Assessment of Structural Dynamic Response and Vehicle-Track Interaction of Precast Slab Track Systems

applied sciences

Article Assessment of Structural Dynamic Response and Vehicle-Track Interaction of Precast Slab Track Systems

Linh Vu 1 , Dong-Doo Jang 2 and Yun-Suk Kang 2,*

1 Department of Transportation System Engineering, KRRI School, University of Science and Technology, 217, Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea; [email protected] 2 Korea Railroad Research Institute 176, Cheoldo-bangmulgwan-ro, Uiwang 16105, Gyeonggi-do, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-10-3895-9112

Featured Application: Structural Dynamic Responses of Precast Slab Track systems.

Abstract: Recently, precast slab tracks have been used widely in railway applications, especially in conventional urban railway lines. These types of tracks are rapidly constructed and limit interrup- tions to train operation. However, the problems of dynamic stability when the trains run on the discontinuous type of tracks must be seriously considered. This paper focuses on analyzing the train-track interaction in two types of tracks under the dynamic load by using the numerical analysis program (APATSI) to evaluate the structural response as well as the running safety to precisely understand the load transfer efﬁciency of precast slab track systems.

Keywords: precast slab track; dynamic analysis; numerical program; urban railway; train-track interaction; load transfer efﬁciency

Citation: Vu, L.; Jang, D.-D.; Kang, Y.-S. Assessment of Structural Dynamic Response and Vehicle-Track Interaction of Precast Slab Track 1. Introduction Systems. Appl. Sci. 2021, 11, 3558. In railway engineering, the ballasted track system with concrete sleeper is the major https://doi.org/10.3390/app11083558 type that is generally used in conventional lines. However, the biggest drawbacks of this system are insufﬁcient ballast depth and ballast fouling that causes the degradation Academic Editors: Juan-Carlos Cano of the track as well as affecting the drainage capacity of the track [1–3]. Moreover, the and Marco Vona maintenance cost of the ballasted track is also mentioned as a limitation when operating this system. As a result, it is necessary to improve the track structure as an innovative solution Received: 11 March 2021 has been offered. Nowadays, with the development of technology, concrete slab track Accepted: 13 April 2021 systems are an alternative method that can solve these problems of the ballasted track with Published: 15 April 2021 their excellent durability under the trainloads created by the high speed or the increasing of the axle load [4]. Although the initial construction cost of concrete track structure is Publisher’s Note: MDPI stays neutral 1.3–1.5 times higher than ballasted track, the Life Cycle Cost evaluation pointed out that it with regard to jurisdictional claims in published maps and institutional afﬁl- is possible in the long term this cost can be recovered after 11–12 years of operation based iations. on the maintenance costs [5]. There are two types of concrete slab track or ballast-less system: (1) The continuous concrete slab track, which is built with cast-in-situ concrete slabs, and (2) the discrete concrete slab track, which uses precast slabs [6–10]. The previous study pointed out that, although the cast-in-place concrete slab track has been used widely over the world, Copyright: © 2021 by the authors. there are many disadvantages of this type of track such as poor quality of concrete slab, Licensee MDPI, Basel, Switzerland. limits on the track installation, and the effects of air pollution that can affect the workers’ This article is an open access article distributed under the terms and health when constructing underground as well as in the tunnel section [11]. In contrast, conditions of the Creative Commons the precast slab track, which is made in the factory, can prevent these issues. The main Attribution (CC BY) license (https:// requirements of precast slab track are rapid installation, huge bearing capacity (huge train creativecommons.org/licenses/by/ loads and train speed), high quality of concrete slab, safety, and that it is friendly to the 4.0/). environment. This type of track is being developed and applied in many countries. There

Appl. Sci. 2021, 11, 3558. https://doi.org/10.3390/app11083558 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 14

Appl. Sci. 2021, 11, 3558 2 of 13

environment. This type of track is being developed and applied in many countries. There are area lot a lotof different of different types types of prefabricated of prefabricated slab slab track track systems systems.. Japan Japan has has the the Shinkansen Shinkansen systemsystem [12], [12 where], where the the5 m 5 length m length of precast of precast slab slab panels panels are aremounted mounted on the on thecontinuously continuously concreteconcrete base. base. After After adjusting adjusting the thelevel level of the of theslab, slab, an asphalt an asphalt cement cement layer layer is poured is poured to to connectconnect the thepanels panels and andbasements. basements. The CRTS The CRTSsystem system was developed was developed in China in [13 China–17], [ 13this–17 ], is thethis most is the popular most popular method method used to usedinstall to in install Chinese in Chinese high-speed high-speed railway railway line. This line. bal- This lastlessballastless system system is composed is composed of a superstructure of a superstructure (rail, (rail,fastening fastening system, system, and andslab slab panel), panel), selfself-compacting-compacting concrete concrete layer, layer, isolator isolator layer layer,, and and plate plate base base [18]. [18 Additionally,]. Additionally, the theBögl Bögl systemsystem was was installed installed in Germany in Germany [19– [1921–].21 The]. The precast precast slab slab tracks tracks usually usually consist consist of three of three layerslayers the theslab slab panels panels on the on thetop, top, the thegrouting grouting layer, layer, and and then then the thesubgrade subgrade,, as can as can be seen be seen in Figurein Figure 1. When1. When construct constructinging the the precast precast slab slab track, track, the the rails rails were were mounted mounted on onthe the panels panels by fasteningby fastening systems systems;; after after that, that, the the whole whole structure structure (rail (rail-fastener-panel)-fastener-panel) was was assembled on on the concrete base. Finally, thethe groutgrout was was poured poured between between the the slab slab panels panels and and the the base base after afteradjusting adjusting the the upper upper structures. structures.

