Road construction in Civil engineering

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Road Construction
Content
• Lead and Lift
• Computation of Earthwork
• Cross Section Area with no transverse slope
• Calculation of Quantities of earthwork FOR
– Mid Section Formula, - MeanSection Formula, -
Prismoidal Formula
• Mass Haul Diagram

Road Construction
What is Road and Why it is needed
• Specially designed route to allow movement from one
place to other.
Items in road construction
Survey Work, Earthworks (Cutting, Filling), Subgrade, Sub
base, Base Course, Bituminous Course
Note: In this chapter, we will study Earthworks calculation

Road Construction
Cutting And Filling
• Why cutting Filling are required?:
• Formation Level of Road may be below the actual ground
level or may be above ground level, hence to provide all
road layers properly executed, sufficient depth/height are
needed.
Lead and Lift
• To dispose or dumping soil at suitable place,
Transportation and Lifting of soil are required
• Lead: It’s a horizontal straight practicable distance through
earth can be transported from source to place of dumping.
– When Unit of Lead is 50 m up to 500 m, Lead is measured as
separate items:-
• 0 to 250 m
• 250 to 500 m

Road Construction
Lead and Lift
• Lead (conti..)
– When Unit of Lead is 500 m to 5000 m, Lead is
measured as a separate item:-
• 500 m to 1000 m
• 1000 m to 1500 m
• 1500 m to 2000 m… Keep on increasing 500 m
– When Unit of Lead is beyong 5 KM, Lead is measured
as a separate item, starting from 1 km or 1/2km
– Lead item shall include loading and unloading.
– Lead is measured from Centre of Exacavted place to
Centre of Dumping Place.

Road Construction
Lead and Lift
• Lift
– Height measured from Ground level.
– Excavation of soil upto 1.5 m meter from ground level
and depositing on ground is included in earthwork
item rate.
– Extra lift is measured in unit of 1.5 m or part thereof.
– Inherent Lift is measured separately (due slope
difference in lead beyond 250 m)
– When earth is to be moved over a bank, dumped
beyond it. Lift is measured difference in level of
centre of gravity to excavated area and TOP of bank.

Road Construction
Volume of Earthwork
• To avoid flooding on Road, The level of formation is designed above the
high flood level. So it forms a trapezium to side slopes of the
embankment
• And when Formation level is below ground level, cutting is required side
slopes. So both in cutting and filling, trapezium is formed.
• The height of banking and depth of cutting is designed as per high flood
level, ruling gradient and for economy in earthwork
• To estimate earthwork, longitudinal levels along the centreline of a road
are taken at certain distance apart.
• The distance between two points depends on topography of surface.
– For Plain surface, distance is 20 to 50 m
– For Hilly areas, distance is 10 to 20 m
• The Scale for Drawings:-
– For Longitudinal Sections : 1 cm = 10 m to 1 cm = 20 m
– For Cross Section : 1 cm = 1 m to 2 m

Road Construction
Volume of Earthwork
• Depth of cutting or banking is difference
between ground level and formation level.
• Slope is Horizontal : Vertical for Sides
• Will follow the Formulas for Calculation of
Earthwork quantity.
– Mid Section Method
– Trapezoidal or Average End area or Mean Section
method
– Prismoidal Method as per Simson’s one-third rule

Road Construction
Volume of Earthwork
• Mid Section Method:
– Area of any Section is Bd + Sd²
– Volume of Earth between Two
sections
• V = Area of Mid Section x L
• V = Am X L
• V = (Bd + Sdm²) x L
Dm = Mean Depth between two
consecutive sections
Dm = (d1 +d2) / 2

Road Construction
Volume of Earthwork
– Table Format for Calculation
Station or
Chainage
Reduced
level of
Ground
Formation
Level
Depth or
Height at
Station
Area of
Centre
Portion
Area of
Sides
Total
Area
Distance
Between
Stations
Quantity
Embankment
Am x L
Cutting
Am X L
When Due to change in Reduced levels of Ground,
Formation level goes up or down with respect to
Ground Level then Crossing chainage shall be found
out. Check Example below
At Chainage CH1 and Depth of Cutting is d1 and At
Chainage CH2 the Height of Embankment is h2

