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For earthwork contractors
the key to survival is an accurate estimate of earthwork quantities.
Without an accurate estimate, the contractor will have little
or no chance to present an accurate bid (let alone a winning bid).
And without an accurate estimate of earthwork volumes, the contractor
will be unable to properly assign construction assets or formulate
a project schedule. Estimating earthwork construction requires
many assumptions and unknowns. Because of this, it is this portion
of the construction project that represents the greatest financial
risk to the contractor.
Minimizing Sources
of Error
There is an old computer acronym called GIGO, which stands
for "garbage in, garbage out." An earthwork estimate is only as
good as the site information used as the basis for the estimate.
No estimator should ever calculate an earthwork volume without
physically walking as much of the site as possible, a copy of
the earthwork plans in hand. In short, there is no substitute
for good old-fashioned job-site reconnaissance, even in this age
of Computer-Aided Design and Drafting (CADD) and global positioning
systems (GPS). Contractors find time and again that site maps
and surveys are wrong to some degree. Either an error was made
during the survey or the site has been physically altered since
the last survey.
To correct these errors, the estimator needs to go back
to the surveyor's source, the benchmarks, and ensure that these
are still valid. At least one third-order benchmark (preferably
three) is needed to accurately survey a site. While it may be
acceptable to use local, site-specific "benchmarks" like a previously
surveyed manhole lid, or relative benchmarks (such as the corner
of a building designated as elevation "100.00"), these improvisations
are inherently prone to a higher degree of error.
A records search for documents relating to the excavation
property is also essential and should be performed as the first
phase of the reconnaissance. How was the site used in the past?
What do the hydrogeological boring logs from onsite drilling operations
show? Is there any unstable or karsts topography? Was the site
ever used for dumping or disposal? Are there wetlands present
that could limit the area of excavation?
Sources of error in calculating earthwork volumes include
carrying out area measurements (either cross-section or contour
areas) beyond the limit justified by the field data, calculating
volumes beyond the nearest cubic yard, and failing to correct
for curvature when a section on a horizontal curve (such as a
roadway alignment) has a cut on one side and fill on the other.
Mistakes in calculating earthwork volumes include math errors,
using the wrong formula for the volume, mixing cut and fill quantities,
and not considering transition sections when passing from cut
to fill. Error can never be eliminated; it only be minimized.
Furthermore, error is cumulative. A daisy chain of a half-dozen
90% accurate measurements would result in a final answer of only
50% accuracy.
Even if mistakes are avoided and the calculations are
mathematically sound, the results are always approximate. Surveys
may not represent the full extent of the excavation area and the
contours established by the survey are interpolations. For example,
even a highly accurate aerial topographic survey is accurate only
to within one half of the smallest contour interval on the map.
So if the resultant topographic map utilizes 2-foot contour intervals,
its accuracy will be plus or minus 1 foot.
When determining acceptable accuracy, the estimator should
remember the differences in volume between in-bank soil, loose
soil that has been excavated, and fill soil that has been compacted.
The current practice is to adopt an assumed shrinkage factor of
20%-30% for adjustment of fill as it is placed and compacted.
For example, a structural fill embankment constructed in controlled
lifts may have an 8-inch-thick layer of loose fill soil spread
in place and then compacted to a thickness of 6 inches. In addition,
a typical swelling factor of 25% is used to account for increases
in volume during transportation or stockpiling. Therefore, 100
bank cubic yards in the ground can become 125 cubic yards loose
in the trucks hauling soil from the excavation area. This loose
soil could be compacted to an embankment fill volume of 94 cubic
yards.
Estimators should also never forget the difference between
precision and accuracy. Precision and accuracy are two completely
different things that even experienced engineers, estimators,
and surveyors can confuse. Precision refers to the number of units
used to describe a measurement. It is a measure of how close together
the measurements are, not how close they are to the correct or
true value. A measurement taken to 10 decimal places will be more
precise than one taken to only two decimal places. However, being
more precise does not improve accuracy. Accuracy of a measurement
describes how close it is to the "real" value, which is not necessarily
precise. Estimators should be concerned with accuracy, as this
will determine profit or loss on a project. Precision is of little
importance except where it actually increases the accuracy of
the measurement.
Calculating Areas
Before volumes can be
calculated, the areas of excavation (either horizontal or vertical)
must be established. Horizontal areas are associated with cross
sections cut through the earthwork volume and vertical surfaces
associated with Digital Terrain Model (DTM) volumes. Horizontal
areas usually refer to either the area extent of the excavation
and horizontal areas enclosed by contour elevation lines. These
areas are defined by a series of discreet points along their boundaries.
