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Load Transfer Efficiency Based on Structural Deflection Assessment of the Precast Floating Track

Load Transfer Efficiency Based on Structural Deflection Assessment of the Precast Floating Track applied sciences Article Load Transfer Efficiency Based on Structural Deflection Assessment of the Precast Floating Track 1 2 , Linh Vu and Yun Suk Kang * Department of Transportation System Engineering, KRRI School, University of Science and Technology, 217, Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea; linhvu2607@krri.re.kr Korea Railroad Research Institute 176, Cheoldo-bangmulgwan-ro, Uiwang, Gyeonggi-do 16105, Korea * Correspondence: yskang@krri.re.kr; Tel.: +82-10-3895-9112 Featured Application: Load Transfer Efficiency of the Precast Floating Track. Abstract: In Korea, a precast floating track with anti-vibration isolators was recently developed to reduce the vibration and noise in urban railway stations, without disrupting train operations. This precast floating slab track is a newly developed structure and differs from existing conventional slab tracks. In this study, a Finite Element Method program (MIDAS CIVIL 2019) was used to analyze the load-carrying ability of structures under the train axle loads. After finishing the design, to understand more precisely about load transfer efficiency of this type of track, an assembly test (two load cases) was conducted with three precast panels (with rail 60 K mounted on) and compared with Finite Element Analysis results. The final results satisfied the test standards in Korea, which confirms that the precast floating track has an acceptable safety factor and structural behavior. Keywords: precast floating track; anti-vibration device; FEA; noise and vibration; structural assembly test; load transfer efficiency 1. Introduction Citation: Vu, L.; Kang, Y.S. Load Trans- There are two common types of railway track are used in railway engineering: (a) fer Efficiency Based on Structural De- ballasted track with concrete sleeper or wooden sleeper, and (b) non-ballasted or slab track flection Assessment of the Precast Float- structure. The ballasted track which is installed with concrete sleepers has been widely ing Track. Appl. Sci. 2021, 11, 120. used for conventional lines. The main advantages of this type of track are good elasticity, https://dx.doi.org/10.3390/ low initial construction cost, and ease of maintenance [1]. However, the ballasted track app11010120 also has essential drawbacks such as high maintenance cost, fouled ballast, or insufficient support to the track structures. The track degradation’s main causes are ballast fouling Received: 30 November 2020 Accepted: 21 December 2020 and insufficient depth of ballast [2]. Therefore, it is necessary to develop and research a Published: 24 December 2020 non-destructive method such as ground penetrating radar (GPR) to limit these problems because the capacity of drainage in railway infrastructure is highly dependent on the Publisher’s Note: MDPI stays neu- fouled ballast [3]. Compared to the ballasted track, the non-ballasted or slab track has tral with regard to jurisdictional claims lower maintenance cost. It has been developed and become more popular in Korea, Japan, in published maps and institutional China, and Europe. Due to the advanced behaviors such as good resistance in lateral affiliations. and longitudinal direction and limiting of the buckling problem the slab track system is a suitable choice to apply for high-speed or metro railway track in tunnels, underground sections and bridges [4]. Nowadays, railway networks have been developed rapidly and the popular way to Copyright: © 2020 by the authors. Li- construct the infrastructure is to use the idle space below the tracks, especially for urban censee MDPI, Basel, Switzerland. This railway stations. However, by using the conventional slab track (cast in-situ method), article is an open access article distributed the ground-borne noises and vibrations generated from railway facilities during the train under the terms and conditions of the operations have become a severe problem [5]. As can be seen in Figure 1, at a railway Creative Commons Attribution (CC BY) station, the dynamic loads of the trains will be transmitted through the rails and slab track license (https://creativecommons.org/ licenses/by/4.0/). to the pillars, walls, and so on, which are the main structures that form the framework Appl. Sci. 2021, 11, 120. https://dx.doi.org/10.3390/app11010120 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 18 Appl. Sci. 2021, 11, 120 2 of 18 pillars, walls, and so on, which are the main structures that form the framework of the pillars, walls, and so on, which are the main structures that form the framework of the of stat the ion [ station 6]. So[, it 6]. iSo, s more e it is mor ffect eive t effective o find to counterme find countermeasur asures that ad es that dress the address sou the rce of the source station [6]. So, it is more effective to find countermeasures that address the source of the of noise, the which noise, which are mor ar ee eco mor nomica e economically lly and intand rinsic intrinsically ally efficient ef for ficient exist for ingexisting railway st railway ations noise, which are more economically and intrinsically efficient for existing railway stations stations [7]. [7]. [7]. Figure 1. The structural vibration transfer path. Figure Figure 1. 1. The The structural vibration transfer pat structural vibration transfer path.h. A floating slab track is one way to minimize the ground-borne vibration noise by A floating slab track is one way to minimize the ground-borne vibration noise by A floating slab track is one way to minimize the ground-borne vibration noise by blocking the vibration transmitted from the vehicle–track interaction [8]. This type of track blocking the vibration transmitted from the vehicle–track interaction [8]. This type of blocking the vibration transmitted from the vehicle–track interaction [8]. This type of track is generally made of the continuous rail, mounted on the massive concrete by the fastening track is generally made of the continuous rail, mounted on the massive concrete by the is generally made of the continuous rail, mounted on the massive concrete by the fastening devices and forming the mass–spring–systems (MSS). The combination of the panel’s fastening devices and forming the mass–spring–systems (MSS). The combination of the devices and forming the mass–spring–systems (MSS). The combination of the panel’s weight with a dead load of superstructures (rails, fastening systems, and sleepers) created panel’s weight with a dead load of superstructures (rails, fastening systems, and sleepers) weight with a dead load of superstructures (rails, fastening systems, and sleepers) created the dynamically active mass [9]. Under this type of track, the anti-vibration device such created the dynamically active mass [9]. Under this type of track, the anti-vibration device the dynamically active mass [9]. Under this type of track, the anti-vibration device such such as the g as the lass glass fiber, rub fiber,breubber r bearing, or bearing, coi or l sp coil ring springs s [10] [i10 s inst ] is al installed led as a s as ua bs substr tructu uctur re to dis e to- as the glass fiber, rubber bearing, or coil springs [10] is installed as a substructure to dis- disconnect connect the tr theack track from from the the ground ground and and decrease the decrease the magnitude o magnitude f the lo of thead load gen generated erated by connect the track from the ground and decrease the magnitude of the load generated by by the wheel-rail, and this method is widely used and accepted for railway tracks in the wheel-rail, and this method is widely used and accepted for railway tracks in Korea the wheel-rail, and this method is widely used and accepted for railway tracks in Korea Kor andea aro and und ar tound he wor the ld [ world 11–18[]11 . In –18 flo ].at In infloating g slab trslab acks, t tracks, he raithe ls ar rails e usu araelly usually used as used the and around the world [11–18]. In floating slab tracks, the rails are usually used as the as connection between panels the connection between p instead of do anels instead wel bar of dowel s to reduce the constructi bars to reduce the constr on cost. uction To si cost. m- connection between panels instead of dowel bars to reduce the construction cost. To sim- To simulate the performance of this type of track system, the easiest way is to consider ulate the performance of this type of track system, the easiest way is to consider it as a ulate the performance of this type of track system, the easiest way is to consider it as a it as a single degree of freedom as shown in Figure 2 with F is load, m is the mass of the single degree of freedom as shown in Figure 2 with F is load, m is the mass of the track single degree of freedom as shown in Figure 2 with F is load, m is the mass of the track track structures, k is the stiffness of substructure and c is the damping factor of the system. structures, k is the stiffness of substructure and c is the damping factor of the system. The structures, k is the stiffness of substructure and c is the damping factor of the system. The The biggest deterrent of this type of railway structure is the huge initial construction cost. biggest deterrent of this type of railway structure is the huge initial construction cost. biggest deterrent of this type of railway structure is the huge initial construction cost. However, recent studies about the life cycle cost of railway structures pointed out that this However, recent studies about the life cycle cost of railway structures pointed out that this However, recent studies about the life cycle cost of railway structures pointed out that this type of track can be an alternative method of the ballasted track or conventional concrete type of track can be an alternative method of the ballasted track or conventional concrete type of track can be an alternative method of the ballasted track or conventional concrete track with several advantages such as lower maintenance cost, rapid construction, and track with several advantages such as lower maintenance cost, rapid construction, and track with several advantages such as lower maintenance cost, rapid construction, and lower structure height [19]. lower structure height [19]. lower structure height [19]. Figure 2. Single degree of freedom scheme. Figure 2. Single degree of freedom scheme. Figure 2. Single degree of freedom scheme. Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 18 Appl. Sci. 2021, 11, 120 3 of 18 In this study, we determined whether a precast floating track, which was manufac- tured in a factory, transported, and installed at a construction site, could be a suitable In this study, we determined whether a precast floating track, which was manufactured solution to reduce the noise and vibration problems. Our study utilized a precast floating in a factory, transported, and installed at a construction site, could be a suitable solution slab track structure, which is a newly developed structure, unlike existing conventional to reduce the noise and vibration problems. Our study utilized a precast floating slab track structures. We assessed the precast floating track panel structure using the finite track structure, which is a newly developed structure, unlike existing conventional track element method (MIDAS CIVIL program) and structural assembly tests to verify its struc- structures. We assessed the precast floating track panel structure using the finite element tural performance. The goal of these tests was to evaluate the displacement of the rail and method (MIDAS CIVIL program) and structural assembly tests to verify its structural pa performance. nel to verify the sa The goal fety of of these thistests system through the was to evaluate the load displacement transfer efficof iency. the rail and panel to verify the safety of this system through the load transfer efficiency. 2. Precast Floating Panel 2. Precast Floating Panel This study focuses on a new type of precast floating panel developed by the Korea This study focuses on a new type of precast floating panel developed by the Korea Railroad Research Institute (KRRI). Figure 3 shows a 3D-modeling and the cross section Railroad Research Institute (KRRI). Figure 3 shows a 3D-modeling and the cross section of of this type of panel. The dimensions of the panel were 4.925 m (length) × 2.4 m (width) × this type of panel. The dimensions of the panel were 4.925 m (length)  2.4 m (width) 0.3 m (thickness). Rail and the slab panel was connected by fastening device (System 300- 0.3 m (thickness). Rail and the slab panel was connected by fastening device (System 300-1, 1, KR type). KR type). (b) (a) Figure 3. (a) Three-dimensional (3D)-modeling of the precast floating panel, and (b) cross-section of precast floating panel. Figure 3. (a) Three-dimensional (3D)-modeling of the precast floating panel, and (b) cross-section of precast floating panel. The fabrication process of the precast floating panel is shown in Figure 4. Rebars D19 (longitudinal direction) and D13 (horizontal direction) were installed in a formwork, The fabrication process of the precast floating panel is shown in Figure 4. Rebars D19 after completing the formwork, concrete was poured (Figure 4b) and the curing process (longitudinal direction) and D13 (horizontal direction) were installed in a formwork, after was carried out (Figure 4c) until the compressive strength of concrete (f’c) reached 45 MPa completing the formwork, concrete was poured (Figure 4b) and the curing process was (Figure 4d). This type of track can be installed in a limited amount of time after the existing carried out (Figure 4c) until the compressive strength of concrete (f’c) reached 45 MPa ballasted track is removed. This design has six anti-vibration devices that are attached to (Figure 4d). This type of track can be installed in a limited amount of time after the existing the bottom of one of the precast track panels. The panel is composed of assembly blocks ballasted track is removed. This design has six anti-vibration devices that are attached to that are connected by concrete crossbeams. The panels are transported to the construction the bottom of one of the precast track panels. The panel is composed of assembly blocks sites for rapid installation and are assembled to a fixed track height by adjusting the base, that are connected by concrete crossbeams. The panels are transported to the construction which is aligned in advance with the upper part of the station slab. The precast floating slab sites for rapid installation and are assembled to a fixed track height by adjusting the base, panels are installed sequentially on a flat plane using a hydraulic jack, and a high-precision which is aligned in advance with the upper part of the station slab. The precast floating survey is used to make linear corrections. The anti-vibration isolator uses a wedge-type slab panels are installed sequentially on a flat plane using a hydraulic jack, and a high- engineering plastic block to attenuate the vibrations in the vertical direction, through precision survey is used to make linear corrections. The anti-vibration isolator uses a frictional resistance. This provides restorative forces through the coil springs, which are wedge-type engineering plastic block to attenuate the vibrations in the vertical direction, arranged in the lateral and vertical directions to insulate against any vibrations. through frictional resistance. This provides restorative forces through the coil springs, which are arranged in the lateral and vertical directions to insulate against any vibrations. Appl. Sci. 2021, 11, 120 4 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 18 (a) (b) (c) (d) Figure 4. Fabrication process of precast floating panel: (a) assembly of rebar, (b) concrete pouring, Figure 4. Fabrication process of precast floating panel: (a) assembly of rebar, (b) concrete pouring, (c) curing, and (d) (c) curing, and (d) prototype of precast floating panels. prototype of precast floating panels. 