Estimating Trench
Excavation
By Steven J. Peterson, PE,
MBA
Introduction
Trench excavation is often performed by hydraulic backhoe excavators. This is because hydraulic excavators are not only good at excavating
below grade, but they may be used to
lift and place utility pipe in the trench,
eliminating the need for a second
piece of equipment.
The purpose of this article is to give
the reader an understanding of how to
accurately calculate the quantity of
earth that needs to be excavated for
trenches. This article discusses determining the volume of excavation using
the average-end method and also presents an alternative method that produces more accurate quantities.
Factors affecting the production of
hydraulic excavators are also discussed.
CSI Divisions and Subdivisions
Trench excavation is part of
Division
2
Site
Construction
Subdivision 02300 Earthwork.
Methods of Measurement
Trench excavation is measured by
the cubic yard (cubic meters) of excavation or by the lineal foot (meter) of
trench. Measuring trench excavation
by the lineal foot (meter) of trench is
only appropriate when the depth of
excavation is constant. For many
trenches, particularly sewer trenches,
the depth changes over the length of
the trench, requiring the trench excavation to be measured in cubic yards
(cubic meters) of excavation. This
10
article will limit its discussion to the
measuring excavation in cubic yards
(cubic meters) of excavation. Feet
may be converted to meters by multiplying the feet by 0.3048, and cubic
yards may be converted to cubic
meters by multiplying the cubic yards
by 0.7646.
Estimating Quantities
A typical trench is shown in Figure
1. In this figure, the sidewalls of the
trench consist of both a vertical component with a constant height of dv
One method of determining the
volume of excavation is the averageend method.
The average-end
method calculates the volume of excavation by taking the average of the
areas representing both ends of the
trench and multiplying them by the
length of the trench. The equation for
the average-end method may be written as follows:
V = L(A1 + A2)/2
Eq. 1
Where:
L = Length of the Trench
A1 = Area of One End of the
and a sloped component with a slope
of s feet horizontal per vertical foot.
The height of the sloped component
of the sides of the trench varies as the
depth of the trench varies. The sloping of the sides of the trench is commonly used to prevent the side slopes
from caving in. The height of dv and
Trench
the slope of the sidewalls (S) are set by
safety regulations and the soil conditions.
In the case of the trench in Figure
1, the areas of the ends may be determined as follows:
A2 = Area of the Other End of the
Trench
A = Wd + S(d – dv)2 Eq. 2
Where:
W = Width of the Trench at the
Bottom
d1 = Depth at One End of the
Trench
d2 = Depth at the Other End of the
Trench
dv = Depth of the Vertical Trench
Figure 1
Wall
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S = Slope of the Trench Walls
The slope of the trench walls is calculated using the following equation:
S = Horizontal Run/Vertical Rise
Eq. 3
The use of the average-end method
is demonstrated in the following
example:
Example 1:
A utility contractor is to install the
sewer line whose plan and profile are
shown in Fig. 2. The trench is to have
the cross-section shown in Fig. 3.
Using the average-end method, determine the volume of excavation in
cubic yards needed to install the sewer
line.
The area of the end of the trench
(A1) at Station 14+30.20 and the area
of the end of the trench (A2) at
tion for the trench in Figure 1 may be
calculated using the following equation:
Station 15+80.20 are calculated as follows:
V = L[W(d1 + d2)/2 + S(d12 + d1d2
A1 = 2 ft(7.82 ft) + 0.75(7.82 ft – 3
ft)2 = 33.1 ft2
A2 = 2 ft(3.33 ft) + 0.75(3.33 ft – 3
ft)2 = 6.7 ft2
The volume of excavation required
for the trench is calculated using Eq. 1
as follows:
V = 150 ft (33.1 ft2 + 6.7 ft2)/2 =
2,985 ft3 (1 yd3/27 ft3) = 111 yd3
To simplify these calculations, Eq. 1
and 2 may be set up in a spreadsheet as
shown in Fig. 4:
Figure 2
Figure 4
Figure 3
The depth of excavation at either
manhole equals the elevation of the
rim less the flow line (FL) of the sewer
line plus the distance between the flow
line and the bottom of the trench.
