Question

Derive an expression for the factor of safety against slope instability for an infinite slope at an angle ?? from horizontal, and with horizontal groundwater seepage emerging from the slope (and then running off). The soil has a total unit weight ?? and the strength is defined by ??′ and ??′. Assume drained conditions. Define the potential failure plane as being located a distance “??” from the slope surface measured vertically.

Answer 1

Let us consider an infinite slope having a failure surface at a depth 'z' from slope surface measured vertically and water table at a height 'h' from base as shown in figure

Consider an element 1234 within the infinite slope.The element has its base along the failure plane

Weight of the element is given as

Effective Weight(W) of the element is given as

The effective vertical stress on 3-4 is equal to W i.e

The normal stress on the element is given as

The tangential stress on the element is given as

Shear strength at depth 'z' is given as

Factor of safety is given as