Group Cable Bolt Interaction and Preliminary Spacing Assessment in Deep Stopes Based on a Dual-Index Interaction Framework

Spacing design for group cable bolt systems remains largely empirical and rarely considers stress interaction and displacement overlap together. This study develops a dual-index interaction framework for two representative cable bolt configurations in deep stope roofs. Mindlin’s semi-infinite body solution and Kelvin’s infinite body solution were combined with a non-uniform interfacial shear stress distribution to model shallow fully grouted and deep end-anchored systems, respectively. The analytical trends were examined using FLAC3D, and the field applicability of the selected spacing scheme was assessed through an industrial test at the Fankou Lead–Zinc Mine. The results show that the fully grouted configuration is strongly affected by the free surface and full-length load transfer, whereas interaction in the end-anchored configuration is concentrated around the deep bonded section. The stress interaction coefficient η provides the primary screening measure for a reference lower spacing bound, while the displacement interaction coefficient α identifies residual displacement overlap. Both are local field interaction indices rather than measures of individual cable capacity or global system stiffness. Using ηref = 0.9 as an engineering tolerance, stress interaction becomes limited at approximately s/D = 30 for the end-anchored configuration, whereas the fully grouted configuration enters a relatively stable interaction–attenuation stage at approximately s/D = 40. Considering both configurations, s/D ≈ 40 is adopted as a reference lower bound, corresponding to 1.6 m for a 40 mm borehole. The field scheme used a spacing of 1.8 m (s/D ≈ 45) and produced a maximum measured roof displacement of 27.6 mm, with no evident roof fall, cable breakage, or anchorage pull-out. Because characteristic rock mass heterogeneity is not explicitly represented and only one field spacing was tested, the proposed spacing ratio should be regarded as condition-specific rather than universal.