## 3 Results  
### Effect of Specim Size on Compressive Strength  
Regarding the results of the numerical simulation experiment, RFC with specimen sizes of 600 mm, 1200 mm, 1800 mm, 2400 mm, and 3000 mm for each particle size type was selected to analyze the failure mode (Figure 6). For RFC of type 1, cracks around the aggregate appeared in all models, and through-cracks appeared in the aggregate in the 1200 mm and 3000 mm specimen size models. For RFC of type 2, there were individual aggregates destroyed in all models. For RFC of type 3 to type 5, there was no obvious law between specimen size and failure mode; in most models, multiple aggregates were  
Figure 5: Numerical experiment design scheme (elastic modulus nephogram, unit: Pa). (**a**) SCC model; (**b**) RFC model; (**c**) Rock model.  
damaged and inclined through-cracks were formed. Overall, as the particle size type increased, i.e., the size of the aggregate decreased, the crack extension area of the RFC gradually shifted from the interface to the aggregate, and as the main crack extended, the quantity of smaller cracks increased and their distribution became more widespread. This was due to the hindrance of coarse aggregate in the transfer of internal force and the expansion of internal cracks in the concrete under static uniaxial compression load; this barrier becomes more pronounced with increasing aggregate size [24]. When the proportion of aggregates is the same, the RFC model containing large-sized aggregates has poor overall deformation coordination ability, and the larger aggregates prevent the initial crack from expanding, causing most cracks to bypass the larger aggregate particles and expand around the weak interface zone.  
Figure 6: Failure modes of RFC with different specimen sizes (shear stress nephogram).  
We compared the stress-strain relationship of RFC with different specimen sizes (600 mm, 1200 mm, 1800 mm, 2400 mm, 3000 mm) under each particle size type (Figure 7). As can be seen, the compressive strength of RFC has an obvious size effect under each particle size type. However, with the increase in specimen size, there is no significant change in the modulus of elasticity of RFC.  
Figure 7: Constitutive relation curves of RFC under different specimen sizes.  
The uniaxial compressive strength data for the three materials, SCC, RFC of each particle size type, and rock, are shown in Table 1, and the resulting data were fitted by using the negative exponential function fitting form:  
\[f_{c}(l)=a+be^{-cl} \tag{5}\]  
where \(l\) is the specimen size;\(f_{c}(l)\) is the corresponding compressive strength; and \(a\), \(b\), and \(c\) are the fitting undetermined parameters.  
The undetermined parameters in Table 2 were obtained by fitting, and the fitting curves of the compressive strength under different specimen sizes were obtained (Figure 8). It can be seen that the three materials have significant size effect. With the increase in specimen size, the compressive strength of the three materials gradually decreased, and the decreasing trend was gradually flat, indicating that RFC, SCC, and rock had the same size effect law. When the size of the specimen was greater than a critical value, there was no obvious change in the strength. This critical value is called the characteristic size of the material strength. The slope of the fitting curve could be obtained by differentiating the fitting function:  
\[{f_{c}}^{\prime}(l)=-cbe^{-cl} \tag{6}\]  
Here, the corresponding \(l\) value when the curve slope is \(-0.005\%\) is taken as the characteristic size of the material (Table 2). There is no obvious law between the particle size type and the characteristic size.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Size (mm)** & **SCC** & **Type1** & **Type2** & **Type3** & **Type4** & **Type5** & **Rock** \\ \hline
150 & 24.07 & 33.50 & 36.30 & 38.63 & 33.27 & 34.67 & 46.33 \\
300 & 24.23 & 31.60 & 30.17 & 34.70 & 31.40 & 34.17 & 44.20 \\
45