## 3 Macroscopic Behavior
### Influence of Particle Size Ratio  
The influence of particle size ratio on the shear behavior of binary mixtures has received considerable attention in previous studies. However, there has been a noticeable gap in investigating the impact of particle shape on such behavior. To address this research gap, the effect of particle shape on the shear behavior of binary samples has been focused on, which consist of cubes and spheres with varying sizes. In this study, five mixtures are generated with a volume ratio of 1:1 for cubes and spheres, as outlined in Table 2. Sample SC represents a case where the particle sizes of cubes and spheres are equivalent. In Samples SS1 and SS2, the size of cubes is maintained while reducing the size of spheres. Conversely, for Samples SC1 and SC2, the size of spheres is kept constant while decreasing the size of cubes.  
Figure 10 presents the deviatoric stress profiles of the five prepared mixture samples. It is observed that the deviatoric stress decreases as the particle size decreases, irrespective of the particle shape. For example, when comparing samples SS1/SC1 or SS2/SC2 with  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **Cube Size** & \begin{tabular}{c} **VF of** \\ **Cube** \\ \end{tabular} & \begin{tabular}{c} **No. of** \\ **Cube** \\ \end{tabular} & \begin{tabular}{c} **Sphere** \\ **Size** \\ \end{tabular} & \
\begin{tabular}{c} **VF of** \\ **Sphere** \\ \end{tabular} &
\begin{tabular}{c} **No. of** \\ **Sphere** \\ \end{tabular} \\ \hline SC & 4.0 mm & 50\% & 2422 & 4.0 mm & 50\% & 2381 \\ SS1 & 4.0 mm & 50\% & 2398 & 3.0 mm & 50\% & 5634 \\ SS2 & 4.0 mm & 50\% & 2425 & 2.0 mm & 50\% & 18,873 \\ SC1 & 3.0 mm & 50\% & 5663 & 4.0 mm & 50\% & 2381 \\ SC2 & 2.0 mm & 50\% & 18,938 & 4.0 mm & 50\% & 2381 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Different particle sizes for mixture samples composed of cubes and spheres.  
Figure 9: Influence of initial porosity on the (**a**) deviatoric stress and (**b**) volumetric strain for the mixture sample of C60S40 under the confining pressure of 1.0 MPa.  
the same particle sizes, their peak strengths are nearly identical. However, the stress at the peak for samples SS1/SC1 is higher. Additionally, samples SC1 and SC2 exhibit a delayed attainment of peak strength compared to SS1 and SS2, indicating that smaller cube particle sizes result in a lower Young's modulus. Although the shear strengths of the five samples are almost identical at the residual state, suggesting that particle size has minimal effect on the residual state, the deviatoric stress curve exhibits the characteristic stick-slip phenomenon. This phenomenon can be attributed to variations in force networks under shear stress [39; 40; 41; 42]. Previous studies have indicated that reducing the size of cube particles can amplify the amplitude of stick-slips.  
Figure 10b presents the volumetric strain profiles of the five mixture samples with equivalent volume fractions of cubic and spherical particles but varying particle sizes under a confining pressure of 1.0 MPa. The results demonstrate that reducing the particle size has a substantial influence on sample expansion, as samples with smaller particle sizes display smaller expansions. This effect can be attributed to the ability of small particles to efficiently fill the void spaces between larger particles without significantly displacing the surrounding particles. Furthermore, it is observed that cubic particles exhibit less dilation compared to spherical particles of the same size. This behavior arises from the inherent characteristics of the particle shapes: spherical particles have a higher tendency to form dense packing structures, while cubic particles of the same volume exhibit a comparatively looser arrangement.