DARTS-NL: Dynamic Analysis of Railway Track Systems

GENERAL INFORMATION

Introduction

Maintenance and design of railway structures is just like the maintenance and design of many other structures dependent on strength and stiffness of the components. To predict the behaviour of the structure we have to analyze the forces and the deformations by means of a structural analysis. The accuracy of this analysis is dependent on the accuracy of the input model and loads.

The simple single degree of freedom (SDOF) models of the structure already gives much insight; a somewhat more complicated model is the beam on an elastic foundation. Loads are modeled either static for the beam models or dynamic for the SDOF models. These models are kept simple for the sake of transparency and easiness to handle.

With the presence of advanced structural analysis programs we can analyze very complicated 3D finite element models, sometimes even with nonlinear properties. Sometimes this is useful, mostly the structure properties are too uncertain for the justification of such an analysis. There above the preparation of the model input and examination of the analysis results is much too much time consuming for the practical applications. Also for many research purposes these models pretend much more accuracy than the application requires.  

Figure 1

In reference to these observations the starting point for the development of the software program DARTS-NL has been the focus on simple models with a maximum of transparency and easiness to handle. Using PC’s these models can be more complicated than the SDOF systems and the simple beam on an elastic foundation, but not that complicated that the supply of relevant material and structure properties are prohibitive for an analysis.

Figure 2

Features

The program DARTS-NL has been written for the analysis of rail tracks loaded by vehicles moving on the track. Basically rail tracks are built up from stiff layers separated from each other by soft layers. A particular case is the classic rail track, a structure that is built up from rail, sleepers and ballast bed. Between rail and sleeper the inserted rail pad provides the soft layer, the ballast bed is usually the bottom soft layer and the sleeper is the stiff component. DARTS-NL can handle a maximum of three stiff and soft layers.

Surface deformations of the rail shape can be taken into account. The stiffness, damping and mass properties of the elastic foundation may vary dependent on the position. Because structural components can be removed from the DARTS-NL model a very flexible way of modelling, as shown in figure 3, is possible.

Model transition classic track to bridge

Figure 3  

Static loads such as dead weight, static point loads, static distributed loads and dynamic loads can load these structures. Dynamic loads are fixed time dependent loads and moving loads. For the numerical simulation of experiments, (the instrumented hammer test), the impulse load has been added.

To model a moving train two ways are possible. The simple way is to model the train by a series of moving loads, travelling on the rail. No interaction between train and track is considered. The more accurate way is to model the train by a moving structure, built up from masses, springs and dampers –see figure 5-. The interaction between train and track is caused by the roughness of the rail surface; DARTS-NL possesses the tools to model this.  

Figure 4

The structure is split up into a number of segments, where a segment has been built up from the structure dependent elements such as rail elements, slab elements, rail pads etc. The response to time dependent loads is calculated by a direct integration process, which evaluates the displacements at each time step. From these results stresses and forces are calculated following the common procedures of the f.e.m. techniques.

 The post-processing capabilities are subdivided into print output, which lists upon request the results, and graphical output. The graphical output capabilities comprise results dependent on geometry per time point or results dependent on time per function value. Envelopes about all time points may be requested too.

Interesting options are the ASCII output files, which are used for input into a MATLAB program. Because MATLAB is used for the processing of experimental data these results can be matched directly with numerical results.

Figure 5

Applications

DARTS-NL can be applied for many purposes. Up to now the following fields have been explored:

	Fixing material properties. The experimental data, obtained with an ‘instrumented hammer’ test are simulated both with laboratory experiments and field tests. This procedure provides a certain validation of the laboratory experiments. The parameters  fixed in this way, are used for more numerical simulations.
	Analysis of strength and stiffness of the rail track. The analysis  is performed to compute the dynamic contact forces between rail and wheel, to compute stresses in the rail and deformations of rail and supporting structure. A structural  analysis can be additional for the analysis of noise hinder, for maintenance problems and more.
	Simulation of vehicle behaviour. The traveler's comfort is dependent on the accelerations of the bodies of the train. Safety is dependent on the transverse displacements of the wheels. These aspects are easily analyzed with the use of DARTS-NL.