The strain response mirrors stress behavior, with maximum volumetric strain occurring at S1 and decreasing substantially with increased spacing. However, the magnitude of strain amplification differed between the two cases. Case One exhibited a stronger interaction effect, with volumetric strain at S1 reaching 1.5 times the single‑shaft value, whereas Case Two showed a more moderate increase of approximately 1.27. This difference indicates that the boundary conditions or material properties assumed in each case influence the degree of shaft interaction, even though the overall trends remain consistent. Backfilling also resulted in stress and strain deduction in Case Two. Overall, the results highlight the sensitivity of shaft interaction to spacing and demonstrate that even modest increases in separation can significantly reduce stress and strain amplification. This has direct implications for shaft layout optimization in underground design. 4. CONCLUSIONS In this study, a numerical model is developed to evaluate the application of VCM in a kimberlite mine and to determine the minimum shaft spacing required to maximize recovery while maintaining shaft stability. Two cases are examined across three spacing configurations, along with single‑shaft reference scenarios, resulting in a total of eight modeled conditions for comparison. The analysis confirms that shaft spacing plays a decisive role in controlling stress and strain interactions between adjacent excavations. The introduction of a second shaft increases the mechanical loading on the first, with the most severe effects occurring at the smallest spacing (S1). As spacing increases, both stress and strain responses decline rapidly, approaching those of the single‑shaft configuration. At the largest spacing considered (S3), the interaction effects become minimal, and the system behaves nearly as if only one shaft were present. The consistent trends observed in both Case One and Case Two, despite differences in the magnitude of strain amplification, underscore the robustness of the findings. These results suggest that maintaining sufficient spacing between shafts is essential for minimizing stress concentrations, reducing deformation, and enhancing overall stability. Consequently, the study provides a clear basis for determining minimum recommended shaft spacing in similar geological and operational conditions. ACKNOWLEDGEMENTS The authors would like to thank the support of Fonds de Recherche du Quebec – Nature et Technologies (FRQNT) in conducting this research.
RkJQdWJsaXNoZXIy MTM0Mzk2