Interpreting differential settlement mechanisms at railway bridge–embankment transitions: a numerical case study

Differential settlement at railway bridge–embankment transitions remains a persistent maintenance challenge due to abrupt stiffness contrasts and complex load-transfer mechanisms within the track substructure. This study presents a representative numerical case study to interpret settlement evolution across a bridge–embankment transition and the influence of material stiffness transitions over time. A three-dimensional train–track–soil modelling framework combined with empirical settlement formulations is used to evaluate stress redistribution and cumulative deformation under cyclic train loading. Four transition configurations are examined, including an untreated case, an auxiliary rail solution, and two earthwork-based treatments with graded stiffness. The results show that settlement mechanisms vary spatially within the transition zone. Localised deformation near the bridge interface is associated with stress concentration, whereas settlement toward the open-track side is governed primarily by progressive subgrade compression. Substructure-based treatments modify long-term settlement evolution by promoting broader stress redistribution, while superstructure measures mainly influence early-stage response. The analysis also indicates that layered earthwork solutions may introduce additional deformation at internal material interfaces. Three complementary definitions of differential settlement are proposed to support interpretation of field observations and maintenance-oriented assessment of railway transition zones.