---
title: "Channel earthwork with drop at 0+090"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:channel-e-drop-0-090"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/channel-e-drop-0-090
site: BCT Engineering
---

# Channel earthwork with drop at 0+090

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2080 Bhadra, 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/channel-e-drop-0-090
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Calculate the quantity of the earthwork of a channel with the following data: Bed width = 6 m, free board = 50 cm, slope of cutting 1:1, side slope of banking 1.5:1, full supply depth is 2 m, width of the banks is 1.5 m. There is vertical drop of 0.5 m at ground surface at chainage 0+090. The longitudinal slope of canal is 1 in 600.

| Chainage | Ground Level (m) | Bed Level (m) |
|---|---|---|
| 0+000 | 225.3 | 224.00 |
| 0+030 | 225.2 | |
| 0+060 | 225.1 | |
| 0+090 | 225.2 / 224.7 (as printed, before and after drop) | |
| 0+120 | 224.8 | |

## Short answer

Mean-area method applied across a drop; all sections have part cutting and part banking. Cutting = 1,139.85 m³, banking = 953.55 m³, total = 2,093.40 m³.

## Answer

#### Given data and assumptions
- Bed width $6$ m; FSD $2$ m; free board $0.5$ m, so $D = 2.5$ m; width (top) of each bank $1.5$ m.
- Side slope in cutting $1:1$; banks $1.5:1$ on both faces.
- Bed falls 1 in 600: 30 m gives 0.05 m, so the bed is 224.00, 223.95, 223.90, 223.85 m up to the drop at 0+090. The 0.5 m drop gives 223.35 m after the drop, and 223.30 m at 0+120. Ground level at 0+090 is 225.2 m before and 224.7 m after the drop.

#### Method
Total depth of canal section $D = \text{FSD} + \text{free board} = 2.00 + 0.50 = 2.50$ 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+000 | 225.300 | 224.000 | 1.300 | part cutting, part banking | 9.490 | 7.920 |
| 0+030 | 225.200 | 223.950 | 1.250 | part cutting, part banking | 9.062 | 8.438 |
| 0+060 | 225.100 | 223.900 | 1.200 | part cutting, part banking | 8.640 | 8.970 |
| 0+090 (before drop) | 225.200 | 223.850 | 1.350 | part cutting, part banking | 9.922 | 7.418 |
| 0+090 (after drop) | 224.700 | 223.350 | 1.350 | part cutting, part banking | 9.922 | 7.418 |
| 0+120 | 224.800 | 223.300 | 1.500 | part cutting, part banking | 11.250 | 6.000 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Banking (m³) |
|---|---:|---:|---:|
| 0+000 – 0+030 | 30.0 | 278.29 | 245.36 |
| 0+030 – 0+060 | 30.0 | 265.54 | 261.11 |
| 0+060 – 0+090 (before drop) | 30.0 | 278.44 | 245.81 |
| 0+090 (after drop) – 0+120 | 30.0 | 317.59 | 201.26 |
| **Total** | | **1,139.85** | **953.55** |

**Answer: Earthwork in cutting = 1,139.85 m³; earthwork in banking = 953.55 m³; total = 2,093.40 m³.**

## Check yourself

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

1. With a bed slope of 1 in 600, how much does the bed fall in 30 m?
   A. 0.05 m
   B. 0.50 m
   C. 0.018 m
   D. 0.20 m
   Answer: A. 30/600 = 0.05 m, so bed levels fall 224.00, 223.95, 223.90 and so on. (Key point: Bed level with gradient)

2. How is the 0.5 m vertical drop at 0+090 handled in the volumes?
   A. The bed level is simply lowered at 0+090 and the usual mean area is taken across it
   B. Two sections are taken at 0+090 (before and after the drop) and no volume is computed between them
   C. The drop is ignored because it is only 0.5 m
   D. The earthwork is increased by 0.5 m x section area
   Answer: B. The bed jumps at the drop, so the reach before and after are calculated separately, with no volume between the two 0+090 sections. (Key point: Handling the drop)

3. What is D, and what is e at 0+120 (GL 224.8, bed 223.30)?
   A. D = 2.0 m and e = 1.5 m
   B. D = 2.5 m and e = 3.5 m
   C. D = 2.5 m and e = 1.5 m
   D. D = 2.0 m and e = 0.5 m
   Answer: C. D = 2.0 + 0.5 = 2.5 m, and e = 224.8 - 223.3 = 1.5 m, so the section is part cutting, part banking. (Key point: Total depth)

## Related in Estimating and Costing

- [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×
- [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
- [Channel earthwork and land area, bed 4 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-land-acquisition-f) — Estimating and Costing, chapter 6, asked 2×
- [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
- [Irrigation canal earthwork with vertical drop](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Acanal-a-drop-0-400) — 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
- [Balancing depth: bed width 20 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed20-cut15-fill2) — Irrigation and Drainage Engineering, chapter 3, asked 3×
- [Crest width, cistern length of vertical drop, Q 1.55](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q155-drop075) — Irrigation and Drainage Engineering, chapter 7, asked 2×
- [Balancing depth: bed width 25 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed25) — Irrigation and Drainage Engineering, chapter 3, asked 3×