Determination of Actual Derailment Loads on Transit Bridges (2025)
Chapter: 3 Derailment Simulations on Rigid Deck
CHAPTER 3
Derailment Simulations on Rigid Deck
The objectives of the derailment simulations are to obtain realistic train motion during derailment and extract important kinematic parameters at the critical moment of impact.
3.1 Approach and Methodology
Following the rationale explained in Section 2.2.1, two derailment scenarios were selected: (1) rail break, corresponding to a discontinuity in one or both rails and (2) rail climb, corresponding to a situation in which the wheel laterally excurses over a continuous rail. An initial velocity of 40 km/h was applied at the start of the analysis, which corresponds to the onset of the derailment scenario. The modeling methodology for both scenarios is elaborated in the following sections.
3.1.1 Rail Break Modeling
The rail break scenario is simplified in the finite element model (Figure 8) through the introduction of an abrupt termination in one or both rails. Although rail breaks, gaps, and other defects are realistically limited to localized spots on the track instead of extending indefinitely, this idealized representation is sufficient in capturing all the similar bridge impact conditions initiated from the myriad of possible track flaws. This simplified approach adequately captures the key conditions affecting the ensuing train kinematics and impact mode of the rail car translating onto the bridge deck, the most important being the rail drop height.
A discontinuity in a single rail represents most rail defects, such as breaks and gaps, and can also apply to other track geometry and car defects (e.g., a broken wheel). Although less likely to occur, a discontinuity in both rails may represent other track geometry-related causes, such as wide gauge and buckled track. Both a single and double rail break on tangent track were simulated in the analyses.
To simulate curved track conditions, a separate analysis case was performed in which a centrifugal load was applied to the entire train. The centrifugal load corresponded to the angular velocity generated from the train traveling at 40 km/h in a curve with a radius of 500 ft. This simplified approach was taken to capture centrifugal effects from a curve without explicitly modeling a specific curved track section. A curve radius of 500 ft was chosen because it is the acceptable minimum for LRV track on tunnels and aerial structures [19].
3.1.2 Rail Climb Modeling
The second derailment type is rail climb, in which the lateral excursion of the wheel is sufficient to cause derailment. This derailment type represents various accident causes, such as train
Long Description.
The schematic illustrates a rail break scenario involving a low-floor light rail vehicle model traveling at an initial speed of 40 kilometers per hour along a curved rigid track surface. The track curve has a radius of 150 meters, equivalent to 500 feet, with the curve center marked. The centrifugal body force acting on the vehicle for the curved path is expressed as omega equals V subscript 0 over r. A rail break is identified on the track ahead of the vehicle. The section view AA shows a detailed wheel-rail interface of the train’s underbody aligned with the 115 RE rail profile, which has a vertical height of 165 millimeters or 6.25 inches. The vehicle and track interaction are analyzed for impact because of the break under curved motion, considering dynamic and centrifugal effects. A coordinate system with X, Y, and Z axes is shown in the lower left.
handling, obstructions, bearing failure, track–train interaction, excessive speed through a curve, and switch-related derailments.
The modeling approach for rail climb (Figure 9) was to impose a kink in the rail to induce wheel climb onto and over the head of the rail. Trial runs were performed with varying angles, and the simulated derailment characteristics were observed. A shallow angle of 0.5° was selected as resulting in the most realistic derailment, which represents both potential derailments at switches and from excessive lateral cornering forces through curves. The effect of restraining rails through curves is not considered to capture a conservative scenario. The intent is to capture the larger drop height and, thereby, the increased impact load when the wheel flange climbs the rail head before the vehicle derails.
3.1.3 Vehicle Speed
An initial speed of 40 km/h was selected for this study because it represents realistic operation conditions on a transit line, particularly for curved track scenarios in which the superelevation is not explicitly modeled. The impact load is not expected to be sensitive to horizontal speed on the tangent track.
Long Description.
