Comparative Study of Wheel–Rail Contact Impact Force for Jointed Rail and Continuous Welded Rail on Light-Rail Transit

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Article Comparative Study of Wheel–Rail Contact Impact Force for Jointed Rail and Continuous Welded Rail on Light-Rail Transit

Jung-Youl Choi 1, Sang-Won Yun 2, Jee-Seung Chung 1 and Sun-Hee Kim 3,* 1 Department of Construction Engineering, Dongyang University, No. 145 Dongyangdae-ro, Pugggi-eup, Yeongju-si, Gyeongsangbuk-do 36040, Korea; [email protected] (J.-Y.C.); [email protected] (J.-S.C.) 2 Technical Director, SAM DONG LAND CO. LTD, 3rd Floor, 23, Samseong-ro 96-gil, Gangnam-gu, Seoul 06167, Korea; [email protected] 3 Department of Architectural Engineering, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do 13120, Korea * Correspondence: [email protected]; Tel.: +82-031-750-4718

Received: 5 March 2020; Accepted: 26 March 2020; Published: 27 March 2020

Abstract: In this study, the measured track impact factor induced by the wheel–rail contact impact force of each test section (two continuous welded rails on slab tracks and rail joint on a ballasted track) was compared with the design track impact factor under service conditions of a curved light-rail transit system. The measured track impact factor (TIF) was estimated from the measured dynamic wheel load and vertical rail displacement at each test section. In the case of the rail joint section, the rail joint was found to directly affect the track impact factor. Moreover, the dynamic wheel load fluctuation and vertical rail displacement were found to be significantly greater than those of the continuous welded rails (CWRs) on slab tracks. In addition, vertical rail displacements were measured by field measurement and finite element analysis (FEA) was conducted to simulate dynamic wheel load on the jointed rail. Using the field measurements, the rate of dynamic wheel load fluctuation and the TIF were calculated for the CWR and rail joint sections. Subsequently, the calculated TIF values were analytically validated through a comparison with the measured vertical rail displacement, the results of FEA, and the designed TIF for rail joints and CWRs. Finally, the TIF measured by field measurement was compared with the result predicted by FEA. The difference between the results of field measurements and FEA for vertical rail displacement was within approximately 4%.

Keywords: track impact factor; rail joint; ﬁnite element analysis (FEA); dynamic wheel load; vertical rail displacement; ﬁeld measurement

1. Introduction The track structure of a light-rail transit system is designed to pass through a city center or connect with other transportation systems both inside and outside a city. Light-rail transit is a form of urban rail transit using rolling stock similar to a tram, but operating at a higher capacity, speed, and often on an exclusive right-of-way. Urban railway is a type of local rail system providing passenger service within and around an urban area. Light-rail systems are characterized by weaker track conditions than a typical urban railway. The Korean light-rail system is built around a city center that has already been formed, making it diﬃcult to secure large areas of land such as for a vehicle base. The form of the vehicle base is thus constructed as a steep curve; nevertheless, as it is the main track rather than the vehicle base, it is constructed as a ballasted track rather than a slab track. Similarly, because it is a vehicle base, joint rails are applied and not CWR. In fact, Korean light-rail vehicle bases frequently undergo rail joint repairs. Moreover, the track geometries of not only the main track, but also station

Appl. Sci. 2020, 10, 2299; doi:10.3390/app10072299 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, x FOR PEER REVIEW 2 of 15 vehicle base. The form of the vehicle base is thus constructed as a steep curve; nevertheless, as it is the main track rather than the vehicle base, it is constructed as a ballasted track rather than a slab track. Similarly, because it is a vehicle base, joint rails are applied and not CWR. In fact, Korean light- rail vehicle bases frequently undergo rail joint repairs. Moreover, the track geometries of not only the main track, but also station tracks, subsidiary main tracks, and side tracks often consist of multiple segmentsAppl. with Sci. 2020sharp, 10, 2299curves owing to a typical lack of available land in the city center. Figure2 of 14 1 shows the typical damage of a rail joint connected to a joint plate without rail welding. As a typical mechanism of rail joint damage, misalignment occurs during train operation at the end of the two tracks, subsidiary main tracks, and side tracks often consist of multiple segments with sharp curves rails in contactowing to with a typical each lack other of available and manifests land in the in city the center. form Figure of pressing1 shows the and typical brea damagekage in of Figure a rail 1. Rail joints arejoint divided connected into tosuspended a joint plate joints without in railwhich welding. the rail As joint a typical is positioned mechanism between of rail joint two damage, sleepers and supportedmisalignment joints, which occurs are during positioned train operation directly at abov the ende the of the sleeper two rails [1]. in The contact upper with photograph each other and in Figure 1 shows manifestsa suspended in the formjoint of and pressing the andlower breakage photograph in Figure 1sh. Railows joints a supported are divided joint. into suspended In the case joints of load in in which the rail joint is positioned between two sleepers and supported joints, which are positioned the area of the joint, the bending lines of both rails are not continuous, but form an angle [1]. The directly above the sleeper [1]. The upper photograph in Figure1 shows a suspended joint and the wheels havelower photographto overcome shows this a supportedangle and, joint. therefore, In the case ofexert load an in the impact area of on the joint,the accepting the bending rail lines [1]. This study measuredof both rails the are typical not continuous, defects butby formrail anjoint angle type [1]. of The supported wheels have joint. to overcome On the this basis angle of and, this study, even fortherefore, a vehicle exert base an impactrather onthan the acceptinga main track, rail [1]. we This applied study measured the design the typical condition defects (impact by rail factor) consideringjoint the type rail of supportedjoint impact joint. in On the the design basis ofof this rail study, joints even for forvehicle a vehicle base base installations, rather than awith main the hope that the newtrack, research we applied results the design for condition reinforcing (impact rail factor) joints considering can be applied the rail jointin the impact field. in the design of rail joints for vehicle base installations, with the hope that the new research results for reinforcing rail Thejoints rail joint can be is applied a necessary in the ﬁeld. component in track system. As the rail joints have low rigidity and strength comparedThe rail jointwith is the a necessary rail centers, component local in settl trackement system. occurs. As the railFurther, joints have the lowimpact rigidity of anda vehicle is generatedstrength to reduce compared the ride with comfort the rail centers, and increase local settlement the maintenance. occurs. Further, Damage the impact canof occur a vehicle in the is wheels and jointedgenerated rail ends to reduce when the a ridetrain comfort passes and over increase discon thetinuity maintenance. gapsDamage in the rail can occurjoints, in which the wheels can impact the rail, railand jointedfastening rail endssystem, when sleeper, a train passes and even over discontinuity the ballast gaps(Figure in the 1). rail This joints, phenomenon which can impact represents a the rail, rail fastening system, sleeper, and even the ballast (Figure1). This phenomenon represents disadvantagea disadvantage of the entire of the track entire system track system as it easily as it easily subjects subjects the trains the trains to impa to impactscts or or vibrations, vibrations, reduces passengerreduces comfort, passenger and comfort, requires and requiresconsiderable considerable manpower manpower and and expenditureexpenditure for trackfor track and wheel and wheel maintenancemaintenance [2]. [2].

