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6C h a p t e r 2 To understand the current state of research and practice in light rail structures, a literature review was conducted. When technical information related to light rail transit was not avail- able, the behavior of conventional rail bridges carrying heavy-haul and high-speed trains was reviewed, which can assist a general understanding of light rail bridges although their loading characteristics are different. 2.1 Light Rail Trains, Tracks, and Decks The advancement of modern light rail trains includes crash energy management principles, improved reliability and propulsion systems, reduced maintenance costs, resilient wheels, and increased capacity. The design of light rail trains includes the following items (Parsons Brinckerhoff et al. 2012): unidirectional versus bi-directional; non-articulated versus articu- lated; size, truck and axle positions; weight; suspension characteristics; high floor versus low floor; and wheel diameter and gage. Car body strength and crashworthiness also are impor- tant to consider. Bumpers are installed to dissipate potential impact energy. Many light rail trains have six axles per car body with a length from 50 ft to 124 ft, whereas four or 10 axles are sometimes used. The wheel diameter of the trains varies from 24 in. to 28 in. Two to four articulated trains are generally operated in the United States. All train components should not experience resonance. TCRP Report 155 states that dampers are required to avoid resonance, and the natural frequency of a car body should be 2.5 times the frequency of the suspension system. The ride quality of light rail trains may be assessed by UIC Code 776-2, âDesign Requirements for Rail-Bridges Based on Interaction Phenomena Between Train, Track and Bridgeâ (UIC 2009) or ISO 2631 âMechanical Vibration and ShockâEvaluation of Human Exposure to Whole-Body Vibrationâ (ISO 1997). The acceleration experienced by light rail passengers may not be greater than 1 ft/s2 or 0.03 g (Parsons Brinckerhoff et al. 2012). Light rail train load consists of several items, as listed below, including a weight of 154 lb (70 kg) per person (ASME 2009, Parsons Brinckerhoff et al. 2012): â¢ AW0 (empty load): the weight of the train with all components â¢ AW1 (fully seated load): AW0 + fully seated passengers and operators â¢ AW2 (system load): AW1 + 3.3 passengers/yd2 (4 passengers/m2) in standing areas â¢ AW3 (crush load): AW1 + 5.0 passengers/yd2 (6 passengers/m2) in standing areas â¢ AW4 (structural load): AW1 + 6.7 passengers/yd2 (8 passengers/m2) in standing areas A comprehensive review of light rail tracks and trains is provided in TCRP Report 155. It includes track geometries, corrosion control, noise and vibration issues, transit power, track in mixed traffic, trackway maintenance, and concise information on structures and bridges. Four types of decks may be available for rail bridges (Parsons Brinckerhoff et al. 2012): State of the Art Review
State of the art review 7 â¢ Open deck: This type was used in the late 1800s with a simple system comprising timber cross- ties installed to a bridge superstructure. Although open deck systems are light, they generate substantial noise and vibration. Some factors to consider include the spacing of timber ties, skew details, anchoring methods, superstructure expansion, material types, track maintenance, emergency walkway, and lateral stability of the superstructure. â¢ Embedded deck: This system was developed for streetcar applications so that trains can share the operation space with regular vehicles at the same elevation. Compared with other deck systems, the embedded deck is noisy and may not be preferred, unless it has to be used (i.e., space sharing with regular vehicles). Typical considerations are dimension requirements for a deck trough, deck thickness beneath track rails, drainage for runoff, joints for thermal expansion, rail gap, and the presence of noise sensitive facilities in the vicinity of the track. â¢ Ballasted deck: This configuration has been used since the 20th century to address noise and vibration problems. The construction and maintenance of ballasted decks, however, require rigorous effort. Some benefits of using a ballasted system involve enhanced ride quality, good track support, and controlled thermal forces from track to bridge. â¢ Direct fixation deck: This type became popular in the 1960s because it resolved concerns resulting from the open and ballasted decks. Direct fixation is a contemporary method for light rail bridges; accordingly, it is broadly used. Resilient fasteners are often employed as in the case of Bay Area Rapid Transit (BART) in San Francisco, Washington Metropolitan Area Transit Authority (WMATA) in Washington, D.C., and Metropolitan Atlanta rapid Transit Authority (MARTA) in Georgia. Direct fixation tracks reduce noise and vibration relative to other track types, require less maintenance, and provide good ride quality and electrical isolation. Bridges with direct fixation tracks will carry reduced dead load in com- parison with those with ballasted tracks, and can save construction expenses. Thermal inter- action between the rail and structure is of interest. Typical tracks used for light rail transit are ballasted, embedded, and direct fixation. 2.2 Use of a Mixed Load Configuration for Bridges or Functional Changes When selecting a bridge type, several factors are taken into consideration (e.g., superstructure details such as continuity, construction and potential maintenance costs, durability, and site condi- tions). A bridge may carry both light rail and highway traffic loads for the convenience of urban dwellers. PESC (2011) studied the potential of changing highway traffic to light rail transit for two bridges in Austin, TX: the Congress Avenue Bridge and the South First Street Bridge. The Congress Avenue Bridge was composed of precast prestressed concrete box girders, while the South First Street Bridge included steel plate girders. The light rail train load used for structural design was 135 kips. Investigations were conducted as per the AASHTO and AREMA specifications. It was found that the capacity of these bridges was not sufficient to accommodate the light rail load, and strengthen- ing was recommended to carry this traffic mode. Although there is a demand for designing bridges subjected to light rail train and highway traffic loadings, specific design guidelines are not available. 2.3 In Situ Response of Bridges Subjected to Rail Load The behavior of constructed bridges has been studied when subjected to rail load. A variety of structural types and loading configurations was emphasized. Axle loads are typically measured by strain gages or load cells (Barke and Chiu 2005). James (2003) examined the distribution of axle load using strain gages bonded to the neutral axis of train rails. Over 7,400 trains were ran- domly operated at an average speed of 64 mph and corresponding loads were monitored. The
