Roads are constructed either in the plain area or in hilly areas. To calculate Earthwork in excavation for road, we have to use the separate formula for plain and hilly areas. Here I have described both types of estimation for road construction step by step with numerical examples. So, let’s start.

## A) Estimate the Earthwork in excavation for Road Construction in Plain Area

#### Volume of earthwork

It is measured in cubic meters without any allowance for an increase in bulk. The volume of earthwork shall be calculated by multiplying the length, breadth, and depth or height measured from the ground from which soil has been taken out.

#### Lead and Lift

Normally earthwork is estimated for 30 m lead for distance and 1.5 m lift for height or depth, and this distance of 30 m and the height of 1.5 m are known as normal lead and lift.

During the estimation of earthwork in the road, the volume of earthwork may be calculated by the various methods of mensuration out of which three methods are given below.

#### Method – 1, Mid sectional area method

Quantity = area of mid section x length

**Area of midsection = Area of rectangular portion + area of two triangular portions.**

Therefore, the Quantity of earthwork,

= (Bd + Sd^{2}) x L

Where,

d = Mean depth or height

B = Formation width

S = Side Slope

The quantity of earthwork may be calculated in a tabular form as below,

#### Method-2: Mean Sectional Area Method

**Quantity = Mid Sectional area x Length**

In this method, it is not necessary to calculate mean depth but, we should calculate the mean area after calculating the area of each station.

The quantity of earthwork may be calculated in the tabular form as given below.

Where,

Am = Mean sectional area

d = Height or Depth

B = Formation width

S = Side Slope

#### Method – 3: Prismodial formula method

Quantity of volume = L/6 x (A_{1}+ A_{2} + 4Am)

Where,

A_{1} = Cross sectional Area at one end

A2 = Cross sectional Area of another end

A_{m} = mid-sectional area

#### Trapezoidal Formula and Prismoidal formula methods for a series of cross-sections.

1) **Volume by trapezoidal formula**

2) **Volume by Prismodial formula**

## Numerical example

#### Q) Prepare an estimate for the portion of a road from chainage 14 to 22 from the data given below. Draw typical cross-sections for cutting and banking. The formation width of the proposed road is 12 m, side slopes 3/2:1 m. cutting and 2:1 in banking.

The road formation is proposed as a uniform falling gradient 1 in 200 passing through G.L at chainage 14 length of one chain = 30 m.

**Solution:-**

Depth of cutting and bankings are denoted by -ve and +ve signs respectively. Depth of cutting or banking = Difference between G.L and F.L.

For a gradient 1 in 200 change of level per chain of 30 m = 30/200 = 0.15

**B = 12 m, S = 1.5 for cutting, S= 2 for banking**

-ve depth = Cutting

+ve depth = Filling

Here from chainage 18 to 19, there is a change from cutting to filling.

Let the distance from 18 chainages up to the portion of cutting = x

Then,

X = 13.63 m, Say 14 m

Therefore length of banking portion = 30-14 = 16 m

## B) Estimate the Earthwork in excavation for Road Construction in hilly area

Earthwork for hill roads having transverse slope i.e for two-level sections where contour lines are very close to each other (as in hilly area) transverse or cross slope cannot be neglected in calculating earthwork.

When these transverse and longitudinal slopes are unknown in between two cross-sections this portion of a road is called two-level sections. The method of estimating the volume of earthwork for such cases has been illustrated below.

#### Case:-1 Wholly in Banking or wholly in cutting

s:1 = Side slope

r:1 = Transverse Slope

H = Height of banking or depth of cutting

b = Half of formation width

#### Case:-2

When the centerline (FG) is in the cutting portion (figure: a)

#### a) Partly in Banking and Partly in cutting

**Area of ABE = Area of banking **

#### b) When center line (FG) is in banking portion (figure:b)

**Area ofABE = Area of Banking**

**Area of EDC = Area of Cutting**

Where,

H = Center depth of cutting or banking

S:1 = Side slope of banking

P:1 = Side slope of Cutting

b = Half of formation width

r:1 =Transverse Slope

The amount of earthwork can be calculated by three methods which are explained in E/w in plain area. The methods are given below,

- Mid sectional Formula
- Average end area of mean sectional formula
- Prismoidal Formula

## Numerical Example

## Q) Calculate the earthwork for or portion of hill road from the following data.

Chainage | 0 | 30 | 60 | 90 |
---|---|---|---|---|

RL of Ground Level | 104 m | 105 m | 106 m | 107 m |

Formation Level | 105 m | 105.5 m | 106.0m | 106.5 m |

Transverse Slope | 20:1 | 15:1 | 12:1 | 10:1 |

Formation width = 10 m, side slope in cutting = 1:1

Side slope in banking = 2:1

**Solution:-**

First, we find the depth of cutting or banking, which are given below:

Chainage | RL of GL (m) | Formation level (m) | Cross Slope | Depth (m) |
---|---|---|---|---|

0 m | 104 | 105 | 20:1 | 1 |

30 m | 105 | 105 | 15:1 | 0.5 |

60 m | 106 | 106 | 12:1 | 0 |

90 m | 107 | 106.5 | 10:1 | -0.5 |

**At chainage 0 m**

s = 2

b = 5 m

H = 1 m

r = 20

**At chainage 30 m**

s = 2

b = 5 m

H = 0.5 m

r = 15

**At chainage 60 m**

s = 2

b = 5

H = 0

r = 12

**At chainage 90 m**

s = 1

b = 5

H =0.5

r = 10

**Hence, earthwork in Cutting = 117.33 m ^{3}**

**Earthwork in filling = 395.82 m ^{3} **

I hope this article on the “**Earthwork in excavation for Road Construction**” remains helpful for you.

Happy Learning – Civil Concept

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