## 3 Numerical Simulation of Early-Age Behaviour of Small Specimens to Actual Rc Deck Slabs
### Preliminary Analysis on Concrete Deck Slab of Shinkesen Bridge to Evaluate the Occurrence of Cracks
Furthermore, at 55% w/b, neither BFS55 nor OPC55 satisfy the JSCE cracking criteria. If attention is paid to the case of 42% w/b, a reduction in maximum tensile strain could be seen in the OPC42 case, whereas higher maximum tensile strain was seen in BFS42 because of the synergistic effect of high autogenous shrinkage and self-desiccation from a low w/b. Although OPC42 seems to satisfy the JSCE cracking criteria, its low resistance against durability issues such as ASR and chloride ingression mean that it might not be a good candidate for areas with severe environments, such as Tohoku. Then, consistent with the universal understanding that prolonged seal curing would reduce the moisture loss through the concrete's surface, seal curing BFS42 up to 28 days significantly helped to reduce the maximum tensile strain. Finally, after incorporating expansive additives inside BFS42, further improvement in reducing the generation of tensile strain was illustrated. In addition to the lower intensity in the maximum crack width, based on the strain contour, the amount of nodal strain that reached a longitudinal strain of 1000 \(\upmu\) is also minimal, which infers that less crack propagation would occur than in the case without expansive additives. Hence, as a conservative measure in cases in which prolonged curing could not be properly conducted or maintained, the recommendation to use expansive additives in the multiple protection strategy is quite reasonable. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Series**} & \multirow{2}{*}{**w/b (\%)**} & \multirow{2}{*}{**Air (\%)**} & \multicolumn{6}{c}{**Unit Proportion (kg/m\({}^{3}\))**} \\ \cline{3-8}  & & & **W** & **C** & **Ex** & **S** & **G** & **Ad** \\ \hline OPC55 & 55 & 4.5 & 170 & 310 & - & 802 & 1044 & 3.14 \\ BFS55 & 55 & 4.5 & 170 & 310 & - & 802 & 1044 & 3.14 \\ OPC42 & 42 & 6 & 153 & 364 & - & 653 & 1112 & 2.24 \\ BFS42 & 42 & 6 & 153 & 364 & - & 662 & 1112 & 2.18 \\ BFS42-EX & 42 & 6 & 153 & 364 & 20 & 662 & 1112 & 2.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mixture designs used for parametric study. Figure 17: FE model of one-fourth of a bridge span. Post-Construction Analysis on Concrete Deck of Shinkesen Bridge: Verification with on-Site Measured Data  
Figure 19 represents the entire overview of the 438-m seven-spanned steel girder-supported bridge. The casting sequence was carried out according to the numbers shown after considering the influence of moment distribution. For long-term monitoring, the strain and temperature gauges were embedded on casting lot 8 over the top of Pier 3 support. The top surface of the concrete underwent wet-curing for approximately 22 days, following by seal-curing for another 7 days before the RC deck  
Figure 18: Parametric study focusing on four different aspects. * \(\epsilon_{\rm max}\) = maximum longitudinal strain; \(\rm w_{max}\) = maximum crack width. was exposed to the ambient environment. Figure 20 illustrates the finite-element model of one-fourth of the Shinkesen Bridge span, which imposes additional elements to consider over the finite-element model mentioned in Section 3.5. To precisely consider the real conditions of the concrete bridge deck, a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. To account for the effect of the expansion joint in the finite-element model, the longitudinal restraint at Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as seen in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion of the rigid body was performed at the end of Lot 8 to maintain the symmetric conditions in the bridge span. The reinforcement ratio was cautiously applied as calculated from the structural detail drawings, whereby lot 8 possesses more reinforcing bars in the top section.