---
title: "Channel earthwork, chainage 0+500 to 1+500"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:channel-b-0500-1500"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/channel-b-0500-1500
site: BCT Engineering
---

# Channel earthwork, chainage 0+500 to 1+500

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2082 Baisakh, 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-b-0500-1500
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Calculate the quantities of earthwork from the following data for channel section from chainage 0+500 to 1+500 m. Bed width = 5 m, side slope in cutting 1H:1V, side slope in banking 1.5H:1V, top width of both banks = 2.5 m, full supply depth = 1.5 m and free board = 0.5 m.

| Chainage | RL of Bed (m) | RL of ground (m) |
|---|---|---|
| 0+500 | 1000.50 | 1001.80 |
| 0+1000 | 1000.00 | 999.50 |
| 0+1500 | 999.50 | 997.50 |

## Short answer

Using ground vs bed level comparison, partial cutting/banking and full banking sections are identified. Volumes: cutting = 2,047.50 m³, banking = 35,930.00 m³, total = 37,977.50 m³.

## Answer

#### Given data and assumptions
- Bed width $5$ m; FSD $1.5$ m; free board $0.5$ m, so $D = 2.0$ m; top width of each bank $2.5$ m.
- Side slope in cutting $1:1$; side slope of banks (inner and outer) $1.5:1$ (H:V).
- Chainages 0+500, 1+000 and 1+500 are 500 m apart.

#### Method
Total depth of canal section $D = \text{FSD} + \text{free board} = 1.50 + 0.50 = 2.00$ 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+500 | 1,001.800 | 1,000.500 | 1.300 | part cutting, part banking | 8.190 | 4.970 |
| 1+000 | 999.500 | 1,000.000 | -0.500 | full banking | 0.000 | 33.375 |
| 1+500 | 997.500 | 999.500 | -2.000 | full banking | 0.000 | 72.000 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Banking (m³) |
|---|---:|---:|---:|
| 0+500 – 1+000 | 500.0 | 2,047.50 | 9,586.25 |
| 1+000 – 1+500 | 500.0 | 0.00 | 26,343.75 |
| **Total** | | **2,047.50** | **35,930.00** |

**Answer: Earthwork in cutting = 2,047.50 m³; earthwork in banking = 35,930.00 m³; total = 37,977.50 m³.**

## Check yourself

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

1. How is the total depth D of the canal section found?
   A. D = FSD + free board = 1.5 + 0.5 = 2.0 m
   B. D = FSD only = 1.5 m
   C. D = FSD - free board = 1.0 m
   D. D = bed width / 2 = 2.5 m
   Answer: A. The banks are built to the full supply depth plus free board, so D = 2.0 m. (Key point: Total depth of section)

2. At 1+000 the bed RL (1000.00) is above the ground RL (999.50). How is the section treated?
   A. Full cutting, because the bed is a known level
   B. Full banking, because e = GL - bed is negative
   C. Part cutting, part banking, because e is less than D
   D. Not counted, because the ground is lower than the bed
   Answer: B. When e <= 0 the canal lies wholly above ground and is in full banking, with banks built to D - e above ground. (Key point: Classifying a station)

3. At 0+500, e = 1.30 m and D = 2.0 m. What is the height of each bank above ground?
   A. 1.30 m
   B. 2.00 m
   C. 0.70 m
   D. 3.30 m
   Answer: C. In part cutting, part banking each bank stands h_b = D - e = 0.70 m above ground. (Key point: Bank height at part section)

4. How are volumes between stations obtained here?
   A. Area at the first station x distance, for cutting and banking combined
   B. Sum of cutting and banking areas x distance only
   C. Prismoidal rule applied on total depth D
   D. Mean of the end areas x distance, done separately for cutting and banking
   Answer: D. The answer averages the two end sectional areas and multiplies by the distance, keeping cutting and banking separate. (Key point: Volume computation)

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