# Characteristics of Restrained Drying Shrinkage on Arched Steel Fiber-Reinforced Concrete
## 4 Drying Shrinkage Strain Prediction Model
### Comparisons between Test Results and Prediction Model Results  
Each prediction model predicts the drying shrinkage strain based on different environmental and material factors. For the F-OPC and F-SFRC20 specimens, we compared the free-drying shrinkage strain results obtained using the prediction models with the test results. Figure 9 and Table 6 present comparisons of the free-drying shrinkage strain measurements of the plain concrete that were obtained via each prediction model versus the free-drying shrinkage test results. Figure 9 shows that the KCI [11], GL2000 [13,14], and Li [15] prediction model results are similar to the experimental results for the first three days of aging, but the predicted drying shrinkage strain levels decrease as the aging increases. The reason for this outcome may be that the KCI and GL2000 prediction models evaluate the material properties of concrete using only cement type and concrete strength as the variables. On the other hand, for the ACI 209R-92 prediction model results, the predicted strain is lower than the experimental results initially, but becomes similar to the experiment results as the aging increases. The reason for this outcome appears to be that the ACI 209R-92 prediction model applies detailed coefficient values that consider the slump, fine aggregate content, and air content of concrete. A comparison of the prediction results and experimental results for the drying shrinkage strain of the plain concrete at 56 days of aging shows that the KCI prediction model has the largest error of \(-52\%\) and the ACI 209R-92 prediction model has the smallest error of \(-4\) percent. Figure 10 and Table 7 present comparisons of the free-drying shrinkage strain results for SFRC20 that were obtained via each prediction model versus the free-drying shrinkage test results. When the predicted results are compared with the experimental results by age of the concrete, the KCI and GL2000 prediction model results are similar to the experimental results initially, but the differences become greater and the strain levels decrease as aging increases, which is similar to the plain concrete results. In the case of the ACI 209R-92 prediction model, the prediction results also are similar to the test results until 28 days of aging, but are overestimated after 28 days. The reason for this outcome may be that the drying shrinkage of concrete is mitigated by the steel fiber as the drying shrinkage strain  
increases for SFRC20, but this effect is not reflected in the prediction models suggested by domestic and overseas codes for concrete. The Li prediction model results are the most similar to the test results for SFRC20 throughout the aging times among the four models, even though slight differences are evident for the plain concrete. The reason for this outcome may be that the Li prediction model considers the fine aggregate and steel fiber contents that affect drying shrinkage when calculating the maximum drying shrinkage strain of concrete. A comparison of the predicted and test results for the drying shrinkage strain of SFRC20 at 56 days of aging indicates that the KCI prediction model shows the largest error of \(-32\%\) and the Li prediction model has the smallest error of \(+6\%\). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**F-OPC**} & **Drying Shrinkage Strain at** & **Predicted** \\  & **56 Days (\(\mu\)c)** & **Value/Experimental Value** \\ \hline This study & 725 & - \\ KCI (2017) & 347 & 0.48 \\ ACI 209R-92 (2008) & 701 & 0.96 \\ GL2000 (2004) & 464 & 0.64 \\ Li Z. (2017) & 557 & 0.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of test results (’This Study’) versus prediction model results for the drying shrinkage strain of plain concrete (F-OPC) at 56 Days.