# Simulation of Rock Failure Cone Development Using a Modified Load-Transferring Anchor Design
## 2 Materials and Methods  
### Assumptions Adopted in the Model  
For simulation purposes, the mechanical parameters characterizing the rock were assumed to be comparable to those measured in field detachment tests [34; 50], in which prototypes of the drive unit and the anchor itself were tested under real geological conditions. Figure 6: Characteristic dimensions of the proposed anchor design, developed based on data from ITG KOMAG. Figure 7: Nominal dimensions of the installation borehole for the newly designed anchor, developed based on data from ITG KOMAG. The rock material was defined in the model as a linear, elastic, and isotropic solid, with the following mechanical properties:  
Young's modulus: 14,275 MPa;  
Poisson's ratio: 0.247. The adopted mechanical parameters correspond to gray sandstone collected from the Brenna mine, which was subjected to both field testing and laboratory characterization (Table 2). This specific rock type is characterized by a layered but relatively homogeneous structure with a stratification thickness of 0.7-1.0 m, which did not influence the detachment pattern or extent (Figure 9d in [63]). The choice of an isotropic, linear elastic model for the rock was a deliberate simplification aimed at isolating and analyzing the influence of the anchor geometry and loading scheme on failure development. While it is recognized that natural rocks often exhibit anisotropy, heterogeneity, and pre-existing discontinuities, the adopted approach is justified by the nature of the tested gray sandstone, which exhibited a homogeneous structure and brittle behavior within the scale of the observed detachment zone. Field experiments confirmed a consistent and repeatable fracture pattern, which supports the use of a simplified material model in the early stage of numerical development. Nonetheless, future work will incorporate more advanced constitutive models to address anisotropy, inhomogeneities, and the presence of bedding planes or joints. Numerical simulations were conducted using ABAQUS v.2022 (ABAQUS, Version 2022, Dassault Systemes Simulia Corp., Providence, RI, USA), incorporating the Extended Finite Element Method (XFEM). A brittle fracture criterion was applied, assuming that the onset of material failure is governed by the value of the maximum principal tensile stress. Crack propagation was defined to occur perpendicularly to the direction of the maximum tensile stress. The evolution of damage was controlled by the fracture energy required to extend the crack. The rock strength parameters used in the numerical simulations are within the range of results obtained from field tests as well as strength tests described in detail by scientific team members [50; 56; 57; 61; 63; 64; 65]. Accordingly, in ABAQUS, the following damage model was implemented:  
* Damage initiation criterion: Max Principal Stress;
* Crack growth direction: perpendicular to the maximum principal tensile stress;
* Damage evolution: energy-based fracture propagation. The critical tensile stress (failure threshold) was set to \(f_{\text{t}}\) = 7.74 MPa, and the fracture energy \(G_{\text{f}}\) was defined as 0.17 N/m, using a linear softening model. A stabilization coefficient of \(1\times 10^{-6}\) was applied to ensure numerical convergence in the XFEM algorithm. The steel used for the anchor components was also modeled as a linear, elastic, and isotropic material, with deformation remaining within the elastic range. The mechanical properties of the steel were defined as follows:  
Young's modulus: 210,000 MPa;  
Poisson's ratio: 0.3. These parameters ensured accurate representation of the elastic behavior of the steel anchor elements while focusing the fracture simulation on the surrounding rock mass.