Figure 1. Concrete slab track systems: (a) Cast-in-place slab track, (b) Precast slab track. Figure 1. Concrete slab track systems: (a) Cast-in-place slab track, (b) Precast slab track. In this paper, we changed the grout layer of the precast slab track by the elastic support systemsIn this paper, and developed we changed new the precast grout slablayer track of the structures. precast slab After track the by design the elastic and sup- testing portof systems the structural and developed behaviors new in theprecast laboratory, slab track we structures. determined After the the dynamic design behavior and testing of the of thestructure structural through behaviors the numerical in the lab analysisoratory, program we determined (All-Purpose the dynamic Analysis behavior of Train Structureof the structureInteraction—APATSI), through the numerical which hasanalysis been developedprogram (All by- thePurpose Korea Analysis Railroad of Research Train Struc- Institute. tureWe Interaction focused on—APATSI the performance), which has of thebeen structures developed under by the the Korea dynamic Railroad load toResearch verify the Institute.structure We deflection.focused on the These performan types ofce tracks of the havestructures no dowel under bar the or dynamic steel plate load to to connect verify eachthe structure panel, and deflection. the trainload These types is transmitted of tracks andhave contributed no dowel bar from or steel the railsplateto to thecon- slab nectpanel. each panel, Therefore, and the it is trainload necessary is to transmitted evaluate the and Load contributed Transfer from Efficiency the rails of theseto the types slab of tracks through the structure deflection. The goal of this study is to evaluate the train-track panel. Therefore, it is necessary to evaluate the Load Transfer Efficiency of these types of interaction and the structural behaviors under the dynamic load (urban conventional tracks through the structure deflection. The goal of this study is to evaluate the train-track trainset) to understand more accurately the safety of these track systems. interaction and the structural behaviors under the dynamic load (urban conventional trains2. Precastet) to understand Slab Panels more accurately the safety of these track systems. Recently, two new types of precast slab track have been studied and improved to 2. Precast Slab Panels apply to conventional railway lines as shown in Figure2. In our study, the grouting layer wasRecently, changed two by new the elastic types supportof precast devices, slab track which have can rapidlybeen studied construct and the improved concrete to track applysystem. to conventional The basic specificationrailway lines ofas these shown precast in Figure slab 2. panels In our is study, listed the in Tablegrouting1. The layer most wasremarkable changed by improvement the elastic support of these devices precast, which slab trackcan rapidly systems construct is that the the trainloadsconcrete track will be system.transmitted The basic between specification the panels of these (the distance precast ofslab panels panels is 75is mm)listed by in theTable rails 1. insteadThe most of the remarkablesteel connection improvement joints. of This these method precast can slab reduce track the systems construction is thatcost the trainloads by 10%, according will be to transmittedthe studies between of concrete the panels pavements (the distance [22]. of panels is 75 mm) by the rails instead of the steel connection joints. This method can reduce the construction cost by 10%, accord- ingTable to the 1. studiesSpecification of concrete of specimen. pavements [22].

Speciﬁcations Type I Type II Dimensions (m) 4.925 (L) × 2.4 (W) × 0.3 (H) 4.950 (L) × 2.38 (W) × 0.23 (H) Concrete Strength (MPa) 45 45 Panel Weight (ton) 7.6 7.6 Support Stiffness of Elastic Device (kN/mm) 22.5 324 Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 14

Table 1. Specification of specimen.

Specifications Type I Type II Dimensions (m) 4.925 (L) × 2.4 (W) × 0.3 (H) 4.950 (L) × 2.38 (W) × 0.23 (H)

Appl. Sci. 2021,Concrete11, 3558 Strength (MPa) 45 45 3 of 13 Panel Weight (ton) 7.6 7.6 Support Stiffness of Elastic Device (kN/mm) 22.5 324

FigureFigure 2. 2.PrecastPrecast slab slab track track systems: systems: ( (aa)) Type Type I: PrecastPrecast FloatingFloating Slab Slab Track, Track, (b ()b Type) Type II: Precast-FastII: Precast-Fast Improvement Improvement slab slab Track. Track. 2.1. Precast Slab Track Type I 2.1. PrecastThe Slab Type Track I slab Type panel I is named “Precast floating slab track,” and it is designed to be usedThe for Type the urbanI slab panel railway. is named The main “Precast function floating of this slab type track is to,” reduceand it is the designed ground-borne to be usenoised for and the vibrationurban railway. issues The generated main function from the of train-track this type is interaction to reduce the when ground operating-borne the train, especially in underground and bridge sections of metro lines. This type has the noise and vibration issues generated from the train-track interaction when operating the dimensions were 4.925 m (length) × 2.4 m (width) × 0.3 m (thickness). Figure3a shows train, especially in underground and bridge sections of metro lines. This type has the di- the details of this precast floating slab track. The design strength of the slab concrete mensions were 4.925 m (length) × 2.4 m (width) × 0.3 m (thickness). Figure 3a shows the is 45 MPa. This type of slab was composed of two concrete blocks connected with the details of this precast floating slab track. The design strength of the slab concrete is 45 crossbeams. Rails were mounted on the slab panel by the fastening device system (Vossloh MPa. This type of slab was composed of two concrete blocks connected with the cross- System 300-1). In the prototype, six coil spring elastic devices (with a vertical stiffness of beams. Rails were mounted on the slab panel by the fastening device system (Vossloh 22.5 KN/mm) were attached at the bottom of each panel. These devices use the frictional System 300-1). In the prototype, six coil spring elastic devices (with a vertical stiffness of resistance of a wedge-shaped block made of engineering plastic applied to an inclined 22.5 KN/mm) were attached at the bottom of each panel. These devices use the frictional surface to attenuate vertical vibrations, providing resilience through coil springs arranged resistance of a wedge-shaped block made of engineering plastic applied to an inclined horizontally and vertically to insulate vibration. By applying the Mass–Spring–Systems surface to attenuate vertical vibrations, providing resilience through coil springs arranged (composed of the rail, fastener, and concrete slab panel) combined with the anti-vibration horizontallydevices, the and floating vertically slab trackto insulate has become vibration. one ofBy the apply mosting typical the Mass methods–Spring to– reduceSystems the (composednoise and of vibration the rail, fastener, problems and in railway.concreteWhen slab panel) constructing combined the with track, the the anti concrete-vibration base devices,was adjusted the floating with aslab fixed track height has ofbecome the track. one Afterof the that, most the typical panels methods were transported to reduce tothe the noisesite and and vibration assembled problems sequentially in railway. by using When the hydraulicconstructing jack the machine. track, the This concrete type of base track can be constructed 10 m per day without interrupting the train operation. Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 14

Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 14

was adjusted with a fixed height of the track. After that, the panels were transported to thewas site adjusted and assembled with a fixed sequentially height of by the using track. the After hydraulic that, jackthe panelsmachine. were This transported type of track to Appl. Sci. 2021, 11, 3558 canthe sitebe constructed and assembled 10 m sequentially per day without by using interrupting the hydraulic the trainjack machine.operation. This type of track4 of 13 can be constructed 10 m per day without interrupting the train operation.