Areas are calculated by connecting these points in a series of continuous
triangles that extend across the area. Given the northing and easting
of each of the three vertices of each triangle, and the lengths
of each of the three sides of the triangles, each triangle's area
can be calculated as follows:
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A
= sqrt[s * (s - a) * (s - b) * (s - c)]
Where,
A = the area of the triangular area (square feet)
a,
b, c, = the lengths of the three sides of the triangle (feet)
s = (a + b + c) / 2
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An alternate method involves
measuring the lengths of parallel lines traversing the area from
one side to the opposite side at a constant interval. The area of
each strip is calculated by multiplying the line's length by the
distance interval between the lines. The sum of all the strips'
areas gives the overall surface area. Computer and CADD programs
use either method, but can perform many more operations, allowing
for a higher degree of accuracy.
Calculating Volumes
There are several ways of calculating bank (in-place)
earth and soil volumes.
The simplest is the Depth Area Method (DAM), which involves
multiplying the thickness of the strata to be excavated by the
surficial area of the strata. This can be done with any reasonable
accuracy only for strata that is consistently thick and whose
area extent is known. It is perfectly suitable for estimating
the amount of topsoil to be stripped at a consistent depth (usually
6 inches). It is also applicable for estimating the volume of
regular (square or rectangular with vertical sideslopes) excavations
of a consistent depth below a relatively flat surface. Remember
to use the sloped surficial area of the excavation zone, not the
projected plain area. Failure to do so will introduce additional
errors into the volume calculation. For example, a plane acre
of a slope with a 25% grade (approximately 14 degrees to the horizontal)
will have a surficial area of about 1.03 acres. Volumes are calculated
as follows:
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V
= T * A * (1/27)
Where,
V = volume (cubic yards)
A
= surficial slope area (square feet)
T
= thickness of strata or even cut (feet)
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The Grid Method (also
known as the Borrow Pit Method) extends DAM to an excavation of
varying depths. Borrow-pit leveling calculates the excavation volume
by applying a grid to the excavation area. The grids can be staked
to squares of 10, 20, 50, 100, or more feet depending on the project
size and the accuracy desired. For each grid square, final elevations
are established for each corner of every grid square. These are
subtracted from the existing elevations at the same location to
determine the depth of cut or height of fill at each corner. For
each grid square an average of the depths/heights of the four corners
is multiplied by the area of the square to determine the volume
of earthwork associated with the grid area. The total earthwork
volume for the project is calculated by adding the volumes of each
grid square in the excavation area. Volumes are calculated as follows:
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V
= ((D1 + D2 + D3 + D4) / 4) * A * (1/27)
Where,
V = volume (cubic yards)
A
= area of the grid square (square feet)
D
= depth of cut/fill at each grid corner (feet)
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The End Area Method (EAM)
utilizes the areas of parallel cross sections at regular intervals
through the proposed earthwork volume. These cross sections are
can be spaced at intervals of 25, 50, 100, or 200 feet depending
on the size of the site and the required accuracy. They are aligned
perpendicular to a baseline that extends the entire length of the
excavation area. There are several types of cross sections, which
can be drawn by hand or generated by CADD. For flat terrain or level
excavation, a level section is suitable. Irregular sections are
used for most excavations in rough terrain. Transition or side-hill
sections occur when passing from excavation cut to embankment fill.
Cross-sectional areas are calculated with either the triangular
area method described above (if the cross sections are geometrically
simple) or by the Length Interval Method for more complicated cross
sections. Volumes are calculated as follows:
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V
= L * ((A1 + A2) / 2) * (1/27)
Where,
V = volume (cubic yards)
A
= areas of the adjacent cross sections (square feet)
L
= distance between cross section along the baseline
(feet)
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The Prismoidal Formula
(PF) allows for greater accuracy than EAM. It is especially useful
when the ground is not uniform or significantly irregular between
cross sections. PF adds an additional cross-sectional area midway
between the two cross sections defining the volume being calculated.