3. Experimental Program 3. Experimental Program To evaluate the structural safety of the prefabricated floating track, we tested the To evaluate the structural safety of the prefabricated floating track, we tested the bending performance of the slab panel in conjunction with a designed trainload. The bending performance of the slab panel in conjunction with a designed trainload. The per- performance of the vibration control system was compared with the stability of the track formance of the vibration control system was compared with the stability of the track sys- system and its ability to resist train loads. The detailed specifications of the slab panel are tem and its ability to resist train loads. The detailed specifications of the slab panel are shown in Table 1. The test was conducted using the same structural assembly specimens, to shown in Table 1. The test was conducted using the same structural assembly specimens, evaluate the behavior of track systems, which consisted of rails, slab panels, and vibration to evaluate the behavior of track systems, which consisted of rails, slab panels, and vibra- isolators composed of precast panels. The test was carried out by applying loads on the tion isolators composed of precast panels. The test was carried out by applying loads on three-panel test, two load cases were conducted: loaded on the 2nd panel at the 2/4 point, the three-panel test, two load cases were conducted: loaded on the 2nd panel at the 2/4 and on the 2nd panel at 4/4 point. Table 2 shows the specifications of the load test. In point, and on the 2nd panel at 4/4 point. Table 2 shows the specifications of the load test. load case I, the maximum bending capacity of the structure was verified through the In load case I, the maximum bending capacity of the structure was verified through the deflection of rail and panel. Meanwhile, the purpose of load case II was to determine the deflection of rail and panel. Meanwhile, the purpose of load case II was to determine the load transfer efficiency between the panels. According to the Korea construction rules load transfer efficiency between the panels. According to the Korea construction rules for for the railroad (Rule number 16), in the tunnel section, the standard live load EL-18 was the railroad (Rule number 16), in the tunnel section, the standard live load EL-18 was used used to apply for the designed load (180 kN) and in preparation for installing this type of to apply for the designed load (180 kN) and in preparation for installing this type of track in track in conventional line [20], more than 250 kN of axle load must be reviewed so that conventional line [20] , more than 250 kN of axle load must be reviewed so that the test was the test was performed through the load up to 440 kN which is calculated based on the performed through the load up to 440 kN which is calculated based on the static axle load static axle load of Korean standard (KRL-2012) for conventional passenger and freight train of Korean standard (KRL-2012) for conventional passenger and freight train (220 kN) and (220 kN) and the dynamic amplification factor (2.00) according to Eisenmann formula [1]. the dynamic amplification factor (2.00) according to Eisenmann formula [1]. In Figure 5 a In Figure 5 a full-scale load test was conducted using monotonic loads of 150, 200, 250, full-scale load test was conducted using monotonic loads of 150, 200, 250, 300, 350, 380, 410, 300, 350, 380, 410, and 440 kN. The load force rate (DIN45673-1) was set to 2 kN/s, then remain and 440 kN. T the maximum he load force load time was rate (DIN45673-1) wa 10 s, and the displacement s set to 2 kN/ of tshe , th rail en rem andapanel in the m wer axim e um measur load time was e while removing 10 s, and the displacement the load at the same of the rail and speed again. The panel were loadingmeasure while r test assemblies e for moving the thr th ee-panel e load at slab the sar am e e shown speed in agFigur ain. The lo es 6 and adin 7g t . First, est as the semblies anti-vibration for the th devices ree-pane wer l sl eab are installed shown at the in Fig bottom ures 6 and 7. First of the panels. Next, , the ant the i-vib panels ration wer de e fixed vices on wer the e in flat stal floor led at by th scr e b ews, ottom of and finally, the load was applied at two load cases as mention above. The linear voltage the panels. Next, the panels were fixed on the flat floor by screws, and finally, the load differential transducers (LVDT) were set to 50 mm mounted on the rails; panels are shown was applied at two load cases as mention above. The linear voltage differential transduc- in Figure 7 to measure the behavior of structures. The load capacity was set to 500 kN ers (LVDT) were set to 50 mm mounted on the rails; panels are shown in Figure 7 to meas- using a dynamic actuator, and the data was collected using a TDS-601 data logger, which ure the behavior of structures. The load capacity was set to 500 kN using a dynamic actu- was manufactured by Tokyo Corp. ator, and the data was collected using a TDS-601 data logger, which was manufactured by Tokyo Corp. Appl. Sci. 2021, 11, 120 5 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 18 Table 1. Table 1. Spe Specification cification of Spe of Specimen. cimen. Table 1. Specification of Specimen. Specifications Dimensions Specifications Dimensions Specifications Dimensions 4.925 (L) × 2.4 (W) × 0.3 Size of Panel (m) 4.925 (L)  2.4 (W)  0.3 (H) Size of Panel (m) 4.925 (L) × 2.4 (W) × 0.3 Concrete Strength (MPa) 45 (H) Size of Panel (m) (H) Weight of Panel (ton) 7.6 Concrete Strength (MPa) 45 Vertical Support Stiffness of Anti-vibration Device (kN/mm) 22.5 Concrete Strength (MPa) 45 Weight of Panel (ton) 7.6 Lateral Support Stiffness of Anti-vibration Device (kN/mm) 18 Weight of Panel (ton) 7.6 Vertical Support Stiffness of Anti-vibration Device (kN/mm) 22.5 Vertical Support Stiffness of Anti-vibration Device (kN/mm) 22.5 Lateral Support Stiffness of Anti-vibration Device (kN/mm) 18 Lateral Support Stiffness of Anti-vibration Device (kN/mm) 18 Table 2. Loading points. Table 2. Loading points. Classification Table 2. Loading points. Loading Point Steps Classification Number of Panel Loading Cases Loading Point Steps Classification Number of Panel Loading Cases Loading Point Steps Load on 2nd panel-2/4 Point Number of Panel Loading Cases Load on 2nd panel-2/4 Point Load case I (Distance: 7.4625 m load on 8 Steps (150–440 kN) Load case I 8 Steps (150–440 kN) Load on 2nd panel-2/4 Point (Distance: 7.4625 m load on both rails) both rails) Load case I 8 Steps (150–440 kN) Three Panels Three Panels (Distance: 7.4625 m load on both rails) Load on 2nd panel-4/4 Point Three Panels Load on 2nd panel-4/4 Point Load case II 8 Steps (150–440 kN) Load on 2nd panel-4/4 Point (Dista Load nce: 10 case .00 m l II oad (Distance: on both ra 10.00 ils) m load on 8 Steps (150–440 kN) Load case II 8 Steps (150–440 kN) (Distance: 10.00 m load on both rails) both rails) (a) (b) (a) (b) Figure 5. Assembly test specifications: (a) full scale static loading diagram and (b) installation of assembly test. Figure 5. Assembly test specifications: (a) full scale static loading diagram and (b) installation of assembly test. Figure 5. Assembly test specifications: (a) full scale static loading diagram and (b) installation of assembly test. (a) (b) (a) (b) Figure 6. Structural assembly of three slab panel with 60 K rail: (a) Load case I: center loading point, and (b) Load case II: Figure 6. Structural assembly of three slab panel with 60 K rail: (a) Load case I: center loading point, and (b) Load case II: Figure 6. Structural assembly of three slab panel with 60 K rail: (a) Load case I: center loading point, and (b) Load case II: 2nd panel at 4/4 loading point test. 2nd panel at 4/4 loading point test. 2nd panel at 4/4 loading point test. Appl. Sci. 2021, 11, 120 6 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 18 (a) Top View (b) Side View Figure 7. Locations of sensors to evaluate the performance of the three precast panels. Figure 7. Locations of sensors to evaluate the performance of the three precast panels. 4. Numerical Analysis 4. Numerical Analysis In railway application, according to the Zimmermann method which is the well- In railway application, according to the Zimmermann method which is the well- known “beam on elastic foundation”, the rail is assumed as a continuous beam supported known “beam on elastic foundation”, the rail is assumed as a continuous beam supported by the elastic foundation system composed by fastening system, ballast, sub-ballast-mat by the elastic foundation system composed by fastening system, ballast, sub-ballast-mat as well as sub-soil. In this study, we focused on the displacement of the structures under as well as sub-soil. In this study, we focused on the displacement of the structures under the static loads to determine the load transfer efficiency of precast floating slab track. To the static loads to determine the load transfer efficiency of precast floating slab track. To model this type of precast floating slab track, based on this method, we considered the rail model this type of precast floating slab track, based on this method, we considered the as a continuous beam mounted on the panels by fastening system and the panels (discon- rail as a continuous beam mounted on the panels by fastening system and the panels tinuous slabs) was attached with the anti-vibration device as the elastic component. (discontinuous slabs) was attached with the anti-vibration device as the elastic component. According to the beam on elastic foundation theory, the deflection and moment of According to the beam on elastic foundation theory, the deflection and moment of the the beam under the concentrated wheel load shown in Figure 8 can be calculated as fol- beam under the concentrated wheel load shown in Figure 8 can be calculated as following lowing formulas: formulas: QL w(x) = h(x) (1) 8EI QL M(x) = m(x) (2) 4EIa where: L: characteristic length = (m); and k : stiffness coefficient of discrete support 1 1 1 and = ; Figure 8. Beam k on ela k stic foundation model. d i a: spacing between centers of discrete supports (m); Q: wheel load (N) = 0.5 P (with P is axle load) 𝑄𝐿 EI: bending stiffness of beam (N/m ); (1) 𝑤 𝑥 𝜂 𝑥 8𝐸𝐼 and, two influence factors are: h i 𝑄𝐿 x x x/L (2) h(x)𝑀 = 𝑥 e co 𝜇𝑥 s + sin x  0 (3) L L h i x x x/L where: L: characteristic length (m); and kd: stiffness coefficient of discrete support m(x) = e cos sin x  0 (4) L L and ; a: spacing between centers of discrete supports (m); Q: wheel load (N) = 0.5 P (with P is axle load) EI: bending stiffness of beam (N/m ); and, two influence factors are: Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 18 (a) Top View (b) Side View Figure 7. Locations of sensors to evaluate the performance of the three precast panels. 4. Numerical Analysis In railway application, according to the Zimmermann method which is the well- known “beam on elastic foundation”, the rail is assumed as a continuous beam supported by the elastic foundation system composed by fastening system, ballast, sub-ballast-mat as well as sub-soil. In this study, we focused on the displacement of the structures under the static loads to determine the load transfer efficiency of precast floating slab track. To model this type of precast floating slab track, based on this method, we considered the rail as a continuous beam mounted on the panels by fastening system and the panels (discon- tinuous slabs) was attached with the anti-vibration device as the elastic component. According to the beam on elastic foundation theory, the deflection and moment of Appl. Sci. 2021, 11, 120 7 of 18 the beam under the concentrated wheel load shown in Figure 8 can be calculated as fol- lowing formulas: Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 18 𝑥 𝑥 𝜂 𝑥 𝑒 𝑐𝑜𝑠 𝑠𝑖𝑛 𝑥 0 (3) 𝐿 𝐿 𝑥 𝑥 Figure 8. Figure Beam 8. Beam on ela on elastic stic fou foundation ndation mo model. de𝜇l. 𝑥 𝑒 𝑐𝑜𝑠 𝑠𝑖𝑛 𝑥 0 (4) 𝐿 𝐿 This type of precast floating slab track was simulated as the double beam model This type of precast floating slab track was simulated as the double beam model with 𝑄𝐿 with discrete support so the finite element method can be used to evaluate the structural discrete support so the finite element method can be used to evaluate the structural be- (1) 𝑤 𝑥 𝜂 𝑥 8𝐸𝐼 behavior of the track [1]. In this paper, we used MIDAS CIVIL 2019, a finite element havior of the track [1]. In this paper, we used MIDAS CIVIL 2019, a finite element program program to model the precast floating slab track. The continuous rail was modeled by to model the precast floating slab track. The continuous rail was modeled by using the 𝑄𝐿 (2) using the profile of KR 60 rail, 𝑀 consider 𝑥 ed 𝜇𝑥 as a continuous beam and the standard gauge profile of KR 60 rail, considered as a continuous beam and the standard gauge (1435 mm) (1435 mm) was applied. The panel was modeled by two concrete slabs connected with each was applied. The panel was modeled by two concrete slabs connected with each other by other by crossbeams using the beam element and the distance between each panel is 75 mm. crossbeams using the beam element and the distance between each panel is 75 mm. The where: L: characteristic length (m); and kd: stiffness coefficient of discrete support The rail and concrete slab were connected by the elastic fastening system (system 300-1, KR rail and concrete slab were connected by the elastic fastening system (system 300-1, KR and ∑ ; type) with the vertical stiffness was 28.7 kN/mm. Six anti-vibration devices were set up at ty pe) with the vertical stiffness was 28.7 kN/mm. Six anti-vibration devices were set up at the bottom of each panel as the spring device (elastic link element), the vertical stiffness of a: spacing between centers of discrete supports (m); the bottom of each panel as the spring device (elastic link element), the vertical stiffness each device was 22.5 kN/mm. The structure system analysis model and specifications are Q: wheel load (N) = 0.5 P (with P is axle load) of each device was 22.5 kN/mm. The structure system analysis model and specifications shown in Figure 9 and Table 3, respectively. EI: bending stiffness of beam (N/m ); are shown in Figure 9 and Table 3, respectively. and, two influence factors are: (a) (b) Figure 9. Modeling of the precast floating slab; (a) overview, and (b) front view. Figure 9. Modeling of the precast floating slab; (a) overview, and (b) front view. Table 3. Specification of track system. Classification Unit Specification Moment of inertia mm 30,640,000 Rail Section modulus mm 395,000 (KR60) Modulus of elasticity MPa 210,000 Appl. Sci. 2021, 11, 120 8 of 18 Table 3. Specification of track system. Classification Unit Specification Moment of inertia mm 30,640,000 Section modulus 395,000 mm Rail (KR60) Modulus of elasticity MPa 210,000 Coefficient of thermal expansion 1/ C 1.14  10 Type System 300-1 Width mm 160 Length mm 290 Fastening Static stiffness (Vertical direction) kN/m 28,734 system Dynamic stiffness (Vertical direction) kN/m 32,770 Static stiffness (Lateral direction) kN/m 40 Dynamic stiffness (Lateral direction) kN/m 60 Thickness mm 300 Width mm 900 Length mm 4925 Precast concrete slab Modulus of elasticity MPa 35,684 (ladder type) Compressive strength MPa 45 Poison’s coefficient - 0.18 Coefficient of thermal expansion 1/ C 1.0  10 Static stiffness kN/m 22,500 Anti-vibration Stability stiffness (longitudinal direction) kN/m 18,000 device Stability stiffness (lateral direction) kN/m 18,000 Modulus of elasticity MPa 35,684 Compressive strength MPa 45 Crossbeam Poison’s coefficient - 0.18 Coefficient of thermal expansion 1/ C 1.0  10 Figure 9 shows the concept of three panels (approximately 15 m length) simulated as the same dimensions of the actual specimens with the continuously rail mounted on by the fastening device. This new type of precast floating slab track has no joint to connect the panels, so the load can be distributed and transmitted directly through the rails. 5. Results and Discussion This study conducted load tests to evaluate the displacement of the structures as well as the load transfer efficiency of the new type of precast floating slab track. The results of the test are compared with the Finite Element Analysis to accurately understand the structure behaviors. 