CONSIDERATIONS FOR DEVELOPMENT OF HIGH SPEED RAIL BRIDGE DESIGN STANDARDS

Y. Edward Zhou URS Corporation 4 North Park Drive Hunt Valley, Maryland 21030 Telephone: 301-820-3539 Fax: 301-820-3009 Email: [email protected] [email protected] Suoting Hu China Academy of Railway Sciences No. 2 Daliushu Road, Haidian District Beijing, China 100081 Email: [email protected] [email protected] Zaitian Ke China Academy of Railway Sciences No. 2 Daliushu Road, Haidian District Beijing, China 100081 Email: [email protected] [email protected] Bin Niu China Academy of Railway Sciences No. 2 Daliushu Road, Haidian District Beijing, China 100081 [email protected] Email: [email protected]

Submitted to:

AREMA 2012 ANNUAL CONFERENCE PROCEEDINGS

Word Count:

Text (including Abstract and References): 4,017 Figures and Tables (equivalent 13 x 250): 3,250 Total: 7,267

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ABSTRACT

Compared with conventional railways, high speed rail (HSR) has stricter requirements on bridge structural stiffness to minimize deformations and avoid excessive vibrations or resonance due to train crossings at high speeds. Bridge design for HSR requires a good understanding of traintrack-structure dynamic interactions, requirements for deflections, rotations, and natural frequencies of bridge spans, as well as continuous welded rail (CWR)-structure interactions. A review of China’s recent developments in HSR can benefit the development of HSR bridge design standards in North America. In China, commercial operation of passenger trains up to 250 km/h (155 mph) began in 2007 on existing rail lines that serve mixed passenger and freight trains. After 2007, construction of commercial passenger dedicated lines (PDL’s) started since further upgrading of mixed-traffic rail lines for higher speeds was considered unpractical and uneconomical. China released its Code for Design of High Speed Railway in late 2009 for passenger train design speed between 250 km/h (155 mph) and 350 km/h (217 mph). The Chinese HSR code is based on the UIC (International Union of Railways) code with adjustments derived from their own research. The document contains 22 chapters, including Alignment, Bridges and Culverts, Tunnels, Tracks, Stations, Traction and Power Supply, etc. This paper provides an overview of the Chinese HSR bridge design standards and three research projects behind the development of the standards, as well as comparisons to the UIC code where possible.

KEY WORDS

High Speed Rail, HSR, Bridge Design, Girder Deflection, Girder Vibration, Girder Natural Frequency, Continuous-Welded-Rail, CWR, China, UIC

© 2012 AREMA

INTRODUCTION

UIC (International Union of Railways) defines high speed rail (HSR) as systems of infrastructure and rolling stock which operate at speeds of 250 km/h (155 mph) or higher on specially built new lines, or the order of 200 km/h (124 mph) on specially upgraded existing lines ( 1). It is commonly recognized that the first modern commercial HSR was Japan’s Shinkansen between Tokyo and Osaka, which started operation in 1964 with a top speed of 256 km/h (159 mph). In Europe, regular HSR services started in the 1970’s in France, Italy, Germany, Spain, and the Great Britain. China began research and planning on high speed rail (HSR) feasibility and technologies in early 1990’s. A long debate was held over the type of technology to be employed for large scale application: conventional rail vs. magnetic levitation (maglev). Finally in 2006, the government decided to adopt the conventional wheel-rail technology for China’s HSR network. Nevertheless the 30 km (18.6 mi) long Shanghai Maglev Demonstration Operation Line began public service in January 2004 with a top operational speed of 431 km/h (268 mph), making it the world's fastest train in regular commercial service as of today. The first HSR in China was a 404 km (251 miles) section of Passenger Dedicated Line (PDL) from Qinhuangdao to Shenyang in Northeast China, constructed between 1999 and 2003. Known as the Qin-Shen PDL with a design speed of 200 to 250 km/h (124 to 155 mph) and test speed up to 300 km/h (186 mph), it served as the research base for development of HSR technologies in China. From 1997 through 2007, six rounds of speed-lift campaigns were carried out across the country, increasing the passenger train top speed from the original 60 km/h (37 mph) to a range varying from 120 km/h (75 mph) to 250 km/h (155 mph) on multiple existing rail lines that served mixed passenger and freight trains. Development of commercial passenger

