Chapter 4 earth work and quantities new

Earth Work & Quantities
CHAPTER 4

2
Introduction
• Is the phase during a highways construction
when the right of way is converted from its
natural condition and configuration to the
section and the grades prescribed in the plans

3
Earth Work Includes
• Clearing
• Grubbing - clear off roots
• Excavation of drainage channels & trenches
• Excavation of structures
• Borrows
• Haul & Overhaul
• Grading
• Preparation of Side Slopes
• Reconditioning of roadway
• Other operations for preparing the subgrade for highway or
runway pavement construction (Highway Eng. II)

4
Earthwork Quantity
• Quantity and Cost are calculated in m3 either in its
original form or by allowing for shrinkage and swell
• The rate of payment generally includes full
compensation for excavation, formation of
embankment, preparing of side slopes, disposal or
borrowing with in the free-haul distance, and the
preparation and completion of the subgrade and the
shoulders
• For borrowing or disposal involving more than the
free haul distance

5
Classification of Excavated Material
Usually the classification is into three categories:
1. Solid Rock: comprises hard rock in place and boulders that
can be removed only by the use of drilling and blasting
equipment.
hard rock and boulders; Volume > 1m3; best
removed by blasting
1. Loose Rock: usually refers to rock which can be removed
with pick and bar, although the use of power shovels or
blasting may be advantageous.
detached masses or rock – 0.025<V<1m3; could
easily be removed
3. Common/Ordinary Excavation: is largely earth, or
earth with detached boulders less than ½ cu yd.

6
Shrinkage & Swell Factors
• When earth is excavated and hauled to form an
embankment, the freshly excavated material generally
increases in volume. However, during the process of
building the embankment it is compacted, so that the
final volume is less than when in its original condition.
This difference in volume is usually defined as
“shrinkage”. The amount of shrinkage varies with the soil
type and the depth of the fill.
• When rock is excavated and placed in the embankment,
the material will occupy a larger volume. This increase is
called “ swell”

CONT…
• Percent shrinkage = ( 1 – ( wt. bank
measure / wt. compacted ) ) *100
% sh. = ( 1 – (γB / γC) ) * 100
• Percent swell = ((wt. bank measure / wt.
loose measure) – 1) * 100
% sw. = ((γB / γL) - 1) * 100
7

8
Shrinkage of compacted fills
Material % of shrinkage
Light excavated soil
(on ordinary ground)
10 – 20%
Light excavated soil
(on swampy ground)
20 – 40%
Heavy Excavated soil Up to 10%
Excavated Rock (Swell) 5 – 25%
Amount of excavation required to make a given fill may be
arrived at by:
Shrinkage: multiply the fill quantity by 1+ %sh
Swelling: divide the fill quantity by 1 + %sw

9
Road Bed Sections
• A highway sub-grade is usually formed with
shoulders and a trench section upon which the
pavement will be constructed, the finished
surface being crowned to facilitate drainage
• Ditches are provided on embankment sections
to transfer water down the fill slops into pipes or
paved gutters to protect the embankment
against erosion
• On curves of 5o or sharper subgrade is banked
and widened. Width of road bed in cut is wider
than on fills to allow for side-ditches.

10
Typical Sections
Fill
Cut
Cut & Fill

11
Side slopes of X-sections
Material Ht. of
Slope
Side Slope Back Slope
Cut Fill
Soil 0 – 1
1 – 2
Over 2
1:4
1:3
1:2
1:4
1:3
1:2
Rock Any ht. See standard details
Black Cotton
Soil
0 – 2
Over 2
- 1:6
1:4

12
Areas of Cross-sections
• For the purpose of calculating the
quantity of earth work, the areas of
cross-sections and the distance between
them must be known
• Methods
– For regular/level ground  simple geometry
– For irregular ground, two methods
1. Graphical or planimeter method .
2. Coordinate or other approximate method