Figure 1.Figure Photograph 1. Photograph of typical of typical defects defects by by rail rail joint joint type.type. (a ()a Suspended) Suspended joint; joint; (b) supported (b) supported joint. joint.

In termsIn of terms rail of joint rail jointtypes, types, most most recent recent railways railways use use continuous continuous welded welded rails (CWRs),rails (CWRs), which which comprise several long or short rails welded together. In conventional CWRs, ﬁshplates are employed comprise several long or short rails welded together. In conventional CWRs, fishplates are employed around the rail joint to connect the web of the adjacent rail by bolts, thereby removing the discontinuity around gapthe inrail the jointedjoint to rail connect and signiﬁcantly the web reducing of the impact adjacent and noise rail during by trainbolts, operation. thereby removing the discontinuity gap in the jointed rail and significantly reducing impact and noise during train operation. Appl. Sci. 2020, 10, 2299 3 of 14

A substantial amount of research both in Korea and abroad has focused on improving rail joints in order to mitigate rail joint impacts. Dynamic wheel–rail forces are generated when a vehicle is subjected to dynamic motions, primarily owing to track irregularities and changes in the track geometry. Geometrical track irregularities, unsprung and sprung masses of vehicle, track stiffness, damping variations in track flexibility, wheel flats, and corrugations on wheels and rails generate dynamic forces on the tracks [2,3]. For example, Lim et al. conducted an analytical study and proposed a method to limit sleeper displacement in the movable section of newly constructed joints to a set value [4]. In addition, Zong et al. proposed a dynamic wheel–rail contact impact modeling method for the determination of impact loads. Their results demonstrated that the free edge of the joint gap draws significant residual stress concentration at the top corner of the end of the railhead, resulting in early material failure at the joint [5]. Mandal and Peach presented limited measurements as analysis and simulations were carried out instead to address mechanical failure, such as failure of the joint bar, joint looseness, and height mismatch of insulated rail joints. From their results, it is known that there is a small reduction in the stress encountered by the rail when joined by bars with an increased moment of inertia [6]. Pombo and Ambrósio proposed a wheel–rail contact model with small-radius curved tracks [7], whereas Sugiyama et al. compared the steady-state lateral force of small-radius curved tracks through track tests and simulations [8]. Wen et al. [9] used finite element analysis simulations to determine the effects of the impact of wheel–rail contact at the rail joint on the axle load, the effect of train speed on dynamic vertical forces, and the distributions of railhead stress and strain. Sharma and Kumar conducted a dynamic analysis of wheel–rail contact and confirmed that the pressure distribution was affected by the rolling distance under various track curvatures [10]. In addition, the wheel–rail impact contact of the insulation rail joint has been simulated through numerical analysis [11]. Choi and Kim studied the impact on the bearings that support the track girder. They performed field measurements and numerical analysis to analyze the characteristics of the structural behavior of a track installed on the Yeongjong Grand Bridge based on the type of bearings and that of the bearings themselves [12]. Raymond found that hardened tracks have smaller differential settlements and cause a lower track impact effect than softer tracks [13]. Selig and Waters found that the subgrade is the important component of the substructure, and it affects track stiffness greatly [14]. Liang and Zhu found the higher deformation and instability of the track structure including the ballast occurring by the reduction of subgrade stiffness [15]. Thus, the majority of the previous studies have analyzed the behavior of main line tracks or the service life of CWRs, which are characterized by a relatively lower track impact during train operation. However, to enter the tracks of the main line, all trains must travel on tracks that have not been converted to CWRs and that contain many rail joints, which include the vehicle base, station tracks, side tracks, and subsidiary main tracks. Therefore, the importance of specifically analyzing the behavior of rail joints cannot be overlooked. The track impact factor (TIF) is a theoretical index used in the track design, which can vary owing to various complex factors such as the structural characteristics of the track, track support stiffness, characteristics of the vehicle, running speed, rail surface roughness, and track irregularity. In this paper, an experimental study of the TIF is discussed. In the “Field Measurement” section, the dynamic wheel–rail contact impact forces are investigated and discussed with the TIF of the rail joint and CWRs. The field measurements were performed using operational trains on different track types such as CWRs of concrete slab tracks in the main line and rail joints of ballasted tracks in the vehicle base. Using these measurements, the rate of dynamic wheel load fluctuation and the TIF were calculated for the CWR and rail joint sections. Subsequently, the calculated TIF values were analytically validated through a comparison with the measured vertical rail displacement, finite element analysis (FEA), and the designed TIF for rail joints and CWRs. Finally, the TIF measured by field measurement was compared with the result predicted by FEA. Appl. Sci. 2020, 10, 2299 4 of 14

2. Field Measurement Two direct ﬁxation concrete slab tracks with CWR on a main line of light-rail transit and one ballasted track with rail joints on a vehicle base of light-rail transit were selected as test sections for the Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 15 ﬁeld measurements. The dynamic wheel load and dynamic vertical rail displacement applied to the CWR and rail joints were measured during train operation. Section A is a jointed 50 kg/m rail with a the CWR and rail joints were measured during train operation. Section A is a jointed 50 kg/m rail ballasted track installed in the vehicle base. The track curvature R is 60 m and the vehicle speed is with a ballasted track installed in the vehicle base. The track curvature R is 60 m and the vehicle speed approximately under 15 km/h. Figure2a,b show the cross-sectional and side view of the rail joint on is approximately under 15 km/h. Figure 2a,b show the cross-sectional and side view of the rail joint Section A, respectively. on Section A, respectively.