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dedicated lines (PDL’s) started after 2007 since further upgrading of mixed-traffic rail lines for higher speeds was considered unpractical and uneconomical. China's HSR network consists of upgraded conventional rail lines and newly-constructed PDL’s. As of June 2011, China has the world's largest in-service HSR network totaling approximately 9,700 km (6,027 miles), including approximately 3,500 km (2,175 miles) with top speed of 300 km/h (186 mph) or 350 km/h (217 mph). The best-known section of PDL is the Beijing-Shanghai High Speed Railway that opened to the public in June 2011 with a design top speed of 380 km/h (236 mph). mph). The Chinese made CRH380 train-sets operate on this line. Bridges account for approximately half of the total length on China’s PDL’s. Prior to opening a line for service, the bridges are usually tested with a special train at a range of speeds up to 110% of the design speed. The primary purpose of the test is to verify the traction and power system and collect wheel-rail interaction data. Acceleration data is often collected from these tests for characterizing the fundamental dynamic behavior of bridges.

KEY ISSUES IN HSR BRIDGE DESIGN

Compared with conventional railways, HSR has stricter requirements on bridge structural stiffness to minimize deformations and avoid excessive vibrations or resonance due to train crossings at high speeds. Bridge design for HSR requires a good understanding of the following subjects:

Requirements for vertical deflections and rotational deformations of bridge spans

•

Requirements for natural frequencies of bridge spans

•

Train-track-structure dynamic interactions and coupling vibrations

•

Continuous welded rail (CWR)-structure interactions

•

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In addition, HSR lines require smoother geometrical alignment for horizontal curves and vertical profiles to ensure safe and comfortable operation of trains traveling at high speeds.

HSR BRIDGE DESIGN CODES

UIC Code Leaflet 776-2 Design requirements for rail-bridges rail-bridges based on interaction phenomena between train, track and bridge (2) provides HSR bridge design requirements specifically for

serviceability limit states concerning deformation and vibration. The UIC Code has other leaflets considered in that contain provisions for HSR bridge design, including Leaflet 776-1 Loads to be considered railway bridge design (3) and Leaflet 774-3 Track/bridge Interaction Recommendations for calculations (4). European standards BS EN 1990:2002 Eurocode – Basis of Structural Design

(5) establishes principles and requirements for structural design and is intended to be used in conjunction with EN 1991 to EN 1999 for the design of various types of civil structures. For example, BS EN 1991-2:2003 Eurocode 1: Actions on structures – Part 2: Traffic loads on bridges defines loads and their dynamic effects for road, pedestrian, and railway bridges ( 6 ). ).

China released its Code for Design of High Speed Railway ( 7 ) on December 1, 2009, for passenger train design speed between 250 km/h (155 mph) and 350 km/h (217 mph). The document contains 22 chapters, including Alignment, Bridges and Culverts, Tunnels, Tracks, Stations, Traction and Power Supply, Communications, Signaling, Rolling Stock Equipment, Environmental Protection, and more. China’s HSR design standards were developed upon reviewing those of UIC (International Union of Railways), Germany, Japan, etc., and incorporating research results of their own. AREMA has no specific HSR bridge design standards as of today.

© 2012 AREMA

HSR TRACK ALIGNMENT REQUIREMENTS

For track horizontal curves, the Chinese HSR code provides radius requirements for different design speeds in the form of: “recommended radius”, “minimum radius – general”, “minimum radius – special” (requiring technical and economical comparison as well as approval by the Ministry of Railway), and “maximum radius”. Table 1 lists the Chinese HSR horizontal curve radius requirements for main lines for different design speeds in Metric and US Customary units. Also provided in the table are the degrees of curve corresponding to the radius requirements. The Chinese HSR Code also has detailed requirements for horizontal transition spirals.

TABLE 1. Main Line Horizontal Curve Radius and Degree Requirements from Chinese HSR Design Code. Track Type \ Design Speed

Recomm'd

Ballasted Track

Min. Gen.

Min. Spec.

Recomm'd

Ballastless Min. Gen. Track

Min. Spec.

