- 2078 Chaitra · 4 marks
Failure mode from stereonet: HS 40/050
Short answer
Only wedge failure is kinematically possible, formed by joints J3 and J4; their intersection plunges 32.4° toward 026°, between the 25° friction angle and the 37.5° face apparent dip. Single planes do not daylight in a sliding sense, and the other intersections are stable or plunge into the hill.
Suggest the possible mode of failure from the following figure. [Figure: equal-angle, lower-hemisphere stereonet with planes HS, J1, J2, J3, J4 plotted] Orientations (Dip/Direction): HS 40/050; J1 46/040; J2 28/200; J3 70/103; J4 39/348. Friction angle: 25°.
Method (lower-hemisphere stereonet, equal-angle): plot the great circle of the slope face and of each discontinuity, draw the friction circle of radius , and mark intersections of great circles. Then apply the kinematic tests below.
Data (dip/dip direction)
HS 40/050; J1 46/040; J2 28/200; J3 70/103; J4 39/348; .
Single planes
| Plane (dip/dip dir) | Diff. of dip dir from slope | Daylights () | Result | |
|---|---|---|---|---|
| J1 (46/040) | 10° | no | yes | Safe (does not daylight) |
| J2 (28/200) | 150° | yes | yes | Safe |
| J3 (70/103) | 53° | no | yes | Safe |
| J4 (39/348) | 62° | yes | yes | Safe |
Intersections
| Pair | Intersection plunge/trend | Face apparent dip along trend | Result |
|---|---|---|---|
| J1 x J2 | 6.9° / 123° | 13.6° | Stable (plunge below ) |
| J1 x J3 | 45.9° / 035° | 39.0° | Safe (does not daylight) |
| J1 x J4 | 38.4° / 360° | 28.3° | Safe (does not daylight) |
| J3 x J4 | 32.4° / 026° | 37.5° | Wedge failure |
(The other 2 intersections plunge into the hill, away from the face, and cannot slide.)
Result
- J1 dips almost with the slope but is steeper (), so it does not daylight.
- J2 dips back into the hill at (far from the face) and is not toppling-type since it is gentle.
- J3 and J4 individually do not daylight in a sliding sense.
- The intersection J3 x J4 plunges towards , which is between and the face apparent dip and points out of the face.
Possible mode of failure: wedge failure formed by joints J3 and J4, sliding along their line of intersection. (Plane and toppling failure are not kinematically possible.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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