## 2 Track-Bridge Interaction Analysis Model  
The analyzed bridge is a simple one, having a span of 40.96 m, whereas the length, width, and height of the track slab segment are 5.12 m, 2.8 m, and 0.53 m, respectively. Eight track slab segments were installed on the bridge. An embankment of 31 m on both sides of the bridge was taken into consideration. The sectional constant and material properties of the bridge, track, and rail are shown in Table 1.  
Figure 1: Concept of the anchor system for a quick-hardening track [22]. The analysis of the track-bridge interaction was conducted using a commercial structural analysis program, ABAQUS [28]. The continuous welded rail, track slab segment, and bridge were modeled using planar Timoshenko beam elements (B21), as shown in Figure 2.  
As rails are connected by rail fasteners installed on the sleepers embedded in the track slab, rails and track slabs are connected to each other using a spring element that replicates the longitudinal resistance of rail fasteners (hereinafter referred to as the \"fastener spring\"). The longitudinal resistance by a fastener is replicated using a bilinear spring that exhibits elastic-perfect plastic behavior, as shown in Figure 3. The displacement that sets the boundary between the elastic and plastic zone is defined as the limit displacement (u\({}_{0}\)). Until the displacement is less than the limit displacement, the rail pad itself deforms due to elastic shearing. After the limit displacement is exceeded, the rail slips over the rail pad, and the longitudinal displacement increases between the rail and the track slab. When there is no train on the track, the longitudinal resistance is determined by the normal force due to the clamping force of a fastener and the friction coefficient of a rail pad. When there is a train on the track, the longitudinal resistance is determined by the vertical load of the train and the friction coefficient of a rail pad. Therefore, the maximum longitudinal resistance of a fastener spring is different when there is a train load (60 kN/m) and when there is no train load (40 kN/m), as suggested in UIC 774-3R [16]. The limit displacement is generally as small as 0.5 mm in the same code. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Equivalent Elastic** & **Section Area** & **Span Length (m)** & **2 nd Moments of Inertia (mm4)** \\ \hline Rail (60E1) & 210,000 & \(1.53\times 10^{4}\) & 100 & \(6.07\times 10^{7}\) \\ QHT slab & 28,571 & \(1.48\times 10^{6}\) & 5.12 & \(3.47\times 10^{10}\) \\ PSC box girder & 28,571 & \(1.19\times 10^{8}\) & 40.96 & \(12.12\times 10^{13}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material and sectional properties of rail and PSC (pre-stressed concrete) box girder. Figure 2: Schematic of rail–track–bridge interaction model for a QHT (quick-hardening track). In QHT, considering the frictional resistance between the track slab and the railway bridge is important [13; 22; 23]. The track slab and the bridge are connected by a nonlinear spring element that replicates the frictional behavior (hereinafter, the \"friction spring\"). When there is an anchor installed, a spring element replicating the resistance due to an anchor block is added to the center of the track segments (Figure 2). The longitudinal resistance due to the friction between track and bridge has a pattern similar to the longitudinal resistance of a fastener. When there is no train on the track, the longitudinal resistance is developed due to the normal force from the self-weight of the track segment and the frictional coefficient between the track slab and the bridge deck. In this study, considering that one QHT track slab has a volume of 7.6 m\({}^{3}\), a unit weight of 24 kN/m\({}^{3}\), and a friction coefficient of 0.7, the maximum kinetic frictional force of a track segment is 127.65 kN without the train.