Stress and Deflection Parametric Study of High-Speed Railway CRTS-II Ballastless Track Slab on Elevated Bridge Foundations Downloaded from ascelibrary.org by GEORGE MASON UNIVERSITY on 01/21/14. Copyright ASCE. For personal use only; all rights reserved.

Lu Sun 1; Liliang Chen 2; and Habtamu H. Zelelew 3

Abstract: Ballastless track slab system (BTS) of China Rail Transit Summit type-II (CRTS-II) is primarily used in China’s Beijing-Shanghai high-speed railway. As a new structural form, CRTS-II has not been extensively tested, and the design and manufacturing processes of CRTS-II BTS systems is not optimized and mature for its load-carrying capacity, structural integrity, deflection, and durability. This study carried out a numerical analysis of stress and deflection responses of the CRTS-II BTS system using SAP 2000. Design parameters include stiffness of the rail fastening, thickness and stiffness of the track slab, the cement emulsified asphalt (CA) mortar cushion, and the concrete supporting layer. Deflection, maximum bending stress, and maximum shear stress of different structural components of the CRTS-II BTS system are investigated under varying design parameters, with the aim to explore an improved set of design parameters. The rail defection is only significantly impacted by the rail fastening stiffness. To reduce the high-speed rail deflection so as to mitigate riding discomfort, higher stiffness of the rail fastening is suggested. To reduce the track slab bending stresses to prevent the high-speed rail from structural failure, the following parameter design strategy can be used: higher track slab thickness, lower track slab stiffness, lower rail fastening stiffness, higher CA mortar, and concrete supporting layer stiffness. All design parameters of the BTS system have negligible influence on the maximum bending stress and shear stress of the elevated bridges. The maximum shear stress of the BTS system is relative low compared with the maximum bending stress of the BTS system, suggesting that the BTS system behaves more like a beam rather than a plate. DOI: 10.1061/ (ASCE)TE.1943-5436.0000577. © 2013 American Society of Civil Engineers. CE Database subject headings: High-speed rail; Slabs; Railroad ballast; Railroad bridges; Bridge foundations; Deflection; Stress. Author keywords: High-speed railway; Ballastless track slab system; Elevated bridge.

Introduction As an alternative to air connections, high-speed railways provide a fast connection among high-density population areas. They meet the challenge of economic competitiveness by providing highoccupancy mass transit system while responding to global climate change and environmental quality issues through promoting energy efficiency (U.S. Department of Transportation 2009). High-speed railways started in Japan in the 1960s and France in the 1980s, and they gained increasing popularity around the globe in recent years (Giannakos 2010; Esveld 2007). The construction of China’s first high-speed railway was launched in 2004. To date, there are 6,000 km of high-speed railways built in China, among which the latest one is the 1,318-km-long Beijing-Shanghai high-speed railway, built in 2010 (Takagi 2011; Okada 2007). Table 1 summarizes 1 Professor, Director, Dept. of Civil Engineering, Catholic Univ. of America, Washington, DC 20064; and School of Transportation Engineering, Southeast Univ., Nanjing 210096, Jiangsu, China (corresponding author). E-mail: [email protected] 2 Post-Doctoral Researcher, School of Transportation Engineering, Southeast Univ., Nanjing 210096, Jiangsu, China. E-mail: chenliliang@ gmail.com 3 Post-Doctoral Researcher, School of Transportation Engineering, Southeast Univ., Nanjing 210096, Jiangsu, China. Note. This manuscript was submitted on February 2, 2013; approved on May 20, 2013; published online on May 22, 2013. Discussion period open until May 1, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Transportation Engineering, Vol. 139, No. 12, December 1, 2013. © ASCE, ISSN 0733-947X/2013/121224-1234/$25.00.

