## 1 Introduction
In [5], a 3D Finite Element Method(FEM) model with solid elements was developed to study the effect of the gap under the unsupported sleepers (one or two sleepers unsupported in their work) together with vehicle velocity; to assess the track settlement with a specific formula based on the output of the simulation. The results show that ballast/sleeper contact forces are gradually amplified over the adjacent sleepers with respect to height of the gap and velocity, whereas it becomes zero for the track section with unsupported sleepers. In case of two unsupported sleepers, the gap could be closed and some contact forces could be produced [5]. Similar conclusions were obtained in [6] in which they expanded the ranges of parametric values and differently, used a 3D numerical model with two rails and a vehicle. By contrast, their study also shows that local maxima could be observed in different configurations considering the number of hanging sleepers, vehicle speed and the height of gap configurations. In another study [7], by meansof configuration, several scenarios for a one-sided partially unsupported sleepers was simulated and resulted in similar conclusions such that higher speed increase the contact force variations. They also show that the effect of triangular configuration, where three assumed voids are sequentially placed under left, right and then left rails, have no significant effect on the contact forces. In another study, the effect of sleeper spacing on the dynamic response of the system is found significant for partially and fully supported sleepers [8]. The larger sleeper bays escalate the rail displacement for both partially and fully unsupported sleepers. Similarly, it is shown in a recent study that the rail displacement was escalated for different number of axles, so-called bogie patterns and axle loads [9]. Surprisingly, researchers have avoided taking advantage of numerical analysis to investigate the unsupported sleepers/beaerrs over a turnout, a complex structured component on a railway track to divert traffic from one route to another one. More importantly, turnouts have an inherent asymmetrical topology (Figure 1) that increases the likelihood of occurrence of unsupported bearers. Only few researches have been encountered in the literature [10; 11]. They show that turnouts also suffer from voided sleepers/beaers and can amplify the contact forces up to four times high. Nevertheless, these models mostly consider static or quasi-static loading, the insufficiency of which is mentioned previously. Furthermore, a single bearer was considered and analyzed in those studies, which was assumed to be sufficient to represent the behavior of whole turnout structure. Nevertheless, it was shown in [12] that the sleepers/beaerrs are subjected to different loading conditions based on their length and location along a turnout. Briefly, it seems that the effect of unsupported sleepers/bearers over a turnout have been investigated insufficiently with reference to above studies. Hence, the aim of this study is to analyze the response of a turnout system with unsupported sleepers/beaers via a more sophisticated numerical model that is capable of capturing dynamic forces. Various scenarios are adopted in numerical process such as one, two and three sleepers/bearers hanging with respect to different vehicle speed. Figure 1: The FEM model. (**a**) The layout of a standard turnout and (**b**) the schematic vehicle–track couple.