5.1. Load Case I In this Load case, the loads were set up at the center of 2nd panel to verify the maximum bearing capacity as well as the maximum deflection of the structures. Table 4 shows the vertical displacement measurement results for the three-panel precast floating slab track, which was mounted on a 60 K continuous rail with a central loading point (2/4 loading point) compare with the FEA results. Appl. Sci. 2021, 11, 120 9 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 18 Table 4. Table 4. Panel Panel vertical vertical d displacement isplacement of three- of three-panel panel precast precast fl floating oating slab slab track panel (centra track panel (centrallloading loadingp point oint in in 2nd 2nd Panel). Panel). Panel Vertical Displacement FEA Results for Panel Vertical Displacement Panel Vertical Displacement FEA Results for Panel Vertical Displacement Support Load Center Left Side Right Average Center Sen- Left Side Right Side Average Support Right Right Load Stiffness Center Left Side Average Center Left Side Average Stiffness (kN) Sensor Sensor Side Sen- Value sor Sensor Sensor Value Side Side (kN) Sensor Sensor Value Sensor Sensor Value (kN/mm) (kN/mm) Sensor Sensor (mm) (mm) sor (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) 150 1.08 0.69 0.54 0.77 32.47 1.39 0.88 0.88 1.05 150 1.08 0.69 0.54 0.77 32.47 1.39 0.88 0.88 1.05 200 1.51 0.91 0.77 1.06 31.35 1.86 1.17 1.17 1.40 200 1.51 0.91 0.77 1.06 31.35 1.86 1.17 1.17 1.40 250 1.96 1.19 1.01 1.39 30.05 2.32 1.46 1.46 1.75 250 1.96 1.19 1.01 1.39 30.05 2.32 1.46 1.46 1.75 300 2.32 1.36 1.23 1.64 30.55 2.78 1.75 1.75 2.09 300 2.32 1.36 1.23 1.64 30.55 2.78 1.75 1.75 2.09 35 3500 2.77 2.77 1.63 1.631.49 1.491.96 1.9629.71 29.71 3.25 2. 3.25 052.05 2.05 2.05 2. 2.4545 380 3.06 1.80 1.66 2.17 29.14 3.53 2.22 2.22 2.66 380 3.06 1.80 1.66 2.17 29.14 3.53 2.22 2.22 2.66 410 3.34 1.97 1.81 2.37 28.79 3.80 2.40 2.40 2.87 410 3.34 1.97 1.81 2.37 28.79 3.80 2.40 2.40 2.87 440 3.62 2.13 1.96 2.57 28.53 4.08 2.57 2.57 3.07 440 3.62 2.13 1.96 2.57 28.53 4.08 2.57 2.57 3.07 Figure 10 shows the vertical deflections of the panel, and the relative deflections of the Figure 10 shows the vertical deflections of the panel, and the relative deflections of right rail, which were measured in Load case I when applying loads in the center of the 2nd the right rail, which were measured in Load case I when applying loads in the center of panel (2/4 loading point). As shown in Figure 5a, under monotonic loads of 150 to 440 kN, the 2nd panel (2/4 loading point). As shown in Figure 5a, under monotonic loads of 150 the vertical displacement of the panel occurred between 1.08 to 3.62 mm, when the sensor to 440 kN, the vertical displacement of the panel occurred between 1.08 to 3.62 mm, when was installed in the center of the panel. However, on the right-side sensor the displacement the sensor was installed in the center of the panel. However, on the right-side sensor the of panel changed from 0.54m to 1.96 mm and this data on the left-side was increased from displacement of panel changed from 0.54m to 1.96 mm and this data on the left-side was 0.69 to 2.13 mm, so that the average vertical deflection value varied from 0.77 to 2.57 mm. increased from 0.69 to 2.13 mm, so that the average vertical deflection value varied from This is because of the greater the load, the greater the vertical displacement. The estimated 0.77 to 2.57 mm. This is because of the greater the load, the greater the vertical displace- support stiffness of the six anti-vibration devices under the slab was calculated by divided ment. The estimated support stiffness of the six anti-vibration devices under the slab was the load by the average deflection and determined to be 28.53–32.47 kN/mm, which is calculated by divided the load by the average deflection and determined to be 28.53–32.47 slightly bigger than the value of the original design. Due to the load was applied in the kN/mm, which is slightly bigger than the value of the original design. Due to the load was center of three panels, the displacement of the panels in Figure 10a and the displacement applied in the center of three panels, the displacement of the panels in Figure 10a and the of the rails in Figure 10b can be compared with others. As can be seen in Figure 10a,b, the displacement of the rails in Figure 10b can be compared with others. As can be seen in Figure loads were transmitted and distributed to three panels through the rails. However, even if 10a,b, the loads were transmitted and distributed to three panels through the rails. How- the loads from 150~440 kN were applied in the 2nd panel, the vertical displacement only ever, even if the loads from 150~440 kN were applied in the 2nd panel, the vertical displace- occurred in the central panel and this value of the left and right panel was exceedingly ment only occurred in the central panel and this value of the left and right panel was ex- small. This situation was also the same for rail displacement. ceedingly small. This situation was also the same for rail displacement. (a) Figure 10. Cont. Appl. Sci. 2021, 11, 120 10 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 18 (b) (c) Figure 10. Three-panel vertical displacement test results (Load case I) (a) vertical displacement of the panel (mm), (b) rail Figure 10. Three-panel vertical displacement test results (Load case I) (a) vertical displacement of the panel (mm), (b) rail vertical displacement (mm), and (c) comparison between FEA and test results (mm). vertical displacement (mm), and (c) comparison between FEA and test results (mm). As can be seen in Figure 10c, the results from the assembly test were moderately As can be seen in Figure 10c, the results from the assembly test were moderately smaller than the FEA results. The panel displacements at the left and right sensors were smaller than the FEA results. The panel displacements at the left and right sensors were similar according to the calculation of the program. The maximum average value of FEA similar according to the calculation of the program. The maximum average value of FEA was roughly 1.2 times larger than this value from the actual test. Moreover, the support was roughly 1.2 times larger than this value from the actual test. Moreover, the support stiffness was measure around 23.8 kN/mm from the program which was almost the same stiffness was measure around 23.8 kN/mm from the program which was almost the same as the design stiffness of the anti-vibration device (22.5 kN/mm). as the design stiffness of the anti-vibration device (22.5 kN/mm). Table 5 shows the results for the relative rail vertical deflections at both the center Table 5 shows the results for the relative rail vertical deflections at both the center endpoints. These deflections occurred in both rails when the load was applied in the center endpoints. These deflections occurred in both rails when the load was applied in the cen- of the 2nd panel. This result was calculated by the difference between the deflection of ter of the 2nd panel. This result was calculated by the difference between the deflection of rail and panel. The displacements in the left and right rails were almost insignificant. rail and panel. The displacements in the left and right rails were almost insignificant. The The maximum displacement of the relative rail to be 2.2 mm, which was 440 kN for the maximum displacement of the relative rail to be 2.2 mm, which was 440 kN for the 60K 60K rail mounted on three-panel assembly test. At the center point, the vertical relative rail mounted on three-panel assembly test. At the center point, the vertical relative dis- displacement of the right rail was 0.91 to 1.80 mm. However, the left rail was between 1.09 placement of the right rail was 0.91 to 1.80 mm. However, the left rail was between 1.09 to to 2.20 mm. The maximum displacement deviation of the left and right sides was 0.43 mm. 2.20 mm. The maximum displacement deviation of the left and right sides was 0.43 mm. Under the same loading conditions, the vertical deflection of the left rail at the endpoint Under the same loading conditions, the vertical deflection of the left rail at the endpoint Appl. Sci. 2021, 11, 120 11 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 18 was 0.06 to 0.39 mm, and 0.10 to 0.25 mm for the right rail. Thus, the average displacement was 0.06 to 0.39 mm, and 0.10 to 0.25 mm for the right rail. Thus, the average displacement of the rails mounted on three-panel at the center point was approximately 8.30 times larger of the rails mounted on three-panel at the center point was approximately 8.30 times larger than at the endpoint. than at the endpoint. Table 5. Maximum relative rail displacement results for the three-panel precast floating slab track Table 5. Maximum relative rail displacement results for the three-panel precast floating slab track (loading at center point (loading at center point of 2nd Panel). of 2nd Panel). FEA Results FEA Results Center Point (mm) Center End Po Point in(mm) t (mm) End Point (mm) Load Center Point (mm) End Point (mm) Load Center Point (mm) End Point (mm) (kN) (kN) Left Right Left Right Left Right Left Right Left Rail Right Rail Left Rail Right Rail Left Rail Right Rail Left Rail Right Rail Rail Rail Rail Rail Rail Rail Rail Rail 150 1.09 0.91 0.06 0.10 0.91 0.91 0.16 0.16 150 1.09 0.91 0.06 0.10 0.91 0.91 0.16 0.16 200 1.35 1.12 0.13 0.12 1.22 1.22 0.22 0.22 200 1.35 1.12 0.13 0.12 1.22 1.22 0.22 0.22 250 1.58 1.31 0.17 0.14 1.51 1.51 0.27 0.27 250 1.58 1.31 0.17 0.14 1.51 1.51 0.27 0.27 300 1.77 1.49 0.23 0.17 1.82 1.82 0.33 0.33 300 1.77 1.49 0.23 0.17 1.82 1.82 0.33 0.33 350 1.95 1.60 0.29 0.20 2.12 2.12 0.38 0.38 350 1.95 1.60 0.29 0.20 2.12 2.12 0.38 0.38 380 2.06 1.67 0.33 0.22 2.30 2.30 0.41 0.41 380 2.06 1.67 0.33 0.22 2.30 2.30 0.41 0.41 410 2.12 1.69 0.37 0.24 2.49 2.49 0.44 0.44 410 2.12 1.69 0.37 0.24 2.49 2.49 0.44 0.44 440 2.20 1.80 0.39 0.25 2.67 2.67 0.48 0.48 440 2.20 1.80 0.39 0.25 2.67 2.67 0.48 0.48 As can be seen in Figure 11, the FEA results present the relative displacements of As can be seen in Figure 11, the FEA results present the relative displacements of both rails have no difference at center point or endpoint. The displacement of both rails both rails have no difference at center point or endpoint. The displacement of both rails at at the center point was 0.91–2.67 mm, and this value at the endpoint was 0.16–0.48 mm. the center point was 0.91–2.67 mm, and this value at the endpoint was 0.16–0.48 mm. The The average deflection of rails at the center point when calculated by the FEM program average deflection of rails at the center point when calculated by the FEM program was was only 5.61 times larger than at the endpoint. When comparing the maximum average only 5.61 times larger than at the endpoint. When comparing the maximum average re- results, the experiment test value was 0.93 times of finite element analysis result. sults, the experiment test value was 0.93 times of finite element analysis result. (a) Figure 11. Cont. Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 18 Appl. Sci. 2021, 11, 120 12 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 18 (b) (b) Figure 11. Comparison of rail relative displacement (Load case I), (a) at center point, and (b) at end Figure 11. Comparison of rail relative displacement (Load case I), (a) at center point, and (b) at end point. Figure 11. Comparison of rail relative displacement (Load case I), (a) at center point, and (b) at end point. point. 5. 5.2. 2. Load Load C Case ase II II 5.2. Load Case II Fig Figur ure e 1 12 2 sho shows ws th the e re rsu esults lts when t when hthe e loa loads ds were wer ap e p applied lied to th to e the 2nd 2nd panel panel at 4/4 at lo4/4 ad- Figure 12 shows the results when the loads were applied to the 2nd panel at 4/4 load- ing po loading intpoints s (Load (Load case II case ). The ma II). The in rea main son o reason f this Lo of ad this case Load is to case deteis rmine to determine the effective the - ing points (Load case II). The main reason of this Load case is to determine the effective- effectiveness of transferring the load from one panel to another. The loading point was set ness of transferring the load from one panel to another. The loading point was set up at ness of transferring the load from one panel to another. The loading point was set up at up at the junction between two panel (2nd and 3rd panel). The loads were transmitted the junction between two panel (2nd and 3rd panel). The loads were transmitted between the junction between two panel (2nd and 3rd panel). The loads were transmitted between between two panel without any dowel bar or connection joint. two panel without any dowel bar or connection joint. two panel without any dowel bar or connection joint. (a) (a) Figure 12. Cont. Appl. Sci. 2021, 11, 120 13 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 18 (b) (c) Figure 12. Vertical displacement results for three-panel testing (at 2nd panel 4/4 loading point), (a) vertical displacement Figure 12. Vertical displacement results for three-panel testing (at 2nd panel 4/4 loading point), (a) vertical displacement of of the panel (mm), (b) vertical displacement of the right rail (mm), and (c) rail relative vertical displacement (mm). the panel (mm), (b) vertical displacement of the right rail (mm), and (c) rail relative vertical displacement (mm). The previous research about concrete pavement pointed out that at least 10% of initial The previous research about concrete pavement pointed out that at least 10% of initial cost increase if install the dowel bars between the panel [21,22]. To limit that issue, this cost increase if install the dowel bars between the panel [21,22]. To limit that issue, this precast floating slab track used rails to transfer the load from the panels and the distance precast floating slab track used rails to transfer the load from the panels and the distance between each slab was 75 mm. In this type of track, the upper part of the panel was between each slab was 75 mm. In this type of track, the upper part of the panel was fas- fastened only by the rails, which were separated from the track slab. Because the train runs tened only by the rails, which were separated from the track slab. Because the train runs on these rails, it is necessary to consider the relative deflection of the connected panel. If a on these rails, it is necessary to consider the relative deflection of the connected panel. If difference occurs in the upper part of the panel of the relative deflection of the rail, then a difference occurs in the upper part of the panel of the relative deflection of the rail, then the railway train will affect the dynamic behavior, such as the vehicle acceleration, and the railway train will affect the dynamic behavior, such as the vehicle acceleration, and body acceleration will increase due to a step difference that occurs when the train passes body acceleration will increase due to a step difference that occurs when the train passes through the connected portion [23]. The vertical deflection of the panel and the rail at the through the connected portion [23]. The vertical deflection of the panel and the rail at the endpoint and the adjacent point were therefore measured. endpoint and the adjacent point were therefore measured. The load transfer characteristics of the slab panel connection can be determined by The load transfer characteristics of the slab panel connection can be determined by using load transfer efficiency (LTE), which is defined as by [24]: using load transfer efficiency (LTE), which is defined as by [24]: 2 2 δ22 2δ LTE =   = (5) LTE = = 2  + 1 2  + (5) δδ δδ 12   where,  : is the rail/panel displacement at panel endpoint (mm). where, δ1: is the rail/panel displacement at panel endpoint (mm). : is the rail/panel displacement at panel adjacent point (mm). δ2: is the rail/panel displacement at panel adjacent point (mm). Appl. Sci. 2021, 11, 120 14 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 14 of 18 As shown in Figure 13, the load transfer efficiency (LTE) of this precast floating track As shown in Figure 13, the load transfer efficiency (LTE) of this precast floating track was based on the displacement of rail and panel between the loaded panel endpoint ( ) was based on the displacement of rail and panel between the loaded panel endpoint (δ1) and unloaded panel adjacent point ( ). In this paper, the precast floating track has used and unloaded panel adjacent point (δ2). In this paper, the precast floating track