high-speed railways worldwide (Esveld 2010; Okada 2007; Thompson 1994; Takatsu 2007). Compared with a ballasted track slab system, a ballastless track slab (BTS) system exhibits better performance in terms of stability, durability, and low maintainability. It has been widely used in highspeed railways in Japan, Germany, and China. One of the major types of BTS system in China is China Rail Transit Summit type-II (CRTS-II). It has been extensively used in the BeijingShanghai high-speed railway. At high speed (greater than 250 km=h), train vibration induced by railtrack irregularities, railway deflection, and uneven foundation settlement may cause significant damage to the track and the train (Zhai et al. 2010), which may further pose a serious threat to transportation safety and ride quality. For this reason, to minimize the deflection and vibration of high-speed railways, BTS systems are often built on elevated bridge foundations. For instance, elevated bridges account for 37% of the total high-speed railways in Japan (Cai 1999), whereas this percentage increases to almost 83% in the Beijing-Shanghai high-speed railway in China (Zhen 2007). Both simply supported concrete bridges and continuously supported concrete bridges have been used in the Beijing-Shanghai high-speed railways. These bridges are designed in a variety of spans. Table 2 lists representative types and spans of bridges used in part of Beijing-Shanghai high-speed railway (Wang 2005a). From Table 2, it is evident that the majority of the elevated bridges are 32-m-span simply supported concrete bridges. A number of studies have been carried out to investigate dynamic train-railtrack-bridge interaction (Dan et al. 2006; Guan et al. 2007). These studies focused primarily on frequency response of the bridge and effect of train speed on bridge response. Other recent

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Table 1. List of High-Speed Railways Worldwide Country

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Japan France Spain Germany United States China

Date of initiation

Length of alignment (km)

Under construction (km)

Top test speed (km=h)

Average operation speed (km=h)

1964 1981 1992 1988 2000 2008

2,118 1,872 2,665 1,032 457 6,158

377 234 1,781 378 900 14,160

443 (conventional) 581 (maglev) 574 404 406 (conventional) 550 (maglev) 300 416 (conventional) 502 (maglev)

300, 260–275, 110–130 320, 300 300, 270, 250 300, 280, 230–250 240 350, 300, 250, 200

Table 2. Representative Bridge Types and Spans in Beijing-Shanghai High-Speed Railway Span (m) 20 24 32 40 24 þ 24 32 þ 32 24 þ 24 þ 24 32 þ 32 þ 32 32 þ 40 þ 32 40 þ 50 þ 40 40 þ 56 þ 40 50 þ 50 þ 50 32 þ 48 þ 32 40 þ 56 þ 40 40 þ 64 þ 40 48 þ 80 þ 48

Bridge type

Length of alignment (km)

Simply supported Simply supported Simply supported Simply supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported Continuous supported

0.4 62.6 237.9 4.4 0.5 41 1.8 1.7 1.2 1.6 1.9 0.2 1.6 0.1 1.6 1.4

Table 3. Benchmark Values of Parameters of CRTS-II BTS System (Zhai 2010) Component Rail track

Fastening system

Slab

Cement emulsified asphalt mortar cushion

Concrete supporting layer

Bridge deck beam

Bridge support

Type

Unit

Default Value

Elastic modulus Density Area Moment of inertia Elastic modulus Density Vertical stiffness Elastic modulus Density Thickness Width Length Elastic modulus Density Thickness Width Length Elastic modulus Density Thickness Width Length Length Supporting condition Area Moment of inertia Elastic modulus Width Depth

Pa kg=m3 m2 m4 Pa kg=m3 N=m Pa kg=m3 m m m Pa kg=m3 m m m Pa kg=m3 m m m m Not applicable m2 m4 Pa m m

2.1 × 1011 7.8 × 103 7.7 × 10−3 3.2 × 10−5 2.1 × 1011 7.8 × 103 6.0 × 107 3.6 × 1010 2.4 × 103 0.2 2.55 6.45 8.0 × 109 1.8 × 103 0.03 2.55 32 3.25 × 1010 2.4 × 103 0.2 2.95 32 32 Simply supported 26 337 3.3 × 1011 3.1 6.8

