# Railway Track Stress-Strain Analysis Using High-Precision Accelerometers
## 4 Numerical Modeling  
In this work, in the environment of finite element modeling software ANSYS, a three-dimensional (3D) model of a section of a railway track was developed, completely repeating the configuration of a real operating track using intermediate rail fasteners of the ZhBR-65 Sh type with a rail R65 and crushed stone ballast 45 cm thick under the sleeper (see Figure 3).  
On the basis of the 3D model, we developed a finite element model of a railway track (see Figure 4). The details of the 3D model's development and the parameters of the numerical model are presented in [57; 58; 59]. The model includes about two million nodes, including the elements of a hexahedral shape, considering the symmetry properties and the specifications of all the necessary contact points and junctions. The model presents the real structure of the railway track line. In places of stress concentration, the size of the element was reduced to achieve the required accuracy of the simulation results.  
Figure 1: Effective locations of accelerometer sensors on a railway track line.  
Figure 2: Sensor equipment used for diagnostic instrumentation.  
We used both the junctions that allow slight movements of the interacting surfaces, and rigid couplings, depending on each specific case of contact point. Rigid embedding was modeled along the lower plane of the roadbed. The size of the element was selected empirically, taking into account the minimization of the computing time while still achieving the maximum accuracy. In places of stress concentration, the size of the element is reduced to achieve the required accuracy of the results of mathematical modeling.  
The initial data for modeling were:  
* Rail type R65;
* Ballast prism of a given type of transverse profile;
* The Mohr-Coulomb plasticity model [58] described the nonlinear properties of the layered structure of the ballast prism;
* Rail fasteners of ZhBR-65 Sh type;
* Track sections and fastening elements were combined into a solid model;
* Standard tightening of the screws was set to hold the rail in the fasteners;  
Figure 4: Finite element model of a track section with fasteners of ZhBR-65 SH type.  
Figure 3: 3D model of a railway track section.  
* The calculated values of the forces on the rails from the rolling stock were formed from the average values observed during the interaction of the track and rolling stocks of different masses when passing sections of different curvature at different speeds: vertical load from 20 to 30 tons per axle, lateral forces from 0 to 10 tons;
* Maximum bending stresses in the rail were determined for the position of the wheel between the two consecutive sleepers. Loading of the model was carried out in several stages: 1. Tightening of rail fasteners; 2. Application of gravity forces; 3. Exposure of the rolling stock. It should be noted that the application of loads was implemented not in the form of concentrated forces directed to finite element units and rail elements, but in the form of the forces applied to the wheel of the rolling stock, transmitted to the rail through contact dependencies. This approach enables removing inaccuracies in the calculations caused by an incorrect application of forces to the rail head, excluding additional torque in the section of interaction between the rail and the wheel.