# Simulation of Rock Failure Cone Development Using a Modified Load-Transferring Anchor Design
## 2 Materials and Methods
### Model Geometry, Finite Element Mesh, and Boundary Conditions
This meshing strategy ensured a balance between computational efficiency and the required resolution in zones where mechanical interaction, stress concentration, and potential crack initiation were anticipated. Although a graphical representation of mesh sensitivity was not included in the present manuscript, it is important to emphasize that a detailed mesh convergence study was conducted in previous works by the authors [33; 55; 60; 66], where the influence of element size, local refinement strategies, and XFEM-based crack tracking accuracy was extensively analyzed. The adopted mesh parameters and refinement strategy used in this study were based on the optimal configurations established in those earlier publications. Furthermore, due to the use of the XFEM algorithm, which is known for its robustness against mesh dependency effects in fracture problems, the influence of global mesh density on the overall crack trajectory was found to be negligible once a critical refinement threshold was achieved [67; 68; 69]. Therefore, to avoid duplication of previously published data and due to space constraints, mesh sensitivity analysis was not presented graphically in this article. The findings reported in prior studies conducted by the authors [33; 55; 60; 66] have repeatedly confirmed that, for both conventional and modified anchor geometries, the selected meshing strategy ensures the adequate resolution of stress fields and accurate crack trajectory prediction within the XFEM framework. The boundary conditions imposed on the model were designed to replicate realistic constraints present in field applications while also ensuring numerical stability and symmetry. The left edge of the model, which represents the axis of symmetry, was fully constrained in the radial (horizontal) direction (U1 = 0) and rotational degrees of freedom (UR2 = 0), allowing displacement only along the vertical axis. The bottom edge of the domain was restrained vertically (U2 = 0) to simulate the presence of a supporting rock mass below the anchor. The right vertical edge was constrained horizontally (U1 = 0), simulating confinement by the surrounding rock and preventing artificial lateral expansion. These constraints reflect a semi-infinite domain approximation commonly used in axisymmetric fracture modeling and ensure that artificial boundary effects do not interfere with the stress distribution and crack propagation around the anchor head. Figure 11: Finite element mesh of the rock mass model with an undercut borehole. The extensive experience gained through these investigations justifies the use of previously validated mesh configurations in the present analysis. Consequently, the current study adopted the optimal mesh structure established earlier, with no additional graphical documentation of mesh sensitivity included herein, as it would not contribute new insights. This approach is further supported by numerous reports in the literature [70; 71; 72], which emphasize that when XFEM is employed, the influence of global mesh size on the quality of fracture predictions becomes significantly reduced, provided that localized refinement is properly applied in critical regions [73]. For the rock mass model, the total number of generated nodes was 1285, and the number of elements was 1195. The radial clearance between the cylindrical surfaces of the anchor and the borehole was set to 0.5 mm, representing one of the analyzed configuration variants. For the anchor body, the mesh included 338 nodes and 294 elements, of which 287 were linear quadrilateral elements of type CAX4R and 7 were linear triangular elements of type CAX3. For the drive screw, the mesh consisted of 103 nodes and 85 elements, including 83 linear quadrilateral elements (CAX4R) and 2 linear triangular elements (CAX3).