Fig. 1. CRTS I slab system

Fig. 2. CRTS II slab system

studies paid attention to stress and deflection analysis of high-speed rail-track on soil foundations (Xu 2008; Liu 2009). What is missing in the literature is the analysis of the effect of design parameters on the deflection and the stress response of a BTS system resting on elevated bridge foundations. Such a study is important, as bridge foundations make up a great percentage of foundations of the highspeed railways in China. In addition, compared with the CRTS-I BTS system, the CRTS-II BTS system adopts different structural dimensions, material properties, and manufacturing processes (Li 2010). The design of the CRTS-II BTS system is not mature and has not been extensively tested to examine its engineering performance in terms of its load-carrying capacity, structural integrity, deflection, and durability. For instance, field observations show that early damage of a BTS system is often observed in cement emulsified asphalt (CA), track slab, and the concrete supporting layer. The current design and operation of the Beijing-Shanghai highspeed railway play the role of a real and large-scale test-bed for future high-speed railway of the CRTS-II BTS system. New structural forms and structural and material parameters can be explored JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / DECEMBER 2013 / 1225

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Fig. 3. Cross section of CRTS-II BTS system

Fig. 4. Cross section of CRTS-II BTS system on a box girder bridge

Table 4. Geometry of Concrete Box Bridge Length (m) 20 24 24 32

Bridge height (m)

Bridge bottom width (m)

2.2=2.4 2.2=2.4 2.8=3.0 2.8=3.0

5.92 5.92 5.92 5.74

to improve the design and to achieve an optimal performance for high-speed railway. For these two reasons, this study carried out a numerical analysis using SAP 2000 to investigate stress and deflection responses of BTS system of the CRTS-II type resting on elevated bridge foundations. Design parameters are all actual values from the BeijingShanghai high-speed railway. The results of the paper provide a

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Vehicle Body Secondary Suspension Rail Rail Fastening CRTS II Slab Track CA Mortar Cushion Concrete Supporting Layer Downloaded from ascelibrary.org by GEORGE MASON UNIVERSITY on 01/21/14. Copyright ASCE. For personal use only; all rights reserved.

Bridge Deck

Fig. 5. Two-dimensional structural model of the CRST-II BTS system

foundation (instead of on a soil foundation). It aims to provide a benchmark analysis for targeting design issues involved in highspeed railway BTS system in practical engineering applications.

Dimensions of CRTS-II BTS System

Fig. 6. Structural model of the CRST-II BTS system in SAP2000: (a) overview of the model; (b) zoom-in view of the model

Table 5. Benchmark Responses of CRTS-II BTS System

Responses Rail Track slab Cement emulsified asphalt mortar cushion Supporting layer Bridge

Maximum bending Deflection Moment stress (mm) (N · m) (kPa) 1.839 0.4883 0.4824

35,766 96.69 6,114.2 359.7 85.9 224.1

0.4783 3,841.4 177.0 0.4737 1,804,240 193.7

Shear force (N)

Maximum shear stress (kPa)

72,348 10,648 584.8

9.41 31.3 11.5

6,299 169,804

16.0 9.68

way to improve structural and material parameter design of components of the BTS system. The contribution of this paper is the analysis of the BTS system using real structural and material parameters of the Beijing-Shanghai high-speed railway on a bridge

BTS systems are initiated by Japan and Germany, from which China’s CRTS system is derived (Xu 2008). The CRTS-I slab shown in Fig. 1 is a customized modification of Japan’s BTS system, whereas the CRTS-II BTS system shown in Fig. 2 is a customized modification of the German Bogl BTS system and has been used in Beijing-Shanghai high-speed railway (Li 2010). The CRTS-II system uses different structural and material parameters as compared with CRTS-I. For example, the CA mortar used in CRTS-II is significantly higher than that used in the CRTS-I. The track slab length used in CRTS-II is relatively shorter than that used in the CRTS-I (Li 2010). Resting on elevated bridge foundations, the CRTS-II BTS system consists of the railtrack, the rail fastening, the track slab, the CA mortar cushion, and the concrete supporting layer. The track slab is prestressed laterally and reinforced longitudinally. Geometrical characteristics of the CRTS-II BTS system includes 6.45 × 2.55 × 0.2-m slab using C60 concrete, 20 650-mm-spaced rail fastenings embedded into each slab, 50-mm gap between slabs, 30-mm-thick CA mortar cushion with elastic of 7,000–10,000 MPa filling between the slab and the concrete supporting layer. Table 3 lists parameters of the CRTS-II BTS system in the BeijingShanghai high-speed railway. Figs. 3 and 4 show the cross section of the CRTS-II BTS system and a two-way CRTS-II BTS system on a concrete box girder bridge in high-speed railway (Third Railway Survey and Design Institute Group Corporation 2010), respectively. The concrete box girder has a varying height and width as specified in Table 4, depending on the bridge length (Wang 2005b).