The depth of excavation (d1) at
Station 14+30.20 and the depth of
excavation (d2) at Station 15+80.20
are calculated as follows:
d1 = 1148.20 ft – 1140.88 ft + 0.50 ft =
7.82 ft
d2 = 1146.71 ft – 1143.88 ft + 0.50 ft =
3.33 ft
OCTOBER 2004
When the length, width, and
depths are measured in feet, the slope
is measured in feet per foot, and the
input variables are set up as shown in
Figure 4. The volume in cubic yards is
calculated by entering the following
equation in Cell B8 of the spreadsheet:
=B1*(B2*B3+B6*(B3B5)^2+B2*B4+B6*(B4-B5)^2)/(2*27)
Care must be used when setting up
spreadsheet formulas because it is easy
to make a mistake that results in inaccurate quantities. After setting up a
formula, the estimator must carefully
test the formula under a wide variety
of conditions. This should be done by
changing each one of the variables
individually and verifying that the
spreadsheet produces the correct
answer.
Alternately, the volume of excava-
+ d22 + 3dv2 – 3d1dv –3d2dv)/3]Eq. 4
Where:
L = Length of the Trench
W = Width of the Trench at the
Bottom
d1 = Depth at One End of the
Trench
d2 = Depth at the Other End of the
Trench
dv = Depth of the Vertical Trench
Wall
S = Slope of the Trench Walls
Equation 4 is based upon four
assumptions. First, the width at the
bottom of the trench is constant.
Second, the height of the vertical sidewall of the trench is constant. Third,
the slope of the sloped sidewalls is constant; and as a result, as the trench gets
deeper the width of the trench at the
surface increases. Fourth, the change
in depth of the trench is uniform over
the length of the trench; therefore,
the depth may be expressed as a linear
function of the distance from one end
of the trench. Provided these conditions are met, Eq. 4 produces an exact
quantity for the excavation of the
trench. The use of Eq. 4 is shown in
the following example:
Example 2:
Solve Example 1 using Eq. 4.
From Example 1 the depth of excavation at the manholes is 7.82 feet and
3.33 feet. The volume of excavation
required for the trench is calculated
using Eq. 1 as follows:
V = 150 ft{2 ft(7.82 ft + 3.33 ft)/2 +
0.75[(7.82 ft)2 + (7.82 ft)(3.33 ft)
+ (3.33 ft)2 + 3(3 ft)2 – 3(7.82
ft)(3 ft) –3(3.33 ft)(3 ft)]/3}
V = 2,607 ft3 = 2,607 ft3(1 yd3/27
ft3) = 97 yd3
To simplify these calculations, Eq. 4
may be set up in a spreadsheet as
shown in Fig. 5:
11
Figure 5
When the length, width, and
depths are measured in feet, the slope
is measured in feet per foot, and the
input variables are set up as shown in
Fig. 5. The volume in cubic yards is
calculated by entering the following
equation in Cell B8 of the spreadsheet:
=B1*(B2*(B3+B4)/2+B6*(B3^2+B
3*B4+B4^2+3*B5^2-3*B3*B53*B4*B5)/3)/27
Switching From Average-End
Method to Eq. 4
Care must be exercised when
switching from the average-end
method to Eq. 4 because the averageend method can overstate volumes by
as much as 50 percent. In Examples 1
and 2, we saw that the average-end
method overstated the excavation
quantity by 14 percent. This overstatement occurs when the sides of the
trench are sloped and the depth of
the trench is not constant. When a
company’s unit costs are based upon
overstated quantities calculated by the
average-end method, the true unit
costs will be understated. If a company switches to Eq. 4—which produces
accurate quantities—and use understated costs, they will underbid a job
and risk losing money. When converting to Eq. 4 estimators need to verify
their unit prices by using Eq. 4 to calculate the volumes for completed jobs
and determine the unit price based
upon Eq. 4.
Factors Affecting Excavation
Production
The productivity of a hydraulic
backhoe excavator is dependent upon
the cycle time, amount of material
excavated during each cycle (load),
and the operational efficiency (the
time that the equipment is being used
for excavation). Production may be
calculated using the following
Equation:
Production = Load(Operational
Efficiency)/(Cycle Time)
Eq. 5
The cycle time is the time it takes
the hydraulic excavator to load its
bucket, swing to the dump location,
dump its load and return to the point
where it will load its bucket. The
more cycles a hydraulic backhoe excavator can perform in one hour, the
greater its production. The cycle time
is dependent on the following factors:
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material being excavated, bucket size,
swing angle, depth of excavation,
placement of excavated material and
obstructions that increase the difficulty of excavation.
The material being excavated
determines the speed at which an
excavation cycle may be completed. It
takes longer to load a bucket full of
hard-to-dig materials (such as rocky
soil, rock and frost-laden soils) than it
does to load a bucket full of easy-to-dig
materials (such as sand and clay).
The cycle time is also a function of
the bucket size: the larger the bucket,
the longer the cycle time. This is
because large loads require more of
OCTOBER 2004
the equipment’s power to excavate
and swing the material to the dump
location.
