# Forensic Analysis on Damage of a Cable-Stayed Bridge without Backstays Using BIM Information
## 4 Numerical Analysis
### Effect of Concrete Shrinkage  
According to the construction records of the pylon, the difference in concrete shrinkage strain generated by the age differences between pylon segments is one of the important effects. Figure 14 gives the concrete casting information between Piers 108 and 109. The age difference between the box girder and Segment 1 is 63 days, and the age difference between the box girder and the first part pylon wall between Piers 108 and 109 is 132 days.  
Considering the structural self-weight and shrinkage effect at each construction stage, a simulation of the whole bridge construction process was carried out to analyze the stress distribution of the pylon. At stage 1, vertical tensile stress due to the shrinkage occurs along the longitudinal direction at the interface of the box girder and Segment 1, as shown in Figure 15. The shrinkage effect continues to develop with time, and the tensile stress in this region has not disappeared.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Construction Stage** & \multicolumn{2}{c}{**Stresses in Region 1**} & \multicolumn{2}{c}{**Stresses in Region 2**} & \multicolumn{2}{c}{**Stresses in Region 3**} \\ \hline
**Stage** & **Construction Content** & **SY (MPa)** & **SZ (MPa)** & **SY (MPa)** & **SZ (MPa)** & **SY (MPa)** & **SZ (MPa)** \\ \hline \multirow{3}{*}{8} & The first part between Piers & & & & & & \\  & 108 and 109 & ++ & + & / & / & ++ & ++ \\ \multirow{2}{*}{9} & The second part between & ++ & + & / & / & ++ & ++ \\  & Piers 108 and 109 in the south & ++ & + & / & / & ++ & ++ \\ \multirow{2}{*}{10} & Segment 8 & ++ & + & / & / & ++ & ++ \\  & Segment 9 & ++ & + & - & - & ++ & ++ \\ \multirow{2}{*}{11} & The second part between & ++ & + & - & - & ++ & ++ \\ \multirow{2}{*}{12} & Piers 108 and 109 in the north & ++ & + & - & - & ++ & ++ \\ \multirow{2}{*}{13} & Power main girder, tension & & & & & & \\  & stayed cables, and & ++ & + & + & + & ++ & ++ \\ \multirow{2}{*}{14} & prestressing tendons & & & & & & \\  & Long-term shrinkage & & & & & & \\  & simulation & & & & & & \\ \hline \hline \end{tabular} Note: “/” indicates the section has not been constructed; “-” indicates compressed stress; “+” indicates tensile stress; “+” and “+++” indicate an increase in tensile stress or tensile zone.  
\end{table}
Table 4: _Cont._  
Figure 14: The concrete casting information between Piers 108 and 109.  
From stage 8 to stage 12, the first and second parts of the pylon walls between Piers 108 and 109 were cast within half a month. However, the age difference between the box girder and the last-casting pylon wall is more than 4 months. As shown in Figure 16, large vertical tensile stress is generated at the interface of concrete, and large longitudinal tensile stress is generated at the upper free edge due to the restraining of the lower pylon wall.  
The long-term shrinkage simulation was continued after the finish of the construction process simulation, and the vertical and longitudinal stress distribution of the pylon is shown in Figure 17.  
Figure 16: Stress distribution in pylon of construction stage 12.  
Figure 17: Stress distribution in pylon under long-term shrinkage.  
Figure 15: Stress distribution in pylon of construction stage 1.  
At the interface of the old and new concrete layers, there is more than 6 MPa vertical tensile stress distributing along the pylon wall, resulting in long longitudinal cracks in this region. Above Piers 108-109, more than 2 MPa longitudinal tensile stress distributes along the outer edge of the last cast pylon wall, resulting in multiple parallel vertical cracks in this region.  
In addition, at the bottom of the pylon near Pier 110, more than 2 MPa shrinkage tensile stresses are generated because the shrinkage deformation of the concrete is constrained by the foundation.