Note that this cross section is calculated separately and is not
an average between the two end areas. Volumes are calculated as
follows:
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V
= L * ((A1 + (4 * Am) + A2) / 6) * (1/27)
Where,
V = volume (cubic yards)
A1,
A2 = areas of the adjacent cross sections (square feet)
Am
= area of the midway cross section (square feet)
L
= distance between cross section along the baseline (feet)
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The Contour Area Method
(CAM) uses the area of the excavation elevation contour lines to
determine volumes. From a topographic map of the site, the areas
enclosed by regular contour intervals are measured. This area measurement
can be done by hand with a planimeter, electronically by a digitizer,
or directly with a CADD program. If the horizontal areas enclosed
by each contour line are large relative to the elevation difference
between the two contour elevations, averaging the two areas and
multiplying the average by the height difference can determine volumes.
However, for relatively small earthworks (like spoil piles and borrow
areas), volumes can be calculated based on the formula for the volume
of a truncated pyramid:
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V
= (h / 3) * (B1 + B2 + sqrt[B1*
B2] ) * (1/27)
Where,
V = volume (cubic yards)
B1, B2 = areas of the contour elevation lines (square feet)
H
= elevation difference between the contour elevations
(feet)
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The Triangulated Irregular
Network (TIN) uses triangles to represent small, continuous surface
areas and is the current standard for accurate terrain modeling.
Each corner of each triangle represents a field survey point with
northing, easting, and elevation coordinates. The TIN model representing
the terrain surface (or boundaries between soil strata) is created
by connecting these points to their nearest neighbors (as determined
by northing and easting, not the nearest in terms of elevation)
to form a series of contiguous, irregular triangles covering the
entire surface (see Figure 1). Of all the methods used, TIN has
the greatest accuracy and can best handle volumes for different
soil strata, but it also requires the greatest amount of calculations.
Therefore it is suitable for CADD and estimation software.
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DTM utilizes surfaces created by the TIN method. DTM
accurately models the ground surface and allows the estimator
to directly calculate volumes without drawing counters. The volumes
are determined by formulas similar to that used by CAM, but use
vertical sections rather than horizontal contour line sections.
DTM can be used to determine the volume between a surface and
a fixed elevation or between two or more DTM generated surfaces.
This allows for accurate measurement of excavations the result
in an unleveled surface. Furthermore, the volumes of differing
types of soils in an excavation can be determined by DTM defining
the boundary surfaces between the various strata.
Major Suppliers
InSite Software provides
a family of software programs for site layout and earthwork analysis.
Its SiteWork utility calculates cuts and fills, stripping, strata
quantities, subgrade materials, topsoil re-spread, areas, lengths,
trench excavation, and backfill from digitizer input or CAD Import.
It will print out 3D drawings, cross sections, and scaled plans.
SiteWork uses a patented algorithm technique based on Delauney Triangulation
to generate the existing, proposed, and underground strata surfaces
(see Figure 2). A surface can be entered into SiteWork as spot elevations,
contours, or sloping lines (where each point along the contour
has a different elevation), or a combination of all three.
The elevations for calculation are taken from the plane created
by each triangle. Once the surfaces are generated, InSite uses the
Grid Method to generate the earthwork volumes.
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Trimble Geomatics and Engineering provides a wide range
of instrumentation and software, including its Terramodel CAD
module package and Paydirt earthwork and material estimating software.
Paydirt is used for calculating site earthwork and material quantities,
and performing detailed analysis of a site project. It comes in
two modules, SiteWork and RoadWork. The software allows estimators
to determine excavation cut and fill volumes, and strip volumes
for an entire site or for selected regions of a site. Material
areas and volumes for asphalt, concrete, base, and other materials
can also be calculated and converted to tons. Paydirt SiteWork
uses Trimble's Terramodel CAD module to import an extensive range
of design data formats. Paydirt SiteWork produces detailed excavation
and material volume reports that allow you to generate bank cut
and fill volumes, and account shrink and swell to get adjusted
cut and fill numbers. Total area of cut and area of fill is provided
to help determine production rates along with strip volumes. Material
areas, volumes, and converted quantities are provided and totaled
by type of material. All text reports can be saved to an Excel
file allowing for the importation of this information into spreadsheets
and construction bidding software.
Accutakeoff and Estimating Services of Knoxville, TN,
is a firm that provides quantity takeoff, budgeting, project management,
estimating, scheduling, and value engineering services to clients
nationwide. These services are provided for a variety of projects
such as site work, dams, landfills, heavy highway, and underground
utility.
AGTEK is a software firm that provides CAD- and GPS-related
software measurement systems. Its Earthwork 3D software streamlines
data input from CAD files and plan drawings. It automatically
corrects for stripping, structural sections, compaction and swelling,
and rock formations. It generates printed reports and 3D project
files that can be used on the job site with a Plan Pilot, optical,
or GPS grade-management systems. A companion software package
is AGTEK's Materials 2000, a high-speed material takeoff system.