FigureFigure 3. Precast 3. Precast Floating Floating Slab Track Slab Track (Type (Type I): (a I):) Detailed (a) Detailed structures, structures, (b) Anti (b) Anti-vibration-vibration Device. Device. Figure 3. Precast Floating Slab Track (Type I): (a) Detailed structures, (b) Anti-vibration Device. 2.2. Precast2.2. Precast Slab SlabTrack Track Type Type II II 2.2. Precast Slab Track Type II The Themain main goals goals of this of thistype typeof track of track are to are rapidly to rapidly replace replace the conventional the conventional ballasted ballasted The main goals of this type of track are to rapidly replace the conventional ballasted tracktrack with with the concrete the concrete track track in difficult in difﬁcult conditions conditions such such as lack as lackof working of working space space and andlack lack track with the concrete track in difficult conditions such as lack of working space and lack of workingof working hours hours,, especially especially in tunnel in tunnel sections sections of urban of urban railway railway lines. lines. The ThePrecast Precast-Fast-Fast Improvementof workingImprovement hours slab, slab Trackespecially Track (P-FIT) (P-FIT)in cantunnel be can constructedsections be constructed of urban20 m 20 per railway m day per dayat lines. ni atghttime nighttimeThe Precast so that so-Fast thatthe the trainImprovementtrain operation operation slab still Track stillcan work can (P-FIT) work on canthe on benext the constructed nextday. day. This This type20 m type ofper slab ofday slabtrack at ni track ghttimehas hasdimensions dimensionsso that the of of 4.950train4.950 moperation (length) m (length) still × 2.38 can× m 2.38work (width) m on (width) ×the 0.23 next ×m 0.23day.(thickness). mThis (thickness). type Figure of slab 4a Figure showstrack4a has the shows dimensionsdetails the of details this of of precast4.950this m slab precast(length) track. slab× 2.38 The track. m design (width) Theed designed ×strength 0.23 m strength (thickness). of the of slab the Figure concrete slab concrete4a shows is 45 is MPa.the 45 details MPa. Rails Rails of were this were mountedprecastmounted slab on the track. on slab the The slabpanel design panel by the byed fastening thestrength fastening device of the device system slab system concrete (Vossloh (Vossloh is System 45 System MPa. 300 Rails- 300-1).1). At were the At the bottommountedbottom of onthe of the panel, the slab panel, 8 panelelastic 8 elastic by devices the devices—rubber fastening—rubber device typetype in system Figure in Figure (Vossloh 4b—4wereb—were System attached attached 300 to-1). support to At support the thebottom lowerthe of lower part the panel, of part the of 8structure. elastic the structure. devices This elastic— Thisrubber de elasticvice type can device in Figurebe ma cannufactured 4b be— manufacturedwere attached by laminated to by support laminated rub- berthe thatlowerrubber meets part that ofthe meets the standard structure. the standard of fireThis ofsituations. elastic ﬁre situations. device The can Rapid The be Rapidma Constructionnufactured Construction Precastby laminated Precast slab slabtrack rub- track hasber 2thathas stoppers 2meets stoppers inthe the standard in middle the middle ofof firethe of situations.panel the panel to resist toThe resist theRapid horizontal the Construction horizontal force force (centrifugal Precast (centrifugal slab force) track force) andhas and2the stoppers longitudinal the longitudinal in the force middle force (brak of (braking ingthe force)panel force) whento resist when the the trains the horizontal trains are operated. are force operated. (centrifugal force) and the longitudinal force (braking force) when the trains are operated.

Figure 4.Figure Precast 4.-FastPrecast-Fast Improvement Improvement slab Track slab (Type Track II): (Type (a) Detailed II): (a) Detailed structures, structures, (b) Rubber (b) RubberElastic Support Elastic Support Device. Device. Figure 4. Precast-Fast Improvement slab Track (Type II): (a) Detailed structures, (b) Rubber Elastic Support Device. 3. Numerical Analysis

The train-track interaction analysis was performed according to the method proposed by Yang et al. [23–25] to investigate and compare the performance of the precast floating and rapid track. The vehicle consists of a rigid bodied car body,2 bogies, and 4 wheels and spring-dampers connecting between them for primary and secondary suspensions, as shown in Figure5. The track consists of rail and slab that are modeled based on the Timoshenko beam theory for rail and the Euler–Bernoulli theory for slab panel. The rail is considered as the first layer and Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 14

3. Numerical Analysis The train-track interaction analysis was performed according to the method proposed by Yang et al. [23–25] to investigate and compare the performance of the precast floating and rapid track. The vehicle consists of a rigid bodied car body, 2 bogies, and 4 wheels and spring-dampers connecting between them for primary and secondary suspen- Appl. Sci. 2021, 11, 3558 5 of 13 sions, as shown in Figure 5. The track consists of rail and slab that are modeled based on the Timoshenko beam theory for rail and the Euler–Bernoulli theory for slab panel. The rail is considered as the first layer and modeled as the continuous beam element, while the modeledslab track as is the the continuous second layer beam and element, simulated while as the the slab discrete track is thesupported second layerbeam and element. simulated Theas spring the discrete-dampers supported of the beamfastener element. are connected The spring-dampers the rail and of slab, the fastener and the are slab connected is sup- the portedrail and by vibrationslab, and the isolators. slab is supported These structures by vibration are isolators. simulate Thesed as thestructures linear are spring simulated and as dampingthe linear elements. spring and damping elements.