8 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads measured axle weight was calibrated with a typical error range of Â± 4%. A comparison showed that the in situ axle weight was greater than the nominal axle weight. This is attributed to the effects of DLA that increased the static axle weight. A coefficient of variation of 0.07 was noted for train load. Ataei et al. (2005) verified the effectiveness of heavy instrumentation for railway bridges. A 118-ft steel truss bridge was monitored with 42 strain gages, 20 displacement transduc- ers, and 27 accelerometers at various structural members (i.e., stringers, floor beams, bracings, and chords). The loads applied were a 245 kip locomotive and a 168 kip freight vehicle. Leander et al. (2010) evaluated the fatigue performance of a steel railway bridge. The 623-ft six-span bridge accommodated about 520 commuter trains per day. Strain gages were bonded to bridge beams, and structural responses were recorded. Damage propagation of the beams was examined along with fatigue load, including investigations into the bridgeâs remaining service life. The need for statistical assessment was discussed to better characterize the performance of railway bridges. Wipf et al. (2000) examined the behavior of a 166-ft long timber bridge (solid sawn stringers) under a 3-car EMD Engine 6870 train. To study dynamic amplification effects, the train was operated at various speeds from 2 mph to 40 mph. The dynamic amplification factor of the bridge at midspan was calculated using a ratio between the maximum dynamic and static deflec- tions. The maximum dynamic amplification factor was 1.22. A dynamic load factor (a ratio between the maximum dynamic and static wheel loads) of 1.32 was also recorded at a train speed of 40 mph. It was found that, unlike the assumption in design, the bridge elements did not act as a single unit. Gutkowski et al. (2003) tested a railroad bridge in quasi-static and dynamic load- ing conditions. A method to calculate load-sharing between bridge girders was discussed using measured deflection and the girdersâ elastic modulus. The load-sharing factor of the girders was from 16% to 29%, depending upon the position of the train load. This observation suggests that a study is necessary to examine live load distribution factors for rail bridges. Xia et al. (2008) instrumented four bridges with a span length varying from 459 ft to 695 ft. The height of piers supporting these bridges was as high as 180 ft. Four train types (140 kips to 289 kips) were operated at variable speeds (20 mph to 44 mph) to measure the displacement and frequency of the bridges. A regression line was developed to engage bridge frequencies with operating speeds. A hunting wave length was then determined. The natural frequency of the piers was affected by lateral resonant train speed. Unlike straight bridges, the resonant speed was not observed for curved bridges. Zhang et al. (2008) monitored the behavior of a hollow-box girder bridge, consisting of 28 simple girders, subjected to a train load with six passenger cars operated at 3 mph to 169 mph. Natural frequencies were measured and numeri- cally predicted. Flener and Karoumi (2009) investigated the dynamic behavior of a composite railway bridge. The 36-ft long bridge system comprised a corrugated steel tube, forming an arch structure to carry train load. Optical speed sensors and linear variable displacement transducers were positioned along the train rail and underneath the steel tube, respectively. Strains were obtained as well. The dynamic displacement of the bridge was approximately 20% greater than its static counterpart. Important parameters were the speed of trains and the span and mass of the bridge. Wiberg and Karoumi (2009) tested a slender box girder reinforced concrete railway bridge. A stochastic subspace identification technique was employed to examine bridge dynamics. The effects of various train passages were studied from extreme bridge acceleration perspec- tives. Test results were compared with existing design guidelines. The maximum acceleration measured was 12 ft/s2, which was lower than the Swedish code limit of 16 ft/s2. Lu et al. (2012) monitored the response of a 26-ft railroad bridge in terms of deflection and acceleration. The predicted results of a numerical model based on a second order dynamic equation were evalu- ated against the data measured. Natural frequencies were determined using a fast fourier trans- form. The importance of a resonant service condition was emphasized. An increase in moving mass tended to decrease the critical speed of a train, which influenced acceleration spikes.
State of the art review 9 Chebli et al. (2008) studied the dynamic response of sleepers subjected to high-speed trains using accelerometers. The sleepers were part of a ballasted railway track, and subgrade- rail interaction was evaluated. Vertical and lateral accelerations were measured, followed by a three-dimensional model that predicted the in situ behavior. Ho et al. (2010) per- formed modal analysis for a bridge carrying high-speed train load. A multi-phase sys- tem identification scheme was developed using the concept of eigenvalue sensitivity. The bridge was 325-ft long, and was composed of steel plate girders and wooden sleepers. A set of high-speed trains with a full load of 1,700 kips was operated at a speed of 190 mph. Three stages of bridge vibration were monitored with multiple sensors: (1) vibration when the train passed (train passage vibration); (2) vibration when the train was passing along the adja- cent bridge (ambient vibration); and (3) vibration after the train passed (free vibration). Modal parameters were acquired by the stochastic subspace identification technique. Numerically obtained responses were compared with in situ data. Natural frequencies and mode shapes for twisting and bending were studied. Rauert et al. (2011) reported a monitoring project for a high-speed rail bridge. A dense grid instrumentation plan was implemented to record strain and acceleration. A numerical approach based on elastic theory was also taken to estimate the behavior of the bridge. A laboratory test with a beam specimen was conducted to confirm the effects of dynamic and cyclic loads. It was concluded that the proposed dense instrumentation scheme properly detected bridge responses. Kishen et al. (2013) assessed the performance of a masonry railway bridge with two arches at a span length of 56 ft. A static load test was carried out using two-truck flat rail-carrying vehicles, in tandem with a dynamic load test at operating speeds varying from 3 mph to 25 mph. Longitu- dinal load was examined. The margin of safety predicted by a nonlinear finite element model was useful to understand the bridgeâs crack initiation and stability failure. Ribeiro et al. (2013) also studied the behavior of an arch bridge under train loading. The bridge type was a bowstring arch with a length of 126 ft. The train was 521 ft long, operated at a speed of 138 mph. Instrumenta- tion included displacement gages, strain gages, and