The schematic illustrates a rail climb derailment scenario for a light rail vehicle traveling at an initial speed of 40 kilometers per hour. The vehicle approaches a rail segment with a manufactured kink, positioned at the interface between a curved and a tangent segment. This kink is intentionally introduced to force the wheel to climb the rail, simulating a derailment. The transition zone spans 5 meters in length, and the misalignment between the segments is 0.5 degrees. The top view shows the vehicle’s placement over the track, while the side and front views show the configuration of the kink in relation to the wheel and rail. Coordinate axes are provided to define orientation in three dimensions.
Long Description.
The schematic presents a low-floor light rail vehicle with labeled translational and rotational motion parameters extracted for analysis. The translational velocities include v subscript y for lateral velocity directed sideways and v subscript z for vertical velocity directed downward. Angular motion parameters are shown as omega subscript x for roll, omega subscript y for pitch, and omega subscript z for yaw. Each rotational parameter is illustrated with a curved arrow along the respective axis. The 3D coordinate system in the bottom left identifies the orientation of the x, y, and z axes. These parameters are used to evaluate vehicle dynamic response during derailment or impact scenarios.
3.1.4 Postprocessing
The goal of the derailment simulations is to obtain realistic rigid body translations in both vertical and lateral directions as well as rotations upon initial impact of the train on the rigid deck. Since the focus of the research is the ramifications of derailment impact on bridges and not the train itself, each train car can be simplified as a rigid body and its behavior examined in aggregate. The methodology to extract aggregated rigid body motions was accomplished using the constrained interpolation feature in LS-DYNA. The constrained interpolation keyword defines a single dependent node kinematically constrained through interpolation by the motion of a set of independent nodes (note that this modeling approach does not rigidize the independent nodes). A dummy node was defined at the center of gravity for each train car, allowing the extraction of translations and rotations of the node set encompassing all parts of the car about its mass center (Figure 10). In addition to velocities, nodal coordinates were also extracted. Both the deformed train and its instantaneous velocity were transferred as initial conditions to the subsequent impact analysis, which are described in Chapter 4. The nodal coordinates effectively define the position and attitude of the train at impact, and the velocities directly correlate to the impact energy on the bridge.
3.2 Results and Discussion
The motion during the derailment of the derailing train car can be extracted from the analysis in the form of velocity time histories. The impact velocities can be directly applied to the trains described in Chapter 4 to evaluate the response of the bridge system. An example of the velocity history during the derailment event is shown in Figure 11, which compares the baseline single rail break scenario across all four train car models.
Important parameters can be extracted from the velocity time histories, such as peak velocities at impact, which correlate directly to the momentum imparted by the derailing train car. The maximum vertical velocity of the train occurs following the initial impact and is a key parameter to capture from the derailment simulation. The angular velocities just before the initial impact of the front truck dictate how much momentum from the total train mass is imparted onto the bridge. The pitch of the train measures the rotation of the train about the lateral axis, and the first peak of the angular velocity plot corresponds to the first full impact of the front truck. Because most of the derailment scenarios are asymmetric, the imbalance in support from the rail as the first train wheel derails on one side causes rotation about the longitudinal axis, denoted as the train roll or twisting. The lateral rotation about the vertical axis, denoted by the term yaw,
Long Description.
A set of seven time history plots from 0.00 to 1.00 seconds, comparing the velocity, angular velocity, and rigid deck force for four vehicle types during a baseline single rail break: low floor LRV, high floor LRV, single level, and bi level. The first plot is labeled X horizontal velocity with a vertical axis from 0 to 10 meters per second. All vehicles start near 10 meters per second and remain constant across the plot. The second plot is labeled Y lateral velocity with a vertical axis from negative 1 to 0 meters per second. All vehicles start near 0 meters per second and show a gradual decline. The third plot is labeled Z vertical velocity, with similar scaling, and shows small initial values that sharply change near 0.40 seconds, particularly for singe level LRV, and after 0.50 seconds, especially for the high floor LRV. The next three plots show angular velocity in radians per second: roll, pitch, and yaw. All vehicle types show minor angular motion until impact, after which significant oscillations occur. The final plot is labeled rigid deck force with a vertical axis from 0 to 2,000 kilonewtons, showing minimal force until the respective impact points, where multiple peaks appear for each vehicle. Vertical dashed lines mark the initial impact times: single level at 0.40 seconds, low floor LRV at 0.53 seconds, high floor LRV at 0.54 seconds, and bi level at 0.62 seconds. These indicate when each vehicle interacts with the rigid deck, causing spikes in velocity changes and rigid deck force.