Figure 5. Train-track interaction analysis model. Figure 5. Train-track interaction analysis model. The motion equation for the vehicle-track interaction system is presented by follow- ingThe formula: motion equation for the vehicle-track interaction system is presented by following formula: .. . MY + CY + KY = F (1) ̈ ̇ Y, the displacement vectorM ofY the + systemCY + canKY be= expressed. F (1) Y, the displacement vector of the system can be expressed. T Y = Y Y (2) v tT Y = {Yv Yt} (2) T = θ θ θ T Yv =Yv {yc,y cθ,v, v y,b1 yb1, ,θb1b1, , y yb2b2, , θb2b2,, yw1, yyw2w2,, y yw3w3,, y yw4w4} (3) (3) T T Yt =Yt = {yriy, ri θ, riθ,ri ,ysi ysi, , θθsisi} i = i =1 1∼ ~ n (4) (4) wherewhere y and y and θ areθ are vertical vertical and and rotational rotational displacement, displacement, subscripts subscripts v and v and t mean t mean vehicle vehicle andand track, track, and and c, b c,, and b, and w windicate indicate car car body, body, bogie, bogie, and and wheel, wheel, respectively. respectively. yri, θθriri,,y siysi, and, andθ siθsiare are i-th i-th nodal nodal displacements displacements of of the the FE FE models, models, which which have have n n nodes, nodes, for for rail rail and and slab, slab,respectively. respectively. The The mass, mass, damping, damping and, and stiffness stiffness matrices matrices of of the the system system can can be be induced induced as as       Mv 0 Cv 0 0 Kv 0 0 M 0 C 0 0 K 0 0 M =  v Mr ,C =  v0 Cr Crs ,K =v 0 Kr Krs  (5) M = [ M ] , C = [ 0 C C ] , K = [ 0 K K ] 0r Ms 0r Crs rsCs 0r Krs Ks (5) 0 Ms 0 Crs Cs 0 Krs Ks in which system matrices of rail, M , K , and slab, M , K , are derived by FE modeling. in which system matrices of rail, M , Kr , andr slab, M , Ks, ares derived by FE modeling. Subscript rs represents coupled partsr r between rail ands s slab by fastener. The force vector F Subscript rs represents coupled parts between rail and slab by fastener. The force vector can be written as F can be written as T F = Fv Ft 02n×1 (6) T Fv = {06×1 FH1 FH2 FH3 FH4} (7) 4 Ft = ∑[Φ(xci) fsi + Φ(xci) FHi ] (8) i

where Φ(xci) is the location vector of wheel-rail contact, which has values of T {ϕ1(xci) ϕ2(xci) ϕ3(xci) ϕ4(xci)} at the corresponding nodes with the contact location and the others are zero; xci is local coordinate of i-th wheel-rail contact point in a FE element; Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 14

T F = {Fv Ft 02n×1} (6)

Appl. Sci. 2021, 11, 3558 T 6 of 13 Fv = {06×1 FH1 FH2 FH3 FH4} (7)

and fsi is static load of vehicleFt acting = ∑ on[Φi-th(xci wheel-rail) fsi + Φ contact(xci) FHi point. ] FHi ( i = 1 ∼ 4) are(8) the contact forces by Hertzian springi between the wheels and rail, and can be obtained as follows [23]. The boundary conditions are simulated by two points. The starting point is where Φ(xci) is the location vector of wheel-rail contact, which has values of from 0 m to the 200 m point of theT rail as a first layer. {φ1(xci) φ2(xci) φ3(xci) φ4(xci)} at the corresponding nodes with the contact location and the others are zero; xci is local coordinate of i-th wheel-rail contact point in a FE  KH {y − y (xci)} if {y − y (xci)} > 0 element; and fsi is static1+ αload(xci) KofH vehiclewi actingr on i-th wheelwi -railr contact point. FHi (i = 1 ~ 4) are theFHi contact= forces by Hertzian spring between the wheels and rail, and can(9) be  obtained as follows [23]. The boundary0 conditions are simulated else by two points. The starting point is from 0 m to the 200 m point of the rail as a first layer. where KH is the linearized Hertzian spring coefficient satisfying the following characteris- K tic equation: H {y − y (x )} if {y − y (x )} > 0 3 2 wi 2 r ci wi r ci α1(+x α)(Kxci)+KHK − c {y − y (x )} = 0 (10) FHi = { ci H H H wi r ci (9) And α(ξc) is given by: 0 else n h io where KH is the linearized Hertzian2 spring 2coefficient3 satisfying2 2 the4 following2 character- xci − (L − xci) 4 xci(L − xci) + xciL − xciL + L ψs + ψs istic equationα(x ) =: (11) ci 12EI(1 + ψ ) 3 2 2 s α(xci)KH + KH − cH {ywi − yr(xci)} = 0 (10) where: And α(ξc) is given by: 12EI ψs = (12) GA L2 {x − (L − x )[4 x2 (L − x r)2 + (x L3 − x2 L2 + L4)ψ + ψ2]} α(x ) = ci ci ci ci ci ci s s and EI, G, Ar,ciand L are the flexural stiffness, shear modulus, cross-sectional area(11 of) 12EI(1 + ψs) the rail, and element length, respectively. In this paper, the precast slab track systems werewhere composed: by the slab panel with a short length (approximately 5-m length per panel) to ensure rapid installation. Moreover,12EI there was a distance (75 mm) between panels without using the dowel bar toψ joins =the slabs.2 Thus, the discontinuous points(12) GArL will occur while operating the train. Besides, the transition zone (ballasted track–slab track)and EI was, G, alsoAr, consideredand L are the and flexural modeled stiffness, in this study.shear modulus, By using thecross APATSI-sectional program, area of thethe structuralrail, and element responses, length, driving respectively safety, and. In load this transferpaper, the efficiency precast ofslab two track types systems of the trackwere werecomposed evaluated. by the slab panel with a short length (approximately 5-m length per panel) to ensureUsing rapid the installation. above mathematical Moreover, there model, was the a distance train-track (75 interactionmm) between analysis panels was without per- formedusing the while dowel a train bar to moved join the at 110slabs. km/h. Thus The, the train discontinuous we used is points an urban will trainset, occur while which op- is beingerating operated the train. in Besides, South Korea, the transition and consists zone of 6(ballasted cars with t 3rack motor–slab cars track) and 3was passenger also consid- cars, asered shown and model in Figureed in6. Sincethis study. the train By using is symmetric the APATSI concerning program, the the longitudinal structural responses, direction, thedriving half modelssafety, and are used,load transfer which is efficiency summarized of two in Tabletypes2 of. the track were evaluated. AUsing 200 mthe length above of mathematical track was simulated, model, the which train is- 100trac mk interaction of ballasted analysis track and was 100 per- m offormed precast while slab a track,train moved as shown at 110 in Figurekm/h. 7The. The train details we used of structures is an urban and trainset, track systems which is werebeing presentedoperated in in South Table 3Korea,. Two and types consists of precast of 6 slabcars with tracks 3 usemotor the cars same and kinds 3 passenger of the superstructure.cars, as shown in The Figure differences 6. Since are the the train elastic is sy devicesmmetric attached concerning at the the bottom longitudinal of each direc- type oftion, slab the track halfand models the distanceare used, between which is the summarized devices as shownin Table in 2. Figures 3 and4.

