---
title: "Irrigation channel earthwork, bed 5 m, 1 in 3000"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:irrigation-channel-j"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/irrigation-channel-j
site: BCT Engineering
---

# Irrigation channel earthwork, bed 5 m, 1 in 3000

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2076 Asoj, 9 marks
- Video: [ESTIMATE & COSTING -III 6TH SEMESTER | 2069 R/B | EARTHWOK CALCULATION OF IRRIGATION CANAL 😍](https://www.youtube.com/watch?v=Vw-Wm_mU2_E) — Er. Dipesh Bhatt
- 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-channel-j
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Calculate the quantity of earthwork of an irrigation channel with the following data: Bed width of channel = 5 m; Top width of both banks = 2 m; Longitudinal slope of bed = 1 in 3000; Side slopes in cutting and filling = 1½:1 (H:V); Fully supply depth = 1 m; Free board = 0.60 m; R.L. of bed at 0 m = 1395.50 m. Ground level along the alignment are as given below:

| R.L. of Ground | 1397.50 | 1397.00 | 1396.50 | 1395.70 |
|---|---|---|---|---|
| Distance | 0 | 300 | 600 | 900 |

## Short answer

Total depth D = 1.6 m. Bed falls 0.10 m per 300 m. At sections 0 and 300 full cutting occurs, sections 600 and 900 are part cutting/part banking. Earthwork in cutting = 8,831.25 m³, banking = 1,828.50 m³, total = 10,659.75 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 $1.5:1$ for cutting and banking (inner and outer).
- Bed RL 1395.50 m at 0, falling 1 in 3000: 1395.50, 1395.40, 1395.30, 1395.20 m at 0, 300, 600, 900 m.

#### 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 | 1,397.500 | 1,395.500 | 2.000 | full cutting | 16.000 | 0.000 |
| 300 | 1,397.000 | 1,395.400 | 1.600 | full cutting ($e = D$) | 11.840 | 0.000 |
| 600 | 1,396.500 | 1,395.300 | 1.200 | part cutting, part banking | 8.160 | 2.080 |
| 900 | 1,395.700 | 1,395.200 | 0.500 | part cutting, part banking | 2.875 | 8.030 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Banking (m³) |
|---|---:|---:|---:|
| 0 – 300 | 300.0 | 4,176.00 | 0.00 |
| 300 – 600 | 300.0 | 3,000.00 | 312.00 |
| 600 – 900 | 300.0 | 1,655.25 | 1,516.50 |
| **Total** | | **8,831.25** | **1,828.50** |

**Answer: Earthwork in cutting = 8,831.25 m³; earthwork in banking = 1,828.50 m³; total = 10,659.75 m³.**

## Check yourself

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

1. At chainage 0 the ground is 2.0 m above the bed and D = 1.6 m. How is it treated?
   A. Part cutting, part banking, with banks 0.4 m high
   B. Full banking, since e is positive
   C. Full cutting but with banks built for the free board
   D. Full cutting, since e >= D, with area (b + s e)e = 16.0 m2
   Answer: D. When e >= D the whole canal is dug below ground and no banks are needed. (Key point: Full cutting condition)

2. Bed falls 1 in 3000 from RL 1395.50. What is the bed at 600 m?
   A. 1395.30 m
   B. 1395.50 m
   C. 1395.70 m
   D. 1395.00 m
   Answer: A. 600/3000 = 0.20 m fall, so 1395.50 - 0.20 = 1395.30 m. (Key point: Bed level at stations)

3. At 900 m, GL = 1395.70 and bed = 1395.20. What is the bank height above ground?
   A. 0.50 m
   B. 1.10 m
   C. 1.60 m
   D. 2.10 m
   Answer: B. e = 0.50 m, so h_b = D - e = 1.6 - 0.5 = 1.10 m. (Key point: Bank height at 900 m)

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