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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 ϕ\phi, 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; ϕ=25∘\phi = 25^\circ.

Single planes

Plane (dip/dip dir)Diff. of dip dir from slopeDaylights (ψp<ψf\psi_p<\psi_f)ψp>ϕ\psi_p>\phiResult
J1 (46/040)10°noyesSafe (does not daylight)
J2 (28/200)150°yesyesSafe
J3 (70/103)53°noyesSafe
J4 (39/348)62°yesyesSafe

Intersections

PairIntersection plunge/trendFace apparent dip along trendResult
J1 x J26.9° / 123°13.6°Stable (plunge below ϕ\phi)
J1 x J345.9° / 035°39.0°Safe (does not daylight)
J1 x J438.4° / 360°28.3°Safe (does not daylight)
J3 x J432.4° / 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 (46∘>40∘46^\circ > 40^\circ), so it does not daylight.
  • J2 dips back into the hill at 200∘200^\circ (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 32.4∘32.4^\circ towards 026∘026^\circ, which is between ϕ=25∘\phi = 25^\circ and the face apparent dip 37.5∘37.5^\circ 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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