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

prises the fill material of the embankment EEM and the other parameters that are needed for
the model, the values considered in the soil classification conducted by the UIC are used as a
reference. These values are listed in Table 1.

Table 1. Values of the geotechnical parameters considered in the model.

Material (/ ) (/ ) (°) (/ )

Steel for rails 2.1x10 0.3 - - 7500
11
Base plates 6.91x10 - - - -
7
Sleeper E1 8.01x10 0.25 - - 2500
10
Sleeper E2 5.02x10 0.25 - - 2500
10
10
Sleeper E3 3.69x10 0.25 - - 2500
Ballast 1.3x10 0.2 0 45 1900
8
Formation layer 0.8x10 0.3 0 35 2000
8
Material QS1 12.5x10 0.3 10000 10 2000
6
Material QS2 25x10 0.3 10000 20 2000
6
Material QS3 80x10 0.3 0.30 30 2000
6
TGM 160x10 0.25 - - 2300
6
Source: Gallego, 2016

EEM values of 12.5, 25 and 80 MPa have been employed. The value of 160 MPa, which corres-
ponds to an embankment that consists of cement-treated granular material (TGM), has also
been considered, as in the case of an embankment-structure transition. For the height of the
embankment hEM, the values 3, 5, 7, 10 and 15 m have been employed. The considered case
studies are determined by the possible combinations between the different values of EEM and
hEM. In this study, only the results obtained at 7 m are employed since that height is considered
to be average in the existing rail tracks.
The load per wheel considered corresponds to the static load of passenger trains on the Ma-
drid-Seville high-speed line (considering all types of trains); it increases to a value of 186.40
kN per axle.

2.2 Dynamic and static vertical rail track stiffness

From the resolution of each case study, the value for the vertical rail track stiffness K was
obtained as follows (refer to Esveld (11):

where Q is the vertical static load per wheel and z is the summation of all deflections in the
vicinity of the load measured on the head of the rail.
The value of K in the Prud’Homme formula is obtained from the dynamic load. Since this load is

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