13
Area for Regular Ground
Area of a trapizod
Cut
d
sd sd
1
b
s s
1
Fill
b
sd
s
sd
2
sd
bd
A 


14
Area for (Regular) cut – fill
sections
)
(
8
)
2
(
)
(
8
)
2
(
2
2
2
1
2
1
s
n
nd
b
A
and
s
n
nd
b
A






)
(
8
)
2
(
)
(
8
)
2
(
2
2
2
1
2
1
s
n
nd
b
A
and
s
n
nd
b
A








A1=Area in cut
A2=Area in fill
When c is to the right
of the point of zero fill
When c is to the left of
the point of zero fill
h1
h2
d1 d2
d
C
L
b/2
s1
1
s2
1
c

Area for Three-Level Section
With three readings taken directly from slope stake notes,
one at the center and one at each slope stake, the area of
cross section may be obtained.
A = ½ [d(x1 + x2) +
½ b(h1 + h2)]
A = ½ (h1x’’ + h2x’)
15

16
Area of irregular section
1. Trapezoidal Rule
A1 A2 A3
An
L
L
L
O1
O2
O3
On+1
On
 
)
...
(
2
2
/
...
3
2
1
1
2
1
n
n
n
O
O
O
O
O
L
A
A
A
A
A











Assumes the boundaries could be approximated by a
straight line, if the interval L between offset
measurements is very small

17
Area of irregular section
2. Simpson’s Rule
Assumes, instead, that the boundaries consist of a series of
parabolic arcs
For this rule to apply, N must be an odd number
)
2
4
(
3
/
)
4
(
3
/
)
4
(
3
/
1
5
4
3
4
3
3
2
1
2
1

 











offsets
odd
remaining
offsets
even
O
O
L
A
O
O
O
L
A
A
O
O
O
L
A
A
N
A1 A2 A3
An
L
L
L
O1
O2
O3
On+1
On

Area by Coordinate Method
• With the coordinates of all the corners of a cross-section known, the
end area may be computed by means of the coordinate method
• Let the corners A, B, C, and D of the area ABCD be located by the
coordinates (x1,y1), (x2,y2), (x3,y3), and (x4,y4). Then the area is given
by the algebraic sum of four trapezoids. Thus,
Area = ABba + BCcb – ADda - DCcd
=1/2 [y1(x4 – x2) + y2(x1 - x3) + y3(x2 – x4)
+ y4(x3 – x1)]
18

19
Computation of Volumes
Two methods will be discussed here:
1. Average End Area Method
2. Prismodal Formula

20
Average End Area Method
Volume of a right prism equals the average
area multiplied by the length
In which: A1 and A2 = area of end sections (m2)
L = length of solid (m)
This formula is applied to areas of any shape, but the
results are slightly too large. The error is small if the
sections do not change rapidly.
)]
...
(
2
)
[(
2
/
2
1
2
3
2
1
2
1
12

 








n
n
n A
A
A
A
A
A
l
V
l
A
A
V

21
Prismodal Formula
• A prismoid is a solid whose ends are parallel and whose
sides are plane or warped surfaces
• The Volume of a prismoid is:
• In which L is the distance between the two parallel bases A1 and A2
and Am is a section midway between the two end bases and parallel
to them. Am is not an average of A1 and A2, but each of its linear
dimensions is an average of the corresponding dimensions of A1
and A2.
))
(
4
)
(
2
(
6
))
(
4
2
(
6
)
4
(
6
)
4
(
6
1
4
2
3
5
1
15
5
4
3
35
3
2
1
13
areas
even
areas
odd
remaining
A
A
l
V
A
A
A
A
A
l
V
A
A
A
l
V
A
A
A
l
V
N 
















)
4
(
6 2
1 A
A
A
l
V m
ab 



22
Mass Diagram
• Is a continuous curve showing the accumulated
algebraic sum of the cuts (+ve) and fills (-ve)
from some initial station to any succeeding
station
• Ordinates of the mass curve are plotted with
reference to a horizontal scale of distances
• It is convenient to tabulate the cumulative sum of
cuts and fills at a station before drawing a Mass
diagram

