# Simulation of Rock Failure Cone Development Using a Modified Load-Transferring Anchor Design
###### Abstract
These anchors are particularly effective in high-load or safety-critical applications due to their ability to transfer loads through a mechanical undercut formed at the base of the drilled hole, thereby reducing the risk of pull-out failure. An example of such an anchorage configuration is illustrated in Figure 1[39]. Figure 1 presents a typical configuration of an undercut anchor system, specifically a commercially available design produced by HILTI. A key area of research interest concerning such anchors is the determination of the maximum safe load that can be applied without causing either pull-out failure or fracture of the anchor shaft. An analysis of catalog  
Figure 1: Example of the design and installation of an undercut anchor system: \(\beta\)–Head angle (undercut in the rock). data [39; 40] showed that the angle of undercut \(\beta\) resulting from the design parameters of HILTI-HDA type anchors is about 15\({}^{\circ}\). Its value depends largely on the precision of the installation [41] and the precision of the hole for the anchor. Several methods for estimating the load-bearing capacity of undercut anchors--particularly in scenarios involving the failure of the surrounding concrete in the form of a conical breakout--are presented in the literature [42; 43; 44; 45]. Most of these approaches share a common framework, as they typically rely on two principal variables: the effective embedment depth \(h_{\text{ref}}\) and the compressive strength of concrete \(f_{\text{cc}}\) measured in cubic specimens (in N/mm\({}^{2}\)) [39; 44; 45; 46]. Other important aspects considered in the study of anchor systems include the shape and extent of the failure zone--commonly referred to as the concrete breakout cone--as well as the phenomenon of interaction between adjacent failure zones [47; 48; 49]. These factors are critical for the safe and effective spacing of anchors under anticipated service loads. An inadequate understanding of these interactions may lead to overlapping failure cones, resulting in a significant reduction in the overall load-bearing capacity of the anchorage system. Therefore, proper anchor layout planning, taking into account breakout cone geometry and interaction effects, is essential to ensure structural reliability and safety in service conditions [50; 51]. Two principal methods are most commonly employed to estimate the design strength of anchor systems with respect to concrete breakout failure: the 45\({}^{\circ}\) cone failure method and the Concrete Capacity Design (CCD) method cone at 35\({}^{\circ}\) or an adequate prism [48; 49; 52]. The 45\({}^{\circ}\) cone failure approach assumes that a conical failure surface develops in the concrete surrounding the anchor, forming an angle of approximately 45\({}^{\circ}\) between the breakout surface and a plane perpendicular to the anchor axis [52]. This method provides a simplified geometric model of the failure mechanism, which is useful for preliminary calculations and conservative design. The second method, the CCD (Concrete Capacity Design) approach, is based on a similar failure mode but refines the geometry of the failure surface. It assumes that the breakout takes the shape of a four-sided pyramid with an inclination angle of 35\({}^{\circ}\) between the failure surface and the concrete member surface [39; 53; 54]. The CCD method is more widely accepted in modern engineering practice, as it accounts for a broader range of influencing parameters, including embedment depth, concrete strength, and edge distances, and is incorporated into international design standards such as the European Technical Guidelines and ACI codes. The authors of this study propose a novel application of undercut anchors, namely as a tool in rock fragmentation technologies (in situ rock mass disintegration) in environments where conventional mechanical excavation methods or the use of explosives are prohibited due to regulatory constraints or operational conditions.