Slope stability: N40W/55 slope, two 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 and assumptions

Slope face N40°W/55° dips south-west, so it is taken as 55/230 (dip/dip direction). Joint set 1 N50°W/37° dips SW: 37/220. Joint set 2 N70°E/67° dips SE: 67/160. $\phi = 28^\circ$.

Individual planes

Intersection of the joint sets

Result

• J1 strikes almost parallel to the face (10° difference), daylights ($37^\circ < 55^\circ$) and dips more than $\phi$ ($37^\circ > 28^\circ$), so plane failure along J1 is possible.
• J2 is steeper than the face ($67^\circ > 55^\circ$), so it alone cannot slide.
• J1 and J2 form a wedge whose line plunges $36.4^\circ$ towards $232^\circ$, within the face (apparent dip of face $55.0^\circ$) and above $\phi$, so wedge failure is also possible.

Conclusion: the slope is unstable (plane failure along J1 and wedge failure along J1-J2). To stabilise it, flatten the cut to below about $35^\circ$ (less than the intersection plunge $36.4^\circ$ and the J1 dip $37^\circ$), or use rock bolts, drainage and benching.