# Simulation of Rock Failure Cone Development Using a Modified Load-Transferring Anchor Design
## 3 Results and Discussion  
In recent years, the growing complexity of engineering problems in geomechanics and material science has intensified the need for advanced computational methods capable of capturing intricate mechanical behaviors of heterogeneous media such as composite materials, rocks, or cementitious systems. In this context, numerical approaches--including the Finite Element Method (FEM) [74; 75; 76], Boundary Element Method (BEM) [77; 78; 79], and various analytical formulations [80; 81]--have proven invaluable for modeling stress distribution, crack initiation, and failure propagation in cases where experimental investigations are constrained by limited access to representative samples, high testing costs, or safety concerns. These methods enable the detailed exploration of failure mechanisms and material responses under controlled boundary conditions, often exceeding what is feasible in laboratory settings. Furthermore, the integration of machine learning algorithms with traditional computational techniques offers new avenues for pattern recognition, inverse problem solving, and model calibration [82; 83; 84; 85]. Particularly in scenarios involving limited experimental data, supervised learning or surrogate modeling can enhance the predictive accuracy of numerical simulations. The synergy between numerical modeling and artificial intelligence thus provides a robust framework for optimizing design, improving failure predictions, and supporting decision-making in engineering applications involving complex material systems [86; 87; 88; 89; 90; 91]. The study revealed a predominant tendency for material cracking to occur beneath the tip of the driving screw (Figures 12 and 13), which differs from failure patterns observed in pull-out anchor models or those related to installation anchor systems, where crack initiation typically occurs at the notch corner created by a conical undercutting head [60]. The results also confirmed a characteristic two-stage evolution of the detachment crack, consistent with findings reported in earlier studies [61]. In the first stage, the fracture propagates deep into the rock mass along a parabolic trajectory, initiated under a negative or zero initial penetration angle (\(\alpha\)), as described in detail in [55; 61]. In the second stage, a deflection in the crack trajectory occurs, and the fracture begins to propagate asymptotically toward the free surface of the rock. This behavior continues until the eventual breakout of the detached rock fragment in the final phase of the process. It should be noted that minor deviations from the expected trajectory may result from limitations in the crack direction algorithm implemented in ABAQUS, which were also documented in previous studies [41; 56; 63]. Figures 12 and 13 demonstrate a strong correspondence between the stress distribution in the anchor-rock interaction zone and the shape and trajectory of the propagating fracture, as compared to the results obtained in numerical simulations of the initial prototype of the detachment anchor [41; 55], as well as earlier studies involving the use of undercut anchors [61; 92; 93], in which the anchor was extracted using specialized equipment. These findings are also consistent with current in situ experimental results involving the newly proposed anchor design. The numerical results obtained in this study reveal notable discrepancies when compared to conventional failure models such as the Concrete Capacity Design (CCD) method  
Figure 12: (**a**) Distribution of maximum principal stress \(\sigma_{\text{max}}\) and bimodal crack development under the action of the detachment/expansion anchor: 1—primary crack, which diminishes during the progressive displacement of the anchor along the OY axis (as imposed by the kinematic loading); 2—secondary crack, responsible for the final detachment of the breakout “cone” of the rock mass; (**b**) stress \(\sigma_{12}\) distribution. or the 45\({}^{\circ}\) cone model.