--- title: "Stability: HS 310/43, BP 306/31" subject: "Engineering Geology II" chapter: 6 key: "semester_4/engineering_geology_ii:stability-hs310-43-bp306-31" source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/stability-hs310-43-bp306-31 site: BCT Engineering --- # Stability: HS 310/43, BP 306/31 Engineering Geology II · Chapter 6: Measurement, analysis and interpretation of structural geological data - Asked in: 2078 Baisakh, 5 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/stability-hs310-43-bp306-31 - Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6 ## Question Discuss the stability analysis of the given planes. Hill slope = 310°/43° Bedding plane (BP) = 306°/31° Joint (J1) = 350°/40° Joint (J2) = 288°/37° Joint (J3) = 237°/32° [Figure: stereonet] ## Short answer Assume phi=30°. Stereoplot shows bedding plane daylighting with dip 31° (>phi) nearly parallel to face, risking plane failure; and wedges BP-J1 (plunge 31.0° towards 306°) and J1-J2 (34.1° towards 314°) lie between friction circle and face, possible wedge failure. Marginally unstable; reduce slope angle below 31° or reinforce. ## Answer **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) HS 310/43; BP 306/31; J1 350/40; J2 288/37; J3 237/32. In dip/dip direction: HS 43/310, BP 31/306, J1 40/350, J2 37/288, J3 32/237. The friction angle is not stated, so $\phi = 30^\circ$ is assumed. #### Single planes | Plane (dip/dip dir) | Diff. of dip dir from slope | Daylights ($\psi_p<\psi_f$) | $\psi_p>\phi$ | Result | |---|---|---|---|---| | BP (31/306) | 4° | yes | yes | **Plane failure** | | J1 (40/350) | 40° | yes | yes | Safe | | J2 (37/288) | 22° | yes | yes | Marginal (dip dir. off by 22°) | | J3 (32/237) | 73° | yes | yes | Safe | #### Intersections | Pair | Intersection plunge/trend | Face apparent dip along trend | Result | |---|---|---|---| | BP x J1 | 31.0° / 306° | 42.9° | **Wedge failure** | | BP x J2 | 28.3° / 332° | 40.8° | Stable (plunge below $\phi$) | | BP x J3 | 26.8° / 273° | 36.7° | Stable (plunge below $\phi$) | | J1 x J2 | 34.1° / 314° | 42.9° | **Wedge failure** | | J1 x J3 | 21.5° / 288° | 40.8° | Stable (plunge below $\phi$) | | J2 x J3 | 31.2° / 251° | 25.9° | Safe (does not daylight) | #### Result - **BP** dips almost in the same direction as the face (4° difference), daylights ($31^\circ < 43^\circ$) and is just above $\phi$ ($31^\circ > 30^\circ$): **plane failure along the bedding** is marginally possible. - J1 (dip direction 40° off) and J2 (22° off) each daylight, but they are outside the $\pm 20^\circ$ range for plane failure. J3 dips across the slope at 32° (73° off). - The **J1 x J2** wedge (plunge $34.1^\circ$ towards 314°) and the **BP x J1** wedge (plunge $31.0^\circ$ towards 306°) lie between the friction circle and the slope great circle: **wedge failure is possible**. **Conclusion: the slope is marginally unstable, with bedding-plane sliding and wedge failure (J1-J2 and BP-J1) as the possible modes.** If the true friction angle is $35^\circ$ or more, all of them become stable. Remedies: reduce the slope angle to less than about $31^\circ$, or use rock bolts, benches and drainage. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is bedding plane failure only marginally possible? A. BP dips 31°, just above phi = 30°, and daylights B. BP dips into the hill C. BP dips less than 10° D. BP is perpendicular to the face Answer: A. 4° from the face, daylights (31° < 43°), and 31° barely exceeds 30°. (Key point: Plane failure on BP) 2. Why are J1 (40° off) and J2 (22° off) not treated as plane failures? A. They dip below phi B. Their dip directions are outside the ±20° range C. They do not daylight D. They are vertical Answer: B. Plane failure needs dip direction within about 20° of the face. (Key point: J2 and J1 plane failure) 3. Which intersections give wedge failure? A. BP x J3 and J2 x J3 B. None C. BP x J1 and J1 x J2, plunging between phi and the face apparent dip D. Only J1 x J3 Answer: C. Their plunges (31.0° and 34.1°) exceed 30° and are below apparent dips of 42.9°. (Key point: Wedge) 4. What happens if the true friction angle is 35° or more? A. Failure becomes worse B. Only wedge fails C. Toppling starts D. All the modes become stable Answer: D. Plunges and dips of 31–34° fall below phi, so no sliding. 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