Figure 6. The urban railway trainset of six cars. Figure 6. The urban railway trainset of six cars. Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 14

Table 2. Specification of trainset (half model).

Motor Car Passenger Car Item Unit (M) (P) Car Body Weight ton 21 19 Appl. Sci. 2021, 11, 3558 7 of 13 Car Body Mass Moment of Inertia ton-m2 791 856.5 Car Body Weight of Bogie ton 0.600 0.585 specifications Bogie Mass Moment of Inertia ton-m2 0.750 0.400 Table 2. Weight of Wheel Specificationton of trainset (half0.860 model). 0.795 Primary Spring Coefficient MN/m 1043 Motor Car0.511 Passenger Car Item Unit Suspension Damping Coefficient MN·s/m - (M) - (P) Secondary Spring CoefficientCar Body WeightMN/m ton0.191 210.176 19 Car Body Mass Moment of Inertia ton-m2 791 856.5 Suspension Car Body Damping Coefficient MN·s/m - - Weight of Bogie ton 0.600 0.585 specifications Balance Interval m 13.8 13.8 Bogie Mass Moment of Inertia ton-m2 0.750 0.400 Length Distance between WheelsWeight of Wheelm ton2.1 0.8602.1 0.795 Radius of Wheel m 0.43 0.43 Primary Spring Coefficient MN/m 1043 0.511 Suspension Damping Coefficient MN·s/m - - A 200 m length of track was simulated, which is 100 m of ballasted track and 100 m Secondary Spring Coefficient MN/m 0.191 0.176 Suspensionof precast slab trackDamping, as shown Coefficient in Figure 7. The details MN·s/m of structures and - track systems - were presented in Table 3. Two types of precast slab tracks use the same kinds of the Balance Interval m 13.8 13.8 superstructure. The differences are the elastic devices attached at the bottom of each type Length Distance between Wheels m 2.1 2.1 of slab track and theRadius distance of Wheel between the devices as shown m in Figures 3 0.43 and 4. 0.43

Figure 7. Track analysis sectionsFigure. 7. Track analysis sections.

Table 3. SpecificationTable 3. ofSpeciﬁcation track systems of (half track model) systems. (half model).

Parameter ParameterUnit UnitType I Type IType II Type II 8 Modulus of ElasticityModulus of ElasticitykPa kPa 2.1 × 10 2.1 × 108 Poisson’s Ratio Poisson’s Ratio 0.3 0.3 Mass ton/m 6.08 × 10−3 Rail –3 Rail Mass Cross Section ton/m m2 6.08 × 10 7.75 × 10−3 Cross Section2nd moment of cross-sectionm2 m4 7.75 × 10–3 3.06 × 10−5 2nd moment of cross-section Stiffness Coefficientm4 kN/mm3.06 × 10–5 196 196 Ballasted track section Ballasted track Stiffness Coefficient DampingkN/mm Coefficient kN.sec/m196 300196 300 Fastener 32,800 32,800 section Damping Coefficient StiffnesskN Coefficient.sec/m kN/m300 300 Precast slab track section (System 300-1) (System 300-1) Fastener Damping Coefficient kN-sec/m32,800 20032,800 200 Precast slab Stiffness Coefficient kN/m Modulus of Elasticity(System kPa 300-1) (System× 5 300-1) × 5 track section 356.8 10 356.8 10 Damping CoefficientPoisson’s RatiokN-sec/m 200 0.18200 0.18 Mass per unit length ton/m 0.772 0.677 Slab panel 5 5 Modulus of Elasticity Cross Section kPa 356.8m2 × 10 0.27356.8 × 10 0.273 Poisson’s RatioSecond Moment of section m0.184 2.025 × 10−0.183 1.203 × 10−3 Elastic Device kN/mm 22.5 (6ea) 324 (8ea) Slab panel Mass per unit length ton/m 0.772 0.677 Stiffness Coefficient kN/mm 314 314 2 Ballast Cross Section Damping Coefficientm kN·s/m0.27 3000.273 300 Second Moment of section m4 2.025 × 10–3 1.203 × 10–3 4. Results and Discussion With the above specifications of train and track structure, the analysis was calculated by using the finite element program All-Purpose Analysis of Train Structure Interaction (APATSI), which was developed by the Korea Railroad Research Institute. The results of train-track interaction and the structural behaviors are shown as follows. Appl. Sci. 2021, 11, 3558 8 of 13

4.1. Wheel Load Variation The driving safety can be evaluated by predicting the possibility of derailment when operating the train. The derailment ratio and the reduction rate of the wheel are calculated in the following formulas. Q 8 αh KQ/P = = (13) P 3 1 − αv ∆P η = = αv (14) P0 where:

KQ/P: Derailment ratio. Q: Lateral force. P: Dynamic wheel weight due to track distortion. αh, αv: Horizontal and vertical accelerations of the vehicle body, respectively. η: Wheel reduction rate. P0, ∆P: Static wheel load and variation in the wheel weight. In this paper, the criteria for the wheel load variation ratio were used by 0.372 according to Jang and Yang [26], and the rules on safety standard for railroad vehicles by the Korea Ministry of Land, Infrastructure, and Transport and the design standard for railway structures by Japanese Railway Technical Research Institute were used. In Figure8, the wheel force variation results are described. The maximum wheel force variation rate in ballasted track was 0.06. Meanwhile, this value of precast slab track Type I and II decreased 33.33% and 50% compared to ballasted track. These results showed that the train runs more stable in the precast slab track sections. The limited rate change of wheel load is 0.372 so that both types of precast slab track acquired the requirement. However, as can be seen in Figure8, the train operated slightly smoother in the Type II than Type I section. There is a small change in wheel force when the train runs from the Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 14 precast ﬂoating track to the ballasted track at the connection zone. Therefore, it is necessary to increase the rigidity at the transition part when designing the ﬂoating slab track.

