---
title: "Road earthwork, grades 1 in 120 and 1 in 90 (0-120)"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:road-earthwork-r-grade-120-90"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/road-earthwork-r-grade-120-90
site: BCT Engineering
---

# Road earthwork, grades 1 in 120 and 1 in 90 (0-120)

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2068 Baisakh (old course), 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/estimating_and_costing/road-earthwork-r-grade-120-90
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Estimate the quantity of earthwork of a portion of road from the following data: Formation width of the road = 10 m. Side slope in banking = 2:1 (H:V), side slope in cutting = 1:1. Downward grade 1 in 120 from distance 0 m to 30 m while it remains in level from distance 30 m to 90 m and has again upward grade 1 in 90 from distance 90 to 120 m. The formation level at distance 60 m = 1197.50 m. The ground levels of the centre line of the road are as under:

| R.L. of ground | 1198.65 | 1196.40 | 1199.30 | 1200.40 | 1198.10 |
|---|---|---|---|---|---|
| Distance in m | 0 | 30 | 60 | 90 | 120 |

## Short answer

Calculate formation levels from given grades and reference, compute cut/fill depths. Using level-section area A=(B+s h)h, determine volumes by mean area method: 1,745.94 m³ cutting and 187.07 m³ filling.

## Answer

#### Given data and assumptions
- Formation width $B = 10$ m; banking slope $2:1$, cutting slope $1:1$. Ground is level across the road.
- Formation levels: 1197.50 m at 60 m; level from 30 m to 90 m; falling 1 in 120 from 0 to 30 m, so the level at 0 m is 1197.50 + 30/120 = 1197.75 m; rising 1 in 90 from 90 to 120 m, so the level at 120 m is 1197.50 + 30/90 = 1197.833 m.

#### Method
Level (plain-ground) sections are used. With centre height $h$, formation width $B$ and side slope $s:1$:

$$
A = (B + s\,h)\,h
$$

Volume between two sections = mean area × distance; where a section changes from cutting to filling, the length of each part is found by proportion of the depths and the volume of each part = ½ × end area × length.

| Chainage | GL (m) | FL (m) | Depth of cutting / height of filling (m) |
|---|---:|---:|---:|
| 0+000 | 1,198.650 | 1,197.750 | cutting 0.900 |
| 0+030 | 1,196.400 | 1,197.500 | filling 1.100 |
| 0+060 | 1,199.300 | 1,197.500 | cutting 1.800 |
| 0+090 | 1,200.400 | 1,197.500 | cutting 2.900 |
| 0+120 | 1,198.100 | 1,197.833 | cutting 0.267 |

#### Sectional areas
| Chainage | Centre ht. $h$ (m) | Cutting area (m²) | Filling area (m²) |
|---|---:|---:|---:|
| 0+000 | cut 0.90 | 9.810 | 0.000 |
| 0+030 | fill 1.10 | 0.000 | 13.420 |
| 0+060 | cut 1.80 | 21.240 | 0.000 |
| 0+090 | cut 2.90 | 37.410 | 0.000 |
| 0+120 | cut 0.27 | 2.738 | 0.000 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Filling (m³) |
|---|---:|---:|---:|
| 0+000 – 0+030 | 30.0 | 66.22 | 110.71 |
| 0+030 – 0+060 | 30.0 | 197.75 | 76.36 |
| 0+060 – 0+090 | 30.0 | 879.75 | 0.00 |
| 0+090 – 0+120 | 30.0 | 602.22 | 0.00 |
| **Total** | 120.0 | **1,745.94** | **187.07** |

**Answer: Earthwork in cutting = 1,745.94 m³; earthwork in filling = 187.07 m³.**

## Check yourself

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

1. Formation level at 60 m is 1197.50 m and the road falls 1 in 120 from 0 to 30 m, level from 30 to 90 m. What is the formation level at 0 m?
   A. 1197.25 m
   B. 1197.50 m
   C. 1197.75 m
   D. 1198.50 m
   Answer: C. Falling in the direction of chainage means the start is higher: 1197.50 + 30/120 = 1197.75 m. (Key point: Formation level from grade)

2. Which formula gives the section area for level ground, centre height h, width B and side slope s:1?
   A. A = B x h
   B. A = (B + s h) h
   C. A = (B + h)/s
   D. A = 1/2 B h
   Answer: B. The section is a trapezoid with bottom width B and side slopes s:1, so A = (B + s h) h. (Key point: Area for level section)

3. Between 0 m (cutting 0.9 m) and 30 m (filling 1.1 m), how is the length of the cutting part found?
   A. Half of the distance, 15 m
   B. By proportion of depths: 30 x 0.9/(0.9 + 1.1) = 13.5 m
   C. 30 x 1.1/(0.9 + 1.1) = 16.5 m
   D. It equals the full 30 m
   Answer: B. The zero-depth point divides the distance in proportion to the end depths, so the cutting length is 30 x 0.9/2.0 = 13.5 m. (Key point: Cutting to filling between sections)

4. After finding the length of each part, how is its volume computed in the answer?
   A. End area x length
   B. 1/2 x end area x length
   C. Mean of both areas x total distance
   D. (B + s h) x length
   Answer: B. Each part tapers to zero at the changeover point, so volume = 1/2 x end area x length. (Key point: Volume of wedge-shaped part)

## Close variants set in other exams

- [Road earthwork, grades from 90 m to 210 m (s)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-s-grade-90-210) — Estimating and Costing, chapter 6, asked 3×

## Related in Estimating and Costing

- [Road earthwork, formation level at 150 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-t-grade-150) — Estimating and Costing, chapter 6, asked 2×
- [Hill road earthwork, cutting 4 m / banking 6 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-k-cut4-fill6) — Estimating and Costing, chapter 6
- [Hill road earthwork, 0-90 m (8 m formation)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-p-0-90) — Estimating and Costing, chapter 6
- [Hill road earthwork, 0 m to 90 m, 10/8 m widths](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-e-0-90) — Estimating and Costing, chapter 6, asked 2×
- [Road earthwork, RD 0-120, gradient 1 in 150](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-o-rds) — Estimating and Costing, chapter 6
- [Road earthwork, upward grade 1:100](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-u-upward-1-100) — Estimating and Costing, chapter 6

## Related in other subjects

- [Cutting volume, 60 m, formation level 279.00](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-cutting-60m-gl-281-50-formation-279) — Surveying I, chapter 9, asked 7×
- [Cutting volume, 120 m, upward slope 1 in 40](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-cutting-120m-formation-380) — Surveying I, chapter 9, asked 8×
- [Cutting volume, 60 m, formation level 278.00](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-cutting-60m-formation-278-upward) — Surveying I, chapter 9, asked 7×
- [Cutting volume, 60 m, GL 540.70, formation 538.20](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-cutting-60m-gl-540-70) — Surveying I, chapter 9, asked 7×