accelerometers installed to the vertical cable, bottom chord, and truss member of the bridge. A finite element model, calibrated with test data employing a generic algorithm, predicted the bridge behavior. Another arch bridge was tested by Malm and Andersson (2006) with an interest in dynamic characteristics such as damping and frequency, when a train load was applied at 50 mph. Free vibration was calculated to identify fatigue-critical members. Murray (2013) used a non-contact testing technique [i.e., digital image correlation (DIC)] to measure the displacement of a two-span bridge in Tweed, Ontario, Canada, subjected to train loading. Summary: The majority of published literature was concerned with heavy-haul and high- speed trains. Typical structural responses monitored were displacement, acceleration, and strain. Finite element models or analytical dynamic approaches were developed to predict the behavior of constructed bridges. Several identification techniques (e.g., stochastic subspace identifica- tion) were useful for extracting the dynamic characteristics of constructed bridges, based on in situ response signals. A few cases discussed the behavior of bridges carrying commuter trains. Scarce information is available on bridge responses associated with light rail trains. As such, there are significant research needs for the field monitoring of light rail bridges. 2.4 Live Load and Associated Effects The live load of light rail structures includes light rail vehicle, maintenance train, and pedestrian loads (AECOM 2008). Light rail transit is typically operated with two to four articulated trains. Appropriately estimated axle loads will prevent excessive ballast settlement and other types of dis- tress, such as weld fatigue. Figure 2.1 shows selected design live loads of light rail transit. There is
10 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads Colorado 75.6ft (train length) California Massachusetts (Orange line rapid) Massachusetts (Red line high speed) Massachusetts (Red line rapid) 6.1ft Minnesota (maintenance train) 6.0ft 44.2ft6.1ft k 0 .23 6.1ft 5.0ft 6.0ft5.0ft 10.1ft10.0ft 17ft k 0 .52 16.75ft 6.1ft 6.1ft k 0 .03 39.7ft 6.1ft 6.0ft6.0ft 17.0ft10ft k 89 .12 Massachusetts (Blue line rapid) 6.1ft 24.5ft 6.1ft 6.2ft 6.0ft Massachusetts 16.8ft6.3ft 16.8ft 6.3ft k 5 .52 28.8ft5.9ft Minnesota 5.9ft 6.3ft 6.0ft Utah 6.0ft28.0ft 28.0ft k 0 .72 28.8ft 5.9ft 6.2ft Arizona 6.2ft27.1ft 27.1ft k 58 .22 k 58 .22 k 54 .03 k 54 .03 k 8 .72 k 8 .72 k 58 .22 k 58 .22 k 5 .81 k 5 .81 k 8 .72 k 8 .72 k 5 .52 k 5 .52 k 5 .52 k 5 .71 k 5 .71 k 0 .72 k 0 .72 k 0 .72 k 0 .72 k 0 .72 k 0 .52 k 0 .52 k 0 .52 k 8 .31 k 8 .31 k 0 .41 k 0 .41 k 8 .31 k 8 .31 k 8 .31 k 8 .31 k 89 .12 k 89 .12 k 89 .12 k 83 .41 k 83 .41 k 0 .23 k 0 .23 k 0 .23 k 0 .71 k 0 .71 k 0 .71 k 0 .71 k 0 .03 k 0 .03 k 0 .03 k 5 .52 k 5 .52 k 5 .52 k 5 .52 Figure 2.1. Various design live loads for light rail transit (axle load).
State of the art review 11 no standard live load for light rail bridges, contrary to the case of highway and railway bridges. For design purposes, one light rail train is loaded per track to determine structural load and associated forces, which is analogous to traffic lanes in design of highway bridges. HL-93 is the standard live load of the AASHTO LRFD BDS (AASHTO 2016), while AECOM (2008) recom- mended HS-25 be used for structures supporting light rail trains. Some researchers attempted to propose alternative train load models. James (2003) studied load effects on the behavior of railway bridges spanning from 13 ft to 98 ft. Two approaches were exploited: the classical extreme value theory and the peaks-over-threshold method. Reliability analysis was incorpo- rated to address the uncertainty of railway loading. Based on the measured axle load and train configurations, a load model was developed. The number of light rail trains (one or more) should be considered when determining the maximum shear force and bending moment of a bridge. To achieve this objective, live load distribution needs to be predicted. The load distribution of light rail transit is, however, not well documented yet. Most design guidelines do not mention this important technical aspect or merely state that AASHTO LRFD BDS should be used (COE 2011). Given that the physical configuration of light rail trains is different from that of highway trucks, such a recommenda- tion may not be valid and could mislead design engineers. Like standard vehicular load on highway bridges, multiple presence factors for light rail trains should be examined. Guidelines for the multiple presence of light rail trains are limited. COE (2011) recommended the following multiple presence factors for light rail transit: two tracks = 100% on each track, three or more = 100% on any two tracks, and 75% on any additional tracks. These recommendations are similar to those of AREMA for heavy-haul trains: â¢ For two tracks: full live load â¢ For three tracks: full live load on two tracks and one-half on the other track â¢ For four tracks: full live load on two tracks, one-half on one-track, and one-fourth on the remaining track The format of the AREMA provision is different from that of AASHTO LRFD BDS that classifies load distribution components based on one lane or two-or-more lane loaded cases. This discrepancy should be addressed for light rail bridges. Research has been conducted to examine the fatigue behavior of railway bridges. Tobias and Foutch (1997) evaluated the fatigue resistance of riveted railway bridges using a reliability model combined with a test database. The performance function of the model was developed using Minerâs damage rule in a Gaussian probability distribution. A parametric study was carried out with a 40-ft simply-supported plate girder bridge subjected to freight load, including 1,600 simu- lations. It was found that train weight and spacing were crucial factors contributing to the fatigue life of short-span bridges. Specific design guidelines are limited for the fatigue of light rail transit. Further, existing documents are arbitrary without rational background. For instance, AECOM (2008) states fatigue design load should be 75% of HS20, and UTA (2010) recommends fatigue design be conducted using the stress at three million cycles. Summary: A variety of live load models were used to design light rail bridges, depending upon transit agencies. In terms of load effects, some design guidelines recommended AASHTO LRFD BDS be used or some suggested the AREMA manual be employed. Discrepancy was found in these two design documents (e.g., live load distribution) and corresponding provisions might not be applicable to light rail structures, given that their load models were different from light rail train load (e.g., light rail load is lighter than E-80 of the AREMA and heavier than HL-93/HS-20 of the AASHTO). Several transit agencies developed design guidelines with their own live load models. A standard live load model for light rail transit is required to achieve uniform design outcomes in the nation.
