In a national park, a narrow maintenance road runs at the edge of a 60 degree rock

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Question:

In a national park, a narrow maintenance road runs at the edge of a 60 degree rock slope. The rock is a bedded sedimentary rock, a limestone. There are weak joints along bedding dipping at 45 degrees. When an unusually large load was carried along the road, a small wedge of rock (shaded in the figure) slipped some 5 cms along a bedding joint. It is estimated that the extra load that caused the slip was around 50 kN per linear meter width in the third direction. Since the stability of the road (and the slope) is of prime concern, your boss was called in to discuss a possible solution to the problem. The following schemes were discussed: I. Move the road out of danger and fence the dangerous part of the surface off from traffic. II. Cut the whole 10 m high slope back from 60 to 50 degrees. III. Keep the 60 degree slope (and the road) and use anchors to bring the safety factor of the whole 10 m high slope to at least 1.25. The supervisor handed you the job with the following instructions:

(a) Investigate the first, the cheapest option first. How far should the road be moved back to avoid a similar problem? At any rate, what is the safety factor for the whole 10 m high rock slope with the 50 kN/m surcharge added? It should be at least 1.1 to keep the 60 degree slope. If it less than that, the first option is untenable. By the way, could the safety factor be less than 1.0?

(b) How much of an improvement would come about if the slope was cut back from 60 to 50 degrees. Could the road still run along the edge? The client would like to have a safety factor of at least 1.25, even with the extra 50 kN/m surcharge. If this condition is satisfied, there is no need to go on to the next problem. Anchors are an expensive business at the best of times.

(c) If the first two schemes are untenable, do you have another solution? If you do not, design an anchoring scheme for the slope. In particular, determine the anchor force required per linear meter width! But, note you do not have to do this if one of option a, option b, or your own option is acceptable.