1884 To evaluate shaft performance under Arctic conditions, numerical modeling techniques have proven essential in simulating excavation behavior and predicting potential instability (Dourado et al., 2024). Initial assessments typically begin with the stress–strain response of a single shaft, establishing a baseline for mechanical stability. However, mining operations rarely involve isolated excavations; shafts are often constructed in close proximity to one another. This introduces the critical issue of spacing, as the interaction between adjacent shafts can significantly alter stress distributions within the surrounding rock mass (Hou et al., 2023). Investigations into shaft spacing have shown that the distance between excavations directly influences the likelihood of stress concentration and deformation. When shafts are positioned too close, the overlapping stress fields can compromise stability and increase the risk of collapse. Conversely, greater spacing reduces these interactions, allowing the shafts to maintain structural integrity under Arctic conditions. By systematically examining multiple spacing scenarios, researchers have been able to identify thresholds where excavation remains safe and where instability becomes probable, applying defined failure criteria to ensure rigorous evaluation (Dourado et al., 2024; Mamot et al., 2021). This focus on spacing underscores the importance of excavation geometry in Arctic mining. Beyond the technical challenge of cutting through permafrost and hard rock, the spatial arrangement of shafts emerges as a decisive factor in balancing resource recovery with geomechanical safety. As climate change continues to expose new Arctic regions for exploration (Tkach, 2021), understanding the role of shaft spacing provides a foundation for developing mining strategies that minimize ecological disruption while ensuring operational reliability. 2. METHODOLOGY The present investigation centers on the application of the VCM in the mining of kimberlite deposits. Particular attention is devoted to understanding the geomechanical behavior of the surrounding rock mass as well as to analyzing the step‑by‑step excavation of the shafts within a cylindrical ore formation. The methodological framework adopted for numerical study is described in detail in the following sections. Numerical simulations were executed using COMSOL Multiphysics. The fundamental local force balance (equilibrium) equation was used based on the continuum mechanics concepts as follows: ∇σ+F=0 (1 where σ is the Cauchy stress tensor and F represents the body/external force per unit volume. For an isotropic solid exhibiting linear elasticity, the governing stress–strain interaction is formally described by Hooke’s law, which provides the mathematical foundation for relating applied stresses to the resulting deformations. σ=C:ε (2 where C corresponds to the elasticity tensor of fourth order, which encapsulates the stiffness characteristics of the material, while “ denotes the infinitesimal strain tensor. The strain tensor is formulated directly from the displacement field Ç, serving as the mathematical expression of how small variations in displacement translate into local deformations of the medium. It is formally defined as: ε= 1 2[(∇u)+(∇u)T] (3 For a linear, isotropic, elastic medium, the stress–strain relation is governed by Hooke’s law:
RkJQdWJsaXNoZXIy MTM0Mzk2