12 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads 2.5 Train-Structure Interaction Train-structure interaction generates several force components to be considered in designing railway bridges, such as impact, rail break, and centrifugal forces. Endeavors have been made to examine these forces associated with train configurations and bridge properties. 2.5.1 Impact or DLA Railway dynamics has a long history over a century. Various approaches have been used from analytical modeling to explicit finite element modeling (Timoshenko 1926; Hou et al. 2003; Gu et al. 2010). Dynamic factors for the displacement and bending moment of bridges are pro- portionally increasing with train speed (Flener and Karoumi 2009). Impact forces, therefore, need to be added to the axle loads of a train when design is carried out. Impact factor or DLA for light rail design varies from 10% to 40% of train load in the vertical direction, depending upon transit agencies. Metro (2007) specifies DLA ranging from 30% to 40%, while AECOM (2008) merely states that loads shall be increased for dynamic effects. A couple of light rail transit agen- cies indicate horizontal impact (e.g., Utah and Massachusetts: 10% of axle load acting normal to the track), although most agencies do not consider this force component. This 10% horizontal force appears to be arbitrary and empirical, which may not be obtainable accurately. Refined analysis may generate uniformly applicable DLA as is for the case of AASHTO LRFD BDS. The most widely used expression for DLA or impact is: DLA R R R dyn stat stat ( )= âï£«ï£ ï£¶ï£¸ Ã100 % (2.1) where Rdyn and Rstat are the maximum dynamic and static responses of the bridge, respectively. If a massive substructure is connected to a superstructure, impact may be ignored (AREMA 2008). Other expressions such as Eq. 2.2 are alternatively used to quantify dynamic effects (Wipf et al. 2000): =DAF maximum dynamic deflection maximum static deflection (2.2) where DAF is the dynamic amplification factor. The Eurocode (CEN 2002) suggests DAF = 1.141; however, the Swedish standard (BV Bro 2006) shows DAF = 1.134. Other researchers recom- mended different values; for example, DAF = 1.22 (Wipf et al. 2000) and 1.45 (Flener and Karoumi 2009). Transient impact force generates higher frequencies and magnitudes than static force during a very short duration (e.g., 2 ms to 10 ms, Lee et al. 2005). Such amplified forces play an important role in design of railway structures, because track components (e.g., rail, sleepers, and fasteners) may be damaged by excessive distress, thereby influencing the safety of passengers. To reduce dynamic impact, hyperelastic pads are sometimes placed underneath track rails (Kim et al. 2009). For design convenience, DLA (or impact) is considered as an additional factor to increase static load. AASHTO LRFD BDS states an increase of 33% for highway traffic, whereas the AREMA manual specifies impact load I depending upon structure type and span length. The dynamic behavior of a wheel-track system may be solved in two distinct ways (Hou et al. 2003): â¢ Time-domain method: Various responses of wheel-track components (e.g., displacement, velocity, and acceleration) are solved in a time domain. â¢ Frequency-domain method: Receptance is engaged with external attributes using mathematical transformation, and the wheel-track interaction is solved without complex differential equations. For continuous bridges, the shortest span controls impact force (AREMA 2008). Although the AREMA design manual stipulates that impact force shall increase by 20% for steam locomotives, this requirement may not be applicable to light rail trains.
State of the art review 13 The following is a summary of selected papers concerning the impact behavior of railway structures. Dukkipati and Dong (1999) studied impact load for a wheel-track system using finite element analysis. Experimental data for model validation were provided by Newton and Clark (1979), which measured impact forces using strain gages in a time domain at a train speed of 73 mph: shear and bending gages were bonded at the neutral axis of rails and to the bottom flange of the rails, respectively. The impact forces obtained from shear strain differentials and wheel-rail contact were similar. The first peak impact force was sensitive to track mass. Several parameters affecting the impact force were examined (i.e., axle load, train stiffness, operating speed, ballast stiffness, tie mass, rail type, impact position, flat size, and longitudinal force). Hou et al. (2003) developed a time-domain-based finite element model to evaluate the dynamic behavior of an asymmetric wheel-track system. It was claimed that symmetric track conditions were rarely found on site, and geometric irregularities needed to be considered (e.g., misaligned rail joints, fatigue damage, surface roughness, and wheel flat). The train body modeled had 10Â° of freedom, including vertical and rotational degrees of freedom in each wheelset and trucks, and the two-layer track model had sleepers, rails, a ballast layer, and a subgrade. A wheel-rail adoptive contact model was used with linear springs (i.e., Hertizian contact theory). The development of wheel-track acceleration was related to impact on account of a dif- ference in mass between the rail and the train. Barke and Chiu (2005) discussed three meth- ods to monitor wheel impact: strain-based, accelerometer-based, and mechanical profile-based approaches. The first strain-based method measures the bending of a rail, and pre-calibration is required to establish a relationship between the applied load and strain (Kalay et al. 1992; Partington 1993; Johansson and Nielsen 2001). The second accelerometer-based method detects the motion of rails (Frederic 1978; Zhai 1996). Contrary to the strain-based method, this method can quantify the impact of the entire rail length between sleepers. Accelerometers can be posi- tioned to the top or bottom flange of a rail. The last method uses a relative position between the wheel flange and rail head. Several techniques (e.g., ultrasound and laser) may be employed to measure the elevation of each component. Gullers et al. (2008) performed field measurement to determine a critical frequency range for rails under high-speed train loading. The site included 10 stretches of track with a length of 0.63 mile. Train wheels were instrumented with eight strain gages at 45Â° apart per wheel to acquire wheel-rail contact force. The frequency range affecting rolling contact force was found to be from 100 Hz to 1,250 Hz. Nielsen (2008) simulated wheel-track interaction with frequencies varying from 20 Hz to 2,000 Hz. A couple of cases were studied: (1) impact load associated with wheel flats and (2) dynamic wheel-rail contact force along corrugated rails. Train models and tracks were linear, and constraint equations were used to couple the wheels and rails. Two types of tracks were com- paratively examined, rail