Modeling of CRTS-II BTS System A CRTS-II BTS system resting on a single-span simply supported concrete bridge is considered in this study. The railway is subjected to a standard static equivalent axle load of 300 kN (see Appendix 1). The BTS system is modeled as multilayer composite beams as shown in Fig. 5 (Esveld 2010). SAP 2000 is used to carry out numerical analysis. A two-dimensional model is developed in this study as demonstrated and validated in Appendix II. The detailed

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Table 6. Variations of Values of Parameters Used in Sensitivity Analysis

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Modulus of rail fastening (kN=mm) Percentage (%) Modulus of track slab (×10 GPa) Percentage (%) Modulus of cement emulsified asphalt mortar cushion (MPa) Percentage (%) Modulus of supporting layer (×10 GPa) Percentage (%) Slab thickness (mm) Percentage (%) Cement emulsified asphalt mortar cushion thickness (mm) Percentage (%) Supporting layer thickness (mm) Percentage (%)

20

30

40

50

60

70

80

90

−67 2.55 −29 7,000

−50 2.7 −25 7,500

−33 3 −17 8,000

−17 3.3 −8 8,500

0 3.6 0 9,000

17 4 11 9,500

33 4.2 17 10,000

50 N/A N/A N/A

−13 2.55 −22 50 −75 10

−6 2.7 −17 100 −50 20

0 3 −8 150 −25 25

6 3.25 0 200 0 30

13 3.6 11 250 25 35

19 4 23 300 50 40

25 4.2 29 350 75 45

N/A N/A N/A 400 100 50

−67 50 −75

−33 100 −50

−17 150 −25

0 200 0

17 250 25

33 300 50

50 350 75

67 400 100

Fig. 7. Effect of design parameters on deflection of railtrack of CRTS-II BTS system 1228 / JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / DECEMBER 2013

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structural model of the CRTS-II BTS system in SAP 2000 is shown in Fig. 6. Constitutive models of all structural components are assumed to be linear under high-speed loading. The high-speed train will result in a transient loading, under which nonlinear behavior of the BTS system can be reasonably ignored. No permanent deformation and strain are considered under linear constitutive models. With the consideration of the shear deformation, the simply supported beam bridge structure is modeled by a 32-m-long Timoshenko beam (Esveld 2010) resting on two end supports. It represents the most commonly used type and span of the elevated bridges in the Beijing-Shanghai high-speed railway, as shown in Table 2. (Wang 2005a; Zhang et al. 2008) The rail track is modeled by a continuously supported beam model resting on distributed springs. These springs are intended to simulate the stiffness fastening. The CA mortar cushion and the concrete supporting layer are modeled by a 32-m-long beam model, whereas the prefabricated track slab is modeled by a 6.45-m-long beam to reflect the actual dimension of the BTS system in the Beijing-Shanghai high-speed railway. The vertical contact among track slab, the CA mortar cushion, the concrete supporting layer, and the bridge are modeled by vertical springs (Biondi et al. 2005; Xia et al. 2003b).

Table 7. Sensitivity of Deflection against Design Parameters Deflection

Design parameters Raul fastening stiffness I Slab stiffness I Cement emulsified asphalt mortar stiffness I Supporting layer stiffness I Slab thickness I Cement emulsified asphalt mortar cushion thickness I Supporting layer thickness I

Cement emulsified asphalt mortar Supporting Rail Slab cushion layer Bridge D N N

N N N

N N N

N N N

N N N

D

D

D

D

D

N N

N N

N N

N N

N N

N

N

N

N

N

Note: “N,” “I,” and “D” indicate that the maximum bending stress remains stable, increases, and decreases, respectively, when the value of a design parameter increases.