Maximum Radius

Radius (m) Radius (ft) Degrees Radius (m) Radius (ft) Degrees Radius (m) Radius (ft) Degrees Radius (m) Radius (ft) Degrees Radius (m) Radius (ft) Degrees Radius (m) Radius (ft) De Deg grees ees Radius (m) Radius (ft) Degrees

350/250 km/h (217/155 mph) 8,000 - 1 10 0, 000 m 26,247 - 3 32 2,8 ,80 08 fftt 0. 22 - 0.17 deg. 7, 000 m 22, 966 ft 0. 25 deg. 6, 000 m 19, 685 ft 0. 29 deg. 8,000 - 1 10 0, 000 m 26,247 - 3 32 2,8 ,80 08 fftt 0.22 - 0. 17 deg. 7, 000 m 22, 966 ft 0. 25 deg. 5, 500 m 18, 045 ft 0.3 .32 2 deg. eg. 12,000 m 39, 370 ft 0.15 deg.

300/200 km/h (186/124 mph) 6,000 - 8 8,, 000 m 19,6 19,685 85 - 26 26,2 ,24 47 ft 0. 29 - 0. 22 deg. 5, 000 m 16,404 ft 0. 35 deg. 4, 500 m 14,764 ft 0. 39 deg. 6,000 - 8 8,, 000 m 19,6 19,685 85 - 26 26,2 ,24 47 ft 0. 29 - 0. 22 deg. 5, 000 m 16,404 ft 0. 35 deg. 4, 000 m 13,123 ft 0. 0.4 44 deg. 12, 000 m 39,370 ft 0.15 deg deg..

250/200 km/h (155/124 mph) 4, 500 - 7 7,, 000 m 14, 4,76 764 4 - 2 22 2,9 ,96 66 fftt 0. 39 - 0.25 deg. 3, 500 m 11, 483 ft 0. 50 deg. 3, 000 m 9, 842 ft 0. 58 deg. 4, 500 - 7 7,, 000 m 14, 4,76 764 4 - 2 22 2,9 ,96 66 fftt 0. 39 - 0.25 deg. 3, 200 m 10, 499 ft 0. 55 deg. 2, 800 m 9, 186 ft 0.6 .62 2 deg. eg. 12,000 m 39, 370 ft 0.15 deg.

250/160 km/h (155/99 mph) 4,500 - 7,000 m 14 14,7 ,764 64 - 22,966 ft 0. 39 - 0. 25 deg. 4, 000 m 13,123 ft 0. 44 deg. 3, 500 m 11,483 ft 0. 50 deg. 4,500 - 7,000 m 14 14,7 ,764 64 - 22,966 ft 0. 39 - 0. 25 deg. 4, 000 m 13,123 ft 0. 44 deg. 3, 500 m 11,483 ft 0. 0.5 50 deg. 12, 000 m 39,370 ft 0.15 deg. deg.

© 2012 AREMA

For main line track vertical profiles, the Chinese HSR code specifies a maximum gradient of 20‰ (2%) in normal condition and 30‰ (3%) in difficult condition pending technical and economical comparisons. In sections that are for trainsets made of motorized cars, the maximum allowed gradient is 35‰ (3.5%). The Chinese HSR Code also has detailed requirements for gradient changes and vertical curves.

OVERVIEW OF CHINA’S HSR BRIDGE DESIGN STANDARDS

The Chinese HSR bridge design specifications are similar to UIC’s with adjustments made for specific situations in China based on results of analytical and field experimental research conducted in the past two decades. In the Chinese Code for Design of High Speed Railway ( 7 ), ), Chapter 7 Bridges and Culverts consists of the following sections: 7.1 General provisions 7.2 Design loads 7.3 Limits for structural deformations, displacements and natural frequencies 7.4 Structural analysis and construction details 7.5 Bridge deck arrangement and auxiliary facilities 7.6 Elevated station structures 7.7 Junctions to other structures and facilities

Design Loads

Design loads for HSR bridges and culverts in China are specified as combinations of the loads listed in Table 2.

© 2012 AREMA

TABLE 2. Design Loads for Bridges and Culverts. Loading Types

Loading Description Selfweight of strutural components and auxiliary facilities Prestressing forces

Permanent Effects of o f concrete co ncrete shrin s hrinka kage ge and creep Earth pressure Static water pressure and buoyan buoyancy cy Effects of foundation movements Primary loads

Vertical train static live loads Vertical erti cal highway highway static live loads (as applic applicable) able) Vertical erti cal dynamic dynamic impa i mpact ct of tr ain loads Longitudinal Longitud inal and fle flexura xurall interactio inte raction n forces forc es with CWR Transient Centrifu Centrifuga gall forces force s La Lateral teral oscillation force s Train live load induced earth pressure pres sure Pe Pedestrian destrian and railing loads Aerodynamic loads