has used the rails mounted on the slabs to transfer the load from one slab to another instead of the the rails mounted on the slabs to transfer the load from one slab to another instead of the connection joint or dowel. If the displacement of loaded slab panel approximated with the connection joint or dowel. If the displacement of loaded slab panel approximated with the unloaded one (   ), the result in LTE will reach 100% [22]. High stresses will occur if 1 2 unloaded one (δ1 ≈ δ2), the result in LTE will reach 100% [22]. High stresses will occur if the load transfer is poor and it may cause the pumping, faulting and breaks at the corner. the load transfer is poor and it may cause the pumping, faulting and breaks at the corner. Therefore, load transfer efficiency is especially important to ensure the running safety of Therefore, load transfer efficiency is especially important to ensure the running safety of floating slab track. floating slab track. Figure 13. Load transfer between slab panel. Figure 13. Load transfer between slab panel. The evaluated results are shown in Tables 6 and 7. According to the measurements, The evaluated results are shown in Tables 6 and 7. According to the measurements, when a load of 150 to 440 kN was applied at Load case II, rail deflection was 2.24 to 6.48 when a load of 150 to 440 kN was applied at Load case II, rail deflection was 2.24 to 6.48 mm at the panel’s endpoint and was 2.21 to 6.4 mm in the adjacent panel. Meanwhile, the mm at the panel’s endpoint and was 2.21 to 6.4 mm in the adjacent panel. Meanwhile, the displacement of the panel was 1.31 to 4.68 at the loaded panel and was 1.29 to 4.59 at the displacement of the panel was 1.31 to 4.68 at the loaded panel and was 1.29 to 4.59 at the adjacent one. However, these values of rail and panel which were calculated by FEA was adjacent one. However, these values of rail and panel which were calculated by FEA was slightly larger as shown in Figure 14. Based on the 250 kN load of Korea’s standardized slightly larger as shown in Figure 14. Based on the 250 kN load of Korea’s standardized cargo design load, the rail deflections difference between the ends was 0.08 mm and the cargo design load, the rail deflections difference between the ends was 0.08 mm and the panel deflection difference between the ends was 0.06 mm, which was within 2 mm of the panel deflection difference between the ends was 0.06 mm, which was within 2 mm of the Japanese usability standard for high-speed railway bridges. When the track slab separa- Japanese usability standard for high-speed railway bridges. When the track slab separation tion distance was 75 mm, the inclination of rail was a maximum of 1.2‰, which is less distance was 75 mm, the inclination of rail was a maximum of 1.2‰, which is less than the than the standard of comfort (2.5 ‰) as well as the safety standard (2.0‰) in Japan. standard of comfort (2.5 ‰) as well as the safety standard (2.0‰) in Japan. Table 6. Load transfer efficiency (LTE) of rail between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading Table 6. Load transfer efficiency (LTE) of rail between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading point). point). Rail Displacement (mm) FEA Result Rail Displacement (mm) FEA Result Load Adjacent Adjacent Loaded Adjacent Incli- Loaded Adjacent Incli- Load Loaded Step Incli-Na- Loaded Step Incli-Nation LTE Step Step LTE (kN) Panel LTE (%) Panel Panel Panel Nation LTE (%) Panel Panel Nation (kN) Panel (δ1) (mm) tion (‰) Panel (δ1) (mm) (‰) (%) (mm) (mm) (%) (δ2) (δ2) ( ) ( ) (‰) ( ) ( ) (‰) 1 2 1 2 150 2.24 2.21 0.03 0.40 99.33 2.40 2.39 0.01 0.13 99.79 150 2.24 2.21 0.03 0.40 99.33 2.40 2.39 0.01 0.13 99.79 200 3.04 3.01 0.03 0.40 99.50 3.20 3.19 0.01 0.15 99.83 200 3.04 3.01 0.03 0.40 99.50 3.20 3.19 0.01 0.15 99.83 250 3.82 3.74 0.08 1.07 98.94 4.00 3.99 0.01 0.13 99.87 250 3.82 3.74 0.08 1.07 98.94 4.00 3.99 0.01 0.13 99.87 300 4.56 4.47 0.09 1.20 99.00 4.80 4.79 0.02 0.21 99.83 300 4.56 4.47 0.09 1.20 99.00 4.80 4.79 0.02 0.21 99.83 350 5.30 5.22 0.08 1.07 99.24 5.60 5.59 0.02 0.25 99.83 350 5.30 5.22 0.08 1.07 99.24 5.60 5.59 0.02 0.25 99.83 380 5.69 5.61 0.08 1.07 99.29 6.09 6.07 0.02 0.27 99.84 380 5.69 5.61 0.08 1.07 99.29 6.09 6.07 0.02 0.27 99.84 410 6.09 6.00 0.09 1.20 99.26 6.57 6.54 0.02 0.29 99.83 440 6.48 6.40 0.08 1.07 99.38 7.05 7.02 0.02 0.31 99.84 410 6.09 6.00 0.09 1.20 99.26 6.57 6.54 0.02 0.29 99.83 440 6.48 6.40 0.08 1.07 99.38 7.05 7.02 0.02 0.31 99.84 Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 18 Appl. Sci. 2021, 11, 120 15 of 18 Table 7. Load transfer efficiency (LTE) of panel between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading point). Table 7. Load transfer efficiency (LTE) of panel between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading point). Panel Displacement (mm) FEA Result Load Adjacent Adjacent Panel Displacement (mm) FEA Result Loaded Step Loaded Panel Step (kN) Panel LTE (%) Panel LTE (%) Adjacent Adjacent Load Panel (δ1) (mm) (δ1) (mm) Loaded Step Loaded Step (δ2) (δ2) Panel LTE (%) Panel LTE (%) (kN) Panel ( ) (mm) Panel ( ) (mm) 1 1 150 1.31 ( ) 1.29 0.02 98.47 1.74 ( ) 1.71 0.03 99.10 2 2 200 1.88 1.85 0.03 98.40 2.33 2.29 0.04 99.13 150 1.31 1.29 0.02 98.47 1.74 1.71 0.03 99.10 200 1.88 1.85 0.03 98.40 2.33 2.29 0.04 99.13 250 2.47 2.41 0.06 97.57 2.91 2.86 0.05 99.13 250 2.47 2.41 0.06 97.57 2.91 2.86 0.05 99.13 300 3.06 2.98 0.08 97.39 3.49 3.43 0.06 99.13 300 3.06 2.98 0.08 97.39 3.49 3.43 0.06 99.13 350 3.67 3.58 0.09 97.55 4.07 4.00 0.07 99.13 350 3.67 3.58 0.09 97.55 4.07 4.00 0.07 99.13 380 4.00 3.90 0.10 97.50 4.42 4.35 0.08 99.13 380 4.00 3.90 0.10 97.50 4.42 4.35 0.08 99.13 410 410 4. 4.34 34 4.24 4.24 0.10 0.10 97.7097.70 4.77 4.77 4.69 4.69 0.08 0.08 99.1399.13 440 4.68 4.59 0.09 98.08 5.12 5.03 0.09 99.13 440 4.68 4.59 0.09 98.08 5.12 5.03 0.09 99.13 As mention above, the purpose when applying the loads at Load case II is to verify As mention above, the purpose when applying the loads at Load case II is to verify the the efficiency of the load transmitted between panels. From the data of the test and pro- efficiency of the load transmitted between panels. From the data of the test and program, gram, the LTE results from the assembly test were smaller than FEA. The evaluated LTE the LTE results from the assembly test were smaller than FEA. The evaluated LTE of rail at of rail at maximum load (440 kN) was 99.38%, and this value from FEA was 99.84% with maximum load (440 kN) was 99.38%, and this value from FEA was 99.84% with a relative a relative difference of 0.46%. Moreover, the error in the panel was 1.05% in the same difference of 0.46%. Moreover, the error in the panel was 1.05% in the same condition. condition. However, these results show that this type of track can transfer the load per- However, these results show that this type of track can transfer the load perfectly with fectly with various kinds of load (150–440 kN) with the LTE more than 99% for the rail various kinds of load (150–440 kN) with the LTE more than 99% for the rail and 97% for the panel. and Table 97% 8 for t presents he pacomparisons nel. Table 8 pof resthe entaverage s comparison load s o transfer f the av efe ficiency rage load t and ransf numerical er efficiency method and n (Midas umeric civi all met program). hod (M The idas c results ivil p show rogram that ). The the L resu TE frlt om s show FEA t was hat t slightly he LTElar from FE ger A and equal was sl to ight 1.01 ly l times argercompar and eqed ual t with o 1.01 the tiexperiment. mes compared with the experiment. (a) Figure 14. Cont. Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 18 Appl. Sci. 2021, 11, 120 16 of 18 (b) Figure 14. Load-displacement results of assembly test and finite element analysis (Load Case II), (a) Figure 14. Load-displacement results of assembly test and finite element analysis (Load Case II), (a) vertical displacement vertical displacement of the right rail (mm), and (b) vertical displacement of the panel (mm). of the right rail (mm), and (b) vertical displacement of the panel (mm). Table 8. Comparison of average LTE. Table 8. Comparison of average LTE. Average Load Transfer Efficiency (%) 𝑨𝑭𝑬 Average Load Transfer Efficiency (%) FEA Structures Structures Experiment Experiment FEA 𝒆𝒏𝒕𝒓𝒊𝒎𝑬𝒙𝒑𝒆 Experiment FEA Rail 99.24 99.83 1.01 Rail 99.24 99.83 1.01 Panel 98.90 99.13 1.01 Panel 98.90 99.13 1.01 In terms of structural safety and ride comfort, the step standard is presented in the In terms of structural safety and ride comfort, the step standard is presented in design guidelines of the Korea Railroad Authority “Honam High-speed Rail Design the design guidelines of the Korea Railroad Authority “Honam High-speed Rail Design Guidelines (Civil Work)” [25], and the design standards such as the Japanese railway Guidelines (Civil Work)” [25], and the design standards such as the Japanese railway structures Displacement Limitation [26], and the European standards. In this case, the Jap- structures Displacement Limitation [26], and the European standards. In this case, the anese standard was used for the concrete slab track. The average LTE of the rail was Japanese standard was used for the concrete slab track. The average LTE of the rail was 99.24%, and the panel was 98.90%. The precast floating track does not have a load-carrying 99.24%, and the panel was 98.90%. The precast floating track does not have a load-carrying structure, such as a dowel, which connects the track slabs directly to each other. However, structure, such as a dowel, which connects the track slabs directly to each other. However, load transfer occurred through the rails (60 K rails), which were fastened at the top of the load transfer occurred through the rails (60 K rails), which were fastened at the top of the panel. panel. 6. Conclusions 6. Conclusions We developed and designed a new type of precast floating slab track structure, which We developed and designed a new type of precast floating slab track structure, which differs from conventional track structures. The main purpose of this type of track is to differs from conventional track structures. The main purpose of this type of track is to reduce the ground-borne noise and vibration generated from the vehicle–track interac- reduce the ground-borne noise and vibration generated from the vehicle–track interaction. tion. As part of this study, the floating track was assessed using experimental methods, As part of this study, the floating track was assessed using experimental methods, and and this type of track were simulated by using MIDAS Civil 2019—a finite element anal- this type of track were simulated by using MIDAS Civil 2019—a finite element analysis ysis to calculate the structural performance base on the beam on elastic foundation theory. to calculate the structural performance base on the beam on elastic foundation theory. Moreover, before operating the train, a precast floating track structure was assembled af- Moreover, before operating the train, a precast floating track structure was assembled after ter installing the slab panel with the anti-vibration devices, which were manufactured in installing the slab panel with the anti-vibration devices, which were manufactured in a a factory and mounted on a continuous rail using a fastening device. As the train passed factory and mounted on a continuous rail using a fastening device. As the train passed through, we determined that the track structure behavior was similar to the structural through, we determined that the track structure behavior was similar to the structural Appl. Sci. 2021, 11, 120 17 of 18 assembly test. After testing and comparing with the results of the FEA, the following conclusions were drawn. First, the measured vertical deflection of the rails and the panels of the structural assembly of the test specimen composed of the three-panel, satisfied the requirements of the track (rail relative displacement  3 mm). Therefore, the design can be considered sufficiently safe. The performance of the track was verified through experimental loading tests. Both the center point and end points of the three panels, which were joined by a rail, exhibited vertical rail deflections satisfied the requirements. The average panel vertical displacement of three-panel by FEM program was 1.2 times greater than the result from assembly test. Meanwhile, the maximum rail displacement from FEA was roughly 1.1 times larger than from the test. Therefore, the train loads were distributed to the adjacent precast floating track through the continuous rail. The reason of these differences can be explained that the average supported stiffness from experimental results was larger than FEA results. Moreover, when applying the assembly test, errors might be occurred that could lead to these differences. Instead of steel plate or steel bar as the dowel joints, the loads were transmitted directly between the slab panels by continuous rail (60 K rail). When trainloads were applied to the rails, a difference in the rail displacement (step difference) and the LTE was measured at the end of the panels. From these results, we found that a step difference in the rails and panels was within the standard limit (2 mm), and the structure was secure during train operations. In addition, the average LTE of the rails was 99.24%, and the panel was 98.90% when measured during train operations. So, this precast floating slab track can secure the trainloads which were sufficiently transmitted through the structures. Author Contributions: Conceptualization, L.V.; methodology, L.V. and Y.S.K.; software, L.V.; val- idation, L.V. and Y.S.K.; formal analysis, L.V.; investigation, L.V.; resources, L.V. and Y.S.K.; data curation, L.V.; writing—original draft preparation, L.V.; writing—review and editing, L.V. and Y.S.K.; visualization, L.V. and Y.S.K.; supervision, Y.S.K.; project administration, Y.S.K.; funding acquisition Y.S.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the railway technology research project (19RTRP-C148760-02) by the Korea Agency for Infrastructure Technology Advancement. 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. Conflicts of Interest: The authors declare no conflict of interest. References 1. Esveld, C. Modern Railway Track, 2nd ed.; Delft University of Technology: Zaltbommel, The Netherland, 2001. 2. Birhane, F.N.; Choi, Y.T.; Lee, S.J. Development of GPR Device and Analysis Method to Detect Thickness of Ballast Layer. J. Korean Soc. Railw. 2020, 23, 269–278. [CrossRef] 3. Koh, T.; Shin, M. Field Tests on Eco-Friendly Railway Precast Concrete Slab. Appl. Sci. 2020, 10, 4140. [CrossRef] 4. Pichler, D. Ballastless Track Systems Experiences Gained in Austria and Germany. In Proceedings of the AREMA Conference, Indianapolis, IN, USA, 29 September–2 October 2013; pp. 81–100. 5. Kwon, S.G.; Kim, J.Y. Development of noise and vibration reduction technology for railway station structures. Railw. J. Korean Soc. Railw. 2018, 21, 14–20. 6. Yang, S.C.; Kang, Y.S.; Kim, M.C. Evaluation method for vibration-reduction efficiency of slab track. J. Korean Soc. Civ. Eng. 2000, 20, 427–435. 7. Yang, S.C.; Kim, T.W.; Kang, Y.S. Measures for noise and vibration of high speed railway track structures. J. Korean Soc. Noise Vib. Eng. 2004, 14, 26–34. 8. Li, Z.G.; Wu, T.X. On vehicle/track impact at connection between a floating slab and ballasted track and floating slab track’s effectiveness of force isolation. Veh. Syst. Dyn. 2009, 47, 513–531. [CrossRef] 9. Wagner, H.G. Attenuation of Transmission of Vibrations and Ground-Borne Noise by Means of Steel Spring Supported Low-Tuned Floating Track-Beds. In Proceedings of the 2002 World Metro Symposium, Taipei, Taiwan, 25–27 April 2002. 10. Jin, H.; Liu, W.; Zhou, S. An experiment to assess vibration reduction ability of the rubber floating-slab tracks with different supporting forms. J. Vibroeng. 2015, 17, 3237–3246. Appl. Sci. 2021, 11, 120 18 of 18 11. Kang, Y.S. 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Sound Vib. 1996, 193, 367–376. [CrossRef] 17. Wagner, H.-G.; Herrmann, A. Floating Slab Track Above Ground for Turnouts in Tram Lines. In Proceedings of the 9th International Workshop on Railway Noise, Munich, Germany, 4–8 September 2007; pp. 86–93. 18. Yuan, J.; Chang, Y.; Meng, Z.; Song, L. Modal Analysis and Parameter Assessment of Floating Slab Track. In Proceedings of the International Conference on Transportation Engineering, Chengdu, China, 25–27 July 2009; p. 543. 19. Montella, G.; Mastroianni, G.; Serino, G. Experimental and Numertical Investigations on Innovative Floating—Slab Track Including Recycled Rubber Elements. In Proceedings of the 25th International Conference on Noise and Vibration Engineering (ISMA 2012), Leuven, Belgium, 17–19 September 2012. 20. Kang, Y.S.; Lee, C.Y.; Du Jang, D.; Kwon, S.G.; Han, W.J.; Vu, L. Study on Structural Performance of Precast Track of Discrete Panel Supporting Type for Rapid Ballast Improvement. J. Korean Soc. Hazard Mitig. 2020, 20, 233–244. [CrossRef] 21. Smith, K.D.; Peshkin, D.G.; Darter, M.I.; Mueller, A.L.; Carpenter, S.H. Performance of Jointed Concrete Pavements, Volume I: Evaluation of Concrete Pavement Performance and Design Features; FHWA-RD-89-136; Federal Highway Administration: McLean, VA, USA, 1990. 22. Chung, W.; Kwon, K.; Jang, S.Y. Deflection-based load transfer efficiency of Floating Slab Track. KSCE J. Civ. Eng. 2014, 18, 616–624. [CrossRef] 23. Jang, S.-Y.; Yang, S.-C. Assessment of Train Running Safety, Ride Comfort and Track Serviceability at Transition between Floating Slab Track and Conventional Concrete Track. J. Korean Soc. Railw. 2012, 15, 48–61. [CrossRef] 24. Jang, S.Y.; Ahn, M.K.; Choi, W.I.; Park, M.H. Investigation of Load Transfer Characteristics at Slab Joints in the Floating Slab Track by Equivalent Shear Spring Model. In Proceedings of the 2011 Autumn Conference, Jeju, Korea, 20–22 October 2011; pp. 2838–2843. 25. Korea Railroad Network Authority. Honam High-Speed Rail Design Guidelines; Civil Work; Korea Railroad Network Authority: Seoul, Korea, 2007. 26. Railway Technology Research Institute (RTRI). Design Standards for Railway Structures and Commentary—Limit for Displacement; Ministry of Land, Infrastructure, Transport, and Tourism: Tokyo, Japan, 2007. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Sciences Multidisciplinary Digital Publishing Institute

