SUMMARY
Determination of Actual Derailment Loads on Transit Bridges

Research Background, Objective, and Scope

Derailment loads in nearly all U.S. transit design criteria follow the AASHTO LRFD Guide Specifications for Bridges Carrying Light Rail Transit Loads, 2nd Edition [1] (hereafter the AASHTO LRFD Guide); in these specifications, vertical impact is defined as 100% of the static load of any truck in the train. However, this derailment impact load has never been verified with any technical basis.

The objectives of the research presented in this report are to (1) establish a reasoned basis for derailment loads on bridges and (2) develop methodologies that engineers can use to calculate realistic derailment impact loading to use in bridge design. The methodologies account for both vertical and horizontal loading. The research team selected methodologies with the goal of meeting the following criteria (subsequent to each criterion are corresponding explanations):

1. The methodology should be geared towards practitioners.
   • Easy to implement
   • Uses tools that bridge designers and/or analysts already use
   • Accounts for the fact that bridge designers and/or analysts have less information about rail cars
2. The methodology should be sufficiently conservative to use in bridge design.
   • Accounts for variability in rail cars, bridges, structural components of interest, and derailment scenarios
3. The methodology should be accurate across a range of derailment scenarios.
   • Validated by high-fidelity simulations
   • Based on engineering principles

To strike a balance between the three criteria, two types of methodologies were developed for vertical impact loading. The first methodology calculates an equivalent static load that can be used to represent the dynamic effects of derailment impact in static analysis models. This methodology is focused on meeting the first two criteria—it is the easiest to implement and provides a conservative approach consistent with the current bridge design tools. The second methodology calculates a force–time history that can be applied to the bridge deck in dynamic analysis models. This methodology is focused on the third criterion—although it is not as easy to implement as the other methodology since it requires dynamic analysis, it does have better accuracy. Bridge designers may use the first methodology (i.e., static) when a simpler analysis method is needed or when more conservatism is desired. Bridge designers may use the second methodology (i.e., dynamic) when providing more conservatism is not possible, such as the evaluation of an existing structure.

Static Vertical Impact Loading Methodology

The static vertical impact loading methodology is outlined in Figure 1. This approach is intended to be applied to one truck from an actual train—it is not intended to be applied to a “notional” live load that does not represent an actual train, such as Light Rail Transit (LRT)-16. Therefore, to calculate the static vertical impact load, the bridge designer will need to know truck loads, which would include the weight of the truck itself and the tributary weight of the carbody (a truck load is typically equal to two rail car axle loads).

Dynamic Vertical Impact Loading Methodology

The dynamic vertical impact loading methodology is outlined in Figure 2. The dynamic vertical impact load is an alternative approach to obtaining the dynamic response of the bridge due to the train derailment impact. This dynamic loading approach involves applying a force–time history to a bridge model at the location of impact. This approach can be used in any structural or finite element analysis (FEA) software that supports dynamic analysis.

Suggested Revisions to Current Codes

The research team suggests incorporating the static vertical load method into Section 3.2.4 (Derailment Load: DE) of the AASHTO LRFD Guide. The team expects that most bridge designers and analysts will prefer to continue using a methodology reasonably similar to the current practice. Vertical derailment impact load should be used with a load factor of 1.0. Vertical derailment impact load does not need to be applied simultaneously with any horizontal derailment impact loads. These suggestions are applicable to both direct fixation and ballasted track.

The research team does not suggest revising the AASHTO LRFD Guide to incorporate the dynamic vertical load method. However, agencies may incorporate this methodology to provide bridge designers and analysts with an option to perform a more accurate analysis with less inherent conservatism.

Long Description.

The illustration depicts the static vertical impact loading methodology, where an impact load is calculated as the product of DAF and P subscript t. The DAF is given by the equation two pi f subscript n multiplied by the square root of 2 H over g, where f subscript n is the bridge natural frequency, H is the vertical drop height, and g is gravity, times lambda subscript t subscript d times lambda subscript e times lambda subscript m. On the left, a table defines the Pulse Duration Reduction Factor lambda subscript t subscript d based on bridge natural frequency ranges, with values of 1.00 for frequencies less than or equal to 1.9 Hz, 0.90 for frequencies between 2.0 and 2.9 Hz, 0.80 for frequencies between 3.0 and 4.4 Hz, 0.65 for frequencies between 4.5 and 5.9 Hz, and 0.50 for frequencies greater than or equal to 6.0 Hz. In the middle, the Energy Restitution Factor lambda subscript e is defined based on impact location, being 1.1 at midspan, 1.2 at quarter span, and 1.3 at the pier. On the right, the System Mass Reduction Factor lambda subscript m is determined from the ratio of P subscript t over W subscript b r, where W subscript b r is the effective weight of the bridge. For ratios less than 0.10, lambda subscript m is 0.90. For ratios between 0.05 and 0.10, lambda subscript m is 0.95. For ratios greater than 0.10, it is 0.90. Notes clarify that P subscript t is the static vertical truck load, W subscript b r includes the bridge span or pier weight, depending on impact location, and that if impact occurs at a pier or abutment, then the weight of the pier or abutment should be added to W subscript b r.

Long Description.

