---
title: "Stability: NS 320/70, F 155/68"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:stability-ns320-70-f155-68"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/stability-ns320-70-f155-68
site: BCT Engineering
---

# Stability: NS 320/70, F 155/68

Engineering Geology II · Chapter 6: Measurement, analysis and interpretation of structural geological data

- Asked in: 2071 Bhadra, 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-ns320-70-f155-68
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

Discuss the stability analysis of the given planes.
NS = 320°/70°; F = 155°/68°; J1 = 240°/80°; J2 = 310°/35°; J3 = 10°/85°; ϕ = 30°.
[Figure: stereonet]

## Short answer

Lower-hemisphere stereonet kinematic tests with 30° friction circle show J2 (310/35) causes plane failure; J1-J2 (34.3°/323°) and J2-J3 (32.0°/283°) cause wedge failure; steep F topples. Slope is unstable; flatten below 35° and support.

## 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)
NS (natural slope) 320/70; F 155/68; J1 240/80; J2 310/35; J3 010/85; $\phi = 30^\circ$. In dip/dip direction: NS 70/320, F 68/155, J1 80/240, J2 35/310, J3 85/010.

#### Single planes
| Plane (dip/dip dir) | Diff. of dip dir from slope | Daylights ($\psi_p<\psi_f$) | $\psi_p>\phi$ | Result |
|---|---|---|---|---|
| F (68/155) | 165° | yes | yes | Toppling possible |
| J1 (80/240) | 80° | no | yes | Safe |
| J2 (35/310) | 10° | yes | yes | **Plane failure** |
| J3 (85/010) | 50° | no | yes | Safe |

#### Intersections
| Pair | Intersection plunge/trend | Face apparent dip along trend | Result |
|---|---|---|---|
| F x J2 | 13.2° / 240° | 24.5° | Stable (plunge below $\phi$) |
| J1 x J2 | 34.3° / 323° | 70.0° | **Wedge failure** |
| J1 x J3 | 72.5° / 296° | 68.3° | Safe (does not daylight) |
| J2 x J3 | 32.0° / 283° | 65.5° | **Wedge failure** |

(The other 2 intersections plunge into the hill, away from the face, and cannot slide.)

#### Result
- **J2** dips at $35^\circ$, only $10^\circ$ off the face direction: $30^\circ < 35^\circ < 70^\circ$, so **plane failure** is possible.
- **F** dips into the hill towards 155° (the direction opposite to the face is 140°, a 15° difference) and is steep ($68^\circ \geq 90^\circ - 70^\circ + 30^\circ = 50^\circ$): **toppling** of slabs is possible.
- J1 and J3 are steeper than the face ($80^\circ$ and $85^\circ > 70^\circ$), so they do not daylight and cannot slide alone.
- **J1 x J2** (plunge $34.3^\circ$/323°) and **J2 x J3** (plunge $32.0^\circ$/283°) lie between $\phi$ and the face apparent dip: **wedge failure** is possible.

**Conclusion: the slope is unstable; plane failure on J2, wedge failure (J1-J2, J2-J3) and toppling on F can occur.** Flatten the slope to less than $35^\circ$ (the J2 dip), install bolts and anchors, and provide drainage.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does J2 (35/310) give plane failure?
   A. 10° from the face direction, with 30° < 35° < 70°
   B. It dips into the hill
   C. Its dip is below phi
   D. It is steeper than the face
   Answer: A. Direction near-parallel, daylights, and dip exceeds phi. (Key point: Plane failure on J2)

2. Why is toppling possible on F (68/155)?
   A. It dips toward the face
   B. It dips into the hill, nearly opposite the face, with dip 68° ≥ 90° − 70° + 30° = 50°
   C. Its dip is less than phi
   D. It is horizontal
   Answer: B. Steep planes dipping into the hill above the toppling limit can topple. (Key point: Toppling on F)

3. Which intersections cause wedge failure?
   A. F x J2 and J1 x J3
   B. None
   C. J1 x J2 and J2 x J3 (plunges 34.3° and 32.0° between phi and the apparent dip)
   D. Only F x J2
   Answer: C. Both plunge over 30° but below the face apparent dips. (Key point: Wedge)

4. What is the recommended treatment?
   A. Steepen the face
   B. Leave as is
   C. Remove J1
   D. Flatten below 35° (J2 dip), install bolts and drainage
   Answer: D. Flatter than J2 dip prevents plane failure and helps others. (Key point: Remedy)

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