(a) (b)

FigureFigure 2. 2.SchematicsSchematics of of the the rail rail joint. joint. ( (aa)) Cross Cross section ofof thethe railrail joint; joint; ( b(b)) side side view view of of the the ﬁshplate fishplate of of thethe rail rail joint joint (unit: (unit: mm). mm).

SectionSection B Bis is a a 50 50 kg/m kg/m railrail withwith direct direct fixation fixation concrete concrete tracks, tracks, with with a track a track curvature curvatureR of 300 R mof and300 m anda designa design vehicle vehicle speed speed of 60 of km 60/ h.km/h. Section Section C is aC 50 is kga 50/m kg/m rail with rail directwith direct fixation fixation concrete concrete tracks, withtracks, witha track a track curvature curvatureR of 100R of m and100 am design and a vehicle design speed vehicle of 30 speed km/h. of The 30 testedkm/h. trains The weretested operated trains were in operateda two-car in formation. a two-car The formation. static wheel The load static of each wheel train load when of fully each occupied train iswhen approximately fully occupied 55 kN. is approximatelyThe test section55 kN. and sensor installation locations are shown in Figure3. The accelerometers were installedThe test at thesection rail and and sleeper, sensor which installation clearly providelocations the are dynamic shown responses in Figure to 3. impact The accelerometers excitations [16,17 were]. Wheel load sensors and displacement transducers were installed on the sleepers or at the centers of installed at the rail and sleeper, which clearly provide the dynamic responses to impact excitations the rail support points to measure the dynamic wheel load and vertical rail displacement as each [16,17]. Wheel load sensors and displacement transducers were installed on the sleepers or at the section was subjected to a passing train load. The properties of the test sections are shown in Table1. centers of the rail support points to measure the dynamic wheel load and vertical rail displacement For the rail joints, the dynamic wheel load and vertical rail displacement were measured. Vertical as each section was subjected to a passing train load. The properties of the test sections are shown in rail displacements were measured using displacement transducers such as linear variable differential Table 1. For the rail joints, the dynamic wheel load and vertical rail displacement were measured. transformers (LVDTs) mounted on a jig anchored on side bridge inspection passage without influence Verticalof train rail load, displacements as shown in Figurewere measured3. LVDTs (CDP-10M)using displacement have sensitivity transducers of 500 such10 as6 /linearmm, a variable rated × − differentialpower of 6.25transformers mV/V 0.3%, (LVDTs) and a mounted frequency on response a jig anchored of 500 Hz. on Displacements side bridge areinspection measured passage and ± withoutrecorded influence automatically of train by load, the computer as shown controlled in Figure data 3. LVDTs acquisition (CDP-10M) system. Thehave wheel sensitivity loads actingof 500 × 10on−6/mm, the low a rated and highpower rails of of6.25 the mV/V curved ± 0.3%, tracks and were a measuredfrequency to response determine of the500 TIFHz. by Displacements evaluating the are measuredamplitude and and recorded characteristics automatically of the dynamic by the comput wheel loader controlled during train data operation acquisition and system. calculating The wheel the loadsdynamic acting wheel on the load low fluctuation. and high Anrails example of the curv of theed measured tracks were waveform measured is shown to determine in Figure 4the. TIF by evaluating the amplitude and characteristics of the dynamic wheel load during train operation and calculating the dynamic wheel load fluctuation. An example of the measured waveform is shown in Figure 4.

Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 15 the CWR and rail joints were measured during train operation. Section A is a jointed 50 kg/m rail with a ballasted track installed in the vehicle base. The track curvature R is 60 m and the vehicle speed is approximately under 15 km/h. Figure 2a,b show the cross-sectional and side view of the rail joint on Section A, respectively.

(a) (b)

Figure 2. Schematics of the rail joint. (a) Cross section of the rail joint; (b) side view of the fishplate of the rail joint (unit: mm).

Section B is a 50 kg/m rail with direct fixation concrete tracks, with a track curvature R of 300 m and a design vehicle speed of 60 km/h. Section C is a 50 kg/m rail with direct fixation concrete tracks, with a track curvature R of 100 m and a design vehicle speed of 30 km/h. The tested trains were operated in a two-car formation. The static wheel load of each train when fully occupied is approximately 55 kN. The test section and sensor installation locations are shown in Figure 3. The accelerometers were installed at the rail and sleeper, which clearly provide the dynamic responses to impact excitations [16,17]. Wheel load sensors and displacement transducers were installed on the sleepers or at the centers of the rail support points to measure the dynamic wheel load and vertical rail displacement as each section was subjected to a passing train load. The properties of the test sections are shown in Table 1. For the rail joints, the dynamic wheel load and vertical rail displacement were measured. Vertical rail displacements were measured using displacement transducers such as linear variable differential transformers (LVDTs) mounted on a jig anchored on side bridge inspection passage without influence of train load, as shown in Figure 3. LVDTs (CDP-10M) have sensitivity of 500 × 10−6/mm, a rated power of 6.25 mV/V ± 0.3%, and a frequency response of 500 Hz. Displacements are measured and recorded automatically by the computer controlled data acquisition system. The wheel loads acting on the low and high rails of the curved tracks were measured to determine the TIF by evaluating the amplitude and characteristics of the dynamic wheel load during train operation and calculating the dynamic wheel load fluctuation. An example of the measured waveform is shown in Appl.Figure Sci. 4.2020 , 10, 2299 5 of 14

Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 15

(a)

(b)

(c)

Figure 3. Test sections and instrumented sensors.sensors. (a) Section A; ((b)) sectionsection B;B; andand ((cc)) sectionsection C.C.

