Stability: HS 175/52, BP 150/48

Method (lower-hemisphere stereonet, equal-angle): plot the great circle of the slope face and of each discontinuity, draw the friction circle of radius $\phi$, and mark intersections of great circles. Then apply the kinematic tests below.

Data (dip direction/dip)

Hill slope 175°/52°, bedding plane 150°/48°, $\phi = 38^\circ$. In dip/dip direction: HS 52/175, BP 48/150.

Stability analysis

• Dip direction of BP is $25^\circ$ from the slope direction: just outside the usual $\pm 20^\circ$ limit.
• $\psi_p = 48^\circ < \psi_f = 52^\circ$ and the apparent dip of the face in the BP direction is $49.2^\circ$, so the bedding plane just daylights.
• $\psi_p = 48^\circ > \phi = 38^\circ$, so the block can slide if it daylights.

So the great circle of BP lies close to the edge of the safe zone: the slope is marginally stable, with a potential for plane (bedding) failure which becomes real if the toe is cut, or if water pressure or weathering lowers the friction.

Suggestions

1. Cut back the slope to $\leq 45^\circ$ (less than the bedding dip) so that bedding does not daylight.
2. Alternatively install rock bolts or anchors across the bedding and shotcrete the face.
3. Provide surface and sub-surface drainage (weep holes) to prevent water pressure.
4. Avoid undercutting the toe; provide a catch ditch or retaining wall.