Parametric Study SAP 2000, a finite-element analysis software package, is adopted to conduct the analysis. Specifically, stress and deflection responses of structural components of the BTS system studied are the maximum bending stress, the maximum shear stress, and vertical displacement (deflection). Here, the maximum bending stress is defined as σmax ¼ Mh=2I, in which M, I, and h are the maximum bending moment, the cross section moment of inertia, and the height of the structure, respectively. The maximum shear stress is defined as τ max ¼ 3V=2A, where V and A denote the maximum shear force and the cross-sectional area, respectively. To better present the result and elaborate the analysis, the parametric study is carried out in two steps. First, a set of benchmark values of design parameters are chosen, adopted from the actual design of the Beijing-Shanghai high-speed railway. These design parameters include stiffness of the rail fastening, and stiffness and thickness of the track slab, the CA mortar cushion, and the concrete supporting layer. Stress and deflection of structural components of the BTS system are computed as benchmark stress and deflection, which are given in Table 5. Second, values of design parameters are perturbed within a reasonable range, one parameter at a time. Stress and deflection of the BTS system are computed again and compared with the benchmark stress and deflection. Table 6 provides variations of values of parameters used in sensitivity analysis, in which the percentage is computed as follows: percentage ¼

value of the parameter − benchmark value of the parameter benchmark value of the parameter ð1Þ

Effect of Design Parameters on Deflection To understand the influence of the design parameters on the deflection of the CRTS-II BTS system and the bridge, the relationship is plotted in Fig. 7 and the results are summarized in Table 7. This table indicates whether the deflection remains stable, increases, or decreases as the value of a specific design parameter increases. In Figs. 7(a and c), rail defection is barely impacted by changing the

BTS parameters, but greatly impacted by changing the rail fastening stiffness. Generally, 20% increase of the fastening leads to approximately 10% decrease of the rail deflection. The higher the fastening stiffness is, the smaller the rail deflection. To effectively mitigate rider discomfort by reducing the rail deflection, it is suggested to use higher stiffness of the rail fastening. Fig. 7(b) shows that, compared with the increase on the stiffness of the track slab and the CA mortar, the increase on the stiffness of the concrete supporting layer has greater effect on the deflection of the track slab, CA mortar cushion, the concrete supporting layer, and the bridge. A 10% increase of supporting layer stiffness leads to approximately 1% decrease of the structural deflection. Effect of Design Parameters on Maximum Bending Stresses To investigate the influence of the design parameters on the maximum bending stresses of the CRTS-II BTS system, the relationships were plotted in Fig. 8 and summarized in Table 8. From the rail fastening–BTS bending stress response plotted in Fig. 8, it was observed that a 30% increase of the rail fastening stiffness resulted in a 10% decrease of the rail maximum bending stress, but a 10% increase of the track slab maximum bending stress. Also, from the track slab stiffness/thickness–BTS bending stress response plotted in Figs. 8(a and b), it was observed that increasing the track slab stiffness or decreasing the track slab thickness resulted in the decrease of the track slab maximum bending stress. So, from the perspective of lowering the track slab bending stress, the rail fastening with lower stiffness, the track slab with higher stiffness, and lower slab thickness are preferred. As can also be seen from Figs. 8(a and b), increasing the CA mortar stiffness and concrete support layer stiffness has the upside of mitigating the track slab bending stress, but also has the downside of increasing bending stress of the CA mortar cushion and the concrete support layer. A possible reason is that more bending effect is taken by the CA mortar cushion and the concrete supporting layer, instead of by the track slab, if the CA mortar cushion and the concrete supporting layer has higher stiffness. Apparently, the track slab bending stress is not greatly impacted by the thickness of the CA mortar and the

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Fig. 8. Effect of design parameters on maximum bending stress of CRTS-II BTS system

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concrete supporting layers, as shown in Figs. 8(d and e). But increasing the thickness of the CA mortar cushion or the concrete supporting layer does increase the bending stress of the CA mortar cushion and the concrete supporting layer, respectively. Fig. 8 also suggests that the maximum bending stress of the bridge is hardly affected by all design parameters.

