## 3 Results
### Effect of Aggregate Size on Compressive Strength  
This study validates the reliability of the numerical experiments by comparing the failure pattern of RFC in the physical and numerical experiments. Figure 9a,b illustrate the damage state of the specimen surface and internal aggregate in the physical experiment, respectively, and Figure 9c shows the corresponding numerical simulation experiment of the RFC. The failure modes of RFC could be divided into interfacial failure and splitting aggregate failure as a whole. For RFC with aggregate size of 150 mm, there were obvious through-cracks in aggregates (marked as A1 and A2) in both the physical and numerical experiments due to the single aggregate being the main body under stress, and the failure mode of the specimens was splitting failure. For RFC with aggregate size of 75 mm, vertical cracks along the interface appeared on the surface of the specimen, and inclined cracks occurred when the aggregate at the B1 mark was destroyed; the aggregate splitting failure at the B2 mark corresponded to the inclined cracks at the B1 mark; the aggregate failure at mark B3 corresponded to that at marks B1 and B2. For RFC with aggregate size of 50 mm, a large amount of the SCC on the surface of the specimen fell off, exposing the internal aggregate; the aggregate at the mark C1 exhibited extrusion phenomena due to the failure of the interface, and the aggregate at the mark D1 exhibited splitting failure; cracks distributed around the aggregate at the C2 mark corresponded to the C1 mark, and inclined cracks through the aggregate at the D2 mark corresponded to the D1 mark. The RFC failure modes of the three aggregate sizes were well compared in the physical experiment and the numerical experiment, which indicated the reliability of the numerical experiment. Figure 8: The fitting curve of size effect of compressive strength. RFC numerical models with aggregate sizes of 3000 mm, 1000 mm, and 600 mm, respectively, were selected to reproduce the process of RFC from micro-element damage to micro-crack development and finally to macro-crack formation (Figure 10). The red color represented tensile damage elements, and the green color represented shear damage elements. For RFC with aggregate size of 3000 mm, when the load was close to the peak strength (strain of 0.43 \(\times\) 10\({}^{-3}\)), a large number of tensile damage elements developed along the interface, forming cracks distributed around the aggregate (marked as A); when the loading strain reached 0.47 \(\times\) 10\({}^{-3}\), it entered the post-peak softening stage, and the cracks at mark A continued to develop along the edge of the aggregates, and the elements inside the aggregates underwent tensile damage; when the loading strain reached 0.67 \(\times\) 10\({}^{-3}\), due to the further expansion of the interface cracks, the SCC stopped working, and as the main body bearing the load, the internal damage elements of the aggregates gradually increased, resulting in the appearance of micro-cracks (marked as B); when the loading strain reached 1.00 \(\times\) 10\({}^{-3}\), the micro-cracks at point B extended into inclined  
Figure 9: Failure mode of RFC with different aggregate sizes. (**a**) Failure mode of specimen surface (front); (**b**) Failure mode of internal aggregate (left side); (**c**) Failure mode of numerical model (shear stress nephogram). cracks that penetrated the aggregates (marked as C), and the failure mode of the RFC was similar to that of Brazilian splitting failure.