Load Transfer Efficiency Based on Structural Deflection Assessment of the Precast Floating Track

Vu, Linh; Kang, Yun Suk
Applied Sciences , Volume 11 (1) – Dec 24, 2020
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applied sciences Article Load Transfer Efficiency Based on Structural Deflection Assessment of the Precast Floating Track 1 2 , Linh Vu and Yun Suk Kang * Department of Transportation System Engineering, KRRI School, University of Science and Technology, 217, Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea; linhvu2607@krri.re.kr Korea Railroad Research Institute 176, Cheoldo-bangmulgwan-ro, Uiwang, Gyeonggi-do 16105, Korea * Correspondence: yskang@krri.re.kr; Tel.: +82-10-3895-9112 Featured Application: Load Transfer Efficiency of the Precast Floating Track. Abstract: In Korea, a precast floating track with anti-vibration isolators was recently developed to reduce the vibration and noise in urban railway stations, without disrupting train operations. This precast floating slab track is a newly developed structure and differs from existing conventional slab tracks. In this study, a Finite Element Method program (MIDAS CIVIL 2019) was used to analyze the load-carrying ability of structures under the train axle loads. After finishing the design, to understand more precisely about load transfer efficiency of this type of track, an assembly test (two load cases) was conducted with three precast panels (with rail 60 K mounted on) and compared with Finite Element Analysis results. The final results satisfied the test standards in Korea, which confirms that the precast floating track has an acceptable safety factor and structural behavior. Keywords: precast floating track; anti-vibration device; FEA; noise and vibration; structural assembly test; load transfer efficiency 1. Introduction Citation: Vu, L.; Kang, Y.S. Load Trans- There are two common types of railway track are used in railway engineering: (a) fer Efficiency Based on Structural De- ballasted track with concrete sleeper or wooden sleeper, and (b) non-ballasted or slab track flection Assessment of the Precast Float- structure. The ballasted track which is installed with concrete sleepers has been widely ing Track. Appl. Sci. 2021, 11, 120. used for conventional lines. The main advantages of this type of track are good elasticity, https://dx.doi.org/10.3390/ low initial construction cost, and ease of maintenance [1]. However, the ballasted track app11010120 also has essential drawbacks such as high maintenance cost, fouled ballast, or insufficient support to the track structures. The track degradation’s main causes are ballast fouling Received: 30 November 2020 Accepted: 21 December 2020 and insufficient depth of ballast [2]. Therefore, it is necessary to develop and research a Published: 24 December 2020 non-destructive method such as ground penetrating radar (GPR) to limit these problems because the capacity of drainage in railway infrastructure is highly dependent on the Publisher’s Note: MDPI stays neu- fouled ballast [3]. Compared to the ballasted track, the non-ballasted or slab track has tral with regard to jurisdictional claims lower maintenance cost. It has been developed and become more popular in Korea, Japan, in published maps and institutional China, and Europe. Due to the advanced behaviors such as good resistance in lateral affiliations. and longitudinal direction and limiting of the buckling problem the slab track system is a suitable choice to apply for high-speed or metro railway track in tunnels, underground sections and bridges [4]. Nowadays, railway networks have been developed rapidly and the popular way to Copyright: © 2020 by the authors. Li- construct the infrastructure is to use the idle space below the tracks, especially for urban censee MDPI, Basel, Switzerland. This railway stations. However, by using the conventional slab track (cast in-situ method), article is an open access article distributed the ground-borne noises and vibrations generated from railway facilities during the train under the terms and conditions of the operations have become a severe problem [5]. As can be seen in Figure 1, at a railway Creative Commons Attribution (CC BY) station, the dynamic loads of the trains will be transmitted through the rails and slab track license (https://creativecommons.org/ licenses/by/4.0/). to the pillars, walls, and so on, which are the main structures that form the framework Appl. Sci. 2021, 11, 120. https://dx.doi.org/10.3390/app11010120 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 18 Appl. Sci. 2021, 11, 120 2 of 18 pillars, walls, and so on, which are the main structures that form the framework of the pillars, walls, and so on, which are the main structures that form the framework of the of stat the ion [ station 6]. So[, it 6]. iSo, s more e it is mor ffect eive t effective o find to counterme find countermeasur asures that ad es that dress the address sou the rce of the source station [6]. So, it is more effective to find countermeasures that address the source of the of noise, the which noise, which are mor ar ee eco mor nomica e economically lly and intand rinsic intrinsically ally efficient ef for ficient exist for ingexisting railway st railway ations noise, which are more economically and intrinsically efficient for existing railway stations stations [7]. [7]. [7]. Figure 1. The structural vibration transfer path. Figure Figure 1. 1. The The structural vibration transfer pat structural vibration transfer path.h. A floating slab track is one way to minimize the ground-borne vibration noise by A floating slab track is one way to minimize the ground-borne vibration noise by A floating slab track is one way to minimize the ground-borne vibration noise by blocking the vibration transmitted from the vehicle–track interaction [8]. This type of track blocking the vibration transmitted from the vehicle–track interaction [8]. This type of blocking the vibration transmitted from the vehicle–track interaction [8]. This type of track is generally made of the continuous rail, mounted on the massive concrete by the fastening track is generally made of the continuous rail, mounted on the massive concrete by the is generally made of the continuous rail, mounted on the massive concrete by the fastening devices and forming the mass–spring–systems (MSS). The combination of the panel’s fastening devices and forming the mass–spring–systems (MSS). The combination of the devices and forming the mass–spring–systems (MSS). The combination of the panel’s weight with a dead load of superstructures (rails, fastening systems, and sleepers) created panel’s weight with a dead load of superstructures (rails, fastening systems, and sleepers) weight with a dead load of superstructures (rails, fastening systems, and sleepers) created the dynamically active mass [9]. Under this type of track, the anti-vibration device such created the dynamically active mass [9]. Under this type of track, the anti-vibration device the dynamically active mass [9]. Under this type of track, the anti-vibration device such such as the g as the lass glass fiber, rub fiber,breubber r bearing, or bearing, coi or l sp coil ring springs s [10] [i10 s inst ] is al installed led as a s as ua bs substr tructu uctur re to dis e to- as the glass fiber, rubber bearing, or coil springs [10] is installed as a substructure to dis- disconnect connect the tr theack track from from the the ground ground and and decrease the decrease the magnitude o magnitude f the lo of thead load gen generated erated by connect the track from the ground and decrease the magnitude of the load generated by by the wheel-rail, and this method is widely used and accepted for railway tracks in the wheel-rail, and this method is widely used and accepted for railway tracks in Korea the wheel-rail, and this method is widely used and accepted for railway tracks in Korea Kor andea aro and und ar tound he wor the ld [ world 11–18[]11 . In –18 flo ].at In infloating g slab trslab acks, t tracks, he raithe ls ar rails e usu araelly usually used as used the and around the world [11–18]. In floating slab tracks, the rails are usually used as the as connection between panels the connection between p instead of do anels instead wel bar of dowel s to reduce the constructi bars to reduce the constr on cost. uction To si cost. m- connection between panels instead of dowel bars to reduce the construction cost. To sim- To simulate the performance of this type of track system, the easiest way is to consider ulate the performance of this type of track system, the easiest way is to consider it as a ulate the performance of this type of track system, the easiest way is to consider it as a it as a single degree of freedom as shown in Figure 2 with F is load, m is the mass of the single degree of freedom as shown in Figure 2 with F is load, m is the mass of the track single degree of freedom as shown in Figure 2 with F is load, m is the mass of the track track structures, k is the stiffness of substructure and c is the damping factor of the system. structures, k is the stiffness of substructure and c is the damping factor of the system. The structures, k is the stiffness of substructure and c is the damping factor of the system. The The biggest deterrent of this type of railway structure is the huge initial construction cost. biggest deterrent of this type of railway structure is the huge initial construction cost. biggest deterrent of this type of railway structure is the huge initial construction cost. However, recent studies about the life cycle cost of railway structures pointed out that this However, recent studies about the life cycle cost of railway structures pointed out that this However, recent studies about the life cycle cost of railway structures pointed out that this type of track can be an alternative method of the ballasted track or conventional concrete type of track can be an alternative method of the ballasted track or conventional concrete type of track can be an alternative method of the ballasted track or conventional concrete track with several advantages such as lower maintenance cost, rapid construction, and track with several advantages such as lower maintenance cost, rapid construction, and track with several advantages such as lower maintenance cost, rapid construction, and lower structure height [19]. lower structure height [19]. lower structure height [19]. Figure 2. Single degree of freedom scheme. Figure 2. Single degree of freedom scheme. Figure 2. Single degree of freedom scheme. Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 18 Appl. Sci. 2021, 11, 120 3 of 18 In this study, we determined whether a precast floating track, which was manufac- tured in a factory, transported, and installed at a construction site, could be a suitable In this study, we determined whether a precast floating track, which was manufactured solution to reduce the noise and vibration problems. Our study utilized a precast floating in a factory, transported, and installed at a construction site, could be a suitable solution slab track structure, which is a newly developed structure, unlike existing conventional to reduce the noise and vibration problems. Our study utilized a precast floating slab track structures. We assessed the precast floating track panel structure using the finite track structure, which is a newly developed structure, unlike existing conventional track element method (MIDAS CIVIL program) and structural assembly tests to verify its struc- structures. We assessed the precast floating track panel structure using the finite element tural performance. The goal of these tests was to evaluate the displacement of the rail and method (MIDAS CIVIL program) and structural assembly tests to verify its structural pa performance. nel to verify the sa The goal fety of of these thistests system through the was to evaluate the load displacement transfer efficof iency. the rail and panel to verify the safety of this system through the load transfer efficiency. 2. Precast Floating Panel 2. Precast Floating Panel This study focuses on a new type of precast floating panel developed by the Korea This study focuses on a new type of precast floating panel developed by the Korea Railroad Research Institute (KRRI). Figure 3 shows a 3D-modeling and the cross section Railroad Research Institute (KRRI). Figure 3 shows a 3D-modeling and the cross section of of this type of panel. The dimensions of the panel were 4.925 m (length) × 2.4 m (width) × this type of panel. The dimensions of the panel were 4.925 m (length)  2.4 m (width) 0.3 m (thickness). Rail and the slab panel was connected by fastening device (System 300- 0.3 m (thickness). Rail and the slab panel was connected by fastening device (System 300-1, 1, KR type). KR type). (b) (a) Figure 3. (a) Three-dimensional (3D)-modeling of the precast floating panel, and (b) cross-section of precast floating panel. Figure 3. (a) Three-dimensional (3D)-modeling of the precast floating panel, and (b) cross-section of precast floating panel. The fabrication process of the precast floating panel is shown in Figure 4. Rebars D19 (longitudinal direction) and D13 (horizontal direction) were installed in a formwork, The fabrication process of the precast floating panel is shown in Figure 4. Rebars D19 after completing the formwork, concrete was poured (Figure 4b) and the curing process (longitudinal direction) and D13 (horizontal direction) were installed in a formwork, after was carried out (Figure 4c) until the compressive strength of concrete (f’c) reached 45 MPa completing the formwork, concrete was poured (Figure 4b) and the curing process was (Figure 4d). This type of track can be installed in a limited amount of time after the existing carried out (Figure 4c) until the compressive strength of concrete (f’c) reached 45 MPa ballasted track is removed. This design has six anti-vibration devices that are attached to (Figure 4d). This type of track can be installed in a limited amount of time after the existing the bottom of one of the precast track panels. The panel is composed of assembly blocks ballasted track is removed. This design has six anti-vibration devices that are attached to that are connected by concrete crossbeams. The panels are transported to the construction the bottom of one of the precast track panels. The panel is composed of assembly blocks sites for rapid installation and are assembled to a fixed track height by adjusting the base, that are connected by concrete crossbeams. The panels are transported to the construction which is aligned in advance with the upper part of the station slab. The precast floating slab sites for rapid installation and are assembled to a fixed track height by adjusting the base, panels are installed sequentially on a flat plane using a hydraulic jack, and a high-precision which is aligned in advance with the upper part of the station slab. The precast floating survey is used to make linear corrections. The anti-vibration isolator uses a wedge-type slab panels are installed sequentially on a flat plane using a hydraulic jack, and a high- engineering plastic block to attenuate the vibrations in the vertical direction, through precision survey is used to make linear corrections. The anti-vibration isolator uses a frictional resistance. This provides restorative forces through the coil springs, which are wedge-type engineering plastic block to attenuate the vibrations in the vertical direction, arranged in the lateral and vertical directions to insulate against any vibrations. through frictional resistance. This provides restorative forces through the coil springs, which are arranged in the lateral and vertical directions to insulate against any vibrations. Appl. Sci. 2021, 11, 120 4 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 18 (a) (b) (c) (d) Figure 4. Fabrication process of precast floating panel: (a) assembly of rebar, (b) concrete pouring, Figure 4. Fabrication process of precast floating panel: (a) assembly of rebar, (b) concrete pouring, (c) curing, and (d) (c) curing, and (d) prototype of precast floating panels. prototype of precast floating panels. 