# Meso-Scale Simulation of Concrete Based on Fracture and Interaction Behavior
## 6 Parametric Study
### The Effect of Aggregates' Mechanical Characteristics  
Although the tensile behavior of concrete is dominated by the properties of ITZs and mortar, damage and fracture may happen in aggregates during compression [45]. Different kinds of aggregates have differences in mechanical characteristics, geometrical shape, and corresponding ITZ properties [46]. To study the effect of aggregates' mechanical characteristics on concrete compressive performance, based on standard models, cohesive elements are inserted into aggregates to simulate aggregate internal interfaces (AII). The material parameters of AII elements are set by referring to the material tests of the following common aggregate rocks: limestone [47], marble [48], granite [49], and basalt [50]. The material parameters of AII elements are listed in Table 4.  
The stress-strain curves of varying aggregates' mechanical characteristics are shown in Figure 21. Compared with the ultimate bearing capacity of the models without considering aggregate damage and fracture, the ultimate bearing capacities of the models with limestone, marble, granite, basalt aggregates fall by averages of 1.1%, 1.0%, 0.23%, 0.18%, respectively. The effect of aggregate type on the stress-strain relationship is mainly reflected in the softening stage. As shown in Figure 22, damage evolution of aggregates accelerates in the early softening stage. Since marble aggregates have the lowest tensile and shear strength, they are more likely to be damaged during the compression process. The energy dissipation of aggregates can lead to stress redistribution at the local area and enhance residual strength.  
Figure 23 shows the failure modes of the models with the same aggregate distribution and different aggregates' mechanical characteristics. It can be seen that the fracture of aggregates only constitutes a minority, but the crack propagation paths at the models' left half are obviously influenced by local crack propagation differences caused by aggregates' fracture. Since the shear bands at the models' right half form earlier than those at left half, the models have very similar failure modes (FZ5-FZ9) at the right half. In view of these observations, it can be concluded that the influence of aggregates' mechanical characteristics on concrete's mechanical characteristics and failure modes is mainly concentrated in the mid-and-late softening stage.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Parameter** & **Limestone** & **Marble** & **Granite** & **Basalt** \\ \hline Maximum nominal stress in normal direction, \(t_{n}^{0}\) (MPa) & 6.0 & 4.5 & 10.0 & 15.0 \\ Maximum nominal stress in shear direction, \(t_{s}^{0}\) and \(t_{t}^{0}\) (MPa) & 45.0 & 40.0 & 90.0 & 120.0 \\ Normal Mode fracture energy, \(G_{n}^{C}\) (N/mm) & 60 & 160 & 400 & 1400 \\ Shear mode Fracture energy, \(G_{s}^{C}\) (N/mm) & 1500 & 4000 & 10,000 & 35,000 \\ B-K criterion material parameter, \(\eta\) & 1.2 & 1.2 & 1.2 & 1.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Material properties of aggregate internal interfaces (AIIs).  
Figure 21: Effect of aggregates’ mechanical characteristics on global stress-strain relationship under compression.  
Figure 22: The relationship between strain and the sum of length of All elements whose SDEG (overall value of the scalar damage variable) values are higher than 0.95.  
Figure 23: Failure modes of a specimen with different aggregate types; in the zoom areas of Figure 23b, the cracks through aggregates are marked by red, the others are marked by black.