The cycle time is also a function of
swing angle: the smaller the swing
angle, the shorter the cycle time.
Swing angles range from 30 degrees
when the excavated material is placed
in spoil piles next to the trench, to 90
degrees when the excavated material
is placed in trucks to the side of the
excavator, to 180 degrees when the
excavated material is placed in trucks
behind the excavator. The placement
of the material is a function of the
space available for the excavation
operation. When a very narrow space
is available for excavation, the trucks
must be located behind the excavator.
The cycle time is also a function of
the depth of excavation. The most
optimal depth for excavation is 30 percent to 60 percent of the excavator’s
maximum
digging
depth
(Schaufelberger, p 145). Excavation
depths deeper or shallower than the
optimal depth of excavation will
increase the cycle time.
Finally, the cycle time is a function
of obstacles that the excavator has to
work around. The operator must
exercise extra care and slow down the
excavating process when digging
around utilities and other obstacles or
13
when working around overhead
power lines and other above ground
obstacles.
In addition to cycle time the
amount of material (load) excavated
during each cycle affects production.
The amount of material is a function
of the bucket size—which is a function
of the excavator size and bucket
width—and the bucket fill factor.
When excavating trenches, the width
of the trench will limit the maximum
width of the bucket. It makes little
sense to increase the bucket width to
increase production if the extra production is used to excavate material
that does not need to be excavated.
The increase in production due to an
increase in bucket size more than offsets the extra cycle time it takes for the
larger bucket.
The type of material also determines how much material can be
loaded into the bucket. When excavating poorly blasted rock, we may
only get material equal to 40 percent
to 50 percent of the bucket’s rated
capacity; whereas, when excavating
cohesive materials (such as clay) we
may get material equal to 100 percent
to 110 percent of the bucket’s rated
capacity (Schaufelberger, p 146).
The operational efficiency is
expressed as the number of minutes
during an hour that the excavator is
excavating. Nonproductive activities
include bathroom and coffee breaks,
waiting for trucks, and performing
other tasks (such as placing pipe). A
typical operational efficiency for an
excavator is 45 to 50 minutes per hour
and includes time spent performing
other tasks.
give the utility company to locate
them.
Special Risk Considerations
Digging into an existing utility line
is not only a hazard for the operator
and personnel in the area, but it can
be very expensive to repair. Cutting a
fiber-optic line can cost the contractor
thousands of dollars per minute.
Before excavation, the contractor
should be familiar with the laws governing the location of existing utilities
and should have the existing utilities
located. There are often laws regulating how often the utilities must be
located, how accurately they are located and how much time you have to
Glossary
Cycle Time – The time it takes a
hydraulic excavator to excavate material, swing to the dump location,
dump and return to the excavation
location ready to excavate the next
load of material.
14
Ratios and Analysis
The cost per cubic yard for one
project may be compared to the cost
per cubic yard from other projects
provided the projects have similar
characteristics. This includes types of
materials being excavated, swing
angle, depth of excavation, placement
of excavated material (stockpile versus
truck), obstructions, bucket size, bucket fill factor, and operational efficiency. These factors must be similar
because they all affect the production
of the excavation process.
Conclusion
Trench excavation is most often
measured in cubic yards. The volume
may be calculated by the average-end
method or Eq. 4, with Eq. 4 producing
more accurate quantities. When bidding trench excavation using unit
prices it is important that the unit
prices are based upon the same
method of determining the volume of
excavation as is being used to calculate the volume of excavation for the
bid. The cost of excavation is a function of production. Production is a
function of material being excavated,
swing angle, depth of excavation,
placement of excavated material,
obstructions, bucket size, bucket fill
factor, and operational efficiency (the
time that the equipment is being used
for excavation). Finally, care must be
taken when performing trench excavation to locate existing utilities to
avoid damaging the utilities and to
ensure the safety of the workers.
Rated Capacity – The rated volume
of a bucket. The rated capacity is
based upon the bucket being heaped
full with a 1:1 angle of repose.
Swing Angle – The horizontal
angel between the point of excavation
and dumping point for a hydraulic
backhoe excavator.
References
Schaufelberger,
John
E.,
Construction Equipment Management,
Prentice Hall, 1999, p. 142–148.
Steven Peterson is an associate professor
in the Parson Construction Management
Technology program at Weber State
University. He teaches courses in estimating, scheduling, and construction finance.
Prior to teaching at Weber State, Steve
worked as a project manager and estimator
in the construction industry. He received a
MBA and a BS in engineering from the
University of Utah. Steven is the author of
Construction
Accounting
and
Financial Management and is working
on a book entitled Construction
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Hydraulic Backhoe Excavator – A
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