Derive a general expression for the Factor of Safety, F of the excavation corresponding to any arbitrary failure plane with angle of inclination, ?.

Figure on next page shows a vertical cut in a clay soil where ?=0? conditions exist.
The soil cohesion = C.
(a) Derive a general expression for the Factor of Safety, F of the excavation
corresponding to any arbitrary failure plane with angle of inclination, ?.
H=height of the vertical cut; Hc= depth of tension cracks in the soil.
(b) Now, find ? such that F is a minimum and hence write down an expression for
the Factor of Safety of the cut for a vertical cut with height, H

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