Analysis of the Rock Failure Cone Size Relative to the Group Effect from a Triangular Anchorage System

This study employs the numerical analysis and experimental testing to analyze the fracturing mechanics and the size of rock cones formed in the pull-out of a system of three undercut anchors. The research sets out to broaden the knowledge regarding: (a) the potential of the undercut anchor pull-out process in mining of the rock mass, and (b) estimating the load-carrying capacity of anchors embedded in the rock mass (which is distinctly different from the anchorage to concrete). Undercut anchors are most commonly applied as fasteners of steel components in concrete structures. The new application for undercut anchors postulated in this paper is their use in rock mining in exceptional conditions, such as during mining rescue operations, which for safety considerations may exclude mechanical mining techniques, mining machines, or explosives. The remaining solution is manual rock fracture, whose effectiveness is hard to assess. The key issue in the analyzed aspect is the rock fracture mechanics, which requires in-depth consideration that could provide the assistance in predicting the breakout prism dimensions and the load-displacement behavior of specific anchorage systems, embedment depth, and rock strength parameters. The volume of rock breakout prisms is an interesting factor to study as it is critical to energy consumption and, ultimately, the efficiency of the process. Our investigations are supported by the FEM (Finite Element Method) analysis, and the developed models have been validated by the results from experimental testing performed in a sandstone mine. The findings presented here illuminate the discrepancies between the current technology, test results, and standards that favor anchorage to concrete, particularly in the light of a distinct lack of scientific and industry documentation describing the anchorage systems’ interaction with rock materials, which exhibit high heterogeneity of the internal structure or bedding. The Concrete Capacity Design (CCD) method approximates that the maximum projected radius of the breakout cone on the free surface of concrete corresponds to the length of at the most three embedment depths (h(ef)). In rock, the dimensions of the breakout prism are found to exceed the CCD recommendations by 20–33%. The numerical computations have demonstrated that, for the nominal breakout prism angle of approx. 35% (CCD), the critical spacing for which the anchor group effect occurs is ~4.5 (a cross-section through two anchor axes). On average, the observed spacing values were in the range of 3.6–4.0.