Road Construction
Volume of Earthwork
– IF formation level (FL) has rising gradient (1 : r or in 1
in r distance) in longitudinal direction
• Then, we can mention:-
– IF formation level (FL) has down gradient (1 : r or in 1
in r distance) in longitudinal direction
• Then, we can mention:-

Road Construction
Volume of Earthwork
Mid Section Method:
Example : A Single railway track is to be at uniform down gradient from point ‘A’ with
formation level of 118.90 to a point ‘B’ with formation level of 118.10. Distance between
two points is 320 m. The ground lvel at different chainages are given in table. Estimate cost
of earthwork involved, Formation width in cutnig is 5.5 m and Banking is 6.0 m. Side Slope
for Cutting 1.5:1 and in Banking 2:1.
GL 120.5 120.1 119.7 119.2 118.5 118.2 117.7 117.3 117.5
Chainage 0 1 2 3 4 5 6 7 8
Station or
Chainage
Reduced
level of
Ground
Formation
Level
Depth or Height
at Station
(GL-FL)
Mean
Depth
dm
Area of Centre
Portion
Bdm
Area of
Sides
Sdm²
Total Area
Am = Bdm + Sdm²
Distance
Between
Stations
L
Quantity
Embankm
ent
Am x L
Cutting
Am X L
0 120.5 118.9 1.6
40 120.1 118.8 1.3 1.45 7.975 3.15375 11.12875 40 445.15
80 119.7 118.7 1 1.15 6.325 1.98375 8.30875 40 332.35
120 119.2 118.6 0.6 0.8 4.4 0.96 5.36 40 214.4
160 118.5 118.5 0 0.3 1.65 0.135 1.785 40 71.4
200 118.2 118.4 -0.2 -0.1 -0.6 -0.02 -0.62 40 -24.8
240 117.7 118.3 -0.6 -0.4 -2.4 -0.32 -2.72 40 -108.8
280 117.3 118.2 -0.9 -0.75 -4.5 -1.125 -5.625 40 -225
320 117.5 118.1 -0.6 -0.75 -4.5 -1.125 -5.625 40 -225
Total 1063.3 -583.6

Road Construction
Volume of Earthwork
Mid Section Method:
Example :
115
116
117
118
119
120
121
0 40 80 120 160 200 240 280 320
Longitudinal Section
Reduced level of Ground Formation Level

Road Construction
Volume of Earthwork
• Trapezoidal Formula or Average End Area or Mean
Sectional Area
– Instead of taking Mean Depth of 2 consecutive section,
Average of Two consecutive cross sectional area is taken.
– First Cross section (A₁) = Bd₁ + Sd₁²
– Next Cross section (A₂) = Bd₂ + Sd₂²
– Mean Sectional Area (Am) = (A₁ + A₂) / 2
– L is length between sections then Volume for n number of
sections (V) =
– V = L (A₁ + A₂ )/2 + L (A₂+ A3)/2 + ………. L (An-1 – An)/2
– V = L /2 (A1 + 2A2 + 2A3 + 2A4 + ……..2An-1 +An)
– That means Volume = Distance between two sections divide by
two and multiplied by addition of FIRST, LAST and two times all
rest section areas.

Road Construction
Volume of Earthwork
• Trapezoidal Formula or Average End Area or Mean Sectional Area
– Repeat Same Example.
Station or
Chainage
Reduced
level of
Ground
Formatio
n Level
Depth or Height
at Station
(GL-FL)
Area of
Centre
Portion
Bd
Area of
Sides
Sd²
Total Area
A = Bd + Sd²
(A1 + A2)/2
Distance
Between
Stations
L
Quantity
Embankm
ent
Am x L
Cutting
Am X L
0 120.5 118.9 1.6 8.8 3.84 12.64
40 120.1 118.8 1.3 7.15 2.535 9.685 11.1625 40 446.5
80 119.7 118.7 1 5.5 1.5 7 8.3425 40 333.7
120 119.2 118.6 0.6 3.3 0.54 3.84 5.42 40 216.8
160 118.5 118.5 0 0 0 0 1.92 40 76.8
200 118.2 118.4 -0.2 -1.2 -0.08 -1.28 -0.64 40 -25.6
240 117.7 118.3 -0.6 -3.6 -0.72 -4.32 -2.8 40 -112
280 117.3 118.2 -0.9 -5.4 -1.62 -7.02 -5.67 40 -226.8
320 117.5 118.1 -0.6 -3.6 -0.72 -4.32 -5.67 40 -226.8
Total 1073.8 -591.2

