---
title: "Cut slope design: quartzite N55W/50"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:cut-slope-quartzite-n55w-50"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/cut-slope-quartzite-n55w-50
site: BCT Engineering
---

# Cut slope design: quartzite N55W/50

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

- Asked in: 2076 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/cut-slope-quartzite-n55w-50
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

An outcrop of quartzite containing discontinuity has orientation N55°W/50° in the rock slope, which has attitude N45°W/70°. If the planes of discontinuities have an average friction angle of 28°, design a cut slope for a stable road with possible mode of failure.

## Short answer

Plane failure along the discontinuity (50/215) is possible because it daylights in the 70° slope and dips above the 28° friction angle. Design the cut at not more than 50°, say 45°, striking parallel to the joint (N55°W). The existing 70° face should be cut back or reinforced with bolts and drainage.

## 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 and assumptions
Rock slope N45°W/70° dipping SW = **70/225**; discontinuity N55°W/50° dipping SW = **50/215**; $\phi = 28^\circ$.

#### Possible failure mode
- Dip directions differ by $10^\circ$ (< 20°).
- $\psi_p = 50^\circ < \psi_f = 70^\circ$: the plane **daylights**.
- $\psi_p = 50^\circ > \phi = 28^\circ$: sliding is possible.

So the existing slope is liable to **plane failure** along the discontinuity.

#### Design
The plane is not exposed in the cut face if the cut angle does not exceed the dip of the plane:
$$
\psi_{cut} \leq 50^\circ
$$

**Answer: design the road cut at not more than 50° (say 45° for a margin of safety), striking parallel to the joint plane (N55°W). The existing 70° face should be cut back by about 20° or reinforced with bolts and drainage.**

## Check yourself

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

1. The slope is 70/225 and the discontinuity is 50/215. Why does the plane daylight?
   A. Its dip (50°) is less than the face dip (70°), so it emerges in the face
   B. Its dip (50°) is greater than the face dip (70°)
   C. Its strike is perpendicular to the face
   D. Its dip direction is opposite to the face
   Answer: A. Daylighting requires the plane dip to be smaller than the face dip (psi_p < psi_f). (Key point: Daylight test)

2. What second condition makes sliding possible on this plane?
   A. Plane dip 50° is less than friction angle 28°
   B. Plane dip 50° exceeds friction angle 28°
   C. Face dip 70° equals the friction angle
   D. Dip directions differ by more than 90°
   Answer: B. Sliding needs psi_p > phi; 50° > 28°. (Key point: Friction test)

3. What is the possible mode of failure of the existing slope?
   A. Toppling
   B. Wedge failure
   C. Plane failure along the discontinuity
   D. Circular failure
   Answer: C. Dip directions within 10°, plane daylights and dips more than phi, so plane failure is possible. (Key point: Failure mode)

4. What cut angle is recommended for the road?
   A. 70°, the existing angle
   B. 60° for economy
   C. Any angle above 50°
   D. Not more than 50° (say 45°), striking parallel to the joint
   Answer: D. Cutting no steeper than the plane's dip (50°) keeps the plane from being exposed; 45° gives a safety margin. (Key point: Cut slope design)

## Related in Engineering Geology II

- [Cut slope design: N41W/56 hillslope](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Acut-slope-n41w-56) — Engineering Geology II, chapter 6
- [Cut slope design: limestone N48E/52](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Acut-slope-limestone-n48e-52) — Engineering Geology II, chapter 6
- [Cut slope design: HS 110/40, B 130/20](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Acut-slope-hs110-40) — Engineering Geology II, chapter 6
- [Slope stability: N40W/55 slope, two joints](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Aslope-stability-n40w-55) — Engineering Geology II, chapter 6
- [Properties of rock mass and discontinuities](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Arock-mass-properties) — Engineering Geology II, chapter 6, asked 3×
- [Rock layer attitude: A 900 m N, C 800 m W](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-rock-layer-a900n-c800w) — Engineering Geology II, chapter 6, asked 2×

## Related in other subjects

- [Planes of discontinuity in rock masses](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aplanes-of-discontinuity-in-rock) — Engineering Geology I, chapter 5
- [Slope orientation and discontinuities for stability](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aslope-orientation-and-discontinuities-for) — Engineering Geology I, chapter 6
- [Strike of quartzite bed, dip 70° towards S20°E](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-quartzite-bed-dip) — Engineering Geology I, chapter 5
- [Rock mass classification and discontinuities](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Arock-mass-classification-and-discontinuities) — Engineering Geology I, chapter 5