Seconda Seco ndary ry loads

Special loads

Train traction tracti on and braking braking forces forc es Wind loads Flow pres pressure sure Ice pressure Effects of temperature temperature changes changes Freezing expansio expansion n pressure Train derailment load l oad Collision forc es from ships and barges barges Collision forces from automobiles automobiles Construction loads Earthquake loads Rail-break forces from CWR (continuous-welded-rail)

Train Live Load and Impact

China’s train live load for HSR bridge design consists of the ZK Standard Live Load and the ZK Special Live Load, as shown in Figure 1 and Figure 2, respectively ( 7 ). ). The ZK Standard Live Load is identical to the UIC Load Model 71 multiplied by a factor of 0.8 ( 3).

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FIGURE 1. China HSR ZK Standard Live Load.

FIGURE 2. China HSR ZK Special Live Load.

Train load vertical dynamic impact for bridge structures is specified as (1 + µ), where

1.44 . 0.2 2 0.

0.18 0.0 0.0

where, Lφ = loading length in meters ≥ 3.61 m (11.84 ft). For simple spans, Lφ is the span length. For continuous spans, Lφ is the average span length times (1 + n/10) where n is the number of spans (2 ≤ n ≤ 5). For continuous superstructures of more than five spans, Lφ equals to the average span length times 1.5.

Requirements for Vertical Girder Deflections

Under the ZK design live loads without dynamic impact, vertical deflection limits for doubletrack simple-span concrete girders shorter than 96 m (315 ft) are specified as in Table 3 ( 7 ). ). For

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continuous superstructures of three or more spans, the limits in Table 3 are to be multiplied by a factor of 1.1. For continuous or simply spans of two or less, the limits in Table 3 are to be factored by 1.4. For single-track simple or continuous spans, the limits in Table 3 are to be factored by 0.6.

TABLE 3. Vertical Deflection Limits for Double-Track Simple-Span Concre Concrete te Girders of Span Lengths less than 96 m (315 ft). Design Speed km/h (mph) 2 5 0 (1 5 5 ) 3 0 0 (1 8 6 ) 3 5 0 (2 1 7 )

L ≤ 4 40 0 (1 3 1 ) L/1,40 0 L/1,50 0 L/1,60 0

Span Length Range, m (ft) 40 ( 131 ) < L ≤ 8 80 0 ( 2 6 2) L/1 ,4 00 L/1 ,6 00 L/1 ,9 00

L > 8 0 ( 2 6 2) L/1,0 00 L/1,1 00 L/1,5 00

For arch and rigid frame bridges, structural deflections must also take into consideration of temperature effects, in addition to live load actions. For prestressed concrete bridges, creep induced residual deformations are also to be taken into account.

Requirements for Vertical Girder End Rotations

Limits for vertical girder end rotations, as depicted in Figure 3, are listed in Table 4 for doubletrack simple-span concrete girders shorter than 96 m (315 ft) under the ZK design live loads without dynamic impact (7 ))..

FIGURE 3. Definitions of Vertical Girder End Rotations of Simple Spans.

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For girder ends at piers, the rotation (θ1 or θ2) of each girder end needs to satisfy the limit for the girder end at abutment (θ) in addition to the requirements for the sum of girder end rotations in adjacent spans ( θ1 + θ2).

TABLE 4. Limits for Vertical Girder End Rotations. Track Type Ballasted

Locatio n between abutment and span between adjacent span s panss between abutment and span

Ballastless between adjacent spans spans

Limit (rad) θ ≤ 2.0‰ θ1 + θ2 ≤ 4.0‰

Girder End Cantilever, Lc , m (f t)

θ ≤ 1. 1.5‰

Lc ≤ 0.55 m (1.80 ft) 0.5 5 (1.80 ) < Lc ≤ 0.75 (2.46) Lc ≤ 0.55 m (1.80 ft) 0.5 5 (1.80 ) < Lc ≤ 0.75 (2.46)

θ ≤ 1. 1.0‰ θ1 + θ2 ≤ 3 3..0‰ θ1 + θ2 ≤ 2 2..0‰

Requirements for Vertical Natural Frequencies of Girders

Requirements for dynamic characteristics of bridge spans are established based upon criteria in consideration of dynamic responses of the structure, safety of crossing trains, as well as ride comfort of passengers. For simple-span concrete girders no longer than 96 m (315 ft), vertical vibration natural frequencies are limited to no lower than the following values ( 7 ): ): n0 = 80/ L,

for L ≤ 20 m (66 ft) -0.592

n0 = 23.58 L

,

for 20 m (66 ft) < L ≤ 96 m (315 ft)

where, n0 = vertical natural frequency (Hz); and L = simple span length (m)

These requirements are based on UIC’s specifications developed primarily for train speeds below 250 km/h (155 mph). For design speeds between 250 km/h (155 mph) and 350 km/h (217 mph), Table 5 provides the vertical vibration natural frequency lower limits for concrete girders of common span lengths that do not require train-structure dynamic analysis (7 ). ).