pads and ballast/subgrade, with an axle load of 13.5 tons. Impact forces consistently rose with an increasing train speed up to 31 mph, beyond which impact tended to stabilize. Remennikov and Kaewunruen (2008) reviewed the impact behavior of rail structures with a focus on rail-track interaction and abnormalities accelerating impact (e.g., rail corruga- tion, wheel flat, welding and joints, and track imperfection). Gu and Franklin (2010) used the concept of structural articulation to evaluate the impact load of railway bridges. A two-span steel plate girder bridge was chosen for analysis. This 70-ft long bridge was loaded with a train set (306 kips) operated at a speed of 90 mph. The natural frequency of the girders was 5.54 Hz. An analytical model was developed to predict the bridge behavior. In the model, track irregularities were represented by a random stochastic method. It was recommended that multi-axle suspen- sion analysis be conducted to predict accurate dynamic impact. Some researchers studied train impact when geometric discontinuities were presented. Kassa et al. (2006) studied the effect of rail switches and crossings on wheel-track impact. A multibody system model was constructed to predict the dynamic interaction between the wheel and rail at a train speed of 38 mph, including train flexibility and track components.
14 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads Summary: Impact increased static load owing to dynamic amplification; however, it tended to converge with train speed. This implies that a threshold train speed exists in design of rail structures. Time- and frequency-domain methods were taken to analyze wheel-track dynam- ics. The response time of train impact was between 2 ms and 10 ms. A number of parameters influenced the impact force of a wheel-track system (e.g., train weight and speed, rail irregulari- ties such as flat and joints, and rail type). In situ impact was measured by various methods with strain gages and accelerometers. In light rail bridge design, impact factors varying from 10% to 40% are typically used. Some design provisions (e.g., AASHTO LRFD BDS and AREMA) state DLA or impact for highway vehicles or heavy-haul trains, whereas their applicability to light rail trains is not known. 2.5.2 Centrifugal Force An article of AASHTO LRFD BDS presents Eq. 2.3 to predict centrifugal force on bridges: (2.3) 2 C f v gR = where C = the centrifugal factor to be multiplied by the live load; f = a constant (4/3 and 1.0 for all load combinations and fatigue, respectively); g = the gravitational acceleration (32.2 ft/s2); and R = the radius of the traffic lane curvature. It is recommended that the centrifugal force be applied at a distance of 6 ft, and the multiple presence factors be used together. The AREMA manual states the following for centrifugal force applied at a distance of 8 ft above the top of rail: â¢ When a maximum speed is not specified: centrifugal force shall be 15% of each axle load without impact. â¢ When a maximum speed is specified: centrifugal force = 0.0117S2D, in which S is the speed (mph) and D is the degree of curve (central angle of curve subtended by a chord of 100 ft). Limited information was found on the centrifugal force of train load relative to that of high- way traffic load. Kravets (2005) evaluated the effects of bridge curvature along with a high-speed train. Several force components (e.g., centrifugal, gyroscopic, and tangential forces) were taken into consideration. A model was developed based on the Euler-Lagrange equation with kinetic parameters obtained from an experimental work. The distribution of internal dynamic load varied with train position and its length. Xia et al. (2006) examined the resonant response of a railway bridge subjected to lateral centrifugal force, employing an analytical dynamic model in conjunction with variable train speeds from 0 mph to 563 mph. The centrifugal force compo- nent affected bridge behavior, like the wind pressure that caused lateral vibration. Summary: Centrifugal force is generated when a train is operated along a curved bridge. Analytical models were developed to predict the intensity of this force with variable train weights and operat- ing speeds. Existing design documents presented equations for practitioners to use when designing curved bridges. The applicability of these equations for light rail trains needs to be studied. 2.5.3 Longitudinal Force Train acceleration and deceleration can generate additional external load. The behavior of sup- porting structures is influenced accordingly. In general, a conductor slowly increases train speed; hence, the effect of acceleration may not be significant. By contrast, braking induces considerable
State of the art review 15 distress to supporting members. A sudden reduction in train speed can impact rail components and bridge substructure (Azimi et al. 2013). The longitudinal force of the AREMA provisions is basically 15% of the Cooper load, based on a scenario of emergency braking (Foutch et al. 2006). Longitudinal force is typically distributed to the supporting structure and its components such as rails and bearings. The behavior of a bridge superstructure due to longitudinal forces should be separated from a bending effect caused by train load (Kumar and Upadhyay 2010). Dynamic braking force may vary by train types. For example, the traction force of AC traction motor diesel- electric locomotives is about 50% greater than that of DC traction motor locomotives (Foutch et al. 2006). Several modeling techniques were proposed to study the effect of train acceleration and deceleration: moving mass and beam model (Fryba 1972, Stanisic 1985), numerical direct integration (Inbanathan and Weiland 1987, Neves et al. 2012), and modal superposition method (Hwang and Nowak 1991, Fryba 1996). Uppal et al. (2001) conducted a longitudinal force test on a 2,196-ft long railroad bridge. The test train was composed of 120 cars with two locomotives at both ends, operated at a speed of 24 mph. Braking action was made to generate longitudinal forces. Test results showed that the forces were well distributed to bridge piers. The maximum shear force for a single pier ranged from 11 kips to 39 kips. Foutch et al. (2006) tested a coal train to examine longitudinal forces on a trestle bridge. The bridge was 2,198 ft with 28-ft precast concrete spans supported by steel H-pile piers. The in situ data measured were longitudinal rail forces, moments at piers, displacements between the abutments and end spans, and the shear strains of selected piers. A total train load of 360 kips was applied at an operating speed of 24 mph. A braking force of 160 kips was measured. Another aspect of the test was to investigate the effects of air braking over a length of 1.2 miles, which were compared with those of dynamic braking. The air braking force was more distrib- uted to the bridge than was the dynamic braking, so that the maximum shear force