## 3 Model Predictions
### Sensitivity Study Regarding the Aggregate Replacement Ratio  
Finally, we study the strength development for aggregate replacement ratios within the interval \(f_{ra}^{a}\in[0,1]\), whereby \(f_{ra}^{a}=0\) refers to conventional concrete without recycled aggregates and \(f_{ra}^{a}=1\) refers to recycled concrete containing recycled aggregates only. The model shows that the strength for early ages and for high \((w/c)_{ncp}\)-ratios is less sensitive to aggregate replacement than for mature ages and for small \((w/c)_{ncp}\)-ratios (see Figure 10); and compare the dashed lines, which refer to \(f_{ra}^{a}=0\), to the continuous lines, which refer to \(f_{ra}^{a}=1\), in Figure 6. The reason is, once again, related to stiffness contrast-driven stress concentrations. At early ages, or for pastes with high \((w/c)_{ncp}\)-ratios, the old cement paste is much stiffer than the new cement paste matrix. The macroscopic load is therefore subdivided relatively equally between all aggregates, even the ones containing the relatively stiff old cement paste. At mature ages, or for pastes with small \((w/c)_{ncp}\)-ratios, however, the stiffness contrast between new cement paste matrix and old cement paste vanishes, and only natural aggregates as well as old plain aggregates are still considerably stiffer than the new cement paste. The macroscopic load is therefore over-proportionally concentrated into natural and old plain aggregates. More aggregate replacement results in a smaller volume of these two aggregate families, and consequently in larger ITZ microstresses around each individual natural and old plain aggregate and this eventually leads to a more pronounced reduction of the macroscopic strength.  
Figure 10: Dimensionless uniaxial compressive strength of recycled concrete (normalized with respect to the strength of conventional with \(f_{ra}^{a}=0\)) as function of the recycled aggregate-related old cement paste volume fraction: (**a**) for \((w/c)_{ncp}=0.35\), and (**b**) for \((w/c)_{ncp}=0.5\).  
Figure 9: Dimensionless uniaxial compressive strength of recycled concrete (normalized with respect to the strength of the benchmark composition with \(f_{cap}^{a}=0.35\)) as function of the recycled aggregate-related old cement paste volume fraction: (**a**) for \((w/c)_{ncp}=0.35\), and (**b**) for \((w/c)_{ncp}=0.5\).  
The model predicts that, for 100% replacement of natural aggregates by recycled ones, the strength is typically by up to 12% smaller (see Figure 10b). Notably, however, the strength reduction is much more pronounced for compositions, where ITZ failure around old covered aggregates triggers the macroscopic failure, as encountered for a composition exhibiting \((w/c)_{ncp}=0.35\) and \(\xi_{ncp}=0.75\) (see the dotted-dashed line in Figure 10a). The macroscopic strength of this recycled concrete composition reduces by more than 20%. We recall that the studied compositions refer to cases for which the ITZ porosity and bulk cement paste porosity are identical. For weak ITZs, the strength reduction due to the use of recycled aggregates is much more pronounced (see also Figure 7). The discontinuity at the limit case of vanishing recycled aggregate volume fraction for the composition with \((w/c)_{ncp}=0.35\) and \(\xi_{ncp}=0.75\), see Figure 10a, is discussed, among other model limitations, in the next section.