# Design of Slopes

All excavated slopes are designed to a chosen factor of safety. This is generally not lower than 1.5 and not greater than about 2.5, but in every slope design there may be ‘hidden’ safety factors obtained by choosing conservative values of strength, or pessimistic views with regard to water pressure. It is important to decide whether the slope should have “long term” or “short-term” stability.

Most road, railway, canal etc. slopes are designed for long-term stability in which case account must be taken of the possible reduction in strength of materials and discontinuities as the result of weathering and erosion of the slope by gullying from rain wash. Slopes with short-term stability could be some open mine slopes and the slopes for foundation excavations. In excavations in soil over rock the critical factor may be the slope of the bedrock topography on which the soil rests.

In slopes in rock where stability problems usually occur by sliding over discontinuities the slope can be designed on the basis of the strength of these discontinuities. The only complication is that the shape of the block is no longer neatly rectangular, but an irregular shape whose weight is difficult to calculate.

However if the geological situation is favourable it may be possible to design a rock slope so that any unfavourably inclined discontinuities do not outcrop on the slope. Thus, in rock slope design one of the simplest design techniques is to arrange for the slope direction and angle to be such that no steeply dipping discontinuity outcrops from the excavated slope (Fig. 1a).

This very simple approach is often the best for road cuttings and similar permanent excavations when space and orientation of the works permits such freedom of choice, for it avoids having to assign values of c and ϕ to discontinuities. Calculating safe slope angle based on c and ϕ values is possible in fresh rock masses such as, perhaps, open pit mines, but in civil engineering excavations, which are often within the weathered zone, it is very difficult to assign a single value to c and ϕ that the designer will be confident will apply to the whole slope. Also civil engineering excavations are permanent and long-term weakening of discontinuities by weathering after excavation has to be considered.

In almost any excavation there must be some discontinuities which outcrop on one slope. Thus in the Fig. 1b discontinuity ‘a’ outcrops and could allow sliding on the east slope if ‘a’ is a very weak discontinuity, particularly prominent and frequent, or liable to long-term deterioration. If so the slope could be flattened to the inclination of ‘a’. Alternatively, it is possible that local support works could be planned for areas in which, after excavation, it seemed likely that local failures on ‘a’ could occur.

The discontinuity set on which sliding may take place need not be continuous through the slope for movement to occur. In Fig. 1c short discontinuous ‘a’ joints serve for sliding surfaces for small instabilities but could also link along ‘x-y’ to give a whole-slope failure.

If the inclination of the slope produced by this method is not acceptable then the slope may be designed using values of c and ϕ for the discontinuities which seem appropriate.

This may require flattening the slope to give the required long-term factor of safety. However, if for reasons of land purchase or adverse environmental impact the plan area of the excavation should be kept as small as possible, then the slope might have to be supported by rock anchorages which, in Fig. 1d are placed to resist collapse along discontinuities ‘c’ and ‘a’.