INTRODUCTION
Three case histories of toppling failures of rock slopes, and the methods used to ensure that failure did not disrupt operations below the slope, are described. The application of Goodman and Bray's limit equilibrium analysis of multi-block toppling failures to these three slopes is demonstrated.
The first failure occurred in a 20 m high granite slope that was stabilized by removing the top 6 m and installing a number of tensioned rock anchors in the toe. The second failure occurred in a sequence of folded sandstone, shale and coal. This slide was too large to stabilize, so the movement rate was monitored while mining continued in the pit below until shortly before failure took place. In the third failure, the top 8 m of a single 12 m high toppling block was removed by blasting to prevent further rotational movement.
Toppling failures can occur in slopes cut in rock with regularly spaced fractures which strike parallel to the slope, and dip into the face. This contrasts with sliding failures which occur when the geological structure dips out of the face (Hoek and Bray (1977)). Although the stability of toppling failures can be studied using numerical models (Burman (1971); Byrne (1974); Cundall (1971)) and physical models (Barton (1971); Soto (1974)), these analyses can be time consuming and the required facilities may not be readily available. However, Goodman and Bray's (Goodman and Bray (1976)) limit equilibrium analysis for multiblock failures now permits the analysis of toppling failures, and the selection of appropriate stabilization measures, to be carried out readily.
This paper describes three toppling failures and shows the stabilization measures which were applied in two cases. In the third case, movement was monitored with electronic distance measuring equipment while operations continued at the toe of the slide. The application of Goodman and Bray's analytical solution to these three examples is demonstrated, and the limitation of the technique in the design of slopes with a geological structure that could cause toppling is discussed.
Toppling movement occurs in slopes where a regularly spaced set of joints or bedding planes strike parallel, or nearly parallel, to the slope face and dip at a steep angle into the face. This geological structure forms a series of tall, narrow slabs (Figure 1). If the dimensions of a slab are such that its centre of gravity acts outside the base of the slab, then there is a potential for the slab to topple. This criteria is given by the relationship (Goodman and Bray (1976)):-
(Equation in full paper)
Short slabs at the crest not meeting the criteria shown in equation (1), and that do not slide on the base, are stable (Figure 1, slabs 6, 7), but longer slabs which topple (slabs 3,4, 5) exert a thrust on the slab immediately below it on the slope. This thrust produces a moment on the lower block which increases its tendency to topple, ie. a “domino effect”.