Table 1. Properties of the test sections.

Track Components Curvature (m) Cant (mm) Vd Vo Rail Type Rail Fastener Sleeper Type Ballast Section A 60 0 15 15 50 kg/m rail joint E-clip Wood Gravel Section B 300 140 63 60 50 kg/m CWR (GPW)1) Fast clip2) -- Section C 100 120 33 30 50 kg/m CWR (GPW)1) E-clip3) -- 1) Vd: maximum design speed (km/h), Vo: operational speed (km/h), CWR: continuous welded rail (GPW: gas 2) 3) pressure welded), spring stiﬀness of rail supporting point: kst = 45 kN/mm (kdy = 68 kN/mm), spring stiﬀness of rail supporting point: kst = 23 kN/mm (kdy = 29 kN/mm). Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 15

Table 1. Properties of the test sections.

Track Components Curvature Cant Vd Vo (m) (mm) Rail Sleeper Rail type Ballast fastener type

Section 50 kg/m rail 60 0 15 15 E-clip Wood Gravel A joint

Section 50 kg/m CWR 300 140 63 60 Fast clip2) - - B (GPW)1)

Section 50 kg/m CWR 100 120 33 30 E-clip3) - - C (GPW)1)

Vd: maximum design speed (km/h), Vo: operational speed (km/h), 1) CWR: continuous welded rail (GPW: gas pressure welded), 2) spring stiffness of rail supporting point: kst = 45 kN/mm (kdy = 68 kN/mm), 3) spring Appl. Sci. 2020, 10, 2299 6 of 14 stiffness of rail supporting point: kst = 23 kN/mm (kdy = 29 kN/mm).

(a)

Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 15 (b)

(c)

FigureFigure 4. Examples 4. Examples of the of the measured measured dynamic dynamic wheel wheel load load and and vertical vertical rail rail displacement. displacement. (a (a) )Section Section A; A; (b) section B; and ( Cc)) sectionsection C.C. 3. Finite Element Analysis 3. Finite Element Analysis ANSYS Ver 17.2 (ANSYS, Inc., Cannonsberg, PA, USA) [18] was used as the ﬁnite element analysis ANSYS Ver 17.2 (ANSYS, Inc., Cannonsberg, PA, USA) [18] was used as the finite element program, and solid elements were used for 3D modeling. The mesh of the track model contained analysis program, and solid elements were used for 3D modeling. The mesh of the track model 20,736 nodes and 80,000 elements. The element size of the sleeper-and-rail joint was assumed to be contained 20,736 nodes and 80,000 elements. The element size of the sleeper-and-rail joint was 15 mm. The ballasted track model for the numerical simulation was conﬁgured as shown in Figure5a. assumed to be 15 mm. The ballasted track model for the numerical simulation was configured as The rails, rail pad, and sleepers are composed of solid elements, and the ballast is composed of shown in Figure 5a. The rails, rail pad, and sleepers are composed of solid elements, and the ballast spring-damper elements. The sleeper sizes were 2500 mm in length, 150 mm in depth, and 300 mm in is composed of spring-damper elements. The sleeper sizes were 2500 mm in length, 150 mm in depth, and 300 mm in width. There is a clearance of 20 mm between the rails at the actual point. The ballast conditions are imposed under the sleeper base using a spring-damper element having the typical ballast properties. The spring stiffness and damping coefficient of the rail pad are 400 kN/mm and 15.683 kNs/m, respectively, and the values for the ballast are 200 kN/mm and 77.877 kNs/m, respectively [2,19,20]. A vertical wheel load of 55 kN was applied using the measured dynamic wheel load illustrated in Figure 4a. For numerical analysis, the rail joint was modeled as shown in Figure 5 by applying section A of the field measurement (Figure 3a). The mechanical properties of light-rail systems are given in Table 2.

(a) Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 15

(c)

Figure 4. Examples of the measured dynamic wheel load and vertical rail displacement. (a) Section A; (b) section B; and (C) section C.

3. Finite Element Analysis ANSYS Ver 17.2 (ANSYS, Inc., Cannonsberg, PA, USA) [18] was used as the finite element analysis program, and solid elements were used for 3D modeling. The mesh of the track model contained 20,736 nodes and 80,000 elements. The element size of the sleeper-and-rail joint was assumed to be 15 mm. The ballasted track model for the numerical simulation was configured as shown in Figure 5a. The rails, rail pad, and sleepers are composed of solid elements, and the ballast is composedAppl. Sci. of2020 spring-damper, 10, 2299 elements. The sleeper sizes were 2500 mm in length, 150 mm7 of in 14 depth, and 300 mm in width. There is a clearance of 20 mm between the rails at the actual point. The ballast conditionswidth. are There imposed is a clearance under of the 20 mmsleeper between base the us railsing ata thespring-damper actual point. The element ballast conditionshaving the are typical ballastimposed properties. under The the spring sleeper basestiffness using and a spring-damper damping coefficient element having of the the rail typical pad ballast are 400 properties. kN/mm and 15.683 ThekNs/m, spring respectively, stiffness and dampingand the coevaluesfficient fo ofr thethe railballast pad areare 400 200 kN kN/mm/mm and and 15.683 77.877 kNs/m, kNs/m, respectivelyrespectively, [2,19,20]. and theA vertical values for wheel the ballast load of are 55 200 kN kN was/mm applied and 77.877 using kNs the/m, measured respectively dynamic [2,19,20]. wheel load illustratedA vertical wheelin Figure load 4a. of 55For kN numerical was applied analysis, using the the measured rail joint dynamic was modeled wheel load as shown illustrated in inFigure 5 Figure4a. For numerical analysis, the rail joint was modeled as shown in Figure5 by applying section by applying section A of the field measurement (Figure 3a). The mechanical properties of light-rail A of the field measurement (Figure3a). The mechanical properties of light-rail systems are given in systemsTable are2 .given in Table 2.

Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 15 (a)

(b)

Figure Figure5. Finite 5. Finite element element (FE) (FE) model model of ofjointed jointed rail rail track: ((aa)) modeling modeling and and boundary boundary conditions; conditions; (b) (b) components of rail joint (ﬁshplate, bolts and nuts, short rail with hole). components of rail joint (fishplate, bolts and nuts, short rail with hole). Table 2. Material properties of jointed rail track. Table 2. Material properties of jointed rail track. Properties Rail (50 kgN) Wooden Sleeper Section area (cm2) 64.2 360 Properties Elastic modulus (kN/cm2) Rail21,000 (50kgN) Wooden 1000 Sleeper 3 5 5 Weight density (kN/cm ) 7.85 10− 0.75 10− Section area (cm2) 64.2× × 360 Poisson ratio (υ) 0.30 0.33

Elastic modulus (kN/cm2) 21,000 1000

Weight density (kN/cm3) 7.85 × 10−5 0.75 × 10−5

Poisson ratio (ʋ) 0.30 0.33

4. Results and Discussion

4.1. Track Impact Factor According to Measured Dynamic Wheel Load In this section, the designed TIF considering the designed speed of the test tracks is compared with the measured TIF for each test section. The wheel load subjected to a passing train includes not only the static load owing to the weight of the train, but also the effect of the dynamic impact load, which is a result of train speed. Therefore, the TIF can be calculated by comparing the dynamic wheel load measured through field measurements [2]. The TIF can be represented by the rate of dynamic wheel load fluctuation, which is obtained by dividing the rate of dynamic wheel load fluctuation subjected to a passing train by the static wheel load, as follows [1–3,21]:

Rate of dynamic wheel load fluctuation = (Pdyn-Psta)/Psta, (1) where Pdyn is the dynamic wheel load and Psta is the static wheel load. TIF was calculated using Equation (2). The equation of the Korean standard for urban transit used for TIF for a train speed of 100 km/h is shown as Equation (2). i = 1 + 0.513 , (2) where V is maximum train speed. Typically, the TIF is calculated by considering the value 2σ, where σ is the standard deviation of wheel load fluctuation [2,19]. The TIF is evaluated based on the dynamic wheel load fluctuation and can be used to determine the dynamic wheel–rail contact force and the track impact. The TIF calculated based on the dynamic wheel load fluctuation is also affected by the track support stiffness and rail surface roughness [2]. The standard TIF used in Korean urban railway track design was applied to that of the American Railway Engineering and Maintenance-of- Way Association (AREMA) [2,3,22]. The rates of all wheel load fluctuations calculated using the dynamic wheel load measurements were greater than zero. This value was compared with the Appl. Sci. 2020, 10, 2299 8 of 14

4. Results and Discussion

4.1. Track Impact Factor According to Measured Dynamic Wheel Load In this section, the designed TIF considering the designed speed of the test tracks is compared with the measured TIF for each test section. The wheel load subjected to a passing train includes not only the static load owing to the weight of the train, but also the effect of the dynamic impact load, which is a result of train speed. Therefore, the TIF can be calculated by comparing the dynamic wheel load measured through field measurements [2]. The TIF can be represented by the rate of dynamic wheel load fluctuation, which is obtained by dividing the rate of dynamic wheel load fluctuation subjected to a passing train by the static wheel load, as follows [1–3,21]:

Rate of dynamic wheel load fluctuation = (P Psta)/Psta, (1) dyn − where Pdyn is the dynamic wheel load and Psta is the static wheel load. TIF was calculated using Equation (2). The equation of the Korean standard for urban transit used for TIF for a train speed of 100 km/h is shown as Equation (2). V i = 1 + 0.513 , (2) 100 where V is maximum train speed. Typically, the TIF is calculated by considering the value 2σ, where σ is the standard deviation of wheel load fluctuation [2,19]. The TIF is evaluated based on the dynamic wheel load fluctuation and can be used to determine the dynamic wheel–rail contact force and the track impact. The TIF calculated based on the dynamic wheel load fluctuation is also affected by the track support stiffness and rail surface roughness [2]. The standard TIF used in Korean urban railway track design was applied to that of the American Railway Engineering and Maintenance-of-Way Association (AREMA) [2,3,22]. The rates of all wheel load fluctuations calculated using the dynamic wheel load measurements were greater than zero. This value was compared with the measured TIF (i = 1.410) at 80 km/h, considering the design speed of the tested section [1–3]. To evaluate the TIF considering the range and frequency of the dynamic wheel load fluctuation measured in each test section, a probability statistical analysis was conducted using a Gaussian probability distribution model [2]. The measured TIF converts the static wheel load to an equivalent dynamic wheel load. Moreover, to consider the increase in weight owing to passengers boarding the train, the static wheel load was measured when the trains were in motion. In reality, it is difficult to estimate the static load of a train and the exact number of passengers boarding the train. Therefore, the variations in the total wheel load were measured during peak hours. Figure6 shows the results of the Gaussian analysis of wheel load fluctuation for each test section. According to the TIF calculation results for each test section, the TIF of rail joints in the ballasted track (Section A) was much higher than that of the direct fixation concrete track CWRs (sections B and C). This suggests that the rail joints amplified the track impact during the train’s passage over the discontinuity gaps. The average probability density function was measured as positive, as shown in Figure6a. The probability of a negative value owing to the normal distribution was negligible because it is close to zero, as shown in Figure6b,c. Therefore, the track impact along section A was gradually amplified. The TIF calculated for the current track conditions for each test section was compared with the designed TIF, and the results are summarized in Table3. Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 15 measured TIF (i = 1.410) at 80 km/h, considering the design speed of the tested section [1–3]. To evaluate the TIF considering the range and frequency of the dynamic wheel load fluctuation measured in each test section, a probability statistical analysis was conducted using a Gaussian probability distribution model [2]. The measured TIF converts the static wheel load to an equivalent dynamic wheel load. Moreover, to consider the increase in weight owing to passengers boarding the train, the static wheel load was measured when the trains were in motion. In reality, it is difficult to estimate the static load of a train and the exact number of passengers boarding the train. Therefore, the variations in the total wheel load were measured during peak hours. Figure 6 shows the results Appl. Sci. 2020, 10, 2299 9 of 14 of the Gaussian analysis of wheel load fluctuation for each test section.

