A General Finite Beam on Tensionless Foundation Model for Rail Track Characterization and Evaluation

Rail infrastructure plays an important role in freight and passenger mobility, and the assessment of rail track structure depends critically on understanding how the rail interacts with the supporting foundation. When rail support degrades (e.g., due to ballast fouling, settlement, etc.), the rail exhibits greater localized deformation that can lead to serious deleterious conditions. Track modulus represents a fundamental diagnostic measure of rail support, encompassing the vertical stiffness characteristics of the foundation and its resistance against downward rail movement. Existing track modulus characterization methodologies typically comprise deflection measurements of railway track (e.g., tie deflections) under known loads. Track modulus estimations result from analyzing deflection and load under assumptions of a traditional Winkler foundation, which can oversimplify mechanic relationships. Specifically, in the context of rail–ballast–subgrade interaction, a tensionless foundation permits gap development which can occur as track structure separates from the supporting ballast; additionally, track modulus may vary along the track length as conditions vary spatially. This paper presents a general analytical solution of ballasted track support characterization based on an iterative algorithm for the static response of a finite beam resting on a tensionless Winkler foundation. The method relates to multiple loads (e.g., concentrated axle loads and distributed self-weight), deflection along the track, and track condition through singularity functions, superposition of discrete support springs, and moment–curvature relationships. The model estimates rail deflections, lift-off points and shear and moment diagrams along the track. The technique permits: (1) validations against benchmark solutions and previously published results, (2) estimations of track modulus from known loads and measured deflections, and ultimately, (3) a framework for designing and processing sensor data streams for use in analyses and evaluations of railway track structure.