General principles

Klaus Lieberenz, Silvio Klügel, René Kipper

Interactions between vehicle and track systems
Interactions between vehicle and track systems

Railways are linear structures which are subject to static and dynamic loads from trains and different weather conditions such as rain, snow, frost and sunlight.

The loads from the trains are applied by the vehicles onto the rails in the track. The vertical, lateral and longitudinal forces resulting from the carrying, guiding and moving between wheel and rail, as well as from temperature, are shown in the adjacent figure. They must be taken and dissipated from the carrying system track-permanent way-subsoil (extended infrastructure) without damage to the environment, in order to guarantee safe operations with a high level of comfort at all times.

The permanent way, made up of track grid and ballast bed or support plate, ensures by a suitable frame stiffness as well as its resistance to slipping, longitudinal and transverse displacement, that it can accept the transverse and longitudinal forces.

The vertical forces are carried into the rails and the sleepers as ballast pressure σB into the multi-layer system ballast-subgrade-subsoil and distributed and dissipated into it.

Under the vertical wheel force or wheelset force P = Pstat+ Pdyn the rail or track experiences an elastic deformation s (spring deflection). This acts due to the flexural strength of the rails as an elastically mounted bearer in a way that the wheel force can be transferred to several sleepers (load distribution) and a reduction in the supporting point force and the ballast pressure.

Bearing system superstructure and subgrade
Bearing system superstructure and subgrade

The deformation behaviour of the layers under the sleeper is described by the ballast bed modulus C = P/s, which is a measure for the elasticity or stiffness of the trackbed system and the deformation behaviour of ballast, substructure and subsoil. The elastic depression of the rail (spring deflection) and the resulting rail foot stress must not exceed certain maximum permissible limits. To do this, the elastic depression of the rail at the top of the trackbed system (at the lower edge of the sleepers) must be limited, and minimum load capacities on the surface trackbed layer or formation are specified for this. On the other hand, the deflection must not fall below a certain level, in order to ensure the elastic load transfer with longitudinal Distribution of the wheel forces over the rail and, thus, avoid overloading of the supporting points and the ballast. Accordingly, in the table below indicative values are given for the ballast bed modulus C.  

The quality of the track bed


Ballast bed modulus
C [N/mm3]

Very bad

Very poor (soft clay, organic soils, homogeneous sand)    

< 0.05 


Cohesive semi-solid clay, silt, loose sand

≥ 0.05 


Clay and sandy stone chips     

≥ 0.10 

Very good

Fine gravel, protective layer

≥ 0.15

Concrete floor

Bridges, tunnels, ballastless track 

 ≥ 0.30


If the subgrade and the subsoil are very good or have low deformation (C ≈ 0.35 N/mm3), the depression s is low and the supporting point force or ballast pressure high. On the other hand, a bad subsoil (e.g. C ≈ 0.05 N/mm3) results in a great depression with a lower support point force and ballast pressure, however, the permissible stress in the rail foot may be exceeded due to the large elastic depression of the rail with corresponding bending line.

In the classic ballasted track the ballast bed works together with the subgrade and subsoil as a spring and damping element. With ballastless track (BT), the track is attached to a much stiffer, low settlement and deformation subgrade with attached base plates and supporting layers, so that an elastic element for suspension and damping under the rail or under the sleeper will be necessary.

It is typical of railway lines that both the effects (static and dynamic loadings from rail traffic) as well as the resistances in the trackbed system track-subgrade-subsoil vary widely depending on the passing trains, the speed, the condition of the track and on condition of the substructure influenced by weather and drainage. 

The track formation should therefore be produced and maintained in a way that

  • the track is available for the planned traffic load and passenger comfort is not restricted (availability),
  • fracture conditions in the structure or in the foundation soil are excluded (carrying capacity) and
  • deformations which arise in the track formation or are produced by it, are harmless to railway operation and third parties (practical suitability).

Stresses and deformations are produced in the track bed system and in its elements under the effect of this complex loading. Stresses must be assimilated by the given mechanical properties, whereas deformations must not exceed certain limits. Accordingly, for the top track-bed layer and the formation, requirements are placed on the deformation modulus, which must be metrologically verified at the time of acceptance.

Metrological verification of the modulus of elasticity by static (left) and dynamic plate pressure test (right)
Metrological verification of the modulus of elasticity by static (left) and dynamic plate pressure test (right) © GEPRO Ingenieurgesellschaft
© GEPRO Ingenieurgesellschaft

The elements of the track-bed system must be dimensioned in a way that the stresses acting on them σp can be absorbed without destructive or damaging deformations. The resistances are intrinsically dependent on the individual deformation moduli of the structural layers and the subsoil and the layer thicknesses. In the case of disturbances to the load transfer, there may be damage to the track structure, subgrade or subsoil and consequently problem areas.

You can find suitable specialist literature about the topic here:

Railway Ground Engineering

Handbuch Erdbauwerke der Bahnen

The second edition of Railway Ground Engineering has been completely reworked and extended. It provides comprehensive information on the essential relationships and dependencies between superstructure, substructure and subsoil subjected to the effects of the rail system. This manual is intended to be a practical reference book for everyone involved in the planning, design and construction of earthworks and other geotechnical structures, as well as a manual for low track maintenance . With the comprehensive presentation of the new partial safety concept in geotechnics, it is also a valuable aid for students and teachers at universities and technical Colleges.