transferred to the substructure was less. The longitudinal force of the air braking was, however, 53% greater than the force of the dynamic braking. It should be noted that the dynamic braking did not mean emergency braking that causes a significant increase in deceleration force. The provisions of the AREMA manual were evaluated with the test data. The measured longitudinal force was up to 5% of the train weight, which was less than the 15% of the AREMA provisions. Toth and Ruge (2001) studied the adequacy of modeling approaches predicting the behavior of railway bridges under dynamic longitudinal loading. A spectral assessment was performed by comparing eigenvalues of the bridge models. Appropriate mesh adaptation was important for the dynamic analysis of railway bridges. Handoko and Dhanasekar (2006) presented the inertial reference frame method to quantify the effects of longitudinal force on the dynamic behavior of railway wheelsets. A braking force mechanism was discussed: FBeff = hFCTit - FRib, where FBeff = effective braking force; h = brake rigging efficiency; FCT = brake cylinder piston thrust; it = total brake rigging ratio; FR = counter force exerted by slack adjuster; and ib = truck brake rigging ratio. The wheelset was subjected to three speeds (33 mph, 56 mph, and 68 mph). By adjusting a braking force, various levels of wheelset braking were simulated (e.g., wheelset dynamics under heavy braking). Pugi et al. (2007) modeled the longitudinal behavior of freight trains in multiple braking phases. Train couplers were emphasized because many freight trains are connected to transport commodities. The developed model was validated with published experimental data having 30 freight trains hauled by two locomotives. Braking forces were cal- culated using a pressure in brake cylinders. Emergency braking was attempted and multi-wave longitudinal load was obtained: the maximum load was approximately 67 kips at the third peak. Huang et al. (2010) examined the longitudinal dynamics of trains along with an asynchronous braking system. A dynamic model was formulated using the equation of motion, and the train model was operated at a speed of 50 mph. A reduction of 40% in speed was simulated to represent braking action. The variation of longitudinal force was then reported. Kumar and Upadhyay (2010) reviewed several train-bridge interaction models, including longitudinal force
16 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads effects. Since each model had its own advantages, careful selection of appropriate models was sug- gested. Hurlebaus (2011) reported longitudinal stresses in rails. A technique called the polarization of Rayleigh surface waves was incorporated to determine the stresses, which were compared with laboratory test results. It was stated that the damage of the rails could be reduced if a longitudinal stress was controlled. Oprea (2012) developed an algorithm to study the longitudinal dynamics of trains based on the generalized matrix-inverse method. A relationship between friction and sliding velocity was established. With a change in velocity, the variation of friction force and displacement was predicted. Azimi et al. (2013) developed a numerical model to estimate the effects of train deceleration on the behavior of a bridge structure (L = 50 ft), with an emphasis on deflection and acceleration at midspan. The model train (42 ton) having 10Â° of freedom was simulated at fric- tion coefficients ranging from 0.1 to 0.7. A sliding effect was taken into consideration. Horizontal inertial forces due to braking were converted to vertical contact forces using a pitching moment. Train velocity and acceleration influenced bridge deflection at midspan and support reaction, respectively. A design factor entitled the acceleration parameter was introduced. Summary: The acceleration and deceleration of trains cause longitudinal forces. Braking force was distributed to supporting structures and their components, such as rails and bearings. In some cases, the implications of air braking and dynamic braking were compared. Although a few experimental programs were reported, most studies were concerned with predictive modeling. Several modeling methods were proposed to predict the forces induced by train acceleration and deceleration (e.g., moving mass and beam model, numerical direct integration, and modal superposition method). Test programs reported that the AREMA provisions on longitudinal force were conservative. The majority of research papers in this subject was dedicated to highway traffic, rather than train loading. 2.5.4 Rail Break Rail break typically takes place because of a thermal change in track rails. A broken rail is defined as âa rail from which a piece of metal becomes detached, causing a gap of more than 50 mm (2 in) in length and more than 10 mm (0.4 in) in depth in the running surfaceâ, accord- ing to the International Union of Railways (UIC 2002). TCRP Report 155 (Parsons Brinckerhoff et al. 2012) denotes that rail break may happen near expansion joints, poorly welded locations, or other weak spots in a rail. Once rail break occurs, a discontinuity is created along the rail. Typical consequences of rail break encompass increased dynamic amplification, derailment, and longitudinal forces at bearings. Table 2.1 summarizes existing design provisions related to rail break. Wu and Thompson (2003) modeled wheel-track interaction at rail joints, where impact force accelerated. A relative displacement excitation approach was employed to study the interaction. The solved model prediction in time domain was converted to frequency domain to extract rail roughness. The presence of rail joints influenced the magnitude of wheel-train impact, and their contribution increased with increasing train speed. Wen et al. (2005) simulated the impact behavior of a wheel-track system at a rail joint using a commercial explicit finite element pro- gram coupled with an implicit analysis. The effects of train load and operating speed (19 mph) on contact forces were examined. The behavior of joint regions was complex owing to the wheel-rail interaction. It was found that axle load substantially influenced the impact of rail joints (i.e., the maximum impact load was 2.6 times static load), whereas train speed was less influential. Kumar (2006) reported a rail deterioration process, including rail break. Several factors influencing rail degradation were identified, namely, rail age, axle load, train speed, traffic density, rail-wheel interaction, track properties, and operational environments. An approach to rail break predic- tion was discussed, supported by in situ data along with Million Gross Tons (MGT). To esti- mate the occurrence of rail break, a reliability program established with a Weibull distribution
