EARTHWORK / VOLUMES
ECV 3501 (Geomatics Engineering)
Prof. Dr. Shattri Mansor
Geomatics Engineering Unit
Department of Civil Engineering
Universiti Putra Malaysia
shattri@eng.upm.edu.my
Outline of lecture




Introduction
Methods of volume measurement
Applications
Summary
Introduction


Earthwork operations involve the
determination of the volumes of materials
to be excavated or embanked on an
engineering project.
Not limited only to earth materials –
concrete structures, stock piles of crushed
stones, gravel, sand etc and reservoirs.
EARTHWORKS


Any operation in an over land which
result in substantial modification to the
existing ground level.
These will include activities such as
excavation, loading, hauling, placing
(dumping & spreading), compacting,
formation, cut & fill and finishing.
The manual method for determining earth excavation and
embankment amounts involves three steps:
- cross
sections of the proposed highway
are placed on the original ground cross
sections,
- the areas in cut and the areas in fill are
calculated,
- the volumes between the sections are
computed.
Exercise:
Draw the
longitudinal
and cross
sections
Contoured plan with sections
EXCAVATION WORKS
Purpose of Earthwork


For development of the structure or
building on the land.
A process so that the ground will meet
the construction needs in terms of
location, elevation, soil density, moisture
content and so on.
Topography Model
Site Model
EARTHWORKS

Three kinds of views are presented in the
contract documents to show earthworks
construction :

Plan view

Profile view

Cross section view
EARTHWORKS
PLAN VIEW
EARTHWORKS
PROFILE VIEW
EARTHWORKS
CROSS SECTION VIEW
Fill section
Cut section
Cutting & Filling Works


Cut – removing of earth from natural
terrain.
Fill – Placement of earth to form an
embankment.
Purposes



To bring the ground surface to a predetermined
grade
To set up stakes to aid in carrying out the
construction work according to plans.
In construction, earthwork volumes are involved
in:



Highways
Railways
Foundations
The role of surveyors and
engineers


Surveyors: Measure quantities of
earthwork for various construction
projects.
Engineers: Design the infrastructures
based on the earthwork plan and cost.
Area calculation





Simpson’s Rule
Trapezoidal Rule
Triangular Equation
Co-ordinates
Planimeter
Cutting & Filling Works
VOLUME

End area
 Average end area

Contour or plan area
 Four corner averaging
Cutting & Filling Works
VOLUME – END AREA (Average End Area)
- Used mainly in route work where
length is infinitely greater than the
width.
- Cross-sections are obtained at
intervals along the route and
volumes are calculated between the
sections.
Volume Calculation Methods



Direct measurement is rarely made.
Normally, indirect measurement is used by
measuring lines and areas.
3 major methods:

Cross-section method





Mean areas
End areas
Prismoidal formula
Unit-area or borrow-pit method or spot heights
Contour-area method
Cutting & Filling Works
VOLUME – END AREA (Average End Area)
Cut and Fill
Section of a
planned
highway
construction
Explanation




Centre-line stakes are shown and mark
locations where cross-sections are taken.
End-areas based on planned gradeline, size of
roadway and selected embankment and
excavation slopes are superimposed (shaded).
Width of base (b) is usually wider in cuts than on
fills to provide for drainage ditches.
Side slopes in fill are flatter than in cuts.
Area of Cross-Section

To determine volumes of cut and fill, we
need to determine areas at cross-sections.
Volume computation



For certain applications such as rock and
underwater excavation, price is so high
which requires cross-sections at very
close intervals ~ 10 ft (3 m)
Ordinary road ~ 50 –100 ft (15 m – 30 m)
After determining the cross-section area,
the next step is to determine the volumes.
Volume calculation

Having determined the various areas of
cross-section, volumes are computed
using:



Mean areas
End areas
Prismoidal formula
Cross-section method


For computing volumes on linear construction
projects (highways, railways, waterways).
Procedures:




Stake the centre line (CL)
Cross-sections are taken perpendicular to the CL
Regular intervals (e.g. 10, 20 or 25 m).
Extension of the application of levelling / total
station m’ment.
End areas




Area of the cross-sections
Can be computed by computation or use
of planimeter.
Also can be computed from field crosssection data and design info.
From end areas, volumes are calculated
from average-end-area or prismoidal
formula.
Area of cross-section

Cross-sections need to be taken at:



Beginning and ending of curves
Locations where unusual changes in
elevation occur
Points where ground elevations coincide with
natural grades
Types of cross-sections






Level section
Three-level section
Five-level section
Irregular section
Transition section
Side-hill section
Level section
- suitable in flat
terrain.
Three-level section
- used when
ordinary ground
conditions
prevail.
Five-level section
- for rough
topography
Irregular section
- for rough
topography
Transition section
-occur in passing
from cut to fill
and on side-hill
locations.
Side-hill section in cut and fill
-occur in passing
from cut to fill
and on side-hill
locations.
Average-End-Area Method
V = {(A1 + A2)/2} x L
A = section area
L = length between areas 1 and 2
V = volume
Prismoidal formula
V = {L (A1 + 4Am + A2)} / 6
2 cross sections with
middle area = approx
For 3 cross sections:

Prismoidal formula =

d/3 (A1 + 4 x A2 + A3)
What will be
the formula if
you have
more than 3
series of cross
sections??
Volume by Prismoidal Formula
Volume from Spot Levels


For large open
excavations –
tanks, basements
Ground levelling
operations –
playing fields,
building sites


Divide the area into

squares
Mark the corner
points and
determine the
heights
Volume per sq =
 {[Ha + Hb + Hc +Hd]/4} l x b


H = side spot height
l, b = side dimensions
Borrow-pit method


Area borrowed from outside project site to
obtain material to construct embankment
at project site.
Contractor pay is based on quantities
borrowed from pit and contract bid item
price. Also, the owner is paid on quantity
used.
Borrow-pit



To calculate volumes at borrow pits,
elevations are obtained at certain points
before and after earth is moved.
Establish a grid system and read
elevations at corners, before and after
excavation.
Find the net depth by adding the
difference between the elevations before
and after.
Volume from Contour method



As an alternative to
calculation of volumes by
vertical cross-sections.
If the contour maps are
available, they can be used
to compute earthwork
volumes.
Area can be determined
using planimeter.
The volume between 145 m and 120 m contours can be
calculated using end areas method etc
Mass-haul diagram



Diagram showing the accumulation of volumes of
materials along a line of road or highway.
Cutting = +ve, Filling = -ve
Function: to find the cost of excavation at one place and
deposition at another.
Mass Haul Diagram
(Source : Fig 2.1 Holmes, R.(1995), Introduction To Civil
Engineering Construction, University of the West of England,
Bristol)
Advanced methods

Photogrammetry



Technology used to extract both 2D and 3D
geographic information from aerial
photographs.
Had received legal and contractor acceptance.
Digital Elevation Models (DEM)

Once this is created, computer software can be used
to create and analyse cross-sections.
EXERCISE : Calculation using
average-end-area method
L

Compute the volume of excavation
between station 2480 with end-area of 711
m2 and station 2500 having an end-area of
515 m2.
End of lecture
