---
title: "Channel earthwork and land area, bed 4 m"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:channel-land-acquisition-f"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/channel-land-acquisition-f
site: BCT Engineering
---

# Channel earthwork and land area, bed 4 m

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2080 Baisakh, 12 marks
- Video: [Calculate the quantity of earthwork in irrigation canal | calculate the permanent width | Type #3](https://www.youtube.com/watch?v=WkcdXvl0XiQ) — SBK Concept
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/estimating_and_costing/channel-land-acquisition-f
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Calculate the quantity of earthwork and area of permanent land required for the land acquisition purpose for a portion of a channel from following data: Bed width = 4 m; Free board = 45 cm; Side slope in cutting = 1:1; Side slope in banking = 1.5:1; Full supply depth = 1 m; Top width of bank = 3 m left and 1.5 m right.

| Chainage | 90 | 120 | 150 | 180 | 210 | 220 |
|---|---|---|---|---|---|---|
| RL Ground | 109.8 | 109.7 | 109.55 | 109.30 | 109.15 | 109.10 |
| RL Bed | 109.52 | Bed slope 1:300 rising | | | | |

## Short answer

Earthwork: cutting = 27.77 m³, banking = 2,316.23 m³. Permanent land obtained from mean width × length = 2,330.70 m².

## Answer

#### Given data and assumptions
- Bed width $4$ m; FSD $1$ m; free board $0.45$ m, so $D = 1.45$ m; top width of bank $3$ m (left) and $1.5$ m (right).
- Side slope in cutting $1:1$, in banking $1.5:1$ (inner and outer faces of banks).
- Bed level 109.52 m at chainage 90, rising at 1 in 300 with chainage (assumed direction): 109.52, 109.62, 109.72, 109.82, 109.92, 109.953 m.

#### Method
Total depth of canal section $D = \text{FSD} + \text{free board} = 1.00 + 0.45 = 1.45$ m. At each station the bed level is compared with the ground level; $e = $ GL − bed level.

- If $e \ge D$: full cutting, area $A_c = (b + s_c e)\,e$ (no banks needed).
- If $0 < e < D$: part cutting, part banking. Cutting area $A_c = (b + s_c e)e$; each bank stands $h_b = D - e$ above ground, so bank area (both banks) $A_b = (t_L + t_R)h_b + (s_i + s_o)h_b^2$ with $s_i, s_o$ the inner and outer bank slopes.
- If $e \le 0$: full banking, bed above ground. Bank top is $H = D - e$ above ground. Gross embankment $= (T + s_o H)H$ with $T = t_L + t_R + b + 2 s_i D$, and the canal space $(b + s_i D)D$ is deducted.

Volume between stations = mean area × distance (separately for cutting and banking).

#### Sectional areas
| Station | GL (m) | Bed RL (m) | $e$ (m) | Condition | Cutting area (m²) | Bank area (m²) |
|---|---:|---:|---:|---|---:|---:|
| 0+090 | 109.800 | 109.520 | 0.280 | part cutting, part banking | 1.198 | 9.372 |
| 0+120 | 109.700 | 109.620 | 0.080 | part cutting, part banking | 0.326 | 11.796 |
| 0+150 | 109.550 | 109.720 | -0.170 | full banking | 0.000 | 15.800 |
| 0+180 | 109.300 | 109.820 | -0.520 | full banking | 0.000 | 22.182 |
| 0+210 | 109.150 | 109.920 | -0.770 | full banking | 0.000 | 26.966 |
| 0+220 | 109.100 | 109.953 | -0.853 | full banking | 0.000 | 28.602 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Banking (m³) |
|---|---:|---:|---:|
| 0+090 – 0+120 | 30.0 | 22.87 | 317.51 |
| 0+120 – 0+150 | 30.0 | 4.90 | 413.93 |
| 0+150 – 0+180 | 30.0 | 0.00 | 569.73 |
| 0+180 – 0+210 | 30.0 | 0.00 | 737.22 |
| 0+210 – 0+220 | 10.0 | 0.00 | 277.84 |
| **Total** | | **27.77** | **2,316.23** |

#### Permanent land
Width of land at a section = distance between the outer toes of the banks (banking) or canal top width plus the two bank/berm widths (cutting).

| Station | Land width (m) |
|---|---:|
| 0+090 | 16.080 |
| 0+120 | 16.880 |
| 0+150 | 17.710 |
| 0+180 | 18.760 |
| 0+210 | 19.510 |
| 0+220 | 19.760 |

Area of land $=$ mean width × length, summed over the reaches $= 2,330.70$ m² $= 0.2331$ ha.

**Answer: Earthwork in cutting = 27.77 m³; earthwork in banking = 2,316.23 m³; total = 2,344.00 m³.** **Permanent land = 2,330.70 m².**

## Check yourself

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

1. Bed rises 1 in 300 from 109.52 at chainage 90. What is the bed at chainage 120?
   A. 109.52 m
   B. 109.42 m
   C. 109.82 m
   D. 109.62 m
   Answer: D. 30 m / 300 = 0.10 m rise, so 109.52 + 0.10 = 109.62 m. (Key point: Bed level at chainages)

2. At 0+150 GL = 109.55 and bed = 109.72. What type of section is it?
   A. Full banking, since e = -0.17 m
   B. Part cutting since e is small
   C. Full cutting since |e| is below D
   D. Neither, since e is not a whole number
   Answer: A. A negative e means the bed is above ground, so the whole canal is in embankment. (Key point: Section type at 0+150)

3. How do the unequal top widths of the banks (3 m left, 1.5 m right) enter the bank area formula?
   A. Only the larger width, 3 m, is used
   B. Through the sum t_L + t_R = 4.5 m multiplied by bank height
   C. The average 2.25 m is used for both banks
   D. They are ignored because slopes decide the area
   Answer: B. Bank area = (t_L + t_R)h_b + (s_i + s_o)h_b^2, so the two widths add. (Key point: Banks of unequal top width)

4. In a full banking section, the width of permanent land is measured as
   A. The bed width plus 2 m
   B. The top width of the banks only
   C. The distance between the outer toes of the two banks
   D. The canal top water width
   Answer: C. Land is needed up to the outer toes of the banks, so land width is between outer toes. (Key point: Permanent land width)

## Close variants set in other exams

- [Channel earthwork and land area, 50 cm fall](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-land-acquisition-h) — Estimating and Costing, chapter 6, asked 2×

## Related in Estimating and Costing

- [Canal earthwork, bed 3 m, free board 0.44 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-q-portion) — Estimating and Costing, chapter 6
- [Irrigation channel earthwork, bed 5 m, 1 in 3000](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Airrigation-channel-j) — Estimating and Costing, chapter 6
- [Channel earthwork with drop at 0+090](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-e-drop-0-090) — Estimating and Costing, chapter 6
- [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
- [Channel fully in banking, 0.5-1.5 km](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Acanal-fully-banking-i) — Estimating and Costing, chapter 6
- [Channel earthwork, chainage 0+500 to 1+500](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-b-0500-1500) — Estimating and Costing, chapter 6

## Related in other subjects

- [Balancing depth with service bank and free board](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed8-service-bank) — Irrigation and Drainage Engineering, chapter 3