State of the art review 17 was developed. Okelo and Olabimtan (2011) constructed a three-dimensional finite element model to determine bearing forces resulting from railâstructure interaction and to quantify a probable rail break gap. A two-track eight-span bridge was modeled using a frame analysis software, whose rails and girders were subjected to a temperature variation range (DT) of 95Â°F. A maximum bearing force of 52 kips was obtained due to the thermal loads with and without rail break. It was recommended that nonlinear analysis be conducted to accurately predict the thermally induced distress associated with rail break, rather than simple elastic analysis. Baxter and Nemovitz (2012) studied rail break caused by thermal load for two direct fixation bridges in Denver, CO. Temperature variation ranges were 70Â°F and 125Â°F for rails and 20Â°F and 55Â°F for structures. Spring elements were involved to simulate railâstructure interaction. The calculated rail break gap length was from 1.8 in. to 3.3 in. (from design perspectives, the maximum rail break State Provision Arizona Consideration shall be given to the impact loading from a rail break. The design shall limit the rail gap due to a rail break. California The final design of structures shall consider the possibility of any one CWR breaking under a tensile load of 200 kips. The break will be restrained by a longitudinal restraint force in the range of 1,600 pounds to 2,200 pounds per rail seat assembly. The structures will be designed for the possibility of only one rail break at one time. Structures shall be designed to resist the lesser of 200 kips from the rail break or the total available restraint available from the rail seat assemblies on the structure for that rail. Rail seat assemblies will be spaced typically at 30 in. on-center except at bonded rail joints and at special trackwork. At special trackwork locations, design details for anchoring rails using the same type of rail fasteners as the typical structures shall be provided. Colorado The analysis shall include evaluation for the condition of continuous rail and for the condition of one broken rail. As a minimum, the broken rail condition shall be investigated for rail break at any rail and at any abutment or other bridge expansion joint location, and at the location of maximum rail stress due to curvature for curved structures. The rail break gap shall be limited to 3 in. maximum. Massachusetts For direct fixation track, provision shall be made for longitudinal forces due to a rail break. Forces from a single broken rail at any one time shall be applied to the structure. Longitudinal break force shall be based on the maximum temperature differential in the rail. The mobilized forces in the structure are equal to the maximum restraint force in fasteners of the broken rail until the thermal force is equalized. The maximum allowable longitudinal gap in a rail due to rail break shall be 2 in . The structure shall be designed to include horizontal forces at the fixed bearing due to the summation of each rail fastener's longitudinal restraint. The structure shall also be designed to include a twisting moment in a horizontal plane at the height of the low rail due to opposing directions of forces in the broken and unbroken rails. Minnesota Structures shall be designed to accommodate the temporary loads associated with rail replacement. In addition, the structures shall be capable of adequately maintaining a broken rail with not more than a 4-in. gap at any one rail supported by the structure. Utah After a rail break occurs, the rails adjacent to the point of break will move apart creating a gap until the cumulative restraints developed by the rail fasteners are large enough to resist further movement. As the rail slides through the fasteners, the force in the rail near the point of rail break reduces to zero. The forces in both the rail and structure then will increase as the rail continues to translate until maximum longitudinal restraint is achieved. The resulting rail pull apart gap and forces shall be calculated based on extreme conditions with the maximum temperature drop and the lowest restraint capabilities of the fastener. Washington Aerial structures shall be designed to accommodate the temporary loads associated with rail break and rail replacement. In addition, the Link aerial structures shall be capable of adequately maintaining a broken rail with not more than a 2-in. gap at any one rail supported by the structure. Table 2.1. Design provisions for rail break.
18 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads gap allowed was 3 in.). The stiffness of longitudinal fasteners did not influence the rail break gap. The predicted rail break lengths were compared with existing empirical equations. Extreme Event III defined in the RTD design manual (RTD 2013) was adopted for a load combination: a load factor of 1.0 for rail break force. Summary: Thermal load can cause a local discontinuity in constructed rails, which is called rail break. A number of parameters were associated with rail break (e.g., fastener stiffness, tem- perature variation, rail condition, traffic frequency and weight, and operational environment). The occurrence of this event increased DLA and could cause train derailment. Longitudinal forces induced by thermal loading were another interest in understanding railâstructure inter- action. Although these force components were transferred to substructure, their effect was not significant. Finite element models were developed to investigate the implications of rail break. Several transit agencies specified requirements for rail break in light rail bridges, whereas a con- sensus was not made yet. 2.6 Load and Resistance Factors for Rail Transit The measure of reliability is important to ensure the safe use of railway bridges. This is also valid for those carrying light rail transit. Extensive research has been conducted to calibrate load and resistance factors for highway bridge structures (Nowak 1995; Barker and Puckett 1997). Given that uncertainty is unavoidable in live load and construction materials, the concept of probability is incorporated. Safety index (b) is a convenient tool to quantify the level of safety in bridge structures: (2.4) 2 2 R E R E Î² = â Ï + Ï where R and E are the mean resistance and applied load effects to the bridge, respectively, and sR and sE are their standard deviations, respectively. NKB (1987) suggested three levels of safety indices for railway structures: b = 3.71 (low safety), 4.26 (normal safety), and 4.75 (high safety). CEN (1996) presented b = 3.8 to 4.7. AASHTO LRFD BDS requires b = 3.5 for new bridges; accordingly, load and resistance factors have been calibrated for bridge members. The AREMA manual states that railway structures can be designed pursuant to the ASD or the load factor design. With technological progress, a safety index tends to decrease (Ellingwood 1996). Cali- bration methods for the load and resistance factors of bridges are well established. For instance, the following is suggested by Barker and Puckett (1997): â¢ Step 1: Compile the statistical