Accounting for the type of freight wagons in determining the statistical distribution of vertical track forces generated by rolling stock with axial loads of 230.5–245.0 kN

Objective: when determining the statistical distribution of vertical forces acting on the track for heavy-haul rolling stock (230.5–245.0 kN axial load), it is essential to account for the specific type of freight wagons. Methods: vertical dynamic wheel-rail forces generated by freight trains with axial loads of 230.5–245.0 kN were measured experimentally. Subsets of the observed data were separated based on wagon type and operational conditions. Separate statistical analysis was performed on each subset. Results: statistical analysis indicated that wagon type (tank, hopper dispenser, or gondola) significantly affects the statistical form of vertical wheel-rail forces. In a number of cases, the actual distribution of vertical forces does not follow the normal probability distribution law (Gaussian distribution), which is traditionally assumed when estimating track stress-strain indicators. Thus, this mismatch may induce errors in stress calculations and, consequently, lead to inefficient decision-making in railway track maintenance planning. To address this, an analytical relation was derived – based on Weibull distribution – linking the maximum dynamic wheel-rail force Pmax (kN) to the parameters of the Weibull distribution functions. This dependence enables a more accurate determination of the area under the probability density curve of vertical forces. Practical significance: the findings of the study can be applied to improve the precision of stress assessments and to inform indicators of the stress-strain state of the track in accordance with the Methodology for assessing the impact of rolling stock on the track to ensure its reliability.