3. Experimental Program 3. Experimental Program To evaluate the structural safety of the prefabricated floating track, we tested the To evaluate the structural safety of the prefabricated floating track, we tested the bending performance of the slab panel in conjunction with a designed trainload. The bending performance of the slab panel in conjunction with a designed trainload. The per- performance of the vibration control system was compared with the stability of the track formance of the vibration control system was compared with the stability of the track sys- system and its ability to resist train loads. The detailed specifications of the slab panel are tem and its ability to resist train loads. The detailed specifications of the slab panel are shown in Table 1. The test was conducted using the same structural assembly specimens, to shown in Table 1. The test was conducted using the same structural assembly specimens, evaluate the behavior of track systems, which consisted of rails, slab panels, and vibration to evaluate the behavior of track systems, which consisted of rails, slab panels, and vibra- isolators composed of precast panels. The test was carried out by applying loads on the tion isolators composed of precast panels. The test was carried out by applying loads on three-panel test, two load cases were conducted: loaded on the 2nd panel at the 2/4 point, the three-panel test, two load cases were conducted: loaded on the 2nd panel at the 2/4 and on the 2nd panel at 4/4 point. Table 2 shows the specifications of the load test. In point, and on the 2nd panel at 4/4 point. Table 2 shows the specifications of the load test. load case I, the maximum bending capacity of the structure was verified through the In load case I, the maximum bending capacity of the structure was verified through the deflection of rail and panel. Meanwhile, the purpose of load case II was to determine the deflection of rail and panel. Meanwhile, the purpose of load case II was to determine the load transfer efficiency between the panels. According to the Korea construction rules load transfer efficiency between the panels. According to the Korea construction rules for for the railroad (Rule number 16), in the tunnel section, the standard live load EL-18 was the railroad (Rule number 16), in the tunnel section, the standard live load EL-18 was used used to apply for the designed load (180 kN) and in preparation for installing this type of to apply for the designed load (180 kN) and in preparation for installing this type of track in track in conventional line [20], more than 250 kN of axle load must be reviewed so that conventional line [20] , more than 250 kN of axle load must be reviewed so that the test was the test was performed through the load up to 440 kN which is calculated based on the performed through the load up to 440 kN which is calculated based on the static axle load static axle load of Korean standard (KRL-2012) for conventional passenger and freight train of Korean standard (KRL-2012) for conventional passenger and freight train (220 kN) and (220 kN) and the dynamic amplification factor (2.00) according to Eisenmann formula [1]. the dynamic amplification factor (2.00) according to Eisenmann formula [1]. In Figure 5 a In Figure 5 a full-scale load test was conducted using monotonic loads of 150, 200, 250, full-scale load test was conducted using monotonic loads of 150, 200, 250, 300, 350, 380, 410, 300, 350, 380, 410, and 440 kN. The load force rate (DIN45673-1) was set to 2 kN/s, then remain and 440 kN. T the maximum he load force load time was rate (DIN45673-1) wa 10 s, and the displacement s set to 2 kN/ of tshe , th rail en rem andapanel in the m wer axim e um measur load time was e while removing 10 s, and the displacement the load at the same of the rail and speed again. The panel were loadingmeasure while r test assemblies e for moving the thr th ee-panel e load at slab the sar am e e shown speed in agFigur ain. The lo es 6 and adin 7g t . First, est as the semblies anti-vibration for the th devices ree-pane wer l sl eab are installed shown at the in Fig bottom ures 6 and 7. First of the panels. Next, , the ant the i-vib panels ration wer de e fixed vices on wer the e in flat stal floor led at by th scr e b ews, ottom of and finally, the load was applied at two load cases as mention above. The linear voltage the panels. Next, the panels were fixed on the flat floor by screws, and finally, the load differential transducers (LVDT) were set to 50 mm mounted on the rails; panels are shown was applied at two load cases as mention above. The linear voltage differential transduc- in Figure 7 to measure the behavior of structures. The load capacity was set to 500 kN ers (LVDT) were set to 50 mm mounted on the rails; panels are shown in Figure 7 to meas- using a dynamic actuator, and the data was collected using a TDS-601 data logger, which ure the behavior of structures. The load capacity was set to 500 kN using a dynamic actu- was manufactured by Tokyo Corp. ator, and the data was collected using a TDS-601 data logger, which was manufactured by Tokyo Corp. Appl. Sci. 2021, 11, 120 5 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 18 Table 1. Table 1. Spe Specification cification of Spe of Specimen. cimen. Table 1. Specification of Specimen. Specifications Dimensions Specifications Dimensions Specifications Dimensions 4.925 (L) × 2.4 (W) × 0.3 Size of Panel (m) 4.925 (L)  2.4 (W)  0.3 (H) Size of Panel (m) 4.925 (L) × 2.4 (W) × 0.3 Concrete Strength (MPa) 45 (H) Size of Panel (m) (H) Weight of Panel (ton) 7.6 Concrete Strength (MPa) 45 Vertical Support Stiffness of Anti-vibration Device (kN/mm) 22.5 Concrete Strength (MPa) 45 Weight of Panel (ton) 7.6 Lateral Support Stiffness of Anti-vibration Device (kN/mm) 18 Weight of Panel (ton) 7.6 Vertical Support Stiffness of Anti-vibration Device (kN/mm) 22.5 Vertical Support Stiffness of Anti-vibration Device (kN/mm) 22.5 Lateral Support Stiffness of Anti-vibration Device (kN/mm) 18 Lateral Support Stiffness of Anti-vibration Device (kN/mm) 18 Table 2. Loading points. Table 2. Loading points. Classification Table 2. Loading points. Loading Point Steps Classification Number of Panel Loading Cases Loading Point Steps Classification Number of Panel Loading Cases Loading Point Steps Load on 2nd panel-2/4 Point Number of Panel Loading Cases Load on 2nd panel-2/4 Point Load case I (Distance: 7.4625 m load on 8 Steps (150–440 kN) Load case I 8 Steps (150–440 kN) Load on 2nd panel-2/4 Point (Distance: 7.4625 m load on both rails) both rails) Load case I 8 Steps (150–440 kN) Three Panels Three Panels (Distance: 7.4625 m load on both rails) Load on 2nd panel-4/4 Point Three Panels Load on 2nd panel-4/4 Point Load case II 8 Steps (150–440 kN) Load on 2nd panel-4/4 Point (Dista Load nce: 10 case .00 m l II oad (Distance: on both ra 10.00 ils) m load on 8 Steps (150–440 kN) Load case II 8 Steps (150–440 kN) (Distance: 10.00 m load on both rails) both rails) (a) (b) (a) (b) Figure 5. Assembly test specifications: (a) full scale static loading diagram and (b) installation of assembly test. Figure 5. Assembly test specifications: (a) full scale static loading diagram and (b) installation of assembly test. Figure 5. Assembly test specifications: (a) full scale static loading diagram and (b) installation of assembly test. (a) (b) (a) (b) Figure 6. Structural assembly of three slab panel with 60 K rail: (a) Load case I: center loading point, and (b) Load case II: Figure 6. Structural assembly of three slab panel with 60 K rail: (a) Load case I: center loading point, and (b) Load case II: Figure 6. Structural assembly of three slab panel with 60 K rail: (a) Load case I: center loading point, and (b) Load case II: 2nd panel at 4/4 loading point test. 2nd panel at 4/4 loading point test. 2nd panel at 4/4 loading point test. Appl. Sci. 2021, 11, 120 6 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 18 (a) Top View (b) Side View Figure 7. Locations of sensors to evaluate the performance of the three precast panels. Figure 7. Locations of sensors to evaluate the performance of the three precast panels. 4. Numerical Analysis 4. Numerical Analysis In railway application, according to the Zimmermann method which is the well- In railway application, according to the Zimmermann method which is the well- known “beam on elastic foundation”, the rail is assumed as a continuous beam supported known “beam on elastic foundation”, the rail is assumed as a continuous beam supported by the elastic foundation system composed by fastening system, ballast, sub-ballast-mat by the elastic foundation system composed by fastening system, ballast, sub-ballast-mat as well as sub-soil. In this study, we focused on the displacement of the structures under as well as sub-soil. In this study, we focused on the displacement of the structures under the static loads to determine the load transfer efficiency of precast floating slab track. To the static loads to determine the load transfer efficiency of precast floating slab track. To model this type of precast floating slab track, based on this method, we considered the rail model this type of precast floating slab track, based on this method, we considered the as a continuous beam mounted on the panels by fastening system and the panels (discon- rail as a continuous beam mounted on the panels by fastening system and the panels tinuous slabs) was attached with the anti-vibration device as the elastic component. (discontinuous slabs) was attached with the anti-vibration device as the elastic component. According to the beam on elastic foundation theory, the deflection and moment of According to the beam on elastic foundation theory, the deflection and moment of the the beam under the concentrated wheel load shown in Figure 8 can be calculated as fol- beam under the concentrated wheel load shown in Figure 8 can be calculated as following lowing formulas: formulas: QL w(x) = h(x) (1) 8EI QL M(x) = m(x) (2) 4EIa where: L: characteristic length = (m); and k : stiffness coefficient of discrete support 1 1 1 and = ; Figure 8. Beam k on ela k stic foundation model. d i a: spacing between centers of discrete supports (m); Q: wheel load (N) = 0.5 P (with P is axle load) 𝑄𝐿 EI: bending stiffness of beam (N/m ); (1) 𝑤 𝑥 𝜂 𝑥 8𝐸𝐼 and, two influence factors are: h i 𝑄𝐿 x x x/L (2) h(x)𝑀 = 𝑥 e co 𝜇𝑥 s + sin x  0 (3) L L h i x x x/L where: L: characteristic length (m); and kd: stiffness coefficient of discrete support m(x) = e cos sin x  0 (4) L L and ; a: spacing between centers of discrete supports (m); Q: wheel load (N) = 0.5 P (with P is axle load) EI: bending stiffness of beam (N/m ); and, two influence factors are: Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 18 (a) Top View (b) Side View Figure 7. Locations of sensors to evaluate the performance of the three precast panels. 4. Numerical Analysis In railway application, according to the Zimmermann method which is the well- known “beam on elastic foundation”, the rail is assumed as a continuous beam supported by the elastic foundation system composed by fastening system, ballast, sub-ballast-mat as well as sub-soil. In this study, we focused on the displacement of the structures under the static loads to determine the load transfer efficiency of precast floating slab track. To model this type of precast floating slab track, based on this method, we considered the rail as a continuous beam mounted on the panels by fastening system and the panels (discon- tinuous slabs) was attached with the anti-vibration device as the elastic component. According to the beam on elastic foundation theory, the deflection and moment of Appl. Sci. 2021, 11, 120 7 of 18 the beam under the concentrated wheel load shown in Figure 8 can be calculated as fol- lowing formulas: Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 18 𝑥 𝑥 𝜂 𝑥 𝑒 𝑐𝑜𝑠 𝑠𝑖𝑛 𝑥 0 (3) 𝐿 𝐿 𝑥 𝑥 Figure 8. Figure Beam 8. Beam on ela on elastic stic fou foundation ndation mo model. de𝜇l. 𝑥 𝑒 𝑐𝑜𝑠 𝑠𝑖𝑛 𝑥 0 (4) 𝐿 𝐿 This type of precast floating slab track was simulated as the double beam model This type of precast floating slab track was simulated as the double beam model with 𝑄𝐿 with discrete support so the finite element method can be used to evaluate the structural discrete support so the finite element method can be used to evaluate the structural be- (1) 𝑤 𝑥 𝜂 𝑥 8𝐸𝐼 behavior of the track [1]. In this paper, we used MIDAS CIVIL 2019, a finite element havior of the track [1]. In this paper, we used MIDAS CIVIL 2019, a finite element program program to model the precast floating slab track. The continuous rail was modeled by to model the precast floating slab track. The continuous rail was modeled by using the 𝑄𝐿 (2) using the profile of KR 60 rail, 𝑀 consider 𝑥 ed 𝜇𝑥 as a continuous beam and the standard gauge profile of KR 60 rail, considered as a continuous beam and the standard gauge (1435 mm) (1435 mm) was applied. The panel was modeled by two concrete slabs connected with each was applied. The panel was modeled by two concrete slabs connected with each other by other by crossbeams using the beam element and the distance between each panel is 75 mm. crossbeams using the beam element and the distance between each panel is 75 mm. The where: L: characteristic length (m); and kd: stiffness coefficient of discrete support The rail and concrete slab were connected by the elastic fastening system (system 300-1, KR rail and concrete slab were connected by the elastic fastening system (system 300-1, KR and ∑ ; type) with the vertical stiffness was 28.7 kN/mm. Six anti-vibration devices were set up at ty pe) with the vertical stiffness was 28.7 kN/mm. Six anti-vibration devices were set up at the bottom of each panel as the spring device (elastic link element), the vertical stiffness of a: spacing between centers of discrete supports (m); the bottom of each panel as the spring device (elastic link element), the vertical stiffness each device was 22.5 kN/mm. The structure system analysis model and specifications are Q: wheel load (N) = 0.5 P (with P is axle load) of each device was 22.5 kN/mm. The structure system analysis model and specifications shown in Figure 9 and Table 3, respectively. EI: bending stiffness of beam (N/m ); are shown in Figure 9 and Table 3, respectively. and, two influence factors are: (a) (b) Figure 9. Modeling of the precast floating slab; (a) overview, and (b) front view. Figure 9. Modeling of the precast floating slab; (a) overview, and (b) front view. Table 3. Specification of track system. Classification Unit Specification Moment of inertia mm 30,640,000 Rail Section modulus mm 395,000 (KR60) Modulus of elasticity MPa 210,000 Appl. Sci. 2021, 11, 120 8 of 18 Table 3. Specification of track system. Classification Unit Specification Moment of inertia mm 30,640,000 Section modulus 395,000 mm Rail (KR60) Modulus of elasticity MPa 210,000 Coefficient of thermal expansion 1/ C 1.14  10 Type System 300-1 Width mm 160 Length mm 290 Fastening Static stiffness (Vertical direction) kN/m 28,734 system Dynamic stiffness (Vertical direction) kN/m 32,770 Static stiffness (Lateral direction) kN/m 40 Dynamic stiffness (Lateral direction) kN/m 60 Thickness mm 300 Width mm 900 Length mm 4925 Precast concrete slab Modulus of elasticity MPa 35,684 (ladder type) Compressive strength MPa 45 Poison’s coefficient - 0.18 Coefficient of thermal expansion 1/ C 1.0  10 Static stiffness kN/m 22,500 Anti-vibration Stability stiffness (longitudinal direction) kN/m 18,000 device Stability stiffness (lateral direction) kN/m 18,000 Modulus of elasticity MPa 35,684 Compressive strength MPa 45 Crossbeam Poison’s coefficient - 0.18 Coefficient of thermal expansion 1/ C 1.0  10 Figure 9 shows the concept of three panels (approximately 15 m length) simulated as the same dimensions of the actual specimens with the continuously rail mounted on by the fastening device. This new type of precast floating slab track has no joint to connect the panels, so the load can be distributed and transmitted directly through the rails. 