KEYBLOCKS
Excavations in jointed rock are frequently affected by keyblocks, unstable blocks of rock bounded by planar discontinuities and excavation surfaces. Formation of keyblocks depends on the geometry of the discontinuities relative to the geometry of the excavation. The size, location and frequency of keyblock occurrence is controlled by the number, size, location and orientation of the discontinuities which intersect the excavation. A probabilistic model has been developed which, once the geometry of the discontinuities present in the rock mass is characterized, can be used to predict keyblock occurrence for proposed excavation geometries. Although the term joint is used throughout this paper, the methods presented are applicable to the analysis of any planar discontinuities.
DETERMINISTIC KEYBLOCK ANALYSIS
Deterministic keyblock analyses determine what shapes of keyblocks are possible for a given excavation geometry and a group of specified joint orientations (Goodman and others, 1982; Priest, 1985; Warburton, 1981). All combinations of excavation surfaces and joints are examined to determine which combinations will form keyblocks. In order to form a keyblock, the joint planes and excavation surfaces must completely isolate a block of rock, the block must be shaped so that it can move into the excavation (the block is not tapered), and the block must have friction which is unable to prevent forces acting upon the block from causing the block to move. Once a combination of joint orientations has been identified which can intersect the excavation to form a keyblock, the joint locations which create the largest possible keyblock for the particular shape (combination of joint orientations) can be determined. A maximum removable area can also be defined (Goodman and Shi, 1985). For a particular excavation cross-section, the union of the projections of all possible keyblocks of a given shape defines an area called the maximum removable area. If an infinite number of keyblocks of the given shape are present along the length of the excavation, the volume of rock removed by keyblock failures per unit of excavation length will be equal to the maximum removable area for the particular keyblock shape. For a particular keyblock shape, no keyblocks will occur outside of the triangular prism defined by the maximum removable area (Figure 1), and depending on the number of joints and their locations, every point in the area could be contained in a keyblock.