(a) (b)

FigureFigure 6. 6.GaussianGaussian analysis analysis of of wh wheeleel load load fluctuations: ﬂuctuations: (a ()a section) section A A (track (track impact impact factor factor (TIF) (TIF) = =1.899);1.899); (b(b) )section section B B(TIF (TIF = =1.207);1.207); (c ()c )section section C C (TIF (TIF = =1.220);1.220); and and (d ()d results) results of of Gaussian Gaussian analysis analysis for for each each sectionsection (R (R2: 2normal: normal distribution, distribution, y0: y0: y yintercept, intercept, xc: xc: mean, mean, w: w: standard standard deviation, deviation, A: A: probability probability density).density).

According to the TIF calculation results for each test section, the TIF of rail joints in the ballasted Table 3. Comparisons of track impact factor (TIF) between the design value and measured result. track (Section A) was much higher than that of the direct fixation concrete track CWRs (sections B and C). This suggests that the rail joints amplifieTestd the Section track impact during the train’s passage over Korean Design TIF the discontinuity gaps. The averageA probability (Rail Joint) density B (CWR) function C wa (CWR)s measured as positive, as shown in Figure 6a. The probability of a negative value owing to the normal distribution was negligible Measured TIF (2σ) 1.899 1.207 1.220 because it is close to zero, as shown in Figure 6b,c. Therefore, the track impact along1.410 section V/80 A was graduallyMeasured amplified./design The value TIF (%) calculated 134.68 for the current 85.60 track conditions 86.52 for each test section was compared with the designed TIF, and the results are summarized in Table 3. The TIFs calculated for sections A, B, and C were 1.899, 1.207, and 1.220, respectively. These values represent 86% and 87% of the current Korean standard TIF for the slab tracks with CWR (sections B and C). However, for section A, the TIF was approximately 134% higher than the Korean standard for urban railways. Therefore, the measured ampliﬁcation of the impact load generated on the rail joints exceeded the track impact level considered during railway design. This could lead to accelerated damage and deterioration of track components and potentially reduce the running stability and riding comfort of the train. Furthermore, an increased dynamic wheel–rail interaction force owing to the structural characteristics of the rail joint is generated regardless of train speed. Hence, a design and maintenance plan should be established to minimize track impact and wheel damage on tracks with multiple rail joints. Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 15

Table 3. Comparisons of track impact factor (TIF) between the design value and measured result.

Test Section Appl. Sci. 2020, 10, 2299 10 of 14 Korean Design TIF A (Rail joint) B (CWR) C (CWR) 4.2. Track Impact Factor Based on the Measured Vertical Rail Displacement Measured TIF (2σ) 1.899 1.207 1.220 The vertical rail displacement measurements in the test sections were used to analyze the track 1.410 V/80 impact effects for a train passing over the rail joint gaps and very sharply curved CWRs. The TIFs Measured/design value (%) 134.68 85.60 86.52 calculated from the displacement response and the dynamic wheel fluctuation were then compared. The track impact effect can be generated simultaneously by the load and displacement, and the typical The TIFs calculated for sections A, B, and C were 1.899, 1.207, and 1.220, respectively. These TIF can be calculated using the dynamic wheel load fluctuation. In this study, however, the effects of values represent 86% and 87% of the current Korean standard TIF for the slab tracks with CWR wheel load on the vertical rail displacement of the rail joint (amplitude of the displacement response) (sections B and C). However, for section A, the TIF was approximately 134% higher than the Korean andstandard the resulting for urban track railways. impact Therefore, were experimentally the measured estimated. amplification These of the values impact were load then generated compared on withthe rail the joints typical exceeded TIF based the on track the impact wheel–rail level contact considered load (dynamicduring railway wheel design. load fluctuation). This could lead On theto basisaccelerated of the displacement damage and measurementdeterioration results,of track the components TIFs were calculated and potentially and compared. reduce the In thisrunning study, thestability dynamic and rail riding displacement comfort of measurement the train. Furthermore, results for track an increased subjected dynamic to a passing wheel–rail train were interaction replaced withforce pseudo-static owing to the displacement structural characteristics values using of lowpass the rail filteringjoint is generated [2]. The TIFs regardless based on of displacementtrain speed. wereHence, calculated a design according and maintenance to the ratio plan of should dynamic be verticalestablished rail to displacement minimize track (Ddyn impact) to pseudo-static and wheel verticaldamage rail on displacement tracks with multiple (Dsta) using rail joints. Equation (3). The results of this conversion are shown in Figure6.