FigureFigure8. 8.Wheel Wheel load load variation variation results: results (a): Precast(a) Precast Floating Floating Slab TrackSlab Track (Type (Type I), (b) Precast-FastI), (b) Precast Improvement-Fast Improvement slab Track slab (Type Track II). (Type II). 4.2. Rail Uplift Force and Rail Stress 4.2. RailWhen Uplift designing Force and a precast Rail Stress slab track, the performance of components such as fasten- ers, slabs,When and designing elastic devicesa precas cant slab be track, secured the by performance applying each of components performance such standard as fasten- or structuralers, slabs, designand elastic standard. devices However, can be evensecured though by applying each component each performance requires performance, standard or structural design standard. However, even though each component requires performance, if they behave systematically in a combined state, the performance of the system’s usability should be confirmed considering long-term maintenance [26]. In the track system, if the rail stresses and rail uplift forces are huge, the life of the rail and fastener become shortened and the maintenance cost will increase by changing the rail pad. There- fore, it is important to evaluate these problems. Figure 9 shows the results of rail uplift force when the train runs on the middle panel of both types of track. The rail uplift force must not be greater than the initial clamping force of the rail fastener so that the rail pad cannot move or twist. In these types of precast slab tracks, the Vossloh System 300-1 type of fastener was used to connect rails with the concrete panel. The initial clamping force of this device is 16.9 kN and the allowable force is 70% of this value, equal to 11.83 kN [26]. As can be seen in Figure 9, the rail uplift force of both types of precast slab track met the requirement. The maximum uplift force of Type I was 1.09 kN, while the force of Type II was slightly larger (1.28 kN).

Figure 9. Rail Uplift Force results: (a) Type I, (b) Type II. Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 14

Figure 8. Wheel load variation results: (a) Precast Floating Slab Track (Type I), (b) Precast-Fast Improvement slab Track (Type II).

4.2. Rail Uplift Force and Rail Stress Appl. Sci. 2021, 11, 3558 9 of 13 When designing a precast slab track, the performance of components such as fasten- ers, slabs, and elastic devices can be secured by applying each performance standard or structural design standard. However, even though each component requires perfor- if they behave systematicallymance, if they in behave a combined systemati state,cally the in performance a combined of state, the system’sthe performance usability of the system’s should be conﬁrmedusability considering should be long-term confirmed maintenance considering [long26].- Interm the maintenance track system, [26]. if the In the track sys- rail stresses andtem, rail uplift if the forces rail stresses are huge, and the rail life uplift of the forces rail and are fastenerhuge, the become life of shortenedthe rail and fastener be- and the maintenancecome costshortened will increase and the by maintenance changing the cost rail will pad. increase Therefore, by changing it is important the rail pad. There- to evaluate thesefore, problems. it is important to evaluate these problems. Figure9 shows theFigure results 9 shows of rail the uplift results force of whenrail uplift the trainforce runswhen on the the train middle runs panel on the middle panel of both types ofof track. both Thetypes rail of uplifttrack. forceThe rail must uplift not force be greater must thannot be the greater initial than clamping the initial clamping force of the rail fastenerforce of the so thatrail fastener the rail pad so that cannot the rail move pad or cannot twist. Inmove these or typestwist. ofIn precastthese types of precast slab tracks, the Vosslohslab tracks, System the Vossloh 300-1 type System of fastener 300-1 type was of used fastener to connect was used rails to with connect the rails with the concrete panel. Theconcrete initial panel. clamping The initial force clamping of this device force is of 16.9 this kN device and theis 16.9 allowable kN and forcethe allowable force is 70% of this value,is 70% equal of this to 11.83value kN, equal [26 ].to As 11.83 can kN be [26] seen. As in Figurecan be9 seen, the in rail Figure uplift 9, force the rail uplift force of both types ofof precast both types slab track of precast met the slab requirement. track met the The requirement. maximum The uplift maximum force of Typeuplift force of Type I was 1.09 kN, whileI was the 1.09 force kN, ofwhile Type the II force was slightly of Type larger II was (1.28 slightly kN). larger (1.28 kN).

Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 14

In this paper, the KR-60 rail was mounted on both types of precast slab tracks. The allowable stress of the KR-60 rail is normally 130 MPa [5]. The reference value to analyze the rail stresses is 70% [27] of 130 MPa and equal to 90 MPa. Figure 10 describes the rail bottom stress of precast slab track systems when operating the train. As can be seen in Figure 10, the rail bottom stress in the precast slab track systems sectionFigure was 9. Raillarger Uplift than Force Figureballasted results: 9. Rail section. (a Uplift) Type ForceThe I, (b )maximum results: Type II. (a) Typerail bottomI, (b) Type stresses II. occurred at the transition point between ballasted section and precast slab track section. This happened dueIn thisto the paper, change the of KR-60 supported rail was stiffness mounted when on the both train types runs of from precast the slabballast tracks. track The to theallowable concrete stress track. of The the KR-60precast rail slab is normallytrack Type 130 II MPahas a[ 5distance]. The reference of the elastic value devices to analyze closerthe and rail stiffer stresses than is 70%Type [ 27I, so] of the 130 maximum MPa and of equal rail bottom to 90 MPa. stress Figure of Type 10 IIdescribes was smaller the rail thanbottom Type I stress. of precast slab track systems when operating the train.

Figure 10. Rail bottom results: (a) Type I, (b) Type II. Figure 10. Rail bottom results: (a) Type I, (b) Type II.