© 2012 AREMA

TABLE 5. Vertical Vibration Natural Frequency Lower Limits for Double-Track Simple-Span Concrete Box Girders of Common Lengths Not Requiring Dynamic Analysis. Span Length m (ft) 1 2 (3 9 ) 1 6 (5 2 ) 2 0 (6 6 ) 2 4 (7 9 ) 3 2 (1 0 5 )

Design Speed, km/h (mph) 25 0 (155) 3 0 0 (1 8 6 ) 10 0/L 1 0 0 /L 10 0/L 10 0/L 10 0/L 12 0/L

1 0 0 /L 1 0 0 /L 1 2 0 /L 1 3 0 /L

3 5 0 ( 2 1 7) 120/L 120/L 120/L 140/L 150/L

For bridges that are beyond the coverage of Table 5, dynamic analysis for train-structure coupling vibrational responses is required based on the actual condition of train crossing and a maximum train speed of 1.2 times the design speed. The following requirements must be satisfied : Wheel-climb derailment factor:

Q/P ≤ 0.8

Axle weight reduction ratio:

∆P/P ∆P/P ≤ 0.6

Wheel lateral force:

Q ≤ 10 + P0 /3

Vertical acceleration of train body:

a z ≤ 0.13g (half-peak value)

Lateral acceleration of train body:

a y ≤ 0.10g (half-peak value)

Sperling ride comfort index:

W ≤ 2.50 excellent

2.50 < W ≤ 2.75 good 2.75 < W ≤ 3.00 acceptable Bridge deck vertical acceleration:

≤ 0.35g for ballasted track

(due to an excitation of ≤ 20 Hz)

≤ 0.50g for ballastless track

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where, Q = lateral wheel load on rail, kN (1 kN = 225 lbs force); P = vertical axle load, kN; P0 = static axle weight, kN; ∆P ∆P = reduction of vertical axle load due to dynamic action; g = standard 2

2

gravity = 9.81 m/s (32.174 ft/s ).

Requirements for Longitudinal Stiffness of Piers and Abutments Ab utments

For simple-span concrete girders located in the fixed zone (no longitudinal rail movements due to temperature) of ballasted continuous-welded-rail (CWR) track, longitudinal stiffness at the top of piers and abutments must be no lower than the limits listed in Table 6 ( 7 ). ).

TABLE 6. Longitudinal Stiffness Limits for Top of Piers and Abutments. Type

Pier

Span m (ft) ≤ 12 1 2 (39 )

Min. Longitudinal Longitudinal Stiffness, Stiffnes s, kN/cm (kip/in) Do uble - Tr ac k Single -Trac k 1 00 ( 5 7 ) 6 0 ( 3 4)

16 (52 ) 20 (66 ) 2 4 (7 9 ) 3 2 (1 0 5 )

1 60 ( 9 1 ) 1 9 0 (1 0 8 ) 2 7 0 (1 5 4 ) 3 5 0 (2 0 0 )

1 00 ( 5 7 ) 1 20 ( 6 9 ) 1 7 0 ( 97 ) 2 2 0 ( 1 26 )

4 0 (1 3 1 ) 4 8 (1 5 7 )

5 5 0 (3 1 4 ) 7 2 0 (4 1 1 ) 3 ,0 00 (1,713)

3 4 0 ( 1 94 ) 4 5 0 ( 2 57 ) 1,500 ( 857 )

Abutme nt

For areas within the departing and approaching limits of elevated stations, the stiffness of the piers and abutments are limited to no lower than 2.0 times the values in Table 5.

RESEARCH BEHIND CHINA’S HSR BRIDGE DESIGN STANDARDS

Significant amounts of research have been conducted in China for the development of the HSR bridge design standards. The following paragraphs briefly discuss three subjects.