4.2. Track Impact Factor Based onTrack the Measured impact factorVertical (TIF) Rail iDisplacement= Ddyn/Dsta (3)

FigureThe vertical7a shows rail thedisplacement TIF based onmeasurements the vertical railin th displacemente test sectionsmeasured were used at to the analyze rail joints the track after theimpact first effects wheel hasfor a passed; train passing the vertical over the rail rail displacement joint gaps and decreased very sharply sharply curved after theCWRs. second The wheelTIFs passes,calculated and from then the increased displacement rapidly response to the maximum and the dynamic value. wheel This is fluctuation because of were the dithenfference compared. in rail displacementThe track impact generated effect when can be the generated wheel passes simultaneously through the twoby the adjacent load and rails displacement, of the joint, resulting and the in atypical sharp displacementTIF can be calculated difference using at the the ends dynamic of the wheel rail joint load and fluctuation. an increase In in this displacement study, however, amplitude. the Theeffects experiments of wheel load suggested on the that vertical this mayrail displacement damage the fishplates of the railof joint the (amplitude rail joint and of atheffect displacement the end rails. However,response) as and shown the inresulting Figure7 b,c,track the impact displacement were expe responserimentally characteristics estimated. of These the rail values joint inwere Figure then7a didcompared not occur with inthe theCWR, typical thereby TIF based confirming on the wheel–rai the continuityl contact of theload time–displacement (dynamic wheel load response. fluctuation). Table4 comparesOn the basis the TIFsof the calculated displacement using themeasurement dynamic wheel results, load the fluctuation TIFs were derived calculated from and the correspondingcompared. In this study, the dynamic rail displacement measurement results for track subjected to a passing train measurements and those calculated using the vertical rail displacement measurements. As shown in were replaced with pseudo-static displacement values using lowpass filtering [2]. The TIFs based on Table4, on the basis of section B, which showed the lowest impact factor, this study compared the displacement were calculated according to the ratio of dynamic vertical rail displacement (Ddyn) to rail joint (section A) with section C, which used the same CWR. According to the comparison of TIF pseudo-static vertical rail displacement (Dsta) using Equation (3). The results of this conversion are evaluation methods in Table4, the TIFs of the rail joints (Section A) are higher than those of the CWRs shown in Figure 6. in terms of both wheel load fluctuation and displacement response by 57.33% and 24.16%, respectively. This is because the load and displacementTrack impact are relativelyfactor (TIF) high i = D owingdyn / Dsta to the rail joint gap and vertical(3) rail displacement difference.

(a) (b) (c)

FigureFigure 7. 7.Comparison Comparison ofof thethe measured vertical rail di displacementsplacement between between dynamic dynamic and and pseudo-static pseudo-static forfor each each test test section: section: ((aa)) sectionsection A;A; ((b)) sectionsection B; and ( c) section C. C. Appl. Sci. 2020, 10, 2299 11 of 14

Table 4. Comparisons of TIF evaluation methods.

Track Impact Factor (i) Description Using Dynamic Wheel Load Ratio (%) Using Vertical Rail Displacement Ratio (%) Section A (rail joint) 1.899 (+) 57.33 1.326 (+) 24.16 Section B (CWR) 1.207 - 1.068 - Section C (CWR) 1.220 (+) 1.08 1.141 (+) 6.84

This study experimentally determined that rail joints amplified the wheel–rail contact load (dynamic wheel load and its fluctuation) and increased the impact load to the track and wheel. The level of impact based on the displacement response according to increased dynamic vertical rail displacement caused by gaps in the rail joints was also higher than that for the CWRs, despite the higher train speed. The TIF evaluated using the dynamic wheel load fluctuation can directly affect the wheel and rail by increasing the damage and the impact load to the track components. The increased TIF owing to increased displacement is expected to cause damage to the fishplates of the rail joints and the rail seats of the rail joint sleepers. Therefore, even at low train speeds, a relatively higher track impact is generated at the rail joints, which may lead to accelerated deterioration of the track components and more serious damage. Thus, future design and maintenance of track components comprising rail joints should consider the track impact factors for rail joints.

4.3. Track Impact Factor Based on the FE Analyzed Vertical Rail Displacement The displacement occurring at the CWR and rail joint was confirmed by FEA. Modal analysis was performed using a jointed rail to confirm the structural responses to wheel–rail contact impacts at the discontinuity of rail joints. The frequencies of the first ten modes of the jointed rail are shown in Table5 and selected modal shapes are shown in Figure8. These modes correspond to vertical translation, rotation, and bending vibration. The ninth mode exhibits a local vibration in the vicinity of the CWR. The ninth mode is similar to the deflection of the impacted jointed rail, and the frequency of the eighth mode (354.11cHz) is close to the frequency of the wheel–rail contact impact force obtained from field measurements. Therefore, the dynamic response of the jointed rail may be closely correlated.

Table 5. Frequencies of the ten modes of the jointed rail.

Number of Model 1 2 3 4 5 6 7 8 9 10 Frequency (Hz) 7.7 24.55 29.59 110.44 157.38 214.70 263.15 354.11 369.68 491.70

The vertical rail displacement according to the wheel–rail contact was confirmed through explicit dynamics analysis. The results of the FEA indicated that the displacement occurred at the rail joint subjected to a passing train wheel using the circular wheel element with sectional properties of an actual wheel (wheel diameter of 860 mm) in order to consider the rolling contact of wheel and rail, as shown in Figure9a,b is the detailed displacement occurring in the rail joint when the wheel and the rail contact. As shown in Table6, the vertical rail displacements predicted by FEA were comparable to the field measurements. The difference between the measured and analytical results was approximately 4%; the analytical results that considered the measured dynamic wheel load and wheel model reflected the measured vertical rail displacement results well. Appl. Sci. 2020, 10, 2299 12 of 14 Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 15

(b) (a)

(d) (c)

(f) Appl. Sci. 2019, 9, x FOR PEER REVIEW(e) 13 of 15

Figure 8. Examples of mode shapes of the jointed rail. (a) Mode 1; (b) mode 3; (c) mode 4; (d) mode 5; wheelFigure model 8. reflectedExamples the of mode measured shapes vert of theical jointed rail displacement rail. (a) Mode 1;results (b) mode well. 3; (c) mode 4; (d) mode 5; (e) mode 8; and (f) mode 10. (e) mode 8; and (f) mode 10. Table 5. Frequencies of the ten modes of the jointed rail.

