**Importance of vertical rail track stiffness on dynamic overloading: Limitations of the Eisenmann formulation**

*28/06/2018*

Since the development of high-speed rail in Europe in the 1970s, the vertical loads that are transmitted to the rail track by vehicles have been measured. The formulations obtained by Eisenmann and Prud’Homme are the most notable formulations of this period due to their extensive application.

The formula proposed by Eisenmann considered the quality of the rail track and was widely proven for maximum speeds of 200 km/h. With the emergence of high speed trains, Eisenmann proposed a modification to the previously proposed formula to adapt it to the case of high-speed vehicles and lines.

Additionally, the formula of Prud’Homme is important because it introduces new criteria and reveals how the vertical rail track stiffness, the unsprung mass of the vehicle and the quality of the rail track, in addition to the speed of the vehicle, affect the dynamic overloads.

As expressed by this formula, for a given speed and rail track quality, different geotechnical and geometric compositions of infrastructure, which determine the stiffness, cause different dynamic overloads. This fact was not considered in the Eisenmann formulation, exposing its limitations.

The objective of this article is to analyze these limitations; for this analysis, a threedimensional (3D) finite element model of the rail track will be employed to calculate static and dynamic stiffness and obtain the dynamic load values for different types of infrastructure. These results will enable us to analyze the relationship between the strength characteristics of the rail track and the dynamic coefficientCd, which is understood to be the ratio between the total dynamic loads and the static loads that are transmitted to the rail track.

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