Road Construction
Volume of Earthwork
• Prismoidal Formula (Simson rule)
– Assumption here is that A1 and A2 are areas at ends
and Am is mid section of them and parallel to them.
– Then Volume of prism L/6x(A1 + A2 +4Am) is
considered Prismoidal Formula
• Note : Am is not average of A1 and A2
– First Cross section (A₁) = Bd₁ + Sd₁²
– Next Cross section (A₂) = Bd₂ + Sd₂²
– Mid Section Area (Am) = Bdm + Sdm²
– L is distance between A1 and A2

Road Construction
Volume of Earthwork
• Prismoidal Formula
– Example : Embankment is 120 m long 8 m wide at crest,
whose side slopes is 1:2 (Vertical to Horizontal). Central
height from 0 to every 30 m intervals are 0.6, 1.2m, 1.6m,
2.0m, 1.3m
CH d dm A Am L V (emb)
AmL
0 0.6 5.52
30 1.2 0.9 12.48 8.82 30 266.4
60 1.6 1.4 17.92 15.12 30 454.4
90 2 1.8 24 20.88 30 627.2
120 1.3 1.65 13.78 18.65 30 561.8
sum 1910

Road Construction
Volume of Earthwork
• Area of Turfing
– Area of one side Turfing = L x Sqrt ((sdm)2+dm
2))
– = L x dm x sqrt (s2+1)
– Area of both side turfing = 2Ldm sqrt(s2+1)
– Table Format

Road Construction
Volume of Earthwork
– Why Mass Haul Diagram required:-
• Haulage distance between excavated place to depositing or
filling place varies in construction of road, canal, drainage
or longitudinal excavation
• For economical transportation of excavated soils, Mass haul
diagram is required.
• Most of the times cutting soil is used in filling in nearby
sections and sometimes have to have from borrow pits
• So it is necessary to place the movement of materials from
cuts to fills so that haul distance be minimum to reduce the
cost of earthwork (specially in undulating areas)

Road Construction
Volume of Earthwork
– What is Mass haul Diagram:-
• Its is curve representing
cumulative volume of
earthwork at any point on the
curve Or algebraic sum of
volume at every chainage.
• It indicates the balance points
of cutting and filling, volume
of free haul, overhaul
• Comparative Economical study
can be prepared whether to
use cut soil or borrow
• Figure shows Mass Haul
diagram as per chainage and
also compare with
Longitudinal sections
Mass Haul Diagram

Road Construction
Volume of Earthwork
• Mass Haul Diagram (MHD)
A few Definition to understand detail of
MHD:-
i. Haul Distance: Distance to which
excavated earth is transported
ii. Haul : Sum of products of each load by its
haul distance ( = Cum x Meter)
iii.Average Haul Distance : Distance from
centre of gravity of a cutting to that of
the tipped material (lead)
iv.Free Haul Distance : Cost of haul within a
specified distance is included in
earthwork item rate is called Free Haul
Distance.
v. Economical Haul : This is limit of
profitable haul distance, beyond which it
is good to waste and borrow. Cost of
excavation and hauling = Cost of
excavation and waste + Cost of borrow
from pits.
Volume XLMA’ hauling to place of
NPZB’ can be uneconomical, so
better to borrow from pits and
waste XLMA’

Road Construction
Volume of Earthwork
A few Definition to understand detail of MHD:-
vi. Over Haul Distance: Extra Distance beyond
Free haul distance to which price is fixed in
contract for haulage. JJ’ and K’K are
overhaul distance.
vi. J and K point are centroid of XLMA and NPZB’
vii. How to find J and K point : Drop line from mid
point of ordinates (at ends of freehaul),
intersecting on curve on both side.
vii. Over Haul : Sum of products of products of
each load by its overhaul haul distance ( =
Cum x Meter)
viii.Balancing Lines : Any horizontal lines which
intersects curve at two points. Quantity of
earthwork for excavation equals to filling
between these two points of sections (EF or
JJ’ or K’K in figure)