Number of Model 1 2 3 4 5 6 7 8 9 10

Frequency (Hz) 7. 24.5 29.5 110.4 157.3 214.7 263.1 354.1 369.6 491.7 7 5 9 4 8 0 5 1 8 0

The vertical rail displacement according to the wheel–rail contact was confirmed through explicit dynamics analysis. The results of the FEA indicated that the displacement occurred at the rail joint subjected to a passing train wheel using the circular wheel element with sectional properties of (b) an actual wheel (wheel diameter(a) of 860 mm) in order to consider the rolling contact of wheel and rail, as shown in Figure 9a,b is the detailed displacement occurring in the rail joint when the wheel and the railFigure contact. 9. Results As shownof finite ﬁnite inelement Table analysis 6, the vert(FEA). ical ( arail)) Rail displacements joint of vertical predicted displacement; by FEA ( b)) detail were of comparablethe rail section. to the field measurements. The difference between the measured and analytical results was approximately 4%; the analytical results that considered the measured dynamic wheel load and Table 6. Comparison of the finite element analysis (FEA) and field measurements results on the vertical rail displacements.

Vertical Rail Displacement (mm) Relative error (%) Description (𝟏) −(𝟐) Measurement (1) FEA (2) (𝟐)

Section A 1.326 1.357 −3

Section B 1.068 1.145 −7

Section C 1.141 1.160 −2

5. Conclusions This study compared and analyzed the track impact factors (TIFs) for rail joints and CWRs in curved light-rail track systems. Field measurements were performed to calculate TIFs based on the dynamic wheel load and dynamic vertical rail displacement during actual train operation for each tested track. The measured TIFs of each tested track were then compared with the Korean standard TIFs for urban railways and the analyzed TIFs by the finite element analysis. The major conclusions of this study are as follows. (1) The effects of track impacts based on wheel–rail contact force and rail displacement can occur simultaneously. The difference of dynamic vertical rail displacement at the rail joint generated when the train load passes over the discontinuity gap of rail joint and the resulting track impact were experimentally evaluated and compared with the force-based TIF using the measured wheel–rail contact load. Even for a vehicle base rather than a main track, we applied the design condition (impact factor) considering rail joint impact in the design of rail joints for vehicle base installations. The track impact factor for rail joints on the sharply curved ballasted track is approximately 1.34 times greater than the Korean TIF standard. Thus, the increased wheel–rail contact force from the rail joints, even with lower-speed trains, is likely to exceed the track impact factor considered in the track design. (2) The results of the vertical rail displacements measured at the rail joints showed that, after the first wheel had passed, the dynamic displacement decreases sharply as the second wheel passes over the rail joint gap before increasing rapidly to the maximum value. Thus, it was experimentally proven that a sudden vertical rail displacement difference occurs at the ends of rail joints, which can damage the components of the rail joint owing to the dynamic wheel–rail contact force induced impact. The results of the FEA and field measurements showed that the vertical rail displacement of the rail joint Appl. Sci. 2020, 10, 2299 13 of 14

Table 6. Comparison of the ﬁnite element analysis (FEA) and ﬁeld measurements results on the vertical rail displacements.

Vertical Rail Displacement (mm) (1) (2) Description Relative Error (%) { − } Measurement (1) FEA (2) (2) Section A 1.326 1.357 3 − Section B 1.068 1.145 7 − Section C 1.141 1.160 2 −

5. Conclusions This study compared and analyzed the track impact factors (TIFs) for rail joints and CWRs in curved light-rail track systems. Field measurements were performed to calculate TIFs based on the dynamic wheel load and dynamic vertical rail displacement during actual train operation for each tested track. The measured TIFs of each tested track were then compared with the Korean standard TIFs for urban railways and the analyzed TIFs by the finite element analysis. The major conclusions of this study are as follows. (1) The effects of track impacts based on wheel–rail contact force and rail displacement can occur simultaneously. The difference of dynamic vertical rail displacement at the rail joint generated when the train load passes over the discontinuity gap of rail joint and the resulting track impact were experimentally evaluated and compared with the force-based TIF using the measured wheel–rail contact load. Even for a vehicle base rather than a main track, we applied the design condition (impact factor) considering rail joint impact in the design of rail joints for vehicle base installations. The track impact factor for rail joints on the sharply curved ballasted track is approximately 1.34 times greater than the Korean TIF standard. Thus, the increased wheel–rail contact force from the rail joints, even with lower-speed trains, is likely to exceed the track impact factor considered in the track design. (2) The results of the vertical rail displacements measured at the rail joints showed that, after the first wheel had passed, the dynamic displacement decreases sharply as the second wheel passes over the rail joint gap before increasing rapidly to the maximum value. Thus, it was experimentally proven that a sudden vertical rail displacement difference occurs at the ends of rail joints, which can damage the components of the rail joint owing to the dynamic wheel–rail contact force induced impact. The results of the FEA and field measurements showed that the vertical rail displacement of the rail joint was greater than that of CWR. The difference between the results of field measurements and FEA for vertical rail displacement was within approximately 4%. Accordingly, it was found that the FEA simulation technique could be used to effectively predict vertical rail displacements of the rail joint with reasonable accuracy. (3) Therefore, the track impact induced by wheel–rail contact force can be amplified by the structural characteristics of rail joints, even if the train speed is not high. Further research is required to design and maintain track components for rail joints according to the design track impact factors of these joints, which are inevitable in light-rail or urban railway track systems.

Author Contributions: Conceptualization, J.-S.C. and J.-Y.C.; investigation, S.-W.Y.; formal analysis, J.-S.C.; field test, J.-Y.C. and S.-W.Y., writing—original draft preparation, J.-Y.C. and S.-H.K.; writing—review and editing, S.-H.K. All authors have read and agreed to the published version of the manuscript. Conflicts of Interest: The authors declare no conflicts of interest.

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