# Simulation of Rock Failure Cone Development Using a Modified Load-Transferring Anchor Design
###### Abstract
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Mine** & \(f_{c}\) **(MPa)** & \
\begin{tabular}{c} **Standard** \\ **Deviation** \(f_{c}\) \\ \end{tabular} & \(f_{t}\) **(MPa)** &
\begin{tabular}{c} **Standard** \\ **Deviation** \(f_{t}\) \\ \end{tabular} & \(k=f_{c}\)**/\(f_{t}\)** & \(\varphi\) **(\({}^{\circ}\))** & \(\epsilon\) **(MPa)** & **Rock** & **Description** \\ \hline Zalas & 106.5 & 23.86 & 5.9 & 1.91 & 18.1 & 54 & 8.6 & porphyry & Deck strongly undulating \\ \hline Braciszów & 155.3 & 29.17 & 8.0 & 0.64 & 19.41 & 49.5 & 14.5 & sandstone & Sandstone, strong, compact \\ \hline Benna & 58.8 & 9.29 & 3.9 & 1.17 & 15.1 & 53 & 6.0 & sandstone & Sandstone, layered, weak \\ \hline Guido & 97.4 & 25.52 & 6.2 & 0.94 & 15.7 & 49.6 & 11.9 & sandstone & Sandstone, compact, medium strength \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical parameters of the studied rocks. Figure 3: (**a**) Components of the experimental setup, measurement signal recording equipment, and recorded parameters: 1—cylinder support; 2—hydraulic cylinder; 3—hand pump set with a pressure gauge; 4—digital receptor; 5—current force acting on the anchor. (**b**) Identification of the geometric parameters of the failure surface using a Shining 3D handheld 3D laser scanner. (**c**) Characteristic parameters of the failure surface: \(h_{\phi}\)—effective anchorage depth; \(\alpha\)—breakout cone angle; \(Z\)—extent of detachment measured on the free surface of the rock medium. Research efforts aimed at automating the detachment process have led to further modifications of the anchor design, as illustrated in Figure 6. The new detachment anchor design, intended to induce material rupture near the borehole bottom via radial expansion, is characterized by the geometric parameters shown in Figure 6[54]. In order to enable comparisons, an important element of the conducted tests was to maintain a comparable value of the undercut angle of the medium \(\beta\) (the angle of the anchor head after spreading in the hole) for typical HILTI-type anchors and the proposed anchor design (Figures 5 and 6) because it is important for the propagation of failure [56; 60], as well as the formation of the pullout force. Hence, an angle value of \(\beta\) =13.3\({}^{\circ}\) was finally used in the anchor design used in the industrial research (Figure 6[54]). Based on previous experimental investigations and numerical analyses conducted on the first prototype version [55], it was determined that the optimal embedment depth for the proposed detachment method is \(h_{\text{ef}}\) = 70 mm. This value was selected taking into account several critical factors: the extent of the induced fracture zone, the mass of the detached rock fragments, the magnitude of the force (torque) required for successful detachment, and the practical feasibility of manipulating the dislodged rock within the confined space of an excavation, particularly in scenarios such as rescue operations. Figure 4: The application of the installation torque (**a**) to the anchor’s threaded bolt (as in position 3, Figure 1) that led to the breakout prism detachment; F—force required to turn the threaded bolt in the anchor; (**b**) electronic force gauge with an external sensor (AX_FC1k). Figure 5: Modified anchor design for rock mass detachment: 1—undercutting element of the anchor head; 2—conical expansion element; 3—drive screw (anchor core); 4—setting ring; 5—induced crack/fracture in the rock mass; R—reaction force of the drive screw acting on the borehole bottom; \(R_{1}\)—reaction force of the anchor head acting on the rock in the undercut zone; \(M\)—applied torque on the drive screw; \(\Delta\gamma\)—incremental (axial) displacement. This type of anchor is installed into a pre-drilled borehole with a specially prepared undercut to accommodate the anchor head.