Its conversion database provides information in tons, square yards,
and linear feet and exports these reports to Excel spreadsheets.
BID2WIN software can be used to estimate all aspects
of site work such as street and highway, paving, bridges, tunnels,
elevated highways, water and sewer lines, earthwork, concrete,
grading and excavation, demolition, environmental, specialty contractor,
mining, railroad, marine, and utility construction. It is compatible
with Microsoft Word or Excel and provides standardized reports.
Additional features allow it to store past cost data (labor, material,
equipment), create reusable task templates, maintain a bid item
database, and calculate project cost estimates.
The Construction Estimating Institute (CEI) provides
training and education in construction estimating. These classes
can be taken at home and are approved for Continuing Education
Credits. According to its Web site, the CEI's Estimating Earthwork
Construction class will teach a student how to accurately measure
quantities of cut and fill by each of the three generally accepted
methods of measurement (average-end area, grid-cell, and digitizer);
properly adjust the measured quantities of cut and fill, allowing
for swell and shrink based on soil type and operation; select
appropriate equipment, both size and type, that represents a cost-efficient
approach to constructing the earthwork portion of the project;
determine accurate productivity rates for projects based on soil
conditions, site restrictions, excavating depths, special requirements,
etc.; zero in on the true cost incurred in the operation of a
specific machine; extend the production-cost estimate of a project
by using the crew-analysis method of estimating; complete the
earthwork estimate by combining the production estimate with the
fixed costs in earthmoving; and convert the cost estimate to a
correct bid by incorporating the four basic pricing premises (business
plan pricing, asset utilization, risk analysis, and market conditions).
This provides a good list of the skills needed by an estimator.
Earthwork Services is an estimating firm providing services
to clients nationwide. Earthwork relies on manual operators who
ensure that every high and low point, ridgeline, swale, break
line, and pad elevation is accounted for in their digital terrain
model. Fast turn-around time is a major feature, with most projects
turned around in 48 hours. The resultant CADD file and grading
plan provides the following information: 3D graphics and cross
sections, color-shaded cut and fill maps, cut/fill grid elevation
plans, DTM in either AutoCAD or AGTEK format, and earthwork volumes
(stripping, subgrade, strata layers, compaction, cut/fill balance,
phasing operations, structural backfill, and roadway templates).
HCSS provides construction estimation and field-management
software. Its HeavyBid construction estimating and bidding software
is suitable for earthwork and infrastructure contractors' bidding
projects. HeavyBid specializes in quote management, analyzing
information from previous quotes and a supplier/vendor database
to provide quote summaries, updates, and financial reports. Its
unit-price bidding is based on historical bid terms going back
17 years. It has access to automated libraries, including activity
codebooks, bid histories, and US Department of Transportation
estimate items. Historical costs from past bids are stored for
future use. It utilizes customized calculations and is exportable
to Excel, Outlook, Word, Primavera, Suretrack, and Microsoft Project.
Intuit provides business-management and accounting software
in its Quickbooks. Its Master Builder software package uses construction
best practices to organize a contracting business into four integrated
steps: estimating, production, accounting, and analysis. While
not specifically designed for earthwork, it manages Certified
Payroll, workers' compensation costs, construction-specific billing
processes, and detailed job-cost and reporting information.
On Center Software (OCS)
produces the QuickBid software package for more than a dozen construction
trades. It has built-in databases for those trades so the operator
need only adjust for local labor and material costs. The latest
version of QuickBid is work-group ready, allowing for easy networking.
In addition to an OCS database manager, it has SQL database server
support. Supporting Quickbid is the OCS estimating software, On-Screen
Takeoff. Electronic plans can be viewed from a CD or computer hard
drive. If a contractor uses paper plans, he can use a digitizer
to send his takeoff quantities directly to the computer screen.
Once a takeoff is completed, it can be moved into the QuickBid Estimating
program for pricing and bid completion.
Quest Solutions produces engineering estimating software
called Civil Solutions. This is a suite of digitized takeoff and
estimating software. It is used in conjunction with Quest Earthwork
and Quest Estimator. Since it relies on digitized site information,
typing quantities into a spreadsheet is not necessary. In its
latest iteration, the suite has improved integration with Intuit's
Quickbooks.
