Stability: H 49/249, F 56/243, three joints

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/dip direction)

H (hill slope) 49/249; F 56/243; J1 58/071; J2 30/175; J3 83/286; $\phi = 25^\circ$.

Single planes

Intersections

(The other 3 intersections plunge into the hill, away from the face, and cannot slide.)

Result

• F has almost the same dip direction as the slope but is steeper ($56^\circ > 49^\circ$), so it does not daylight: no plane failure.
• J1 dips into the hill (071, against 249 - 180 = 069). The toppling limit is $90^\circ - 49^\circ + 25^\circ = 66^\circ$, but $\psi = 58^\circ < 66^\circ$, so toppling is not expected.
• J3 is very steep, and J2 is gentle and dips almost at right angles to the face direction: neither slides alone.
• The intersection J2 x J3 plunges $27.7^\circ$ towards $200^\circ$. This is greater than $\phi = 25^\circ$ and smaller than the apparent dip of the face in that direction ($36.9^\circ$), so it plots between the friction circle and the slope great circle.

Conclusion: the slope is stable against plane and toppling failure, but wedge failure along the intersection of J2 and J3 is possible. It can be treated by bolting, or by flattening the face to below about $39^\circ$, so that the apparent dip of the face towards 200° becomes less than the $27.7^\circ$ plunge of the wedge ($\tan\psi\cos 49.7^\circ = \tan 27.7^\circ \Rightarrow \psi \approx 39^\circ$).