database for load and resistance parameters. â¢ Step 2: Estimate the level of reliability inherent in current design methods to predict the strengths of bridge structures. â¢ Step 3: Observe the variation of the reliability levels with different span lengths, dead load to live load ratios, load combinations, bridge types, and methods of calculating strengths. â¢ Step 4: Select a target reliability index based on the margin of safety implied in current designs. â¢ Step 5: Calculate load factors and resistance factors consistent with the selected target relia bility index. Various load factors were proposed by Eurocode 1 for railroad design (e.g., gself-weight = 1.35, gballast = 1.80, gprestress = 1.0, and gtraffic = 1.45). Snidjer and Rolf (1996) explain how the Eurocode was calibrated. Many design guidelines for light rail structures do not specify load and resistance factors dedi- cated to light rail trains, and recommend following AASHTO LRFD BDS or the AREMA manual (load factors only); examples include Central Corridor, Minneapolis, MN; Metro Light Rail,
State of the art review 19 Phoenix, AZ; UTA Light Rail, Salt Lake City, UT; and SoundTransit, Seattle, WA. It is, therefore, worthwhile to calibrate load factors associated with light rail transit loadings. Summary: Contrary to highway bridges, limited effort has been made for railway bridges in terms of reliability investigations and the calibration of load and resistance factors. Further research is necessary to develop these design factors for light rail bridges. 2.7 Summary and Challenges Unlike the design of highway bridges based on AASHTO LRFD BDS or railway bridges based on the AREMA manual, there are no broadly accepted standards or codes for bridges subjected to light rail transit. Many design manuals recommend AASHTO LRFD BDS be used for design- ing bridge structures carrying light rail trains or the AREMA manual be referenced, although light rail loading is not specified in these technical documents. The design guidelines developed by individual transit agencies are valuable, whereas their contents are empirical in many occa- sions. Unified design criteria and guidelines for light rail bridges should thus be developed. Technical contents are incomplete because standard light rail trains are not available and the design provisions of AASHTO LRFD BDS and the AREMA manual are not dedicated to light rail structures. Below is a summary of findings from the literature review: â¢ Most studies were concerned with heavy-haul and high-speed trains, while few studies were about commuter rails. Limited information is available on light rail structures. Experimental and numerical investigations were conducted to examine the behavior of railway bridges. Nonlinear finite element models or analytical models were frequently utilized. â¢ The dynamic and static responses of bridges carrying train loads were measured by strain gages, potentiometers, accelerometers, and load cells. Strain gages were bonded at the middle height of a rail to record train loading. Potentiometers and accelerometers were positioned underneath the top flange of the rail. Structural identification techniques such as stochas- tic subspace identification were employed to extract the dynamic characteristics of bridges loaded with trains. â¢ DLA or impact amplifies static load and needs to be considered when designing railway bridges. Existing design guidelines for light rail bridges showed a DLA of up to 40%. Although train impact was influenced by operating speed, it tended to converge beyond a certain threshold speed. Wheel-track dynamics was studied in time and frequency domains. Typi- cal response time for train impact was from 2 ms to 10 ms. Several parameters affected the dynamic behavior of railway bridges: train weight and speed, rail irregularities such as flat and joints, and rail types. Thermally induced rail break also increased the magnitude of DLA. â¢ Train deceleration causes longitudinal force. Literature reports that train speeds varying from 24 mph to 68 mph were used to study such a force component. The longitudinal force effects of trains were predominantly examined by numerical modeling. Some test programs reported in situ braking forces along with dynamic braking and air braking. The provisions of the AREMA manual on longitudinal force appeared to be conservative. Centrifugal force is a function of bridge curvature and train speed. The dynamic models mentioned above can also estimate the centrifugal force of a curved bridge. Empirical factors are used to calculate centrifugal forces in design. â¢ As in the case of highway bridges, light rail structures should be designed with a standard live load model. Load factors need thorough examinations, because each transit agency has its own factors arbitrarily taken (or modified) from AASHTO LRFD BDS. Some transit agencies recommend the ASD method. Although light rail transit is a promising transportation mode in urban areas and operated in many states, present knowledge and practice are limited. Of interest are live load and the
20 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads corresponding effects on the behavior of bridge structures, as well as forces related to trainârailâ structure interaction. To better utilize light rail transit systems and to advance the state of the art of light rail bridges, the following challenges should be addressed: â¢ There is a practical need for the design of light rail bridges carrying both light rail train and highway traffic loads, which is not actively considered in practice. A unified design approach is necessary. â¢ The absence of a standard live load (e.g., HL-93 of AASHTO LRFD BDS and Cooper E80 of the AREMA manual) results in various design products, depending upon transit agencies. A standard live load model should be proposed for design convenience and uniform outcomes, which will facilitate light rail bridge design. â¢ The live load effects of light rail transit such as load distribution, multiple presence, and DLA are not fully addressed. AASHTO LRFD BDS and the AREMA manuals are frequently referenced, although their live load characteristics are different from light rail trains. Refined investigations are required. â¢ Load factors for light rail structures are directly obtained or modified from AASHTO LRFD BDS. Because the loading characteristics of light rail trains are different from those of highway traffic, an assessment is imperative to propose alternative design factors, where necessary. â¢ The ambiguous article of AASHTO LRFD BDS should be updated: Art. 184.108.40.206 (âwhere a bridge also carries rail-transit vehicles, the owner shall specify the transit load characteristics and the expected interaction between transit and highway trafficâ) and C.220.127.116.11 (âIf the rail transit is supposed to mix with regular highway traffic, the owner should specify or approve an appropriate combination of transit and highway loads for the designâ).