## 4 Analysis of Force Chain Network Characteristics in Anchored Granite with Different Fissure Angles
Figure 13a shows the force chain rose diagrams for all force chains that were not threshold screened for force chains. Overall, the force chain rose diagrams for both the anchored and unanchored samples closely resemble a spherical shape, and the volume of the force chain rose diagrams for samples with inclined fractures, whether anchored or unanchored, is similar, with no significant differences in coloration. However, the volume of the rose diagrams of the anchored samples is reduced and the color is lightened to some extent from the unanchored samples compared to the unanchored samples. This implies that the number of force chains inside the unanchored sample is more. As the sieving threshold increases, the force chain rose diagrams for both the unanchored and anchored samples no longer exhibit a spherical shape. Among samples with the same \(\alpha_{\mathrm{s}}\), when the sieving threshold is increased from 50 N to 150 N, the volume of the force chain rose diagrams for both types of samples gradually decrease. This indicates that only a small number of force chains within the samples are influenced by the external load. Additionally, Figure 13b-d show that after threshold sieving, the volume of the force chain rose diagrams for the anchored samples is larger than that for the unanchored samples. Moreover, as the sieving threshold increases, this phenomenon becomes increasingly evident. This suggests that compared to the unanchored samples, the anchored samples carry a higher level of load within the sample under external loading and are able to retain more force chains with higher force chain values, thereby possessing greater load-bearing capacity. Figure 13: Variations in orientation distribution of force chains in samples with different \(\alpha_{\mathrm{s}}\) under different filtering thresholds. Figure 14 illustrates a comparative plot of the number of force chains in the unanchored and anchored samples of the fissure containing different \(\alpha_{\rm s}\) screened with different thresholds. As can be observed from Figure 14, the number of force chains inside the unanchored sample is also consistently larger than that of the anchored sample without threshold screening. In Figure 14, it can be clearly observed that the number of force chains inside the unanchored sample is always lower than that of the anchored sample at different screening thresholds. The increase in the number of force chains of the anchored sample compared to the unanchored sample tends to diminish with the increase in \(\alpha_{\rm s}\). Among them, when the force chain screening threshold is set to 50 N, as \(\alpha_{\rm s}\) increases from 30\({}^{\circ}\) to 75\({}^{\circ}\), the number of force chains within the anchored samples increases by 32.81%, 23.98%, 16.18%, and 3.23% compared to the unanchored samples, respectively. When the force chain screening threshold is set to 100 N, the number of force chains within the anchored samples increase by 68.30%, 52.53%, 38.75%, and 13.66%, respectively; when the force chain screening threshold is set to 150 N, as \(\alpha_{\rm s}\) increases from 30\({}^{\circ}\) to 75\({}^{\circ}\), the number of force chains within the anchored samples increases by 105.67%, 85.75%, 66.99%, and 24.59% compared to the unanchored samples, respectively. From the above results, it can be inferred that the increase in the number of force chains in the anchored samples relative to the unanchored samples gradually decreases, which may be related to the influence of the fracture dip angle on the anchoring effect. The mechanism by which the fracture dip angle affects the anchoring effect warrants further research. Figure 14: Variations in force chain numbers in samples with different \(\alpha_{\rm s}\) under different filtering thresholds.