler, E. Die Lehre von der Elasticitaet und Festigkeit mit Besondere Ruecksicht auf ihre Anwendung in der Technik, fuer Polytechnische Schuhlen, Bauakademien, Ingenieure, Maschienenbauer, Architecten, etc.; H. Dominicus: Prague, Czech Republic, 1867. 32. Rapp, C.T.; Dersch, M.S.; Edwards, J.R.; Barkan, C.P.L.; Wilson, B.; Mediavilla, J. Measuring Concrete Crosstie Rail Seat Pressure Distribution with Matrix Based Tactile Surface Sensors. In Proceedings of the American Railway Engineering and Maintenance-of-Way Association Annual Conference, Chicago, IL, USA, 16–19 November 2012. 33. Edwards, J.R.; Aaron, C.; Dersch, M.S.; Qian, Y. Quantiﬁcation of rail transit wheel loads and development of improved dynamic and impact loading factors for design. J. Rail Rapid Transit 2018, 232, 2406–2417. [CrossRef] 34. Selig, E.T.; Waters, J.M. Track Geotechnology and Substructure Management; Thomas Telford Services: London, UK, 1994.