The mass haul diagram can be used
to determine:
Proper distribution of excavated
material
Amount and location of waste
Amount and location of borrow
Amount of overhaul in kilometer-cubic
meters
Direction of haul.
23

24
Drawing a mass-haul diagram
Procedures
1. Calculate areas at cross-sections
2. Calculate the volume of fill and cut; cut is +ve and fill –ve.
3. Correct the volume calculated by shrinkage and swell
factors
4. Tabulate the corrected aggregate volume
5. Plot the mass haul diagram
(e.g. scale: 1:2000 H and 1:500 or 1:1000 (cm:m3)V)
6. Join points by a straight line or curves
Sta Individual
volume
Bulking/ Shrinkage
factors
Corr. Indiv. volumes Aggregate
Vol.
Cut Fill Cut Fill

25
Mass-Haul Diagram -
Characteristics
i. The Ordinate at any point represents the cumulative material to
that point on the profile
ii. With in the limits of a single cut, the curve rises from left to right;
within the limits of a single fill, it falls from left to right
iii. Sections where the profile changes from cut to fill correspond to a
maximum (and the opposite for ch. from fill to cut). Evidently the
maximum and minimum points on the mass diagram occur at or
near grade points on the profile
iv. Any horizontal line cutting a loop of a mass curve, intersects the
curve at two points b/n which the cut is equal to the fill (adjusted
for shrinkage); such a line is called a BALANCE LINE
v. The loop convex upward indicates that the haul from cut to fill is
to be in one direction
vi. The final point on a mass diagram for a given project gives the
overall net amount of earthwork for the entire project. This
amount, if positive, would indicate a surplus of excavation
material and a need to waste that quantity of material. If the final
point on the mass diagram is a negative amount, it indicates a net
shortage of earthwork for the project and a need to borrow that
quantity of earthwork material.

26
Mass-haul Diagram - Example
Chainage (km+m)
Aggregate
volume
(m3)
Natural ground profile
Proposed grade line
O
H J
I
K
L
M
h
i
j k
l
m

27
Distribution Analysis of Earthwork
Terminologies
• Haul Distance: distance from point of excavation to point where the
material is to be tipped
• Average Haul Distance is the distance from the centre of gravity of the
excavation to the centre of gravity of the tip
• Free-haul Distance: is the distance (usually specified in the contract) over
which a charge is paid only for the volume of earth excavated and not for
its movement (300m). Free-haul is part of the haul which is contained
within the free haul distance.
• Over-haul Distance: is the distance in excess of the free-haul distance, over
which it is necessary to transport material. An extra charge will be paid for
transport. Over-haul is part of the haul which remains after the free haul
has been removed.
• Haul: is the sum of the product of each volume of material and the distance
through which it is moved. On the mass-haul diagram, it is the area
contained b/n the curve and the balance line

28
Distribution Analysis of Earthwork
Terminologies (cont.)
• Waste: is the volume surplus or unsuitable material
which must be exported from a section of the site.
• Borrow: is the volume of material which must be
imported in t a section of the site due to deficiency of
suitable material

Haul and Overhaul
• In grading contracts for roads it is usually stipulated that
the contractor shall be paid a certain price per cubic
meter for excavating, hauling, and dumping the material,
regardless of distance hauled, provided it does not
exceed a specified limit called free haul. The free haul
distance may be as low as 150m and as high as 900m or
more.
• If there is an overhaul on some of the material, that is, if
the distance from excavation to embankment is beyond
the free haul limit, then an extra charge may be allowed.
• A mass diagram is helpful in determining the amount of
overhaul and the most economical distribution of the
excavated material.
29

30
Limit of Economical Haul
• When there are long hauls, it may be more economical to
waste and borrow materials rather than pay for the cost of
overhauling. Equating the cost of excavation plus overhaul to
the cost of excavation from both the roadway and borrow pit,
one can estimate the limit of economic haul for making the
embankment.

