---
title: "Cut slope design: N41W/56 hillslope"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:cut-slope-n41w-56"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/cut-slope-n41w-56
site: BCT Engineering
---

# Cut slope design: N41W/56 hillslope

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

- Asked in: 2080 Chaitra, 6 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-n41w-56
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

A hill slope with orientation N41°W/56° has outcrop of quartzite rock containing discontinuity orientation N50°W/37°. The friction angle of the plane of discontinuity is 28°. Design a cut slope for a stable road with the possible mode of failure by using the stereographic projection method.

## Short answer

Kinematic checks show plane failure along the discontinuity (37/220) because it daylights in the 56° slope and exceeds the 28° friction angle. Design the road cut at about 35°, not more than 37°, keeping the strike near N41°W. If a steeper cut is needed, use rock bolts, shotcrete 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
Hill slope N41°W/56° dipping south-west = **56/229**; discontinuity N50°W/37° dipping SW = **37/220**; $\phi = 28^\circ$ (both are assumed to dip towards the same side, which is the critical case).

#### Possible failure mode
- The dip directions differ by only $9^\circ$ (< 20°).
- Joint dip $37^\circ <$ slope $56^\circ$, so the joint **daylights** in the natural slope.
- Joint dip $37^\circ > \phi = 28^\circ$.

All the plane-failure conditions are satisfied, so the possible mode is **plane failure** along the discontinuity.

#### Design of the cut slope
Plane failure is avoided if the cut slope does not expose the plane, i.e. the cut angle is not steeper than the dip of the discontinuity:
$$
\psi_{cut} \leq \psi_p = 37^\circ
$$
On the stereonet, the great circle of the cut slope must then lie outside (nearer the primitive than) the great circle of the joint, so the joint's dip vector no longer falls between the slope great circle and the friction circle.

**Answer: cut the slope at about 35° (not more than 37°), keeping the road face along the existing strike (about N41°W). If a steeper cut (up to 56°) is needed for the road, support it with rock bolts or shotcrete and drain the slope, because the joint dip (37°) exceeds the friction angle (28°) and sliding will occur on any cut steeper than 37°.**

## Check yourself

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

1. Which failure mode is possible for the hill slope 56/229 with joint 37/220?
   A. Toppling
   B. Wedge failure
   C. Plane failure
   D. None
   Answer: C. Dip directions differ by 9° (<20°), the joint daylights and 37° > 28°. (Key point: Failure mode)

2. What cut angle avoids plane failure?
   A. Not steeper than the joint dip (37°)
   B. Steeper than 56°
   C. Exactly phi 28° only
   D. Any angle if dry
   Answer: A. If the cut does not expose the plane, it cannot slide. (Key point: Design rule)

3. Why is the sliding risk real?
   A. Joint dip 37° is above friction angle 28°
   B. Joint dip is below 28°
   C. Slope is below 30°
   D. Cohesion is zero
   Answer: A. Dip above phi means the block can slide once daylighted. (Key point: Friction check)

4. What if a steeper cut up to 56° is required?
   A. Impossible
   B. Leave unsupported
   C. Support with rock bolts or shotcrete and drain
   D. Raise friction angle by wetting
   Answer: C. Reinforcement and drainage compensate. (Key point: Steeper cut)

## Related in Engineering Geology II

- [Cut slope design: quartzite N55W/50](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Acut-slope-quartzite-n55w-50) — 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
- [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
- [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

## Related in other subjects

- [Hill road earthwork, cross slope 1 in 5 (0-60)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-r-cross-slope-1-5) — Estimating and Costing, chapter 6