Analytical Elastic Modeling of Rail and Fastener Longitudinal Response

Abstract

The rail fastening system plays a critical role in maintaining proper railroad track geometry by transferring vertical, lateral, and longitudinal forces from the rails to crossties. Broken spikes in elastic fastening systems have been linked to inadequate transfer of longitudinal loads, posing a safety risk for timber crosstie ballasted track. Longitudinal track demand caused by passing trains has been investigated in previous research, but the magnitude and distribution of longitudinal fastener loads is not well understood or documented. To address these track component failures and improve fastener design, this paper presents a validated analytical model that estimates longitudinal rail seat loads, advancing current formulations to focus specifically on the rail seat. The validated method was used to quantify the distribution and magnitude of longitudinal loads in both the rail and fastening system caused by passing trains. Further, this paper quantifies the effect of track stiffness, number of powered locomotives, and wheel spacing on these distributions and magnitudes. This information provides valuable insight into the specific type of spike failures that have led to at least ten derailments and the requirement of manual walking inspections on multiple North American heavy axle load railroads as detailed in this paper. Further, this method can be used to quantify the longitudinal fastener loads for different track conditions to advance the mechanistic-empirical track design philosophy for elastic fastening systems.

Analytical Nonlinear Modeling of Rail and Fastener Longitudinal Response

“…Dersch et al quantified the vertical, lateral, and longitudinal rail and fastener loads at one given location ( 32 ), and Khachaturian et al quantified the effect of fastening system stiffness on longitudinal fastener load magnitude ( 17 ). However, in both cases, the researchers leveraged a one-dimensional (1D) analytical model that was validated by Trizotto et al’s limited model ( 33 ).…”

“…Additionally, track resistance is simplified by representing the fastener and ballast as a single, combined spring. This approach was further investigated by Trizotto et al, who focused on the effect of longitudinal train loads on fastener and rail loads ( 33 ). However, this model only accounted for the linear approximation of the load-displacement response of the track, and thus did not account for slip or the interaction of the applied vertical load.…”

“…Illi3D was validated by comparing the rail load, fastener rail displacement, and/or fastener load to two field-validated models found in the literature: an analytical linear model developed by Trizotto et al ( 33 ) and an approach that accounts for the nonlinear behavior of track developed by Samavedam et al ( 36 ). The Trizotto et al model was selected to validate the linear behavior of Illi3D, as it had been validated using revenue-service field data and output rail load, fastener load, and rail displacement ( 33 ). The Samavedam et al model was selected to validate the nonlinear response of Illi3D, as it had been validated using field data from the Transportation Technology Center ( 36 ).…”

Quantification of vertical, lateral, and longitudinal fastener demand in broken spike track: Inputs to mechanistic-empirical design

“…This value is comparable to measured longitudinal modulus of vertically loaded ballasted track sections 38 and is believed to bound actual field conditions. Further, Trizotto et al 54 found that while there is a direct nonlinear relationship between longitudinal track modulus and fastener loads, a quadrupling of modulus was required to see a 30% increase in fastener load. Therefore, it is reasonable to believe that any small changes in longitudinal track modulus will have a small effect on the longitudinal fastener loads.…”

“…The analytical method developed by Kerr 27 and expanded by Trizotto et al. 54 quantifies longitudinal rail seat loads by assuming they are proportional to longitudinal rail displacement Equation (1) in the condition that there is no slip at the rail-fastener interface. Moreover, a parametric study was conducted to identify the effect of the superposition of multiple wheel loads and varying track stiffness.…”