31
Limit of Economical Haul (cont…)
Let: Ce=cost of excavation per unit volume (including free haul)
Cb=cost to excavate borrow pit (including free haul)
Coh=cost of overhaul per m3m
Le=Economical Length of over-haul
Cost to excavate 1m3 of material from cut and move to fill
=Ce+CohLe (1)
Cost of excavate from cut, waste, borrow and place 1m3 material
in fill = Cb+Ce (2)
Equating (1) & (2): Ce+CohLe= Cb+Ce  Le=Cb /Coh
Total Distance, D=Le+F
where: F=free haul distance

32
Example
If the cost of roadway excavation, Ce, is 800
cents/m3, cost of borrow, Cb, is 700 cents/m3,
and cost of overhaul, Coh, is 12 birr/m3-station,
what is the economical length of overhaul? The
free haul distance is 1.5km and a station is
100m long.
Ans: Le =1558m

Example 2
Cross-section data for “Jimma-Didesa” road segment from station 1+200 to
2+000 was given in Table 1. The section is to be constructed entirely on cut
up to station 1+600 and entirely on fill up to station 2+000 at uniformly rising
gradient of 2 percent. The original ground was level in the transverse
direction with center line elevations given in Table 1. The finished formation
elevation at station 1+200 is 1220.0 and the formation width including
shoulders is 8 m. The side slopes are 1 vertical to 2 horizontal.
Cross-section data
37
Station 1+200 1+300 1+400 1+500 1+600 1+700 1+800 1+900 2+000
NGL
Elevation
1220.0 1223.75 1226.5 1227.5 1228.0 1228.0 1229.5 1233.0 1236.0
1. Plot the road template
2. Calculate the areas of the cross-sections
3. Estimate the volume of earthwork and
4. Draw mass haul diagram by considering
5. Shrinkage factor of 15% and show direction haul.

Home works
1. For the natural ground level given in Table, plot the road template and
calculate the areas of the cross-sections and estimate the volume of earthwork.
The section is to be constructed entirely on fill at rising gradient of 4% up to
station 0+100 and downward gradient of G2 up to station 0+200. The original
ground is level in the transverse direction with the elevations given in Table.
The finished subgrade elevation at station 0+000 and 0+200 is 1122.0 and
1124.0 respectively. The formation width including shoulders is 10 m. The
side slopes 1H:2V. (no need to consider the vertical alignment)
Cross-section data
38
Station 0+000 0+050 0+100 0+160 0+200
Elevation 1121.0 1122.0 1123.0 1123.3 1123

2. The following table shows the station and ordinate for a mass diagram. The free haul
distance is 200. Overhaul cost is 10 birr per cubic meter per station, cost of borrow is
80 birr per cubic meter. And the cost of excavation is 30 birr per cubic meter. Station
length is 100m
39
Station 1 2 3 4 5 6 7 8 9 10 11
Coordinate of mass diagram 0 130 420 870 1250 1310 1250 1120 760 230 0
Determine the following:
a) Limit of economic haul distance
b) Total excavated volume
c) Total fill volume
d) Volume of free hauling
e) Volume of borrow
f) Volume of economical haul
g) Cost of excavation
h) Cost of borrow
i) Cost of hauling

3. The following a mass diagram. Determine the following:
a) Limit of economic haul distance
b) Total excavated volume
c) Total fill volume
d) Volume of free hauling
e) Volume of borrow
f) Volume of economical haul
g) Total cost of earthwork
The free haul distance is 400. Overhaul cost is 10 birr per cubic meter per
station, cost of borrow is 40 birr per cubic meter. And the cost of excavation is
20 birr per cubic meter. Station length is 100m
40

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