## 3 Results and Discussion
### Fracture Energy  
Figure 8A shows the normalized fracture energy versus FT cycles, which were obtained by dividing the \(G_{F}\) with the control. Different from the loss in \(E_{dyn}\) and strength under FT damage, there was even an increase in the fracture energy for both water- and sulfate-exposed samples. The fracture energy showed an increasing trend to 60 FT cycles, followed by an overall decrease until 180 FT cycles. After being subjected to 60 FT cycles, the fracture energy showed a maximum increment of about 45% and 39% for water- and sulfate-exposed samples, respectively. Generally, for the sulfate-exposed specimens, the fracture energy decreases more sharply compared to that of water-exposed specimens. After being subjected to 180 FT cycles, there was about a 16% decrease in fracture energy for the sulfate-exposed specimen, which is higher than that of the water-exposed one (9%). [PERSON] et al. [42] reported a similar variation trend in the study of the effects of internal frost damage on the fracture energy of aerated and non-aerated concrete.  
Figure 8: Evolution of fracture energy (**A**) and area percentage of aggregate splitting failure (**B**) and pulled-out failure (**C**) at different FT cycles.  
The fracture energy, \(G_{\text{F}}\), required for the creation of a fracture surface can be expressed as  
\[G_{\text{F}}=2(A_{m}\cdot\gamma_{m}+A_{a}\cdot\gamma_{a}+A_{i}\cdot\gamma_{i}) \tag{5}\]  
where A is the area of fracture surface and \(\gamma\) represents the energy dissipated for the crack propagation, with the subscripts \(m\), \(a\) and \(i\) indicating the matrix, aggregate and interface phases, respectively. Consequently, the fracture surface were analyzed to investigate the increase in \(G_{\text{F}}\). The area percentage of different failure modes of aggregates were obtained using a MATLAB code. It is worth pointing out here that the fracture of mortar parts in RCA, mainly the crushed mortar, is considered as the mortar failure.  
Figure 8B,C show the area percentage of different failure modes of aggregates with different FT cycles. In general, a noticeable increase in the interface damage (Figure 8C), which corresponds to a sharp decrease in the splitting damage (Figure 8B). For the control specimen with zero FT cycle, the area percentages of the fractured aggregate (Figure 8B) and interface failure (Figure 8C) were 18.5% and 7.3%, respectively. However, specimens subjected to 120 FT cycles in sulfate solution showed 9.6% and 14.9%, respectively. After being subjected to 180 FT cycles, the area percentage of splitting and pulled-out failure were around 5% and larger than 17.3% respectively. For pulled-out aggregate failure, specimens subjected to FT under sulfate-exposed showed a higher area percentage at all studied FT cycles when compared to the water-exposed ones. After being subjected to 180 FT cycles, the area percentage of pulled-out aggregate failure was 22.1% and 17.3% for the sulfate- and water-exposed specimens, respectively. This indicates that a significant deterioration in the binding force of mortar occurs during the cyclic FT damage. Compared to the area of ligament, the failure of the curved interface eventually results in a larger area of the fracture surface. However, the fracture energy is calculated based on the effective cross-section area (i.e., \(t\cdot h\)) and thus contributes to higher fracture energy.