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Effect of Design Parameters on Maximum Shear Stresses Another stress that was evaluated in the analysis is the maximum shear stress. The effect of the design parameters on the maximum shear stresses of CRTS-II BTS system are plotted in Fig. 9 and summarized in Table 9. The results show that the maximum shear stress is tremendously lower than the maximum bending stress, which is understandable in that the structural response of the BTS is closer to the behavior of a thin beam, not a deep beam. From the rail fastening–BTS stress response plotted in Figs. 9(a and b), higher stiffness of the rail fastening decreases the maximum shear stress of the rail but increases the maximum shear stresses of the slab and the concrete supporting layer. A 10% increase of the rail fastening stiffness leads to a 10% increase of the track slab maximum shear stress, as can been seen in Fig. 9(b). In contrast to the effect of the rail fastening stiffness on shear stresses of the tack slab and the concrete supporting layer, the slab thickness will have a negative impact on the shear stresses of the track slab and the concrete supporting layer, which means higher slab thickness leads to lower maximum shear stress of the slab and the concrete supporting layer, as seen in Fig. 9(c). As with the maximum bending stresses of the bridge, the maximum shear stresses of the bridge are insignificantly affected by all design parameters, as shown in Fig. 9.

as to mitigate rider discomfort, higher stiffness of the rail fastening is suggested. • To reduce the track slab bending stresses to prevent the highspeed rail from structural failure, the following parameter design strategy can be used: higher track slab thickness, lower track slab stiffness, lower rail fastening stiffness, higher CA mortar, and concrete supporting layer stiffness. • All design parameters of the BTS system have negligible influence on the maximum bending stress and shear stress of the elevated bridges. • The maximum shear stress of the BTS system is relative low, as compared with the maximum bending stress of the BTS system, suggesting the BTS system behaves more like a beam than a plate.

Appendix I. The Railway is Subjected to a Standard Static Equivalent Axle Load of 300 kN The China CRH380A train is used in the Shanghai-Beijing highspeed rail. The total weight of the train is 3,885 kN with eight train carriages. Each train carriage has a weight of 485 kN (Xia et al. 2003a; Auersch 2005). The static axle load is half of the train carriage weight, which is 243 kN. When the train is moving above 200 km=h, the dynamic load can be calculated as (Yang 2008) Pd ¼ Ps ð1 þ α þ βÞð1 þ α1 Þð1 þ α2 Þ where Pd = dynamic equivalent load; Ps = static load; α, α1 , α2 = dynamic amplification factors; and β = eccentricity factor = 0.15 (see Table 10). Pd ¼ 0.5 × 243 × ð1 þ 0.6 × 120=100 þ 0.15Þ × ð1 þ 0.3 × 40=100Þ × ð1 þ 0.45 × 40=100Þ ¼ 300 kN

Discussion The preceding analysis demonstrates that the model proposed in the paper can be an effective research tool to investigate the effect of design parameters. The current study is based on 32-m simple-span bridge. To evaluate the variation of different structural types, bridges with different lengths, multiple spans, and varied supporting conditions can be studied. A three-dimensional finite-element model may also be used in the future to evaluate the structural response. The high-speed train has been modeled as a static load in this study. In future study, a train-rail-BTS-bridge coupled system can be established to investigate structural dynamic response and mode analysis of such a coupled system under a high-speed train.

Appendix II. Validation between a SAP 2000 Model and other Computation Method To validate the SAP 2000 model for evaluating the structural behavior of BTS, a two-dimensional finite-element model has been Table 8. Sensitivity of Maximum Bending Stress against Design Parameters Maximum bending stress

Conclusions This paper investigates the stress and deflection response of CRTS-II BTS on the elevated bridge foundations that occupy a great portion of high-speed railway network in China. Numerical simulation is carried out using SAP 2000 models to study the effect of stiffness of the rail fastening, stiffness and thickness of the slab, CA mortar cushion, and the concrete supporting layer on structural deflections and stresses. Values of design parameters of the BeijingShanghai high-speed railway are used to conduct the sensitivity analysis. The study provides an actual case study of an existing high-speed railway BTS system, which serves as a benchmark analysis for improvement of future BTS systems. The following conclusions can be drawn from the parametric study: • The rail defection is only significantly impacted by the rail fastening stiffness. To reduce the high-speed rail deflection so

Design parameters Raul fastening stiffness I Slab stiffness I Cement emulsified asphalt mortar stiffness I Supporting layer stiffness I Slab thickness I Cement emulsified asphalt mortar cushion thickness I Supporting layer thickness I

Cement emulsified asphalt mortar Supporting Rail Slab cushion layer Bridge D N N

I I D

N N I

I N N

N N N

N

N

D

N

N

N N

D N

N I

D D

N N

N

D

N

I

N

Note: “N,” “I,” and “D” indicate that the maximum bending stress remains stable, increases, and decreases, respectively, when the value of a design parameter increases.