5. Results and Discussion This study conducted load tests to evaluate the displacement of the structures as well as the load transfer efficiency of the new type of precast floating slab track. The results of the test are compared with the Finite Element Analysis to accurately understand the structure behaviors. 5.1. Load Case I In this Load case, the loads were set up at the center of 2nd panel to verify the maximum bearing capacity as well as the maximum deflection of the structures. Table 4 shows the vertical displacement measurement results for the three-panel precast floating slab track, which was mounted on a 60 K continuous rail with a central loading point (2/4 loading point) compare with the FEA results. Appl. Sci. 2021, 11, 120 9 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 18 Table 4. Table 4. Panel Panel vertical vertical d displacement isplacement of three- of three-panel panel precast precast fl floating oating slab slab track panel (centra track panel (centrallloading loadingp point oint in in 2nd 2nd Panel). Panel). Panel Vertical Displacement FEA Results for Panel Vertical Displacement Panel Vertical Displacement FEA Results for Panel Vertical Displacement Support Load Center Left Side Right Average Center Sen- Left Side Right Side Average Support Right Right Load Stiffness Center Left Side Average Center Left Side Average Stiffness (kN) Sensor Sensor Side Sen- Value sor Sensor Sensor Value Side Side (kN) Sensor Sensor Value Sensor Sensor Value (kN/mm) (kN/mm) Sensor Sensor (mm) (mm) sor (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) 150 1.08 0.69 0.54 0.77 32.47 1.39 0.88 0.88 1.05 150 1.08 0.69 0.54 0.77 32.47 1.39 0.88 0.88 1.05 200 1.51 0.91 0.77 1.06 31.35 1.86 1.17 1.17 1.40 200 1.51 0.91 0.77 1.06 31.35 1.86 1.17 1.17 1.40 250 1.96 1.19 1.01 1.39 30.05 2.32 1.46 1.46 1.75 250 1.96 1.19 1.01 1.39 30.05 2.32 1.46 1.46 1.75 300 2.32 1.36 1.23 1.64 30.55 2.78 1.75 1.75 2.09 300 2.32 1.36 1.23 1.64 30.55 2.78 1.75 1.75 2.09 35 3500 2.77 2.77 1.63 1.631.49 1.491.96 1.9629.71 29.71 3.25 2. 3.25 052.05 2.05 2.05 2. 2.4545 380 3.06 1.80 1.66 2.17 29.14 3.53 2.22 2.22 2.66 380 3.06 1.80 1.66 2.17 29.14 3.53 2.22 2.22 2.66 410 3.34 1.97 1.81 2.37 28.79 3.80 2.40 2.40 2.87 410 3.34 1.97 1.81 2.37 28.79 3.80 2.40 2.40 2.87 440 3.62 2.13 1.96 2.57 28.53 4.08 2.57 2.57 3.07 440 3.62 2.13 1.96 2.57 28.53 4.08 2.57 2.57 3.07 Figure 10 shows the vertical deflections of the panel, and the relative deflections of the Figure 10 shows the vertical deflections of the panel, and the relative deflections of right rail, which were measured in Load case I when applying loads in the center of the 2nd the right rail, which were measured in Load case I when applying loads in the center of panel (2/4 loading point). As shown in Figure 5a, under monotonic loads of 150 to 440 kN, the 2nd panel (2/4 loading point). As shown in Figure 5a, under monotonic loads of 150 the vertical displacement of the panel occurred between 1.08 to 3.62 mm, when the sensor to 440 kN, the vertical displacement of the panel occurred between 1.08 to 3.62 mm, when was installed in the center of the panel. However, on the right-side sensor the displacement the sensor was installed in the center of the panel. However, on the right-side sensor the of panel changed from 0.54m to 1.96 mm and this data on the left-side was increased from displacement of panel changed from 0.54m to 1.96 mm and this data on the left-side was 0.69 to 2.13 mm, so that the average vertical deflection value varied from 0.77 to 2.57 mm. increased from 0.69 to 2.13 mm, so that the average vertical deflection value varied from This is because of the greater the load, the greater the vertical displacement. The estimated 0.77 to 2.57 mm. This is because of the greater the load, the greater the vertical displace- support stiffness of the six anti-vibration devices under the slab was calculated by divided ment. The estimated support stiffness of the six anti-vibration devices under the slab was the load by the average deflection and determined to be 28.53–32.47 kN/mm, which is calculated by divided the load by the average deflection and determined to be 28.53–32.47 slightly bigger than the value of the original design. Due to the load was applied in the kN/mm, which is slightly bigger than the value of the original design. Due to the load was center of three panels, the displacement of the panels in Figure 10a and the displacement applied in the center of three panels, the displacement of the panels in Figure 10a and the of the rails in Figure 10b can be compared with others. As can be seen in Figure 10a,b, the displacement of the rails in Figure 10b can be compared with others. As can be seen in Figure loads were transmitted and distributed to three panels through the rails. However, even if 10a,b, the loads were transmitted and distributed to three panels through the rails. How- the loads from 150~440 kN were applied in the 2nd panel, the vertical displacement only ever, even if the loads from 150~440 kN were applied in the 2nd panel, the vertical displace- occurred in the central panel and this value of the left and right panel was exceedingly ment only occurred in the central panel and this value of the left and right panel was ex- small. This situation was also the same for rail displacement. ceedingly small. This situation was also the same for rail displacement. (a) Figure 10. Cont. Appl. Sci. 2021, 11, 120 10 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 18 (b) (c) Figure 10. Three-panel vertical displacement test results (Load case I) (a) vertical displacement of the panel (mm), (b) rail Figure 10. Three-panel vertical displacement test results (Load case I) (a) vertical displacement of the panel (mm), (b) rail vertical displacement (mm), and (c) comparison between FEA and test results (mm). vertical displacement (mm), and (c) comparison between FEA and test results (mm). As can be seen in Figure 10c, the results from the assembly test were moderately As can be seen in Figure 10c, the results from the assembly test were moderately smaller than the FEA results. The panel displacements at the left and right sensors were smaller than the FEA results. The panel displacements at the left and right sensors were similar according to the calculation of the program. The maximum average value of FEA similar according to the calculation of the program. The maximum average value of FEA was roughly 1.2 times larger than this value from the actual test. Moreover, the support was roughly 1.2 times larger than this value from the actual test. Moreover, the support stiffness was measure around 23.8 kN/mm from the program which was almost the same stiffness was measure around 23.8 kN/mm from the program which was almost the same as the design stiffness of the anti-vibration device (22.5 kN/mm). as the design stiffness of the anti-vibration device (22.5 kN/mm). Table 5 shows the results for the relative rail vertical deflections at both the center Table 5 shows the results for the relative rail vertical deflections at both the center endpoints. These deflections occurred in both rails when the load was applied in the center endpoints. These deflections occurred in both rails when the load was applied in the cen- of the 2nd panel. This result was calculated by the difference between the deflection of ter of the 2nd panel. This result was calculated by the difference between the deflection of rail and panel. The displacements in the left and right rails were almost insignificant. rail and panel. The displacements in the left and right rails were almost insignificant. The The maximum displacement of the relative rail to be 2.2 mm, which was 440 kN for the maximum displacement of the relative rail to be 2.2 mm, which was 440 kN for the 60K 60K rail mounted on three-panel assembly test. At the center point, the vertical relative rail mounted on three-panel assembly test. At the center point, the vertical relative dis- displacement of the right rail was 0.91 to 1.80 mm. However, the left rail was between 1.09 placement of the right rail was 0.91 to 1.80 mm. However, the left rail was between 1.09 to to 2.20 mm. The maximum displacement deviation of the left and right sides was 0.43 mm. 2.20 mm. The maximum displacement deviation of the left and right sides was 0.43 mm. Under the same loading conditions, the vertical deflection of the left rail at the endpoint Under the same loading conditions, the vertical deflection of the left rail at the endpoint Appl. Sci. 2021, 11, 120 11 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 18 was 0.06 to 0.39 mm, and 0.10 to 0.25 mm for the right rail. Thus, the average displacement was 0.06 to 0.39 mm, and 0.10 to 0.25 mm for the right rail. Thus, the average displacement of the rails mounted on three-panel at the center point was approximately 8.30 times larger of the rails mounted on three-panel at the center point was approximately 8.30 times larger than at the endpoint. than at the endpoint. Table 5. Maximum relative rail displacement results for the three-panel precast floating slab track Table 5. Maximum relative rail displacement results for the three-panel precast floating slab track (loading at center point (loading at center point of 2nd Panel). of 2nd Panel). FEA Results FEA Results Center Point (mm) Center End Po Point in(mm) t (mm) End Point (mm) Load Center Point (mm) End Point (mm) Load Center Point (mm) End Point (mm) (kN) (kN) Left Right Left Right Left Right Left Right Left Rail Right Rail Left Rail Right Rail Left Rail Right Rail Left Rail Right Rail Rail Rail Rail Rail Rail Rail Rail Rail 150 1.09 0.91 0.06 0.10 0.91 0.91 0.16 0.16 150 1.09 0.91 0.06 0.10 0.91 0.91 0.16 0.16 200 1.35 1.12 0.13 0.12 1.22 1.22 0.22 0.22 200 1.35 1.12 0.13 0.12 1.22 1.22 0.22 0.22 250 1.58 1.31 0.17 0.14 1.51 1.51 0.27 0.27 250 1.58 1.31 0.17 0.14 1.51 1.51 0.27 0.27 300 1.77 1.49 0.23 0.17 1.82 1.82 0.33 0.33 300 1.77 1.49 0.23 0.17 1.82 1.82 0.33 0.33 350 1.95 1.60 0.29 0.20 2.12 2.12 0.38 0.38 350 1.95 1.60 0.29 0.20 2.12 2.12 0.38 0.38 380 2.06 1.67 0.33 0.22 2.30 2.30 0.41 0.41 380 2.06 1.67 0.33 0.22 2.30 2.30 0.41 0.41 410 2.12 1.69 0.37 0.24 2.49 2.49 0.44 0.44 410 2.12 1.69 0.37 0.24 2.49 2.49 0.44 0.44 440 2.20 1.80 0.39 0.25 2.67 2.67 0.48 0.48 440 2.20 1.80 0.39 0.25 2.67 2.67 0.48 0.48 As can be seen in Figure 11, the FEA results present the relative displacements of As can be seen in Figure 11, the FEA results present the relative displacements of both rails have no difference at center point or endpoint. The displacement of both rails both rails have no difference at center point or endpoint. The displacement of both rails at at the center point was 0.91–2.67 mm, and this value at the endpoint was 0.16–0.48 mm. the center point was 0.91–2.67 mm, and this value at the endpoint was 0.16–0.48 mm. The The average deflection of rails at the center point when calculated by the FEM program average deflection of rails at the center point when calculated by the FEM program was was only 5.61 times larger than at the endpoint. When comparing the maximum average only 5.61 times larger than at the endpoint. When comparing the maximum average re- results, the experiment test value was 0.93 times of finite element analysis result. sults, the experiment test value was 0.93 times of finite element analysis result. (a) Figure 11. Cont. Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 18 Appl. Sci. 2021, 11, 120 12 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 18 (b) (b) Figure 11. Comparison of rail relative displacement (Load case I), (a) at center point, and (b) at end Figure 11. Comparison of rail relative displacement (Load case I), (a) at center point, and (b) at end point. Figure 11. Comparison of rail relative displacement (Load case I), (a) at center point, and (b) at end point. point. 5. 5.2. 2. Load Load C Case ase II II 5.2. Load Case II Fig Figur ure e 1 12 2 sho shows ws th the e re rsu esults lts when t when hthe e loa loads ds were wer ap e p applied lied to th to e the 2nd 2nd panel panel at 4/4 at lo4/4 ad- Figure 12 shows the results when the loads were applied to the 2nd panel at 4/4 load- ing po loading intpoints s (Load (Load case II case ). The ma II). The in rea main son o reason f this Lo of ad this case Load is to case deteis rmine to determine the effective the - ing points (Load case II). The main reason of this Load case is to determine the effective- effectiveness of transferring the load from one panel to another. The loading point was set ness of transferring the load from one panel to another. The loading point was set up at ness of transferring the load from one panel to another. The loading point was set up at up at the junction between two panel (2nd and 3rd panel). The loads were transmitted the junction between two panel (2nd and 3rd panel). The loads were transmitted between the junction between two panel (2nd and 3rd panel). The loads were transmitted between between two panel without any dowel bar or connection joint. two panel without any dowel bar or connection joint. two panel without any dowel bar or connection joint. (a) (a) Figure 12. Cont. Appl. Sci. 2021, 11, 120 13 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 18 (b) (c) Figure 12. Vertical displacement results for three-panel testing (at 2nd panel 4/4 loading point), (a) vertical displacement Figure 12. Vertical displacement results for three-panel testing (at 2nd panel 4/4 loading point), (a) vertical displacement of of the panel (mm), (b) vertical displacement of the right rail (mm), and (c) rail relative vertical displacement (mm). the panel (mm), (b) vertical displacement of the right rail (mm), and (c) rail relative vertical displacement (mm). The previous research about concrete pavement pointed out that at least 10% of initial The previous research about concrete pavement pointed out that at least 10% of initial cost increase if install the dowel bars between the panel [21,22]. To limit that issue, this cost increase if install the dowel bars between the panel [21,22]. To limit that issue, this precast floating slab track used rails to transfer the load from the panels and the distance precast floating slab track used rails to transfer the load from the panels and the distance between each slab was 75 mm. In this type of track, the upper part of the panel was between each slab was 75 mm. In this type of track, the upper part of the panel was fas- fastened only by the rails, which were separated from the track slab. Because the train runs tened only by the rails, which were separated from the track slab. Because the train runs on these rails, it is necessary to consider the relative deflection of the connected panel. If a on these rails, it is necessary to consider the relative deflection of the connected panel. If difference occurs in the upper part of the panel of the relative deflection