An infinitely long Euler-Bernoulli beam resting on a tensionless Winkler foundation is considered. Steady-state solutions are obtained for a downward directed concentrated force moving with constant speed. First, the critical load necessary to initiate separation of the beam from the foundation is determined for a range of speed. For loads greater than critical, one or more regions of noncontact can be expected to occur. Closed-form solutions of the differential equations are obtained in terms of local coordinate systems which significantly reduces the coupling among the various regions. The extent and location of the noncontact regions, as well as the corresponding beam deflections, are then determined for a range of force and speed. The results show that many solutions are possible and the final determination is based on an energy criterion.

With the first major installation in North American railroads during the 1960's, concrete ties were believed to last longer than timber ties and have the potential for reduced life cycle costs. However, their characteristic response to initial pretension release as well as dynamic track loading is not well understood. In North America, concrete ties have been found vulnerable to rail seat deterioration (RSD), but the mechanisms contributing to RSD failures are not well understood. To improve such understanding, a comprehensive computational study of the tie response to dynamic track forces is needed. This paper presents an initial research effort in this direction that models concrete crossties as heterogeneous media in threedimensional finite element analyses, i.e., the prestressing strands, concrete matrix and the strand-concrete interfaces are represented explicitly.Damaged plasticity models are employed for the concrete material, and linear elastic bond-slip relations, followed by damage initiation and evolution, are adopted for the strand-concrete interfaces. Further, the ballast is modeled with an Extended Drucker-Prager plasticity model, and the subgrade is modeled as an elastic half space. All material parameters are obtained from the open literature. Currently the rail fastening systems are not included in modeling.Two loading scenarios are simulated: pretension release and direct rail seat loading. The modeling approach is able to predict the deformed tie shape, initial interface deterioration, the compressive stress state in concrete and residual tension in the strands upon pretension release. The transfer lengths of the prestressing strands can be readily calculated from the analysis results. Further predicted are the rail seat force-displacement characteristics and the potential failure mode of a concrete crosstie under direct rail seat loading. The responses of two railroad concrete crossties with 8-strand and 24-wire reinforcements, respectively, are studied using the presented modeling framework. The analyses indicate a potential failure mode of tensile cracking at the tie base below the rail seats. The results show that the 24-wire tie is better able to retain the pretension in the reinforcements than the 8-strand tie, resulting in slightly stronger rail seat force-displacement characteristics and higher failure load. The effects of the load application method and the subgrade modeling on the predicted tie response are further studied.

Concrete tie rail seat abrasion/deterioration (RSA) has been an issue since the inception of concrete ties. As a result of recent derailments involving abraded concrete ties on curved track, the Federal Railroad Administration set up a task force to study abrasion/deterioration mechanisms and develop automated detection methods using existing research vehicles. A portion of this study reviews historical development of concrete abrasion due to moisture or foreign materials incorporated under the rail seat that tend to abrade concrete ties evenly across the rail seat area. This report discusses a newly identified concrete tie deterioration mechanism characterized by material loss in a triangle toward the field side of the rail seat, resulting from wheel rail interaction involving track geometry variations.The NUCARS™ model was used to evaluate the vertical and lateral loading at one of the recent derailment sites using the track geometry measured approximately one month before the derailment. Wheel loads predicted from the model, based on P-42 Amtrak Locomotive, were used to evaluate the pressure distribution at the rail concrete tie interface and were compared with allowable design bearing pressure for concrete used in the manufacture of concrete ties. The results indicate that applied stress on the field side of a concrete tie due to outward rail roll can exceed the design values. Applied pressure distribution exceeding the design strength on the field side tends to abrade concrete ties in a triangular wear pattern that produces wide gage. Charts were developed to convert measured field side abrasion/deterioration to additional gage widening under an applied vertical load for identifying critical locations with wide gage defects. Further, techniques for field inspectors to detect, measure, and evaluate rail seat abrasion/deterioration (RSA) based on commonly used inspection technology are discussed.

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Recent gage restraint measurement system (GRMS) developments include the redesign of GRMS vehicles using a deployable split-axle instead of a freight truck mounted split-axle. This new test configuration results in boundary condition changes in the applied loads and split axle location, which influence test results. To ensure the equivalence of test results from these two systems, a comprehensive evaluation of the mechanistic basis for previous GRMS rulemaking was conducted and coupled with a fundamental investigation of factors influencing GRMS performance and inspection accuracy followed by field-testing to verify conclusions. Comparison tests between the original GRMS vehicle design and the redesigned vehicles identified the need to enhance the current gage widening ratio (GWR) equation to accommodate the increased range of vertical test loads represented by the different GRMS vehicles. GWR has been the leading source of test result discrepancies between the original GRMS design and redesigned vehicles over the same territory. The discrepancy between the inspections likely resulted from the increased range of vertical test loads represented by the distinct test vehicles, since GWR has treated vertical load as a constant. The Gage Widening Projection (GWP) parameter was proposed to replace GWR as a result of an ongoing investigation. GWR was originally developed as an indicator of fastener and tie performance by providing an extrapolated total gage widening deflection at a limiting load condition. Testing at the limiting load condition is not conducted because of the potential for damage to track components. A deflection at a lower load is extrapolated based on conservative track load-deflection behavior to the limit load, which represents an extreme but not unexpected gage widening event. The concept behind both GWP and GWR is similar. However, the GWP parameter includes vertical load as a variable, where GWR treated vertical load as a constant. The large variation in vertical load represented by the various test scenarios requires the consideration of variable vertical load in the extrapolation process to ensure an equivalent basis for inspection and safety. Based on analytical modeling and field-testing, the GWP parameter was found to perform more consistently between vehicles than GWR. A limiting condition based on a combination of deflection and load was selected to provide comparable inspection results and safety for both parameters. Additional testing has been conducted to further evaluate the data and indicates excellent performance of the GWP parameter, and perhaps merits further consideration regarding the limits.