Stability of Rock Wedges and Excavation Surfaces - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 317

Setting μ = 1 and solving (11.75) for A d yields:

(11.76)

Sliding of a pseudo-three-dimensional rock wedge
In order to check the stability of the temporary face of a tunnel against sliding a rock
wedge such as illustrated in Fig. 11.25 is often investigated. This wedge may be bounded
by a discontinuity D dipping towards the temporary face and two vertical lateral planes.
The free surface of this sliding wedge is modeled by an equivalent rectangle that has the
same surface area as the temporary face. Such a wedge in a certain sense can be referred
to as “pseudo-three-dimensional”.

Figure 11.25 Pseudo-three-dimensional wedge to check the stability of the temporary face of a tunnel
against sliding

If this wedge is loaded only by its self-weight G and part of the weight of the overlying
rock mass P, the components of G and P parallel to D, denoted as G T and P T , respec-
tively, are driving forces that must be balanced by the resisting forces T D and T L due
to friction and cohesion of the discontinuity D and the lateral planes. According to the
partial safety factor method, the stability against sliding is then assessed by the follow-
ing utilization factor (Fig. 11.25):

(11.77)