VECTOR ANALYSIS OF KEYBLOCK ROTATIONS

The mechanical response of rock slopes and excavations depends largely on the geometry of discontinuities and associated rock blocks. Common ly used rigid black models for determining stability, such as the slid ing wedge model or the keyblock analysis, assume that initial displace ments are pure translations. This paper examines kinematic and kinetic constraints on block rotations. The kinematic constraints include con ditions that are independent of the free surface and therefore belong uniquely to the joint pyramid, as well as conditions that depend on th e orientation of the free surface. The relevant criteria, expressed in terms of vector inequalities are represented on the stereographic pro jection, allowing graphical solution of the kinematical inequalities. Additionally, rotational equilibrium of tetrahedral blocks is consider ed, the failure modes of block theory are generalized to include rotat ional modes and procedures for evaluating rotational stability are dis cussed. The results show that blocks found to be stable with respect t o the translational modes of sliding and falling may yet fail by rotat ion.