---
title: "Irrigation canal earthwork, 0-600 m"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:irrigation-canal-k-drop"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/irrigation-canal-k-drop
site: BCT Engineering
---

# Irrigation canal earthwork, 0-600 m

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2075 Chaitra, 6 marks
- Video: [Earthwork calculations of a canal | Canal Construction | Earthing Techniques #canal #earthwork](https://www.youtube.com/watch?v=g0YL_G9geJg) — 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/irrigation-canal-k-drop
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Calculate the quantity of earthwork of an irrigation canal with the following data. Bed width = 5 m, freeboard = 0.6 m, fully supply depth = 1 m, top width of both the bank = 2 m, side slope in cutting = 1:1, side slope in banking = 1½:1.

| Distance (m) | 0 | 300 | 600 m |
|---|---|---|---|
| Ground level (m) | 325.24 | 324.80 | 324.43 |
| Proposed bed level (m) | 324.00 | 1 in 3000 downward | |

## Short answer

Total depth D = 1.6 m, cutting slope 1:1, banking slope 1.5:1. All three stations are part cutting and part banking. Volumes: cutting = 3,285.68 m³, banking = 2,560.72 m³, total = 5,846.40 m³.

## Answer

#### Given data and assumptions
- Bed width $5$ m; FSD $1$ m; free board $0.6$ m, so $D = 1.6$ m; top width of each bank $2$ m; side slope in cutting $1:1$ and in banking $1.5:1$ (inner and outer faces of banks).
- Bed RL 324.00 m at 0, falling 1 in 3000: 324.00, 323.90, 323.80 m at 0, 300, 600 m. (No drop is mentioned in the data.)

#### Method
Total depth of canal section $D = \text{FSD} + \text{free board} = 1.00 + 0.60 = 1.60$ 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 | 325.240 | 324.000 | 1.240 | part cutting, part banking | 7.738 | 1.829 |
| 300 | 324.800 | 323.900 | 0.900 | part cutting, part banking | 5.310 | 4.270 |
| 600 | 324.430 | 323.800 | 0.630 | part cutting, part banking | 3.547 | 6.703 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Banking (m³) |
|---|---:|---:|---:|
| 0 – 300 | 300.0 | 1,957.14 | 914.82 |
| 300 – 600 | 300.0 | 1,328.54 | 1,645.90 |
| **Total** | | **3,285.68** | **2,560.72** |

**Answer: Earthwork in cutting = 3,285.68 m³; earthwork in banking = 2,560.72 m³; total = 5,846.40 m³.**

## Check yourself

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

1. Which slope is used for the cutting area and which for the bank area?
   A. Both use 1.5:1
   B. Cutting uses 1.5:1 and banks 1:1
   C. Cutting area uses 1:1 and the banks use 1.5:1
   D. Both use 1:1
   Answer: C. The question gives different side slopes, so cutting area uses s_c = 1 and bank slopes s_i = s_o = 1.5. (Key point: Different slopes for cutting and banking)

2. Bed 324.00 at 0 falling 1 in 3000. What is the bed at 300 m?
   A. 324.10 m
   B. 323.00 m
   C. 323.70 m
   D. 323.90 m
   Answer: D. 300/3000 = 0.10 m fall. (Key point: Bed levels)

3. At 0, GL = 325.24 and bed = 324.00 with D = 1.6 m. What is the bank height above ground?
   A. 0.36 m
   B. 1.24 m
   C. 1.60 m
   D. 2.84 m
   Answer: A. e = 1.24 m, so h_b = 1.60 - 1.24 = 0.36 m. (Key point: Bank height at station 0)

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