# How do you calculate the amount of earthwork in a canal

We need to calculate the amount of earthwork to estimate the probable cost of the canal. Earthwork means the digging work of the soil below the ground. The ground is dug to provide the foundation of the structure.

But in some cases, it is dug to construct the channel like drainage, canal, manage river embankment, etc. To design a canal we have to calculate the balancing depth along with the nature of the ground. Here we will see in detail the calculation of the earthwork for a canal. So, let’s start.

## What is Balancing depth or Economical depth?

While designing the canal project, if the bed levels of the canals are so adopted, that the quantity of earth, excavated is just sufficient for making the two banks on either side of the canal, the depth of excavation is then called economical depth.

For calculating the balancing depth,

Area of cutting = Area of filling

Bd + sd2 = 2[b(H−D) + S1 (H-d)2]

where,

d = Balancing depth in cutting

B = Bed width of the bank

b₁ & b₂ – Top width of the bank

H- d Height of the bank about NSL

S:1 = Slope in cutting

S₁1 = Slope in filling

FSL Full supply level

FSD= Full supply depth

#### Permanent Land Width:

Permanent land width is that land width that is acquired permanently by the Government and it includes the sum of the widths of the bed and two banks, plus the widths required for slopes, plus extra widths required beyond the outer toes of the bank as per design.

#### Dowel or Daula:

Generally, on the side of the canal bank, a service road is provided for inspection purposes. Thus on the inner edge of the bank, an earthen bund of small sections (30 cm to 5 cm high above the service road, 30cm to 50 cm in top width, and (1.5:1) to 2:1 side slopes) called dowel.

## Earthwork in ca nals:

Case I: Fully in excavation

The quantity of earthwork is calculated in the same manner (principle) of road estimate (Bd + sd²) × L, in a tabular form. Width of permanent land = B + 2sd + road widths on the sides + extra land widths beyond the roads

.’. Area of permanent land = width of permanent land x length

Case II: Partly in excavation and partly in embarkment

The quantity of earthwork is calculated, both in cutting and filling by any above methods. However, if the quantity of the earth work in cutting is more than the quantity required in banking, the surplus earth is thrown away to form a spoil bank, otherwise, if the quality of earth work in cutting is less than that required for embarkment, the extra earth is taken from borrow pits in temporary land.

Area of excavation = Bd+sd2

Area of banking = (b1+b2)h + sh2 +s1h2

H= H-d

Width of permanent land = B + b1 + b2 + 2sd + 4s1(H-d) + 2 bern widths + extra widths beyond the outer toes of bank.

.’. Area of permanent land = width of permanent land x length

Case III: Fully in filling or fully above Ground Level or N.S.L.

There can be three sections of this category

a) When bed level of canal coincides with N.S.L.The quantity of earthwork is calculated in the same manner as above. Width of permanent land = B + b₁ + b₂ + 4s₁d + extra widths beyond the outer toes of bank

Area of permanent land = width of permanent land x length

b) When bed level of canal is above NSL and the width occupied by the side slopes (i.e. 2s, H) as shown in the figure is less than bed width of the channel

Area of filling = Area of the two banks + area of the trapezium below the bed

Or

= Area of the whole section – Area of the channel section

Width of permanent land = B+ b + b₂ + 2s₁H + 2s1d + extra widths beyond the outer toes of bank

Area of permanent land = width of permanent land x length

c)  When bed level of canal is above NSL and the width occupied by the side slopes i.e. (2s1H) as shown in figure is more than Bed width of channel.

Area of filling = Area of two banks + Area of triangles below bed – Area of common triangle formed by the inside bank sides (as shown)

Width of permanent land = B + 2s1d + b₁ + b₂ + 2s₁H – 2s/d₂ + extra widths beyond the outer toes of banks

Area of permanent land = width of permanent land X length

## Numerical Examples:

#### Q) Calculate the quantity of earthwork of an irrigation channel with the following data

Bed width = 5 m

Top width of both the bank = 2m

Free board = 0.6 m

Full supply depth = 1m

Side slope in cutting = 1:1

Side slope in banking = 1   1/2:1

a) Calculate the quantity of earthwork of an irrigation channel

b) Also find the economical depth of cutting

Solution:-

#### a) Calculate the quantity of earthwork of an irrigation channel

Here

B = 5 m, b₁ = b₂ = 2 m

FB = 0.6 m, FSD = 1 m

.. Total depth = 1 + 0.6 = 1.6 m Ht. of bank above ground level,

h = H – d

s = 1 and s₁ = 1.5

Cutting

Embarkment

.’. From table.

Quantity of earthwork in excavation = 6445.4 m³

Quantity of earth work to be taken from borrow pit = 4086.3 m³

#### b) To find the economical depth of cutting

Depth of cutting = depth of filling

Bd + sd² = (b1 + b₂) h + 2s₁h²

B = 5 m, s= 1,

b₁ = b₂ = 2m,

s₁ = 1.5

h = H – d= 1.6 – d

or, sd + 1d²+ (2+2) (1.6 – d) + 2×1.5 (1.6 – d) ²

or, 2d²- 18.6 d + 14.08 = 0

on solving,

d = 8.47 m & 0.83 m

But, the value of 8.47 m being too high can’t be adopted

.’.Economical depth = 0.83 m

I hope this article on “How do you calculate the amount of earthwork in a canal” remains helpful for you.

Happy Learning – Civil Concept