Analysis of tetrahedral and pentahedral key blocks in underground excavations

Abstract This paper presents a study the non-pyramidal key blocks of the rock mass. After a review of the Key Blocks Method (KBM), the study focuses on the analysis of key blocks formed by three and four discontinuity planes in underground excavations. The concept of non-pyramidal key blocks is described and their generation from a geometric operation called dislocation, thus determining the pentahedral key blocks that may be formed. To do so, the software program ASTUR (Analysis of the Support of Tunnels in Rock) was used, which develops a ubiquitous approach and allows the analysis of both pyramidal and non-pyramidal tetrahedral and pentahedral blocks. From this analysis, it is possible to ascertain the behavior of the block stability as a function of the trend and plunge of the tunnel axis. Isoplethograms have been used to illustrate how the block assembly might affect the design of an excavation. It may be concluded from the study that it is necessary to analyze the non-pyramidal key blocks with four discontinuity planes, since these may generate blocks with a large volume and a much lower safety factor than that obtained by blocks with three planes. In this respect, the ASTUR software improves on existing programs in the analysis of instability in ubiquitous rock mass. The results obtained were applied to the design of an access tunnel in an underground marble mine situated in the south east of Spain.