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Fig. 9. Effect of design parameters on maximum shear stress of CRTS-II BTS system

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P=300KN Rail Rail Fastening Slab Track Soil Foundation

Fig. 10. BTS system resting on soil foundation

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Table 9. Sensitivity of Maximum Shear Stress against Design Parameters

Table 12. Comparison between the Structural Responses

Maximum shear stress Cement emulsified asphalt mortar Supporting Rail Slab cushion layer Bridge

Design parameters Raul fastening stiffness I Slab stiffness I Cement emulsified asphalt mortar stiffness I Supporting layer stiffness I Slab thickness I Cement emulsified asphalt mortar cushion thickness I Supporting layer thickness I

D N N

I N N

N N I

I D I

N N N

N

N

D

N

N

N N

D N

N I

D N

N N

N

N

N

N

N

Structural behavior Maximum displacement of the rail (mm) Maximum bending moment of the rail (N·m) Maximum bending moment of the rail (N·m) Maximum displacement of the track slab (mm) Maximum bending moment of the track slab (N·m) Minimum bending moment of the track slab (N·m)

Numeric solution

ANSYS result

SAP2000 result

3.22

3.34

3.29

5.10 × 104

5.10 × 104

4.60 × 104

−9.72 × 103

−9.95 × 103

−8.00 × 103

0.87

0.99

0.85

1.83 × 104

1.36 × 104

2.40 × 104

−7.94 × 103

−6.50 × 103

−7.00 × 103

Note: “N,” “I,” and “D” indicate that the maximum bending stress remains stable, increases, and decreases, respectively, when the value of a design parameter increases.

compared using analytical-numerical solution, SAP 2000 and ANSYS, as shown in Table 9. The results show significant similarity among key structural responses, so SAP 2000 models can be confidently used for other computational analysis for the BTS system in this study (see Tables 11 and 12).

Table 10. Dynamic Speed Coefficient under Different Speed Ranges

Acknowledgments

Speed coefficient

This study is sponsored in part by the National Science Foundation under Grant Nos. CMMI-0408390 and CAREER award CMMI-0644552, by the American Chemical Society Petroleum Research Foundation under Grant No. PRF-44468-G9, by the National Natural Science Foundation of China under Grant Nos. 51050110143, 51150110478, 51250110075, and U1134206, by the Ministry of Communication of China under Grant No. 0901005C, by the Jiangsu Natural Science Foundation under Grant No. SBK200910046, and by the Fok Ying Tong Education Foundation under Grant No. 114024, to which the authors are very grateful.

α α1 α2

Speed range

Speed difference

Default value

v ≤ 120 120 < v < 160 160 < v < 200

— Δv1 ¼ v − 120 Δv2 ¼ v − 160

0.6v=100 0.3Δv1 =100 0.45Δv1 =100

Table 11. Structural Parameters of the Model in Fig. 10 Component Rail track

Fastening system

Slab

Slab-soil interaction Load

Type

Unit

Default value

Elastic modulus Density Area Moment of inertia Elastic modulus Density Vertical stiffness Elastic modulus Density Thickness Width Length Vertical stiffness Axle load

Pa kg=m3 m2 m4 Pa kg=m3 N=m Pa kg=m3 m m m N=m3 N

2.1 × 1011 7.8 × 103 6.73 × 10−3 1.95 × 10−5 2.1 × 1011 7.8 × 103 6.0 × 107 3.6 × 1010 2.4 × 103 0.2 2.40 4.9 15 × 107 3 × 105

developed using analytical-numerical solution, SAP 2000, and ANSYS. Physical parameters of the railway structure used in the computation are given in Table 8. The standard axle load is 300 kN. The maximum displacement, the maximum and minimum bending stress of the rail, and the track slab are computed and

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