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Girder Vibration Frequency Requirements

Crossing trains act as vibration excitation sources to bridge girders. The excitation frequency varies with train speed. As the excitation frequency approaches the natural frequencies of the structure excessive vibrations or even resonance may occur. These dynamic responses can cause damages to the track system and the structure, or even threaten the safety of the crossing train or the bridge. Factors affecting train-bridge dynamic responses include natural frequencies of the girder, damping ratio of the structural system, train speed, car length and truck spacing, track irregularities, flat wheels, etc. Previous research suggested that the primary factors affecting the vertical excitation frequency of train loading are the train speed and car length. The effects of other factors such as the axle spacing and truck spacing are secondary because their repeated actions are not continuous. Thus the excitation frequency is simply:

where f = = frequency of vertical excitation, V = = train speed, and Lv = car length. This conclusion has been supported by analytical and experimental research results in China. Figure 4 shows test data that demonstrates a consistent correlation between field measured vertical excitation frequency and train speed for two different types of train sets and two different span lengths ( 8 and 9).

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(a) 32 m (105 ft) Box Girders

(b) 24 m (79 ft) Box Girders

FIGURE 4. Field Measured Correlation between Vertical Excitation Frequency and Train Speed.

UIC’s requirements for bridge girder natural frequencies consist of the upper bound and lower bound for varying span lengths. The lower bound is to control excessive vibration or resonance due to train crossings; and the upper bound is to limit train-track dynamic responses due to track irregularities. For bridge girders of natural frequencies within the required envelope stipulated in design specifications, structural design can be based on the static design loads amplified by the dynamic impact. Experience and research in Europe and China have suggested that the UIC lower bound cannot eliminate excessive vibration or resonance due to dynamic train loads at high speeds ( 8 and 9). The main reason is that the original UIC requirements were developed primarily for train speeds below 250 km/h (155 mph). As a result, extensive analytical and experimental research was conducted in China to develop limits for vertical vibration natural frequencies of bridge girders of varying span lengths for train speeds between 250 km/h (155 mph) and 350 km/h (217 mph). Table 5 is the result of the research and provides girder natural frequency lower limits that are higher than those of UIC’s. It was found that an upper limit is not necessary considering the

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high magnitudes of these lower limits for actual girders and the low magnitudes of track irregularities permitted by inspection requirements. Figure 5 shows comparisons between computed and field measured dynamic impact for 32 m (105 ft) simple-span concrete box girders due to the CRH2 train sets ( 8 ). ). The figure clearly demonstrates that girders not satisfying the natural frequency requirements in Table 5 ( ≥130/L at 300 km/h, ≥150/L at 350 km/h) can be subject to excessive dynamic response or resonance at train speeds higher than 300 km/h (186 mph).

Computed Compute d (natural freq. = 150/L) ) µ + ( 1 t c a p m I c i m a n y D

Computed Compute d (natural freq. = 120/L) Field Measured (loaded trains) Field Measured (empty trains)

Speed (km/h)

FIGURE 5. Comparison between Computed and Field Measured Dynamic Impact for 32 m (105 ft) Simple-Span Concrete Box Girders.

Girder Stiffness Requirements

Design limits for bridge girder stiffness serve to ensure the safety of crossing trains at high speeds as well as ride comfort of passengers. Live load induced girder deflection is the most commonly used parameter for specifying the stiffness limit. Typically, bridge structural stiffness is controlled through specifying limiting values for the span to deflection ratio (L/ δ) based on limiting the vertical acceleration to values that ensure passengers ride comfort, say 1.0 m/s 2 (3.28

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ft/s2), for varying train speed. However, different countries use different live loads for the calculation of maximum girder deflection ( δ) for double-track bridges. For example, UIC uses single-track design live load with dynamic impact; Japan uses single-track operating live load including dynamic impact; China uses the standard ZK design live load on both tracks but not including dynamic impact. Comprehensive comparative studies were made in China for varying span lengths considering factors such as single-track vs. two-track loading, variation of design live load among different countries, tolerances for track irregularities, etc. Figure 6 depicts computer models used for calculating static and dynamic responses of concrete box girders to crossing train loads. Such research yielded Table 3 as the result.

A Simple Span Girder

Half of a 3-Span Continuous Girder

FIGURE 6. Computer Models for Dynamic Responses R esponses of Concrete Box Girders.