Timberline Software is
a firm specializing in accounting software for construction and
real estate development. Timberline Office is an integrated family
of financial and operations software providing a cross-functional
system to pull everything together for streamlined, single-source
control. It has access to a full range of databases and can be integrated
with digitizers or CADD, allowing for takeoffs from CADD files and
plan drawings. Its Model Estimating software allows for fast, conceptual
costs.
Vertigraph Inc. produces takeoff and estimating software
for the construction industry. Its SiteWorx software calculates
cut and fill earthwork volumes. SiteWorx will digitize into the
computer existing and proposed contour lines, spot elevations
and areas, along with project boundaries, topsoil strip areas,
and topsoil respread areas. With a mouse click, cut and fill volumes
are automatically and accurately calculated. Areas are also calculated
with subgrade volumes. SiteWorx even tells how to adjust proposed
elevations to arrive at a balanced site.
User Anecdotes
Among the users of the InSite family of software is Landmark
Enterprises in Auburn, NY. Takeoffs done from CADD files allow
for easy staking of critical stake points. The associated Field
General software guides the staker accurately to any referenced
display point. As the surveyor walks around a site, a running
readout of the surface data (existing, proposed, stripping depth,
subgrade elevation, cut or fill depth, strata layers, etc.) is
reported on the screen. The robotic hardware used by InSite even
allows for vehicle mounting of the prism rod, resulting in very
fast topographic surveys and site staking.
For BID2WIN users, its main selling points are ease of
use and operational flexibility. According to Robert Slear of
Eastern Industries Inc., "It keeps us from duplicating work. It
downloads DOT bids directly, so we don't have to re-key the data.
It prints and faxes bids directly from the program, so we don't
have to retype them onto paper forms. It even exports data directly
to our mainframe accounting system without much modification.
Plus the screens are so easy to understand that anyone could sit
in front of the screen and get right into it." Jack Hobbs of the
Penhall Company cites its compatibility with Microsoft: "We like
the fact that BID2WIN is Windows and that it works like the Microsoft
products we already use."
Earthwork Software Services provides AGTEK training to
clients nationwide. Its experience with AGTEK software has been
very positive. Due to promotions, employee turnover, and ongoing
AGTEK product improvements, many AGTEK users are under-trained
and not leveraging all the power of their investment in AGTEK
software. At best, under-trained users can waste hours of valuable
time on every takeoff or 3D grading model; at worst, they make
mistakes that can lose a job (or much of the profit on a job).
Productive AGTEK users avoid these risks by getting regular, up-to-date
professional training. According to Kurt Dulle, an estimator in
St. Louis, MO, such training can help even the most experienced
operator. "Because I had used Earthwork 3D for about five months
prior to this seminar, I thought it wasn't necessary for me to
attend the first day. But I was amazed at how much I learned in
this class and at how little I was utilizing the capabilities
of this software."
As a construction estimating and bidding software, HCSS's
HeavyBid has a devoted following. Tom Gunther of DeSilva Gates
Construction has this to say about HeavyBid versus old manual
methods of estimating: "We really like using HCSS HeavyBid because
it has significantly improved the accuracy and the consistency
of our estimates. In our previous system of Excel spreadsheets,
we were constantly encountering formula errors, errors that were
made in transferring subtotals from one worksheet to another,
and errors that were made when we would forget to update a material
or subcontract price change in multiple locations in our spreadsheets.
Now with HeavyBid we spend more time analyzing our estimates and
less time checking our math extensions. We can update a material
or subcontract price in one place and be confident that the update
is made accurately throughout the estimate."
Conclusions
So what is a good earthwork estimate? What constitutes
an acceptable degree of accuracy? Well, by definition, an accurate
earthwork estimate is one that results in the contractor not losing
money on the job. So needed accuracy is almost defined by the
job's contract conditions. Competition is too intense and guesstimates
are no longer an acceptable basis for bids. However, a contractor
does not need to account for every shovel full of dirt. On most
jobs, small errors in cut and fill will average out to almost
nothing. And given the inherent inaccuracies in ground surveys
and aerial topography, a slight elevation difference can often
be safely ignored. A usable survey is one that allows a DTM to
be made to current accuracy standards, such as 90% of the surface
points being within 3 inches of actual ground location and elevation.
If the survey numbers are good, then use of the TIN methodology
to create a DTM will lead to the greatest accuracy in your earthwork
estimate.
Daniel P. Duffy, P.E., is an environmental engineer
for Rumpke Waste Inc. in Cincinnati, OH.
GEC
- September/October 2004
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