---
title: "Highway earthwork for one km length"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:highway-1km-earthwork"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/highway-1km-earthwork
site: BCT Engineering
---

# Highway earthwork for one km length

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2081 Baisakh, 8 marks
- Video: [Calculation of Volume of Earthwork from Cross Sections | Road Estimate | Earthwork Calculation](https://www.youtube.com/watch?v=zMl6OVLeKWM) — Civil Engineering Edu
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/estimating_and_costing/highway-1km-earthwork
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Estimate for the construction of highway for one km length. Cut slope be 1.5:1 and fill slope be 2:1, mid depth of cutting be 0.35 m for two lane road and ground slope be 9:1. The pavement thickness be wearing coat, base course and sub-base over the subgrade 50 mm, 250 mm and 350 mm respectively.

## Short answer

Multiply side-hill section areas by length: cutting 4428.2 m³, filling 244.5 m³ per km. Pavement layers: wearing coat 350 m³, base 1750 m³, sub-base 3500 m³ (width × thickness × 1000 m).

## Answer

#### Given data and assumptions

- Two-lane road: carriageway $7.0$ m with $1.5$ m shoulders on both sides (Nepal Road Standard 2070), so formation width $B = 10.0$ m. The earthwork is taken to subgrade (formation) level.
- Cut slope $1.5:1$, fill slope $2:1$, ground cross slope $9:1$, centre depth of cutting $h = 0.35$ m at every section, so the section is uniform along the 1 km.
- Wearing coat and base course 7.0 m wide; sub-base spread over the full formation width of 10 m.

#### Earthwork (side-hill section)

At the up-hill edge the ground is $0.35 + 5/9 = 0.906$ m above formation (cutting), and at the down-hill edge it is $0.35 - 5/9 = -0.206$ m (so that side falls below formation and needs filling). The ground cuts the formation level at $9 \times 0.35 = 3.15$ m from the centre line.

- Up-hill toe: $x_u = 6.630$ m from the centre line, ground $1.087$ m above formation
- Down-hill toe (filling slope): $x_d = 5.529$ m, ground $0.264$ m below formation
- Area of cutting $= 4.428$ m²; area of filling $= 0.244$ m² (from the co-ordinates of the section).

$$
\begin{aligned} V_{cut} &= 4.428 \times 1000 = 4,428.2\ \text{m}^3\\ V_{fill} &= 0.244 \times 1000 = 244.5\ \text{m}^3 \end{aligned}
$$

#### Pavement quantities for 1 km

| Layer | Working | Volume (m³) |
|---|---|---:|
| Wearing coat 50 mm | $7.0 \times 0.05 \times 1000$ | 350.0 |
| Base course 250 mm | $7.0 \times 0.25 \times 1000$ | 1,750.0 |
| Sub-base 350 mm | $10.0 \times 0.35 \times 1000$ | 3,500.0 |

**Answer: cutting = 4,428.2 m³, filling = 244.5 m³ per km; wearing coat 350 m³, base 1,750 m³, sub-base 3,500 m³.** The cost follows by multiplying each quantity by its rate (District Rate) and adding overhead, profit and VAT.

## Check yourself

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

1. How is the formation width obtained for the two-lane road in this answer?
   A. Carriageway 7.0 m plus 1.5 m shoulders on both sides = 10.0 m
   B. Carriageway 7.0 m only
   C. Two lanes of 3.5 m plus 1.5 m on one side = 8.5 m
   D. Taken as 12 m by default
   Answer: A. 7.0 + 2 x 1.5 = 10.0 m is used as the formation width B. (Key point: Formation width)

2. With centre cutting depth 0.35 m and ground slope 9:1, the ground meets formation level at what distance from the centre line?
   A. 0.35/9 = 0.039 m
   B. 9 x 0.35 = 3.15 m
   C. 9 + 0.35 = 9.35 m
   D. 5 m
   Answer: B. Ground rises or falls 1 m per 9 m horizontally, so a 0.35 m height difference is reached at 9 x 0.35 = 3.15 m. (Key point: Where ground crosses formation)

3. Why does this section need both cutting and filling although the centre is in cutting?
   A. The ground falls below formation level at the downhill edge, so that side needs filling
   B. The pavement adds extra volume
   C. Fill slope is steeper than cut slope
   D. The road is two-lane
   Answer: A. At the downhill edge the ground is 0.206 m below formation, so that part must be filled while the uphill side is cut. (Key point: Why filling occurs)

4. Why is the sub-base volume 10.0 x 0.35 x 1000 while the wearing coat is 7.0 x 0.05 x 1000?
   A. Sub-base is spread over the full 10 m formation width; wearing coat only over the 7.0 m carriageway
   B. Sub-base is thicker so it uses a bigger width factor
   C. Wearing coat has a side slope
   D. It is a mistake in the answer
   Answer: A. Wearing coat and base are 7.0 m wide, but the sub-base extends across the full formation width. (Key point: Pavement quantities)

## Related in Estimating and Costing

- [Hill road earthwork, km 8.50 to km 9.00](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-t-km-8-5) — Estimating and Costing, chapter 6
- [Road earthwork, four lane NRS-1070](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-g-four-lane) — Estimating and Costing, chapter 6
- [Road earthwork, 80 m length (v)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-v-0-80) — 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
- [RCC slab culvert: brick, wearing coat, GI pipe, steel](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aslab-culvert-a-fig-b) — 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

## Related in other subjects

- [Plain CC pavement thickness by IRC, 7 m highway](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Aplain-cc-pavement-thickness-irc-7m) — Transportation Engineering II, chapter 2
- [Equipment for highway and pavement construction](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Ahighway-pavement-equipment) — Construction Management, chapter 4, asked 3×
- [Cut and fill volume, 20 m formation width](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-road-20m-width-cut-fill-1-1-1-2) — Surveying I, chapter 9
- [Converting two-way slope to one-way slope](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Asuper-attainment-drainage) — Transportation Engineering I, chapter 3, asked 2×