4.3. Rail Relative Displacement Figure 11 shows the rail relative deflection of the Precast Floating slab track and Pre- cast-Fast Improvement slab Track under the urban railway trains at a speed of 110 km/h. Based on the Japanese standard for railway structure, the relative displacement of rails should not exceed 3 mm to ensure the running safety of the vehicles [28]. In general, the rail displacement of both types of precast slab track met the allowable criteria (under 3 mm). It can be seen in Figure 11a that the rail displacement increased by 2.1 mm when the vehicle runs over the connection from the ballasted track to precast Type I. However, in Figure 11b, at the same part, the rail deflection only raised 0.5 mm. When applying the moving load, the maximum rail displacement of Type I was 3 times higher than Type II. Therefore, the stiffness of the elastic device greatly affected the rail deflection because both types of precast slab track used the same type of fastener and rail pad. Appl. Sci. 2021, 11, 3558 10 of 13

As can be seen in Figure 10, the rail bottom stress in the precast slab track systems section was larger than ballasted section. The maximum rail bottom stresses occurred at the transition point between ballasted section and precast slab track section. This happened due to the change of supported stiffness when the train runs from the ballast track to the concrete track. The precast slab track Type II has a distance of the elastic devices closer and stiffer than Type I, so the maximum of rail bottom stress of Type II was smaller than Type I.

4.3. Rail Relative Displacement Figure 11 shows the rail relative deflection of the Precast Floating slab track and Precast-Fast Improvement slab Track under the urban railway trains at a speed of 110 km/h. Based on the Japanese standard for railway structure, the relative displacement of rails should not exceed 3 mm to ensure the running safety of the vehicles [28]. In general, the rail displacement of both types of precast slab track met the allowable criteria (under 3 mm). It can be seen in Figure 11a that the rail displacement increased by 2.1 mm when the vehicle runs over the connection from the ballasted track to precast Type I. However, in Figure 11b, at the same part, the rail deflection only raised 0.5 mm. When applying the Appl. Sci. 2021, 11, x FOR PEER REVIEW moving load, the maximum rail displacement of Type I was 3 times higher than11 ofType 14 II. Therefore, the stiffness of the elastic device greatly affected the rail deflection because both types of precast slab track used the same type of fastener and rail pad.

Figure 11. Rail Relative Displacement results: (a) Type I, (b) Type II. Figure 11. Rail Relative Displacement results: (a) Type I, (b) Type II. 4.4. Load Transfer Efﬁciency 4.4. Load Transfer Efficiency Both types of precast slab tracks used rail to transmit the wheel load between slab Both types of precast slab tracks used rail to transmit the wheel load between slab panels with a distance of 75 mm instead of dowel bars or steel joints. This advantage can panels with a distance of 75 mm instead of dowel bars or steel joints. This advantage can reduce the initial construction cost of concrete slab track [22]. To evaluate the safety when reducethe the train initial is operating construction on the cost track, of concrete the relative slab displacementtrack [22]. To betweenevaluate panelsthe safety is particularly when the trainimportant. is operating If a step on the difference track, the occurs relative in the displacement rail, the dynamic between performance panels is particularly of the train will important.be affected, If a ste suchp difference as increasing occurs of in car the body rail, the acceleration dynamic asperformance well as high of stressesthe train of will rail [1]. be affectTherefore,ed, such it isas necessaryincreasing to of measure car body the acceleration Load Transfer as well Efﬁciency as high (LTE) stresses of the of rail track [1]. under Therefore,the moving it is necessary load. This to characteristicmeasure the Load can be Transfer calculated Efficiency by the (LTE) following of the formula. track under the moving load. This characteristic can be calculated by the following formula. δ2 2δ2 LTE = = (15) δ1+δ2 δ + δ δ222δ 1 2 LTE = = 2 δ12+ δ δ12+ δ (15)  where: 2 whereδ1:: is the rail displacement at loaded panel (mm).

1: is the rail displacement at loaded panel (mm). 2: is the rail displacement at adjacent panel (mm). The results of LTE are shown in Table 4. According to the results, the step difference, inclination and LTE were calculated from the 1st panel to the 20th panel in both types of the track (equal to the 100-m length of slab track). The rail relative deflection of Track Type I is 4 times larger than Type II in both loaded panels and adjacent panels. The Precast Floating slab track had the rail relative displacements ranging from 2.62 to 2.71 mm at loaded panels and from 2.57 to 2.66 mm at the unloaded ones. These values of the Precast- Fast Improvement slab Track were 0.689 to 0.694 mm at loaded panels and 0.648 to 0.659 mm at the adjacent panels. The reason is the supporting devices of Type I are more elastic than Type II. Meanwhile, the average Load Transfer Efficiency in both types of precast slab track was 98.80% and 97.28%. These results show that they can transfer almost completely the trainload from panel to panel without using any connection joints. Based on the Japanese standard usability for high-speed railway structure, the limit angular rotation values in the vertical direction by riding comfort is 2.5‰, and by running safety is 2.0‰. When the distance of the panel is 75 mm, the maximum rail inclination of Type I is 1.07‰ and Type II is 0.53‰ between the 19th and 20th panels. It means these types of precast slab tracks can secure safety as well as riding comfort when the train passes by.

Appl. Sci. 2021, 11, 3558 11 of 13

δ2: is the rail displacement at adjacent panel (mm). The results of LTE are shown in Table4. According to the results, the step difference, inclination and LTE were calculated from the 1st panel to the 20th panel in both types of the track (equal to the 100-m length of slab track). The rail relative deﬂection of Track Type I is 4 times larger than Type II in both loaded panels and adjacent panels. The Precast Floating slab track had the rail relative displacements ranging from 2.62 to 2.71 mm at loaded panels and from 2.57 to 2.66 mm at the unloaded ones. These values of the Precast-Fast Improvement slab Track were 0.689 to 0.694 mm at loaded panels and 0.648 to 0.659 mm at the adjacent panels. The reason is the supporting devices of Type I are more elastic than Type II. Meanwhile, the average Load Transfer Efﬁciency in both types of precast slab track was 98.80% and 97.28%. These results show that they can transfer almost completely the trainload from panel to panel without using any connection joints. Based on the Japanese standard usability for high-speed railway structure, the limit angular rotation values in the vertical direction by riding comfort is 2.5‰, and by running safety is 2.0‰. When the distance of the panel is 75 mm, the maximum rail inclination of Type I is 1.07‰ and Type II is 0.53‰ between the 19th and 20th panels. It means these types of precast slab tracks can secure safety as well as riding comfort when the train passes by.

