**1. Introduction**

Transport volume is one major trigger of track maintenance [1]. For all structures, the loading drives damage, wear and overall system deterioration. In the case of railway track, the loading can be described in different ways. The number of trains gives information on the track utilization. This indicator is important in terms of capacity and linked issues like timetabling, but does not directly influence the maintenance as trains range from heavy freight trains to fast long-distance passenger trains to regional trains. The number of trains does have influence on the maintenance costs as most maintenance tasks need closed-down tracks. Line utilization specifies that the duration of track closures which in turn defines the possible length maintenance tasks can be carried out and thus impacts the cost per meter [2]. Additionally, so-called cost of operational hindrances emerges as trains are delayed, re-routed or simply do not run [3, 4]. Alternatively, the accumulated weight of trains can be applied which describes the intensity of track usage. The calculated gross-tonnage is widely used as an indicator for track loading and used for both classifying tracks [5] and defining maintenance frequencies [6–8]. Consequently, track maintenance cost is allocated to

gross-ton-kilometers [9, 10]. Also charging is based on this unit [11, 12]. On the other hand, tracks are designed, constructed and classified for a maximum permissible static axle load and a maximum allowed speed [13–15]. Forces are generally used as loading for the design of structures, and the static axle load at least approximates the vertical loading. Summarizing, the gross-tonnage is a feasible indication for the vertical loading and thus works as an approximation for ballast maintenance and possible rail fatigue. However, the gross-tonnage is definitely not sufficient for all damage mechanisms that are additionally triggered by lateral forces, slip and/or applied traction forces and thus for determining maintenance requirements for rails and turnouts. Moreover, gross-tonnage does not cover axle loads and speed.

There are some approaches covering those—and even more—aspects in calculating so-called equivalent gross-tons. In [16, 17] speed and high axle loads act as increasing factors, so does the aggressiveness of powered axles. [18, 19] additionally address the unsprung mass. Those models improve the description of vertical impacts, but still do not address lateral aspects. The approach of Burstow adds these in providing a damage index for the rails [20].

Finally, there are existing track deterioration models combining all the mentioned aspects [18, 21]. These models have been the inspiration for the proposed model in this paper which is close to the SBB-model. We specified the loading for crossings in turnouts and also added an additional damage term for the entire track structure being restored by a track renewal only. In the result section, we give several examples using this model for both the prediction of track maintenance and the effects of different train service and vehicles. These examples leave out the damage mechanisms for turnouts and the entire track and turnout structures so that one can follow the examples well.
