Failure mode: HS 170/50, BP 160/42

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 HS = 170°/50°, bedding plane BP = 160°/42°, $\phi = 26^\circ$. In dip/dip direction form: HS = 50/170, BP = 42/160.

Result

• The dip directions differ by only $10^\circ$ (within $\pm 20^\circ$).
• $\psi_p = 42^\circ < \psi_f = 50^\circ$, so the bedding plane daylights in the face.
• $\psi_p = 42^\circ > \phi = 26^\circ$.

On the stereonet, the dip vector of BP lies between the slope great circle and the friction circle (equivalently, its pole falls inside the daylight envelope). Possible mode of failure: plane failure (sliding along the bedding plane). It can be controlled by reducing the slope angle below $42^\circ$ or by bolting and drainage.