# Simulation of Rock Failure Cone Development Using a Modified Load-Transferring Anchor Design
###### Abstract
The authors' previous experience shows that in the case of rocks (sandstone) the extent of the failure zone described, among other things, by the value of the angle of the failure cone \(\alpha\) and the value of the diameter of the base of this cone measured at the free surface significantly differs from the characteristic values (taken as standard) for concrete. The Concrete Capacity Design (CCD) method approximates that the maximum projected diameter of the breakout cone on the free surface of concrete corresponds to the length of at most three embedment depths (\(h_{\text{ref}}\)). The numerical computations have demonstrated that, for the nominal breakout prism angle of approx. 35\({}^{\circ}\) (CCD), the critical spacing for which the anchor group effect occurs is \(\sim\)4.5 (a cross-section through two anchor axes). On average, the observed spacing values were in the range of 3.6-4.0. Previous experimental work on the disintegration of intact rock using mechanical anchors clearly indicates that, for this application, undercut anchors are the most suitable solution due to the specific nature of load application [41; 55; 56]. The rationale for employing undercut anchors in the proposed rock detachment technology lies in the mechanism of stress induction within the rock mass. Specifically, the stresses generated by the applied load are concentrated at the geometric undercut formed by the cutting head, resulting in a localized stress field that facilitates fracturing of the surrounding rock. This method of inducing rock failure using an anchor can be conceptually compared to the failure mechanism observed in conventional anchorage systems, where pull-out failure occurs through the formation and detachment of a concrete breakout cone. An example application area of the proposed technology is the excavation of mine workings (Figure 2), where the process involves local rock disintegration by pulling out individual anchors in locations that allow for the effective detachment of rock lumps. Tests of the proposed technology under industrial conditions are described in [57; 58; 59]. In order to gain a closer understanding of the phenomenon of the effect of the interaction of successive detachments in such a proposed technology, the phenomenon was analyzed numerically and experimentally. For particular rock types, a significant correlation was found between the structural parameters of the head, the strength parameters of the rock, and the depth of the \(h_{\text{ref}}\) anchorage [33; 46; 51; 60; 61]. Table 1 summarizes the number of successful detachment tests performed for rock samples collected from four mining locations. A total of 115 tests were conducted across the Zalas, Braciszow, Guido, and Brenna mines. The dataset provides the experimental basis for subsequent mechanical analysis and interpretation of rock behavior under load. Field studies were carried out at several rock extraction sites [50]. The number of detachment experiments conducted is summarized in Table 1.  
Table 2 presents the basic mechanical and strength parameters of rocks collected from four different mining sites in Poland. The data include uniaxial compressive strength fc, tensile strength ft, the ratio of compressive to tensile strength (\(k=f_{\text{c}}/f_{\text{t}}\)), internal friction angle (\(\varphi\)), and cohesion (c). Additionally, the rock type and a brief geological description of each sample are provided. These parameters are essential for characterizing the mechanical behavior of the rock masses and assessing their suitability for engineering applications. Mechanical parameters of the studied rocks are illustrated in Table 2[50]. \begin{table}
\begin{tabular}{c c} \hline
**Mine** & **Number of Successful Detachment Tests Conducted** \\ \hline “ZALAS” & 30 \\ “Braciszow” & 27 \\ “Guido” & 36 \\ “Brenna” & 22 \\  & \(\Sigma\)115 \\ \hline \end{tabular}
\end{table} 
Table 1: Number of conducted, successful detachment tests. Figure 2: Example of using the proposed technology for local rock detachment in an excavation site.