is particularly accentuated in the derailment case, with centrifugal load from a curve. Tables 1 and 2 show the peak vertical and pitch velocities of the entire mass of the derailing train for each analyzed scenario, which correspond most to the momentum transfer onto the bridge deck.
The following observations can be made from the overall kinematics of these derailment simulations:
- Some variance is present in peak vertical impact velocities across trains for the rail climb scenario. The variance in vertical impact velocities for rail break is less than that observed for the rail climb scenario.
- The maximum vertical velocity for all analyzed cases does not differ significantly, indicating that the constant rail height is a predominant factor in derailment physics.
- Pitch velocity is highly dependent on train car geometry, such as mass and inertial distribution.
- The wide range of peak impact velocities shows the complex nature of derailments and that the kinematics vary based on many different factors, such as train type and derailment conditions.
Long Description.
The table presents derailment scenario values for four rail vehicle types labeled Low Floor LRV, High Floor LRV, Single Level Commuter, and Bi Level Commuter. Under the derailment scenario Single Rail Break with AW0 Load, the values are 0.671 for Low Floor LRV, 0.675 for High Floor LRV, 0.660 for Single Level Commuter, and 0.557 for Bi Level Commuter. Under Single Rail Break with AW4 Load, the values are 0.665 for Low Floor LRV, 0.795 for High Floor LRV, and NA for Single Level and Bi Level Commuter. Under Single Rail Break with Centrifugal Effects from a Curve with AW0 Load, the values are 0.697 for Low Floor LRV, 0.817 for High Floor LRV, 0.558 for Single Level Commuter, and 0.612 for Bi Level Commuter. Under Double Rail Break with AW0 Load, the values are 0.713 for Low Floor LRV, 0.612 for High Floor LRV, 0.706 for Single Level Commuter, and 0.749 for Bi Level Commuter. Under Rail Climb with AW0 Load, the values are 0.728 for Low Floor LRV, 0.466 for High Floor LRV, 0.493 for Single Level Commuter, and 0.659 for Bi Level Commuter. Under Rail Climb with AW4 Load, the values are 0.763 for Low Floor LRV, 0.478 for High Floor LRV, and NA for Single Level Commuter and Bi Level Commuter.
Long Description.
The table displays derailment scenario data for Low Floor LRV, High Floor LRV, Single Level Commuter, and Bi Level Commuter. Under the scenario Single Rail Break with AW0 Load, the values are 0.072 for Low Floor LRV, 0.132 for High Floor LRV, 0.066 for Single Level Commuter, and 0.069 for Bi Level Commuter. For Single Rail Break with AW4 Load, the values are 0.097 for Low Floor LRV, 0.162 for High Floor LRV, and NA for both Single Level Commuter and Bi Level Commuter. For Single Rail Break with Centrifugal Effects from a Curve under AW0 Load, the values are 0.098 for Low Floor LRV, 0.143 for High Floor LRV, 0.066 for Single Level Commuter, and 0.056 for Bi Level Commuter. For Double Rail Break under AW0 Load, the values are 0.107 for Low Floor LRV, 0.130 for High Floor LRV, 0.066 for Single Level Commuter, and 0.084 for Bi Level Commuter. For Rail Climb under AW0 Load, the values are 0.139 for Low Floor LRV, 0.094 for High Floor LRV, 0.068 for Single Level Commuter, and 0.067 for Bi Level Commuter. For Rail Climb under AW4 Load, the values are 0.131 for Low Floor LRV, 0.120 for High Floor LRV, and NA for both Single Level Commuter and Bi Level Commuter.