An overview depicts the dynamic vertical impact loading methodology, where the applied force P subscript DERL of t is defined as a sinusoidal function: P subscript 0 times sine of pi t over t subscript d for time t less than or equal to t subscript d, and 0 for t greater than t subscript d. Here, t subscript d represents the pulse duration, given as 0.15 seconds. P subscript 0, the amplitude of the force, is defined by the equation P subscript t times pi over t subscript d times the square root of H over 2 g, multiplied by lambda subscript e and lambda subscript m. P subscript t is the static truck load, H is the vertical drop height, and g is gravity. A diagram illustrates the sinusoidal curve of P subscript DERL of t peaking at P subscript 0 within the duration t subscript d. Below, tables provide the Energy Restitution Factor lambda subscript e and System Mass Reduction Factor lambda subscript m. The lambda subscript e values are 1.1 at midspan, 1.2 at quarter span, and 1.3 at the pier. The lambda subscript m values are 1.00 when the load ratio is less than 0.05, 0.95 for ratios between 0.05 and 0.10, and 0.90 when the ratio exceeds 0.10. A note explains that P subscript t is the static vertical truck load and W subscript b r is the effective bridge weight, which may be half the bridge span weight unless impact is at a pier or abutment, in which case the full pier or abutment weight should be added to W subscript b r.

The research team also developed a methodology for applying horizontal derailment impacts; however, it does not suggest revising the AASHTO LRFD Guide to incorporate this methodology. The research for this project shows that vertical derailment impact forces are more significant than horizontal impact forces. The longitudinal braking loads prescribed by the AASHTO LRFD Guide govern the longitudinal derailment impact loads. The research does not justify modifying the barrier wall loads prescribed by the AASHTO LRFD Guide, and these loads govern the transverse derailment impact loads.

Research Approach

The research for this project began with an extensive literature review to gather information on the background and basis of the current design practice regarding train impact loads on bridges. The team also researched common derailment scenarios to design the study for this project.

The bulk of the project work involved a detailed analysis of derailment scenarios. It is impractical to conduct this research through physical derailment impact testing because of the scope, scale, cost, and safety concerns. Over the past two decades, advances in computational capabilities have made detailed analysis of combined bridge–rail vehicle impact interactions practical. The research for this project utilized LS-DYNA to perform numerical simulations of train derailments. Figure 3 illustrates the research team's detailed analysis methodology with a light rail vehicle (LRV) on a bulb-tee girder bridge.

The analysis was performed in phases, building in complexity with specific effects studied at each stage and dominating effects carrying over to the next stage. The research was divided into three sequential modeling tasks:

1. An explicit derailment simulation on a rigid surface was performed to determine the kinematics of the train car upon impact.
2. The kinematic parameters extracted from the derailment simulation were then applied to vehicles impacting a simplified bridge model.

Long Description.

The illustration depicts a light rail vehicle traveling at a velocity of 40 kilometers per hour on a bulb-tee girder bridge. The rail break is located slightly off the midspan of the bridge, and an arrow indicates the approximate distance from the break to the impact location, which was determined from previous analyses. A detailed section view of the track with the train is shown below it, illustrating the internal structure of the track and the vehicle. The bridge is supported by vertical piers beneath the girder, and the rail extends along the full length of the span. The setup is intended to simulate and evaluate the dynamic effects caused by a sudden rail break while the train is in motion.

3. A subset of the same train derailment scenarios was then simulated on detailed finite element bridge models.

These derailment simulations were used to validate the static and dynamic derailment impact methodologies described in the previous sections.

Key Findings from Bridge Derailment Simulations

The research team performed train car derailment simulations to study the effect of derailment on bridges. These simulations progressed from simplified bridge and derailment modeling to more detailed bridge modeling. The first round of simulations modeled the bridge as a rigid surface, which was done to understand the rigid body kinematics of the derailment in isolation from its effects on a bridge structure. The second round of simulations modeled the bridge as a simple single-degree-of-freedom (SDOF) system. It used rigid body kinematics from the first round of simulations as the initial conditions, which was done to understand the primary effects of the principal variables (i.e., derailment scenario, class of rail car, weight of passenger loads, and bridge frequency). The third and final round of simulations included detailed modeling of bridges, with detailed train models in motion across the bridge before derailment. This final round of simulations was intended to have the greatest level of accuracy and to primarily use these results to inform the teamʼs proposed methodology for derailment loading in bridge design and analysis. The following are specific findings from the bridge derailment simulations:

1. Peak vertical rigid body velocities varied less than 40% for the different derailment scenarios, rail car classes, and passenger loads that the research team considered in its analysis. Peak rotational pitch rigid body velocities varied by as much as 90%. This result indicated that rotational pitch velocity is more sensitive to the variables than vertical velocity.
2. The peak displacement of the simplified SDOF bridge system did not vary significantly for the different derailment scenarios for a given rail car class and passenger weight. This result indicated that the type of derailment (e.g., single rail break, double rail break, rail climb) is not a primary consideration in determining the derailment loading in bridge design and analysis.

3. Increasing the stiffness of a bridge structure (and thus increasing its natural frequency) increased the dynamic amplification factor (DAF) on the bridge structure. This result indicated that the dynamic properties of a bridge structure are a primary consideration in determining derailment loading in bridge design and analysis.
4. The dynamic properties of a bridge structure vary based on the impact location. In the simulations, impacts occurring closer to bridge piers or abutments had higher frequency dynamic responses and higher contact force impulses. This result indicated that increasing the stiffness of the underlying structure effectively increases the coefficient of restitution for the derailment impact.
5. The dynamic motion of the bridge before the derailment impact did not significantly affect the peak bridge displacement due to the derailment impact. This result indicated that the derailment impact may be considered in isolation from the dynamic motion of the bridge because of regular train operation before the derailment.
6. The peak contact forces and impulses in the horizontal direction due to the derailment impact were much smaller than those in the vertical direction. Contact forces in the transverse direction were consistent with friction due to the static wheel load. Frictional forces in the longitudinal direction were of a smaller magnitude due to the wheel rotation. Governing horizontal impact forces do not occur simultaneously with governing vertical impact forces.
7. Compared to the industry practice of using 100% for the DAF, the detailed modeling of the research team indicates equivalent DAFs can range between 91% and 359% over the range of considered parameters.