Analyzing the stability of the three-dimensional wedges created around underground excavations in rock masses is a common problem in rock engineering. Most existing algorithms for wedge failure analysis assume wedges to be in low stress environments. Under such conditions the influence of stresses on the wedge factor of safety can be ignored. In blocky rock masses experiencing high in situ stresses, however, such analysis can lead to conservative results. This paper discusses the incorporation of stresses calculated from boundary element analysis into the analysis of wedge stability. The new formulation assumes complete plane strain, allowing the analysis of tunnels arbitrarily oriented with respect to principal stress directions. The approached described in the paper is implemented in the program Unwedge.


The stability of wedges formed around underground excavations in blocky rock masses is a common problem in rock engineering. The wedges are formed by intersecting discontinuities and the free face created through excavation of an underground opening.

Under the influence of gravity and other forces, roof and wall wedges may fail either by falling, sliding or rotating out of their sockets. The factors that control wedge stability include geometry (the size, shape and spatial location of a wedge), the strength characteristics of the discontinuity planes that create the wedge, and stresses within the rock mass.

Most existing algorithms for underground wedge stability analysis assume that stresses are sufficiently low and can therefore be ignored. This is fine for wedges in low in situ stress environments, such as those encountered in shallow excavations [1]. When in situ stresses are high, however, exclusion of the effect of stresses leads to error.

The assumption of zero stress results in very conservative results for certain cases. The stability of a wedge in the roof of an excavation is an example. Such a wedge fails by falling under the influence of self-weight. Traditional stability analysis approaches (which do not take stress into account) predict that this wedge has a factor of safety of zero, and can remain in place only when supported.

Many practical situations defy this prediction. Roof wedges located in deep underground excavations have been observed to be stable. Kaiser et al [2] suggest that conventional underground wedge stability analyses are commonly too conservative because they ignore stress.

The stability of wedges at significant depths can be explained by the clamping effect of the surrounding stress field. The components of confining stress normal to the discontinuity planes, which form a wedge, mobilize shear resistance sufficient to keep the wedge in place.

Unfortunately, including stresses in wedge stability analysis is not a trivial exercise. To simplify the problem, techniques that have been suggested use assumptions such as:

  • Two-dimensional wedge and stress geometry, and/or

  • In situ stresses acting on wedges.

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