Girder end rotation is another design parameter that needs to be subjected to limiting values in order to ensure the stability of ballast for ballasted tracks and the performance of the fasteners and slab systems for ballastless tracks. As illustrated in Figure 7, live load induced

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girder end rotation imposes push-down and uplift forces, respectively, to the rail on either side of the gap between the girder ends. These forces may cause damages to the ballast, rail fasteners, or the slab system if not controlled properly. Research in China suggested limits for vertical girder end rotations (9), as summarized in Table 4, for ensuring proper performance of the rail-fastenerslab system, reducing maintenance needs, and ensuring the safety of crossing trains at high speeds.

Fastener 扣件 Rail 钢轨 梁 Girder

梁 Girder

FIGURE 7. Illustration of Bridge Girder End Rotation and Impact to Rail-Fastener-Slab System.

CWR-Structure Interactions

High speed rail (HSR) requires the use of continuous-welded-rails (CWR) to ensure track smoothness and ride comfort. Good understanding of CWR-structure interactions is essential to the design of both the bridge structure and the track system consisting of rails, fasteners and the slab, with or without ballast. Forces are generated at the CWR-structure interfaces due to temperature induced deformations, live loads, train braking forces, and accidental rail breaks. Proper considerations are necessary to minimize structural deformations of the bridge and ensure the stability of CWR and the safety of train operations. Extensive research has been conducted in China in the past few decades on CWRstructure interactions, CWR anchorage requirements on bridges, variations of the CWR neutral temperature over time, impact of rail breaks on train safety, proper use of rail expansion joints,

© 2012 AREMA

etc. (10). The results from such research have provided great value and detailed provisions to proper design of bridges and track systems for HSR. Distribution of train braking forces among bridge substructure depends on the longitudinal stiffness of adjacent bridge piers and abutments. Research in China suggested that the longitudinal stiffness of bridge substructure is an important design parameter; and Table 6 was developed as a result to provide longitudinal stiffness limits for the top of piers and abutments in the fixed zone of ballasted CWR. Since the braking force only considers one train for double-track bridges in the Chinese bridge design standards, values in Table 6 are to be multiplied by a factor of 2.0 for piers and abutments supporting elevated train stations within the departing and approaching limits to consider the simultaneous occurrence of traction and braking forces on both tracks.

CONCLUSIONS

High speed rail (HSR) has strict requirements on bridge structural stiffness to minimize deformations and avoid excessive vibrations or resonance for ensuring the safety and comfort of trains crossing at high speeds. These requirements need to be established based upon analytical and experimental research for specific train loads, speeds, track systems, and bridge configurations. China has successfully developed and implemented HSR technologies in a relatively short time period based on effective employment of foreign experiences and technologies plus significant research efforts addressing the specific situations in China. Detailed requirements for bridge design are stipulated in the Chinese Code for Design of High Speed Railway released in 2009 for passenger train design speed between 250 km/h (155mph) and 350

© 2012 AREMA

km/h (217 mph). Much of their research results and bridge design standards can be used as a good resource for the development of HSR bridge design standards in North America.

REFERENCES

(1) UIC

(International

Union

of

Railways),

General

definitions

of

highspeed

http://www.uic.org/spip.php?article971,, retrieved June 2012 http://www.uic.org/spip.php?article971 (2) UIC (International Union of Railways), Leaflet 776-2, Design requirements requirements for railnd

bridges based on interaction phenomena between train, track and bridge, 2 edition, June

2009 (3) UIC (International Union of Railways), Leaflet 776-1 Loads to be considered considered in railway bridge design, 5th edition, August 2006

(4) UIC (International Union of Railways), Leaflet 774-3

Track/bridge

Interaction

nd

Recommendations Recommen dations for calculations calculations, 2 edition, October 2001

(5) BSI (British Standards Institution) / CEN (European Committee for Standardization), BS EN 1990:2002, Eurocode – Basis of structural structural design, December 2005 (6) BSI (British Standards Institution) / CEN (European Committee for Standardization), BS EN 1991-2:2003, Eurocode 1: Actions on structures – Part 2: Traffic loads on bridges, September 2003 (7) People’s Republic of China Ministry of Railway, Code for Design of High Speed Railway (in Chinese), TB 10621 – 2009/ J 971 – 2009, China Railway Press, Beijing, 2009 (8) Hu, S., Niu, B., Du., B., Ban, X., Su, Y., Establishment of Structural Stiffness and Natural Frequency Limits for China Code for Design of High Speed Railway (in Chinese),

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