of the rail, then a difference occurs in the upper part of the panel of the relative deflection of the rail, then the railway train will affect the dynamic behavior, such as the vehicle acceleration, and the railway train will affect the dynamic behavior, such as the vehicle acceleration, and body acceleration will increase due to a step difference that occurs when the train passes body acceleration will increase due to a step difference that occurs when the train passes through the connected portion [23]. The vertical deflection of the panel and the rail at the through the connected portion [23]. The vertical deflection of the panel and the rail at the endpoint and the adjacent point were therefore measured. endpoint and the adjacent point were therefore measured. The load transfer characteristics of the slab panel connection can be determined by The load transfer characteristics of the slab panel connection can be determined by using load transfer efficiency (LTE), which is defined as by [24]: using load transfer efficiency (LTE), which is defined as by [24]: 2 2 δ22 2δ LTE =   = (5) LTE = = 2  + 1 2  + (5) δδ δδ 12   where,  : is the rail/panel displacement at panel endpoint (mm). where, δ1: is the rail/panel displacement at panel endpoint (mm). : is the rail/panel displacement at panel adjacent point (mm). δ2: is the rail/panel displacement at panel adjacent point (mm). Appl. Sci. 2021, 11, 120 14 of 18 Appl. Sci. 2021, 11, x FOR PEER REVIEW 14 of 18 As shown in Figure 13, the load transfer efficiency (LTE) of this precast floating track As shown in Figure 13, the load transfer efficiency (LTE) of this precast floating track was based on the displacement of rail and panel between the loaded panel endpoint ( ) was based on the displacement of rail and panel between the loaded panel endpoint (δ1) and unloaded panel adjacent point ( ). In this paper, the precast floating track has used and unloaded panel adjacent point (δ2). In this paper, the precast floating track has used the rails mounted on the slabs to transfer the load from one slab to another instead of the the rails mounted on the slabs to transfer the load from one slab to another instead of the connection joint or dowel. If the displacement of loaded slab panel approximated with the connection joint or dowel. If the displacement of loaded slab panel approximated with the unloaded one (   ), the result in LTE will reach 100% [22]. High stresses will occur if 1 2 unloaded one (δ1 ≈ δ2), the result in LTE will reach 100% [22]. High stresses will occur if the load transfer is poor and it may cause the pumping, faulting and breaks at the corner. the load transfer is poor and it may cause the pumping, faulting and breaks at the corner. Therefore, load transfer efficiency is especially important to ensure the running safety of Therefore, load transfer efficiency is especially important to ensure the running safety of floating slab track. floating slab track. Figure 13. Load transfer between slab panel. Figure 13. Load transfer between slab panel. The evaluated results are shown in Tables 6 and 7. According to the measurements, The evaluated results are shown in Tables 6 and 7. According to the measurements, when a load of 150 to 440 kN was applied at Load case II, rail deflection was 2.24 to 6.48 when a load of 150 to 440 kN was applied at Load case II, rail deflection was 2.24 to 6.48 mm at the panel’s endpoint and was 2.21 to 6.4 mm in the adjacent panel. Meanwhile, the mm at the panel’s endpoint and was 2.21 to 6.4 mm in the adjacent panel. Meanwhile, the displacement of the panel was 1.31 to 4.68 at the loaded panel and was 1.29 to 4.59 at the displacement of the panel was 1.31 to 4.68 at the loaded panel and was 1.29 to 4.59 at the adjacent one. However, these values of rail and panel which were calculated by FEA was adjacent one. However, these values of rail and panel which were calculated by FEA was slightly larger as shown in Figure 14. Based on the 250 kN load of Korea’s standardized slightly larger as shown in Figure 14. Based on the 250 kN load of Korea’s standardized cargo design load, the rail deflections difference between the ends was 0.08 mm and the cargo design load, the rail deflections difference between the ends was 0.08 mm and the panel deflection difference between the ends was 0.06 mm, which was within 2 mm of the panel deflection difference between the ends was 0.06 mm, which was within 2 mm of the Japanese usability standard for high-speed railway bridges. When the track slab separa- Japanese usability standard for high-speed railway bridges. When the track slab separation tion distance was 75 mm, the inclination of rail was a maximum of 1.2‰, which is less distance was 75 mm, the inclination of rail was a maximum of 1.2‰, which is less than the than the standard of comfort (2.5 ‰) as well as the safety standard (2.0‰) in Japan. standard of comfort (2.5 ‰) as well as the safety standard (2.0‰) in Japan. Table 6. Load transfer efficiency (LTE) of rail between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading Table 6. Load transfer efficiency (LTE) of rail between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading point). point). Rail Displacement (mm) FEA Result Rail Displacement (mm) FEA Result Load Adjacent Adjacent Loaded Adjacent Incli- Loaded Adjacent Incli- Load Loaded Step Incli-Na- Loaded Step Incli-Nation LTE Step Step LTE (kN) Panel LTE (%) Panel Panel Panel Nation LTE (%) Panel Panel Nation (kN) Panel (δ1) (mm) tion (‰) Panel (δ1) (mm) (‰) (%) (mm) (mm) (%) (δ2) (δ2) ( ) ( ) (‰) ( ) ( ) (‰) 1 2 1 2 150 2.24 2.21 0.03 0.40 99.33 2.40 2.39 0.01 0.13 99.79 150 2.24 2.21 0.03 0.40 99.33 2.40 2.39 0.01 0.13 99.79 200 3.04 3.01 0.03 0.40 99.50 3.20 3.19 0.01 0.15 99.83 200 3.04 3.01 0.03 0.40 99.50 3.20 3.19 0.01 0.15 99.83 250 3.82 3.74 0.08 1.07 98.94 4.00 3.99 0.01 0.13 99.87 250 3.82 3.74 0.08 1.07 98.94 4.00 3.99 0.01 0.13 99.87 300 4.56 4.47 0.09 1.20 99.00 4.80 4.79 0.02 0.21 99.83 300 4.56 4.47 0.09 1.20 99.00 4.80 4.79 0.02 0.21 99.83 350 5.30 5.22 0.08 1.07 99.24 5.60 5.59 0.02 0.25 99.83 350 5.30 5.22 0.08 1.07 99.24 5.60 5.59 0.02 0.25 99.83 380 5.69 5.61 0.08 1.07 99.29 6.09 6.07 0.02 0.27 99.84 380 5.69 5.61 0.08 1.07 99.29 6.09 6.07 0.02 0.27 99.84 410 6.09 6.00 0.09 1.20 99.26 6.57 6.54 0.02 0.29 99.83 440 6.48 6.40 0.08 1.07 99.38 7.05 7.02 0.02 0.31 99.84 410 6.09 6.00 0.09 1.20 99.26 6.57 6.54 0.02 0.29 99.83 440 6.48 6.40 0.08 1.07 99.38 7.05 7.02 0.02 0.31 99.84 Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 18 Appl. Sci. 2021, 11, 120 15 of 18 Table 7. Load transfer efficiency (LTE) of panel between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading point). Table 7. Load transfer efficiency (LTE) of panel between panel endpoint and panel adjacent (Load at 2nd panel 4/4 loading point). Panel Displacement (mm) FEA Result Load Adjacent Adjacent Panel Displacement (mm) FEA Result Loaded Step Loaded Panel Step (kN) Panel LTE (%) Panel LTE (%) Adjacent Adjacent Load Panel (δ1) (mm) (δ1) (mm) Loaded Step Loaded Step (δ2) (δ2) Panel LTE (%) Panel LTE (%) (kN) Panel ( ) (mm) Panel ( ) (mm) 1 1 150 1.31 ( ) 1.29 0.02 98.47 1.74 ( ) 1.71 0.03 99.10 2 2 200 1.88 1.85 0.03 98.40 2.33 2.29 0.04 99.13 150 1.31 1.29 0.02 98.47 1.74 1.71 0.03 99.10 200 1.88 1.85 0.03 98.40 2.33 2.29 0.04 99.13 250 2.47 2.41 0.06 97.57 2.91 2.86 0.05 99.13 250 2.47 2.41 0.06 97.57 2.91 2.86 0.05 99.13 300 3.06 2.98 0.08 97.39 3.49 3.43 0.06 99.13 300 3.06 2.98 0.08 97.39 3.49 3.43 0.06 99.13 350 3.67 3.58 0.09 97.55 4.07 4.00 0.07 99.13 350 3.67 3.58 0.09 97.55 4.07 4.00 0.07 99.13 380 4.00 3.90 0.10 97.50 4.42 4.35 0.08 99.13 380 4.00 3.90 0.10 97.50 4.42 4.35 0.08 99.13 410 410 4. 4.34 34 4.24 4.24 0.10 0.10 97.7097.70 4.77 4.77 4.69 4.69 0.08 0.08 99.1399.13 440 4.68 4.59 0.09 98.08 5.12 5.03 0.09 99.13 440 4.68 4.59 0.09 98.08 5.12 5.03 0.09 99.13 As mention above, the purpose when applying the loads at Load case II is to verify As mention above, the purpose when applying the loads at Load case II is to verify the the efficiency of the load transmitted between panels. From the data of the test and pro- efficiency of the load transmitted between panels. From the data of the test and program, gram, the LTE results from the assembly test were smaller than FEA. The evaluated LTE the LTE results from the assembly test were smaller than FEA. The evaluated LTE of rail at of rail at maximum load (440 kN) was 99.38%, and this value from FEA was 99.84% with maximum load (440 kN) was 99.38%, and this value from FEA was 99.84% with a relative a relative difference of 0.46%. Moreover, the error in the panel was 1.05% in the same difference of 0.46%. Moreover, the error in the panel was 1.05% in the same condition. condition. However, these results show that this type of track can transfer the load per- However, these results show that this type of track can transfer the load perfectly with fectly with various kinds of load (150–440 kN) with the LTE more than 99% for the rail various kinds of load (150–440 kN) with the LTE more than 99% for the rail and 97% for the panel. and Table 97% 8 for t presents he pacomparisons nel. Table 8 pof resthe entaverage s comparison load s o transfer f the av efe ficiency rage load t and ransf numerical er efficiency method and n (Midas umeric civi all met program). hod (M The idas c results ivil p show rogram that ). The the L resu TE frlt om s show FEA t was hat t slightly he LTElar from FE ger A and equal was sl to ight 1.01 ly l times argercompar and eqed ual t with o 1.01 the tiexperiment. mes compared with the experiment. (a) Figure 14. Cont. Appl. Sci. 2021, 11, x FOR PEER REVIEW 16 of 18 Appl. Sci. 2021, 11, 120 16 of 18 (b) Figure 14. Load-displacement results of assembly test and finite element analysis (Load Case II), (a) Figure 14. Load-displacement results of assembly test and finite element analysis (Load Case II), (a) vertical displacement vertical displacement of the right rail (mm), and (b) vertical displacement of the panel (mm). of the right rail (mm), and (b) vertical displacement of the panel (mm). Table 8. Comparison of average LTE. Table 8. Comparison of average LTE. Average Load Transfer Efficiency (%) 𝑨𝑭𝑬 Average Load Transfer Efficiency (%) FEA Structures Structures Experiment Experiment FEA 𝒆𝒏𝒕𝒓𝒊𝒎𝑬𝒙𝒑𝒆 Experiment FEA Rail 99.24 99.83 1.01 Rail 99.24 99.83 1.01 Panel 98.90 99.13 1.01 Panel 98.90 99.13 1.01 In terms of structural safety and ride comfort, the step standard is presented in the In terms of structural safety and ride comfort, the step standard is presented in design guidelines of the Korea Railroad Authority “Honam High-speed Rail Design the design guidelines of the Korea Railroad Authority “Honam High-speed Rail Design Guidelines (Civil Work)” [25], and the design standards such as the Japanese railway Guidelines (Civil Work)” [25], and the design standards such as the Japanese railway structures Displacement Limitation [26], and the European standards. In this case, the Jap- structures Displacement Limitation [26], and the European standards. In this case, the anese standard was used for the concrete slab track. The average LTE of the rail was Japanese standard was used for the concrete slab track. The average LTE of the rail was 99.24%, and the panel was 98.90%. The precast floating track does not have a load-carrying 99.24%, and the panel was 98.90%. The precast floating track does not have a load-carrying structure, such as a dowel, which connects the track slabs directly to each other. However, structure, such as a dowel, which connects the track slabs directly to each other. However, load transfer occurred through the rails (60 K rails), which were fastened at the top of the load transfer occurred through the rails (60 K rails), which were fastened at the top of the panel. panel. 6. Conclusions 6. Conclusions We developed and designed a new type of precast floating slab track structure, which We developed and designed a new type of precast floating slab track structure, which differs from conventional track structures. The main purpose of this type of track is to differs from conventional track structures. The main purpose of this type of track is to reduce the ground-borne noise and vibration generated from the vehicle–track interac- reduce the ground-borne noise and vibration generated from the vehicle–track interaction. tion. As part of this study, the floating track was assessed using experimental methods, As part of this study, the floating track was assessed using experimental methods, and and this type of track were simulated by using MIDAS Civil 2019—a finite element anal- this type of track were simulated by using MIDAS Civil 2019—a finite element analysis ysis to calculate the structural performance base on the beam on elastic foundation theory. to calculate the structural performance base on the beam on elastic foundation theory. Moreover, before operating the train, a precast floating track structure was assembled af- Moreover, before operating the train, a precast floating track structure was assembled after ter installing the slab panel with the anti-vibration devices, which were manufactured in installing the slab panel with the anti-vibration devices, which were manufactured in a a factory and mounted on a continuous rail using a fastening device. As the train passed factory and mounted on a continuous rail using a fastening device. As the train passed through, we determined that the track structure behavior was similar to the structural through, we determined that the track structure behavior was similar to the structural Appl. Sci. 2021, 11, 120 17 of 18 assembly test. After testing and comparing with the results of the FEA, the following conclusions were drawn. First, the measured vertical deflection of the rails and the panels of the structural assembly of the test specimen composed of the three-panel, satisfied the requirements of the track (rail relative displacement  3 mm). Therefore, the design can be considered sufficiently safe. The performance of the track was verified through experimental loading tests. Both the center point and end points of the three panels, which were joined by a rail, exhibited vertical rail deflections satisfied the requirements. The average panel vertical displacement of three-panel by FEM program was 1.2 times greater than the result from assembly test. Meanwhile, the maximum rail displacement from FEA was roughly 1.1 times larger than from the test. Therefore, the train loads were distributed to the adjacent precast floating track through the continuous rail. The reason of these differences can be explained that the average supported stiffness from experimental results was larger than FEA results. Moreover, when applying the assembly test, errors might be occurred that could lead to these differences. Instead of steel plate or steel bar as the dowel joints, the loads were transmitted directly between the slab panels by continuous rail (60 K rail). When trainloads were applied to the rails, a difference in the rail displacement (step difference) and the LTE was measured at the end of the panels. From these results, we found that a step difference in the rails and panels was within the standard limit (2 mm), and the structure was secure during train operations. In addition, the average LTE of the rails was 99.24%, and the panel was 98.90% when measured during train operations. So, this precast floating slab track can secure the trainloads which were sufficiently transmitted through the structures. Author Contributions: Conceptualization, L.V.; methodology, L.V. and Y.S.K.; software, L.V.; val- idation, L.V. and Y.S.K.; formal analysis, L.V.; investigation, L.V.; resources, L.V. and Y.S.K.; data curation, L.V.; writing—original draft preparation, L.V.; writing—review and editing, L.V. and Y.S.K.; visualization, L.V. and Y.S.K.; supervision, Y.S.K.; project administration, Y.S.K.; funding acquisition Y.S.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the railway technology research project (19RTRP-C148760-02) by the Korea Agency for Infrastructure Technology Advancement. 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. Conflicts of Interest: The authors declare no conflict of interest. References 1. Esveld, C. 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Published: Dec 24, 2020

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