## 3 Numerical Simulation of Early-Age Behaviour of Small Specimens to Actual Rc Deck Slabs
### Experimental Outline and Model Validation via Small-Scale Specimens (Decimetres)
#### 3.2.1 Influence of Environmental Conditions: Rainfall, Shade and Indoors  
Figure 3a represents a one-fourth finite-element model of the 200 \(\times\) 200 \(\times\) 800 mm\({}^{3}\) prismatic specimens that were used in the experiments on concrete shrinkage under direct rainfall, shade and indoor environment. Apart from the indoor case, for which numerical models have been verified, the fluctuation in environmental conditions necessitates further model validation because it significantly affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, the mechanical properties. The displacement restraints were applied based upon the symmetric condition and actual placement of the specimens. In other words, a vertical displacement restraint was applied at the bottom surface, whereas longitudinal and transverse displacement restraints were applied at the X-symmetric plane and the Y-symmetric plane, respectively. As necessitated by the computational platform, the mix proportion, casting temperature and curing conditions were identical to the experimental conditions. The implemented mixture designs for the specimens were OPC55 and OPC45 as indicated in Table 1. Figure 3b depicts the environmental condition. The environmental data, which consist of the temperature and relative humidity of rainfall, shade and indoor conditions, were obtained from data loggers at each corresponding location. The rainfall specimens were exposed to direct sunshine and rainfall, as shown in Figure 4a, whereas shaded specimens were sheltered from direct sunshine and rain (Figure 4b). The indoor specimens were kept in a storage room without direct exposure to the ambient environment. Rainfall is of paramount important in determining concrete shrinkage behaviour. To simply account for the water absorption of concrete via rainfall, the emissivity coefficient in the surface mass flux is assumed to increase one hundred times from its original value. However, the actual hydraulic pressure on the exposed surface could be acquired in the model [12]. The rainfall data of Koriyama in Fukushima prefecture was retrieved from the Japan Meteorological Agency and applied in the analysis. \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 Content (kg/m\({}^{3}\))**} & \multirow{2}{*}{**Seal-Cured**} \\ \cline{4-9}  & & & & **W** & & **C** & **Ex** & **S** & **G** \\ \hline OPC55 & 55 & 4.5 & 172 & 313 & - & 834 & 997 & 7 days \\ OPC45 & 45 & 6 & 164 & 338 & 20 & 791 & 992 & 7 days \\ \hline \hline \end{tabular} Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Gravels.  
\end{table} 
Table 1: Mix proportion of 200 \(\times\) 200 \(\times\) 800 mm\({}^{3}\) prismatic specimens and curing condition. Figure 4: (**a**) Specimens with direct rainfall exposure; (**b**) shaded specimens. Figure 3: (**a**) Finite-element (FE) model of one fourth of the specimen; (**b**) environmental condition. Figures 5-7 portray a comparison between the measured values from data loggers and the analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the specimens could be simulated well for the shaded and indoor cases. The analytical results for the specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with direct rainfall, similar to the behaviour in mass change, a minimal discrepancy was found in the trend between the measured and analytical strain. As extra water from rainfall was supplied to the concrete through the exposed surfaces, the measured strain reflected this phenomenon through concrete expansion.