Table 4. Load Transfer Efﬁciency (LTE) of rail between loaded panels and adjacent panels.

Type I Type II Panels Loaded Adjacent Loaded Adjacent Step Incli-Nation Step Incli-Nation LTE Panel Panel LTE (%) Panel Panel (mm) (‰) (mm) (‰) (%) (δ1) (δ2) (δ1) (δ2) 1st–2nd 2.62 2.57 0.05 0.67 99.04 0.689 0.657 0.03 0.43 97.623 2nd–3rd 2.64 2.58 0.06 0.80 98.85 0.690 0.656 0.03 0.45 97.474 3rd–4th 2.64 2.58 0.06 0.80 98.85 0.690 0.656 0.03 0.45 97.474 4th–5th 2.65 2.59 0.06 0.80 98.85 0.691 0.657 0.03 0.45 97.478 5th–6th 2.66 2.60 0.06 0.80 98.86 0.692 0.659 0.03 0.44 97.557 6th–7th 2.67 2.61 0.06 0.80 98.86 0.693 0.658 0.03 0.47 97.409 7th–8th 2.67 2.61 0.06 0.80 98.86 0.693 0.658 0.03 0.47 97.409 8th–9th 2.67 2.60 0.07 0.93 98.67 0.693 0.658 0.03 0.47 97.409 9th–10th 2.67 2.61 0.06 0.80 98.86 0.694 0.657 0.04 0.49 97.261 10th–11th 2.68 2.62 0.06 0.80 98.87 0.694 0.657 0.04 0.49 97.261 11th–12th 2.69 2.63 0.06 0.80 98.87 0.694 0.656 0.04 0.51 97.185 12th–13th 2.70 2.63 0.07 0.93 98.69 0.693 0.656 0.04 0.49 97.257 13th–14th 2.70 2.63 0.07 0.93 98.69 0.693 0.655 0.04 0.51 97.181 14th–15th 2.70 2.63 0.07 0.93 98.69 0.693 0.654 0.04 0.52 97.105 15th–16th 2.69 2.62 0.07 0.93 98.68 0.692 0.653 0.04 0.52 97.100 16th–17th 2.69 2.63 0.06 0.80 98.87 0.690 0.651 0.04 0.52 97.092 17th–18th 2.70 2.62 0.08 1.07 98.50 0.690 0.650 0.04 0.53 97.015 18th–19th 2.71 2.66 0.05 0.67 99.07 0.688 0.648 0.04 0.53 97.006 19th–20th 2.70 2.62 0.08 1.07 98.50 0.688 0.648 0.04 0.53 97.006

5. Conclusions In this paper, the Precast Floating Slab track (type I) and Precast Fast Improvement slab track (type II) were developed and designed as the alternative method to ballasted track. These types of tracks are supported discretely and the gap between each panel (75 mm). Moreover, there is no connection joint or dowel bar to transmit the load from the slabs so the rail will take on the role of transferring the wheel load when operating the trains. Therefore, it is necessary to consider the dynamic performance of the structures as well as the running safety of the precast slab tracks through the train-track interaction. This study focused on analyzing 200 m length combined of these types of precast slab track and ballasted track with conventional metro trainset (designed speed 110 km/h) by using the numerical program All-Purpose Analysis of Train-Substructure Interaction (APATSI). After calculating and comparing the results, these conclusions are summarized as below: • The wheel force variation of both types of tracks was almost similar and met the requirement (smaller than the limitation is 0.372). However, when the train runs from the ballasted track to the Precast Floating slab track (Type I), there was a sudden Appl. Sci. 2021, 11, 3558 12 of 13

change of wheel load. The reason is the huge difference in elasticity between the ballast layer and the anti-vibration device attached at the bottom of this type of track. Thus, it will be needed to increase the rigidity at the transition zone when designing this section. • To ensure comfort when the train running, the rail uplift force of precast slab track systems should not exceed 11.83 kN (which is 70% of the clamping force of fastening systems Vossloh 300-1 system-16.9 kN). The results showed that the maximum rail uplift force of Type II was slightly larger than Type I. In general, these results of both types of tracks satisfied the acceptance criteria and guarantee the riding comfort of the train. • Both types of tracks used the same kind of rail (KR 60 type). When applied to the conventional trainset, the rail bottom stress of Type I is 1.24 times larger than Type II, especially at the transition zone between the ballasted track and slab track. The main cause was that Type II had the stiffer elastic devices, and the distance of these devices was closer than Type I. However, the result of stress in both types of the track was smaller than the allowable stress (90 MPa). • According to the Japanese standard for displacement limit of structure in railway application, the rail displacement must be smaller than 3 mm. From the results, the maximum rail relative displacement of Type I was 3 times higher than Type II. When the train was operating at the connection zone between ballasted track and slab track, the rail deflection of Type I rose 4.2 times higher than Type II. This means the elasticity of the supporting device has a huge effect on rail displacement. • Finally, instead of using steel bars to connect the slab panels, the trainload was transmitted by the KR-60 rail. The step and inclination as well as the load transfer efficiency (LTE) between 20 slab panels were evaluated. As can be seen from the results, the step was smaller than the standard (2 mm), and the maximum inclination of the rail at the 75 mm distance of slabs was 1.07‰ for Type I and 0.53‰ for Type II, which met the requirement of the standard for riding comfort (2.5‰) and running safety (2.0‰) in Japan. The average LTE of Type I and Type II was 98.80% and 97.28%, respectively. Thus, these types of tracks can perfectly transmit the wheel load when the train passes by.

Author Contributions: Conceptualization, L.V.; Data curation, L.V.; Formal analysis, L.V.; Funding acquisition, Y.-S.K.; Methodology, D.-D.J.; Project administration, Y.-S.K.; Software, D.-D.J.; Supervi- sion, Y.-S.K.; Writing—original draft, L.V.; Writing—review & editing, D.-D.J. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by a grant from R&D Program (PK2103B1) of the Korea Railroad Research Institute, Korea. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: This research was supported by a grant from R&D Program (PK2103B1) of the Korea Railroad Research Institute, Korea. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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