# Track-Bridge Interaction of CWR on Chinese Large-Span Bridge of High-Speed Railway
## 4 Special Problems of Track-Bridge Interaction
### Shrinkage and Crep  
The span of a long-span, prestressed concrete, continuous rigid-frame bridge with a double-track ballastless track is (72 + 128 + 72) m. The bridge adopts a single-box single-chamber box section, the beam body is C55 concrete, the deck width is 12 m, and the mid-span beam height is 4.8 m (as shown in Figure 19). The pier adopts a rectangular \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**City** & \(a\) & \(b\) & **City** & \(a\) & \(b\) & **City** & \(a\) & \(b\) \\ \hline Beijing & 27 & \(-\)5 & Hefei & 29 & 1 & Shenyang & 25 & \(-\)12 \\ Chengdu & 26 & 3 & Huhehot & 23 & \(-\)12 & Shijiazhuang & 28 & \(-\)4 \\ Changchun & 24 & \(-\)16 & Jinan & 28 & \(-\)3 & Taipei & 30 & 12 \\ Changsha & 30 & 3 & Kunming & 20 & 4 & Taiyuan & 25 & \(-\)7 \\ Chongqing & 29 & 5 & Lasa & 22 & \(-\)6 & Tianjin & 27 & \(-\)5 \\ Kuzhou & 29 & 8 & Lanzhou & 24 & \(-\)7 & Urumqi & 24 & \(-\)15 \\ Guangzhou & 29 & 10 & Nanchang & 30 & 3 & Wuhan & 29 & 1 \\ Guiyang & 25 & 2 & Nanjing & 29 & 1 & Xian & 27 & \(-\)2 \\ Harbin & 30 & \(-\)19 & Nanning & 29 & 9 & Xining & 20 & \(-\)9 \\ Haikou & 29 & 13 & Macao & 29 & 11 & Yinchuan & 25 & \(-\)9 \\ Hangzhou & 29 & 2 & Shanghai & 29 & 2 & Zhengzhou & 28 & \(-\)1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Adjustment coefficients of typical regions in China. thin-walled pier, which is made of C40 concrete. The heights of P1 and P2 piers are 96 and 102 m, respectively. The relative humidity of curing is 70. The beam element with a rigid arm is used to simulate the beam body, and the beam pier is rigidly connected. According to the actual situation of pier modeling, the pier bottom is set to be consolidated. A double-line ballastless track is laid on the bridge without a rail expansion regulator, and the rail is 60 kg/m. The rail on the 200 m subgrade is built on both sides of the abutment. The linear spring is used to simulate the vertical stiffness (50 MN/m), and the fastener resistance is used as the longitudinal resistance of the line. The relationship between the longitudinal resistance of the line (kN/m) and the relative displacement of the beam rail (mm) can be expressed as follows:  
\[r(x)=\left\{ \begin{array}{ll}12.0x&|x|\leq 2.0\ \mathrm{mm}\\ 24.0&|x|>2.0\ \mathrm{mm}\end{array} \right. \tag{4}\]  
When building the bridge structure model, the construction stages of formwork erection, concrete pouring, tension prestress, and demolding are simulated accurately according to the actual situation, and the simulation model of the prestressed concrete, continuous rigid-frame bridge-track system is established, as shown in Figure 20.  
Figure 19: Beam cross-section (unit: m). Figure 20: Simulation model for the track–bridge interaction. Based on the shrinkage creep model proposed by the China Railway code (TB10002.3-2005), China Highway code (JTG D62-2004), and Eurocode 2, the concrete material properties are defined as a time-dependent function. When extracting the force and deformation of key components, only the shrinkage and creep conditions are extracted. The force and deformation of the system after 120 days of track laying are calculated (for the sake of simplification, the influence of rail change, fastener change, and stress release are not considered), as shown in Figure 21.  
Under the action of shrinkage and creep, the rail stress and displacement of the long-span continuous steel frame bridge are basically symmetrical. The maximum value of rail stress appears near the abutment, and the maximum value of rail vertical displacement appears in the middle of the span [74]. With the extension of the service time, the stress and deformation of the system increase gradually, which increases rapidly in the first five years, then gradually slows down, and gradually stabilizes after 10 years of track laying [74; 75; 76]. The additional force caused by concrete shrinkage and creep is much larger than that caused by bending and braking. It is not safe to ignore the influence of concrete shrinkage and creep on rail longitudinal force [39; 75].