Road Construction
Volume of Earthwork
– Characteristics of MHD
a) As curve (A’C) upwards, it shows cutting (+ve) and curve reaches at
maximum(C). Then curve (CB’) moves downwards it shows filling (-
ve)
b) Take a scale of free haul distance (EF) and insert between curve in
such a way that it remains parallel to Baseline(A’B’) and intersects(E
& F) to curve at two points, it will show free haul distance and
vertical distance(CC’) to upto maximum point(C) is volume to be free
haul

Road Construction
Volume of Earthwork
c) Vertical Distance(EJ’) between two points (E & J) with no maximum &
minimum between them, is volume of earth between the length(J”G)
of these two points. Similarly JJ” is the volume of earth between
point A’ and J”
d) Wherever Curve intersects with Baseline, volume of cut becomes
equals to volume of filling up to that point. At B’ the cut volume
(XA’Y) equals to fill volume (YB’Z)
e) Algebric sum of volume of cut and fill is zero at intersection point (B’)

Road Construction
Volume of Earthwork
f) When Curve is above the balance line then volume is be moved from
left to right.
g) When curve is below the balance line then volume is to be moved
from right to left.
h) Length(A”B”) of balancing line intercepted by a loop of curve,
represents the maximum haul distance (A”B”) in that section.

Road Construction
Volume of Earthwork
Preparation of MHD
1. Work out accumulated volume at every
station.
2. Positive sign for cutting and Negative sign for
filling
3. Draw a horizontal line as abscissa (baseline)
and select a scale (1 cm = 20 m or 30 or 50
m). Mark chainage or station points.
4. Select a scale (1 cm = 200 cum,
250/300/500/1000) for quantity of earth
work
5. At every station point draw vertical lines
equal commulative volume at that point
(positive above abscissa and negative below)
6. Join all the ends of ordinates and the baseline
by a smooth curve.
7. The whole enclosed area within curve and
baseline is called Mass Haul Diagram.

Road Construction
Volume of Earthwork
Example-1:

Road Construction
Volume of Earthwork
Example-2: Plot the ground profile and mass haul diagram of the road
section from the data given below. And calculate
a) Economical Haul Distance b) Division points in cut for least possible
total haul c) Total Free Hual d) Total Overhaul e)Total borrowed
earth f) Total cost of earthwork
Following information is given:- Free haul distance is 90 m. Cost of
excavation with free haul is Rs 6.00 per cum. Cost of borrowed earth is
Rs 7.5 per cum for stage of each. Cost of overhauling is Rs 1.5 per cum
for each additional lead of 30 m over free haul distance.
Solution is in next slide
CH 0 30 60 90 120 150 180 210 240 270 300 330 360
Volum 0 350 450 250 100 -350 -550 -625 -475 -175 250 525 500
Accumulated 0 350 800 1050 1150 800 250 -375 -850 -1025 -775 -250 250

Road Construction
Volume of Earthwork
Example (Solution)

Road Construction
Volume of Earthwork
Example (Solution)
• Limit of Economical Haul is when cost of overhaul = cost of borrow
C1 (X-ff) = C2 x 30
1.5 (X-90) = 7.5 x 30
X = 240 m
• Total Free haul distance = 90 m, Free haul volume is 1.4x250+2.0x250 = 850 cum
• Total overhaul distance = (o1k1 + o2k2) carrying 800 cum and (o3k3 + o4k4) carrying 550
cum
= 1.8x 30 = 54 m (in upper loop)
= 0.9x 30 = 27 m (in lower loop)
• Total Borrowed earth = bb2 = 250 cum
• Total Cost of Earthwork = Total freehaul cost + Total overhaul cost + Total borrow cost
=850 x 6 + (54x800/30+27x550/30) x 1.5 + 250 x 7.5
= 5100 + 2902.5 + 1875
= Rs 9877

Road construction in Civil engineering

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