# Estimation of Earth work excavation – Types, With Numerical Examples

Estimation of Earth work excavation in civil engineering is the process of calculations of expected quantity required, amount of work to be done, the number of worker and equipment required and total expenditure cost to complete any project.

Different types of quantities are required to be estimated accordingly to their types of work. For example, the amount of excavation, cutting and backfilling is required to be calculated in earthwork, the amount of concrete and reinforcement in RCC work and so on.

The earthwork excavation is taken in cubic meters, so the detail of length, breadth and height of the work that is to be excavated is the first thing we required in estimation.

Excavation shall include throwing of excavated earth material at least 1m to clear the edge of the excavation. The excavation includes setting out of work, profile, site clearance, dewatering and removal of soil.

However, if the structure is to be dismantled before excavation, they are not included within it and separate estimation and rate analysis are required.

The cubic rate estimate method is generally preferred for earthwork (cost estimate) in which the amount of estimate is measured in cubic meters and are directly multiplied by cubic rate to determine the cost.

Different types of earthwork excavation are performed for building construction, road construction, pile and pier construction, irrigation and drainage purpose.

## Different methods are used to determine the estimate of quantities in the building construction work. They are;

### A) Central line method

In this method, the total centerline length is calculated in the first order. The centre to centre length is denoted by (l) and breadth by (b). Thus, the total length of the centre line is given,

Total length = 2(l+b)

Quantity of earthwork excavation = T. L. * w * h (h is height of trench and w is width of trench)

As shown in Figure, it is clear that the inside intersected corner repeats twice when area through length and breadth is taken. And the outside corner is completely neglected. Thus, the intersected corner compensates the area od outside corner which is exactly equal giving the actual area.

Special consideration is needed when more no of cross wall is included within.

Total length = 2l+nb- no of junction *w/2

### B) Crossing method

This method is also similar to center line method, but the calculation of length is different here. The total outside perimeter is taken instead of perimeter of center line. Thus, here each corner repeats during calculations and thus they are deducted.

Total length = 2(L+B) –  4w

And total quantity of earthwork excavation = T. L. * w * h (h is height of trench and w is width of trench)

Special consideration for more number of cross wall is given by;

Total length = 2L+ n *B- no of junction including corner *w

### C) Long wall and short wall method

In this method the long wall and short wall are first of all identified. Then their respective length is calculated. And the separate quantity of both long wall and short wall is calculated and sum up at last.

Long wall length (lw) = c/c length + w/2+ w/2

Short wall length (sw) = c/c length – w/2 – w/2

So,

Total long wall quantity of excavation = nl * lw*w*h (nl is no. of long walls)

Total short wall quantity of excavation = ns*sw *w*h (ns is no. of short walls)

### D) Bay method

This method is generally use for the slab and raft foundation. The plane area of panel is calculated and then by multiplying with depth quantity is determine. And multiplying by each number of panel the total quantity is estimated

And, the different types of method used to calculate the earthwork excavation in road construction (in plain area), irrigation canal and drainage are:

### E) Mid section area method

Here the area of mid cross section is taken for certain portion of length of road to be excavated (also for embankment). And then are multiplied with length to get volume of earthwork.

Quantity of excavation = Area of mid section * length of the section considered

And,

Area of mid section = area of rectangular portion + area of triangular portion (reference to figure shown)

= B* d + ½*s*d² + ½*s*d²

= Bd + sd²

So, quantity of excavation = (Bd + sd²) * L

Where;

d is height (depth) at mid section

B is formation width

s is side slope

### F) Mean sectional area method

In this method instead of depth of mid section, the mean area of the two ends of the certain length portion of road to be excavated are calculated to determine the estimate. So,

Quantity of excavation = Mean of the area * length of section considered

Area of the both cross section (front and end face) are calculated same as above. So,

Area of front face (A­­­1) = B*d1 + s*d1²

Area of end face (A2) = B*d2 + s*d2²

Mean area (Am) =(A1+A2) /2

So,

Quantity of earthwork excavation = Am* L

### G) Prismodial formula method

This method is the more accurate and precise approach to calculations. Here, the Mean depth of the section is calculated to determine the area of the midsection of the considerable length of road excavation along with calculations of the area of the front end and back end of it.

And, thus by Prismodial formula quantity of earth excavation is calculated.

Quantity od earthwork excavation = L/6 (A1+A2+4*Am);

1 = B*d1 + s*d1²

A2 = B*d2 + s*d2²

Am = B*dm+ s*dm²; dm = (d1+d2) /2

The method to be used depends upon their suitability along with work type and the user.

Some simple example of each for more illustration are given below.

## 1) Estimation of Earth work excavation calculations for building

#### Sept 1:

First of all, the necessary drawing with proper and detail dimensioning should be made ready for estimation.

The specification also must be read properly before any estimate. If possible, trench plan drawing can be prepared separately for easy estimation. The trench plans are required especially when the formworks are to be placed beneath the ground for footing purpose.

Thus, the extra width of 20-30 cm is added to the width of the actual plan structure (wall or footing foundation) for such trench.

#### Step 2:

Determine the most bottom width of trench required to be constructed and according to it, the full depth is to be excavated.

(Note: But when the height of excavation is too deep the trench are constructed in step wise such that width increase upwards or in slope (increasing width upward) to maintain stability.

#### Step 3:

determine the depth of excavation needed.  Different structures are located at different depth so it must have noted carefully. For example, the depth of footing is higher than the depth of the foundation beam.

#### Step 4:

Determine the volume of excavation needed using any od techniques of estimate the quantity.

Footing: excavation for footing is determined. If the footings are of the same dimensions overall building, then at the first volume required doe one footing is calculated and then multiplied by its numbers.

Foundation beam: Any one of the techniques above explain can be used. For footing, the long wall and short wall method are comparatively easier so it is select here for calculating.

## 2) Estimation of Earth work excavation calculations for simple plain road construction

Given data:

Formation width (B) = 12m

Side slope for cutting (s:1) = 1.5: 1

Formation road gradient is(downward) 1 in 200. (So, change of level per chainage should be 30/200 =0.15)

Solution:

#### Step 1:

Find out R.L of formation level. This is done by deducting 0.15 from top R.L of 0 chainages (108.6) per each chainage.

#### Step 2:

Find out depth of cutting or banking required.

Depth of earthwork = R.L of F.L – R.L. of G.L

If the depth value is in -ve sign then cutting(excavation) is indicated and if it is +ve then filling (banking) is indicated. (Note, here we only deal with excavation)

#### Step 3:

Determine the chainage at which the process of excavation and filling gets change by linear interpolation techniques.

(X-20)/(0-0.5) = (150-120)/(-0.6-0.5)

On calculation value of x is 133.63 which can be taken as approx. 134 for easier calculation.

#### Step 4:

Calculate the quantity of earthwork to be excavated using any one of the methods as explained above (Here, we use the midsectional method)

Calculation is as shown in table: (note only excavation is shown so -ve sign is neglected)

Happy Learning – Civil Concept

Contributed by,

Civil Engineer – Rajan Shrestha

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