CE 142
Principles of Transportation
Engineering
EARTHWORKS
LESSON 5
Transportation construction projects almost always
involve a certain amount of earthwork. In many cases,
one of the objectives in the geometric design of the
facility will be to minimize the cost of earthwork. The
present chapter covers techniques for estimating
earthwork quantities and costs, and for planning haul
strategies so as to minimize these costs. These techniques
are presented both as an example of how construction
costs are estimated and for the insight they offer into how
problems of horizontal and vertical location may be
approached.
EARTHWORK CROSS SECTIONS
Earthwork quantities are normally expressed as
volumes; in metric units, they are given in cubic meters
(cubic yards in traditional units). For “linear” facilities
such as, highways or railways, these volumes are usually
calculated by estimating the areas of earthwork on cross
sections taken at intervals along the facility and
multiplying the average of adjacent cross-sectional areas
by the distance between them.
Fig 1. Earthwork cross section for a roadway.
Figure 1 illustrates an earthwork cross section for a roadway.
The cross section shows both the existing ground and the
constructed section, and is drawn as seen by an observer facing in
the direction of increasing stations. The top of the earthwork, as
actually constructed, is the subgrade elevation at the bottom of the
pavement; in drawing the earthwork cross section, however, the
usual practice is to represent the top of the constructed section as
a horizontal line at profile grade elevation. A standard correction is
later applied to cross-sectional areas to account for the thickness of
the pavement and the cross-slopes of the normal crown section.
Vertical distances are measured from the profile grade elevation,
and horizontal distances are measured left and right from the
centerline.
EARTHWORK VOLUMES
Earthwork volumes are normally calculated by the
average end area method In this method, the two end
areas as determined from the earthwork cross section are
averaged and multiplied by the distance between them.
In other words, the earthwork volume is approximated by
where A1 and A2 are the end areas and L is the distance
between them. This method is entirely accurate only if
the two end areas are equal.
If one end area is zero the earthwork volume is a pyramid,
and the proper formula for its volume is
Thus, as the area of one end of the earthwork volume
approaches zero, the error in the volume calculated by the
average end area method approaches 50 percent. A more
accurate formula, known as the prismoidal formula, is
available. This is
where Vp is the volume as given by the prismoidal formula
and Am is the area of plane surface midway between cross
sections with areas A1 and A2. The prismoidal formula is
sometimes used in computerized calculations but use of the
average end are method is more common because only
approximate volumes are required for purposes of
estimation.
The usual practice is to use the average end area
method except in cases in which the area of one end of the
earthwork is actually 240. In that case the volume is
calculated by using the pyramid formula. Such pyramid
sections are often involved in
transitions between cut & fill.
The usual surveying practice to
take a cross section at the
points at which the transition
occurs on each edge of the
roadway and at the point it
occurs at the centerline. Such
a practice results in two
pyramid volumes, one in cut
and the other in fill, as
illustrated by Figure 4.
Fig 4. Earthwork calculations
in transition from fill to cut.
MASS DIAGRAMS
Calculation of optimum haul strategies and earthwork costs is done
by means of a mass diagram. The mass diagram is a graph of
cumulative volume of earthwork versus distance in stations from
the beginning of the job, in which cut is considered to be positive
and fill negative. Consequently, a rising mass diagram indicates an
excess of cut over fill in a particular section and a falling mass
diagram indicates an excess of fill over cut. Use of the graph of
cumulative earthwork makes it easy to identify sections for which
the volume of cut equals that of fil, since any horizontal line
spanning a loop of the diagram, as illustrated in Figure 5, will
identify such a section.
Fig 4. Properties of mass diagrams.
Such lines are called balance lines, since the amounts of cut and fill
within the loop they span are said to balance each other. Of course,
what is actually being equated is the masses of cut and fill material,
so that either the cut or fill volume must be corrected for shrinkage
or swell before the diagram is plotted.
Mass diagrams are plotted from tables known as
summary sheets. These tables list the cut and fill volumes
for each section and the cumulative volumes of earthwork
that are to be plotted as the mass diagram ordinates at each
station. The table shows an example of a summary sheet.
The optimum haul strategy is determined on the basis
of the properties of the mass diagram and the prices of
various earthwork items for which contractors are paid. The
exact definition of these pay items may vary from agency to
agency and is normally determined by the standard
specifications of the owner of the project. Common pay
items include excavation, borrow, overhaul, and
occasionally, waste.
COSTS OF COMMON PAY ITEMS
The cost of excavation normally includes the cost of
removing the material from its existing state, hauling it up
to some specified distance referred to as the free haul
distance, and placing it in a properly compacted fill. In most
cases, the cost of excavation will also include the cost of
removing excess cut material. The cost of excavation will be
quoted in dollars per cubic meter.
The cost of overhaul is the cost of hauling material beyond
the free haul distance. It is quoted in dollars per stationmeter.
Costs of Common Pay Items … continuation
• The cost of borrow, also quoted in dollars per cubic meter,
is the cost of any material that has to be obtained off the
job site in order to make a fill. The cost of borrowed
material is usually several times that of material excavated
locally.
• In the event that disposal of excess cut material is not
included in the item for excavation, there will be a separate
pay item for waste, also quoted in dollars per cubic meter.
Earthwork quantities for transportation projects are usually
estimated by drawing vertical cross sections and estimating the
volumes between them. Cross-sectional areas may be measured by
planimeters, calculated by computer using a coordinate method, or
calculated by hand. Earthwork volumes are normally calculated by
the average end area method. Optimum haul strategies and
earthwork costs are calculated by means of a mass diagram. Haul
strategies are determined by fitting the optimal balance lines to the
diagram. Excavation costs are calculated by summing the cut
column of the summary sheet used to make up the mass diagram.
Costs of overhaul, borrow, and waste (where applicable) are
determined from the mass diagram.