Stability of Rock Wedges and Excavation Surfaces - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 291

hibit components pointing away from both discontinuities (movement away from D1 and
D2). The translation of practical relevance here is directed parallel to D1 (Fig. 11.4, right).
Methods of identification of kinematically admissible translations are the stereographic
projection technique (Goodman 1980) and the so-called “block theory”. The latter is based
on a mathematical branch of topology which allows a systematical identification of wedges
or blocks that are most critical for stability referred to as “keyblocks”. These methods are
not considered in this topic. For a detailed description of block theory see Goodman &
Shi 1985, Mauldon & Goodman 1990, Mauldon 1992, Chern & Wang 1993, Hatzor 1993,
Mauldon & Goodman 1996, Tonon 1998 and Pötsch & Schubert 2006, for example.
Figure 11.4 Potential translations of two-dimensional rock wedges supported by one and two
discontinuities
Sliding on one discontinuity
Figure 11.5 shows the forces acting on a two-dimensional rock wedge that is supported
by one discontinuity D and loaded by self-weight. The state of limit equilibrium of
such a wedge is achieved when the resisting shear force due to the normal force acting
on the discontinuity balances the shear force acting on the sliding surface. Adopting
Mohr-Coulomb's failure criterion the limit equilibrium of the wedge can be formulated
as