## 4 Modeling and Results with Discussion
### States without Settlement of the Three Cases
layer, the stresses of the second and third cases are higher than the first case due to the effect of friction between sleepers and ballast stones. Figure 16 shows the deformation values for the track substructure. It can be seen that the difference of the deformation values in the substructure layers of the three cases could be diminished for each case separately. [PERSON] et al. [42] stated that the vertical deformation values of the fresh ballast layer after applying the wheel load were between 2 mm and 3 mm, while the maximum deformation values in the three cases ranged from 2 mm to 2.25 mm. This shows that, despite the difference in track conditions, the ballast deformation values of the three cases are in the same range and reasonable. In most of the track elements, the first and second cases have the lowest stress values compared with the third case. In reality, it is hard to apply bonded contacts between all elements in the ballasted tracks as in the first case. Hence, the second case has lower stresses compared with the third case, and the contact types in that case could also be applicable compared with the first case. Therefore, the second case has been selected as a case study according to its characteristics for studying the effect of subgrade settlement on the track elements. At the beginning of wheel running, it can be seen that there is a large difference, which is gradually minimized, in the sequence of stresses and deformation values for  
Figure 16: Substructure deformation values. Figure 15: Substructure stresses. about the first 700 mm. That is because this is the beginning of the calculation by ANSYS Workbench for the dynamic motion. That distance is called the starting zone, and its results are neglected. Furthermore, it must be noted that the values of the stresses are lower than the exact values because we selected a large mesh size for all elements and analyzed the track models in 2D, with the aim of decreasing the needed time to solve each model. Comparison between States with and without Settlement of the Second Case (Frictional Contact between Slepeers and Ballast)  
We assumed that there was a settlement that increased gradually from 5 mm to 10 mm to present the settlement of the sewer pipeline beneath the track. The shape of the stress distributions of the track elements would be changed as follows. Figure 17 shows that the wheel/rail pressure values in the settlement states are not as regular as those in states without settlement. That would negatively affect both the wheels and rails and reduce their lifetime by creating surface irregularities. [PERSON] and [PERSON] [39] concluded that the maximum wheel/rail contact pressure equals 1000 MPa, where the applied dynamic wheel load is 8 tons with a 4 mm mesh size at the wheel/rail contact area. Moreover, the maximum wheel/rail contact pressure equals 1200 MPa by applying 10 tons of dynamic wheel load with a 1 mm mesh size. After comparing the maximum contact pressure of this 2D model, which was about 790 MPa, with that of [PERSON] and [PERSON] [39], it can be concluded that the wheel/rail contact pressure values are logical. In Figure 18a, it can be seen that stresses of the railhead grow gradually by increasing the settlement value of the subgrade layer. The highest stress values belong to the settlement, with 10 mm. Figure 18b introduces the stresses in the 11 th sleeper, as the stress rates have irregular values during the wheel running in states with settlement. The maximum stress in the ballast layer without settlement equals 0.34 MPa, as shown in Figure 18c. The maximum stresses in ballast layers, with different track properties and loading conditions, were registered to be 0.2 MPa by [PERSON] et al. [42], 0.45 MPa by [PERSON] and [PERSON] [33], and 0.28 MPa by [PERSON] and [PERSON] [34]. Thus, the results of the modeled ballast layer stresses are reasonable. Figure 18d,e show the stress distributions in the subballast and subgrade layers, respectively.