## Code Predictions
### Improved Creep Model for AAS Concrete with a Wide Range of Stress-Strength Ratios  
In the previous section, we use adjustment models to predict the creep of AAS concrete. When the four models predict the creep of OPC concrete, the use of more parameters typically means better accuracy. However, more parameters mean the model is more firmly bound to the OPC concrete. Thus, a model with fewer parameters may be more suitable for predicting the creep in new materials. So, the CEB-FIP 2010 and GL2000 creep models with fewer parameters show the better accuracy for predicting the creep of AAS concrete. The CEB-FIP 2010 model has similar prediction accuracy with GL2000 model and superiority in the early time prediction. However, there are more data points in early time than the later time, which means the GL2000 has more superiority in accuracy and long time prediction. Furthermore, the residual values of the GL2000 model are positive value which means the predicted value is higher than the actual data values. It is safer from the perspective of practical engineering application. For several reasons above, we propose an improved creep model for AAS concrete with a wide range of stress-strength ratios based on the GL2000 model with an improved formula of the secant modulus used to replace the elastic modulus. The calculation of the secant modulus is based on Figure 9.  
\[E_{secant}=E_{elastic}-(-1)^{\sigma-\sigma_{E}}\times\left(\frac{17.3\sigma}{ f_{cm28}}\right)\]  
where \(E_{secant}\) is the secant modulus, \(E_{elastic}\) is the elastic modulus determined through the testing, \(\sigma\) is the actual stress corresponding to the sample, \(\sigma_{E}\) is the stress of the elastic modulus test, and \(f_{cm28}\) is the compressive strength of the concrete. The \(\sigma-\sigma_{E}\) is used for control the symbol of \(-1\) which mean when the stress-strength ratio is higher than the stress-strength ratio of the elastic modulus test, the secant modulus would lower than the elastic modulus. When the stress-strength ratio is lower than the stress-strength ratio of the elastic modulus test, the reverse is also true. The \(\sigma\)\(f_{cm28}\) means the stress-strength ratio, which is also the independent variable in Figure 9. The 17.3 is the slope based on the linear fit result of the Figure 9.  
We then use \(E_{secant}\) to replace the elastic modulus to calculate the specific creep and stress-dependent strain. The prediction of stress-dependent strain and the specific creep of AAS concrete under a wide range of stress-strength ratios using the improved creep model (curves containing \"M\" in their name), as well as the test results, are shown in Figure 11. The average and standard deviation of residual values by improved model are shown in Table 8. The prediction of the stress-dependent strain is fairly accurate, whereas the prediction of the specific creep under a stress-strength ratio of 0.45 is insufficient \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Stress-Dependent Strain** & **Specific Creep** & **Creep Coefficient** \\ \hline \hline \(\mathrm{ACI}\) 209R-92 & \(-\)242/77 & \(-\)18.8/6.0 & \(-\)0.325/0.104 \\ \(\mathrm{B}\)3 & \(-\)567/130 & \(-\)20.9/10.1 & \(-\)0.757/0.193 \\ \(\mathrm{CEB}\)-FIP 2010 & \(-\)74/30 & \(-\)5.7/2.3 & \(-\)0.100/0.041 \\ \(\mathrm{GL}\)2000 & 76/36 & 5.6/2.8 & 0.098/0.049 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The average and standard deviation of residual values by adjustment models predicted value minus experimental data value (shown as average/standard deviation). Figure 11: Test values compared with improved creep model. (**a**) stress-dependent strain; (**b**) specific creep; (**c**) creep coefficient.