Blogs and Articles

# Taking the Measure of Methods for Estimating Earthwork Volumes

## A review of methods for estimating earthwork volumes

•  Email This Post

For earthwork contractors the key to survival is an accurate estimate of earthwork volumes. 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.

 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
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:
 V = T * A * (1/27) Where, V = volume (cubic yards) A = surficial slope area (square feet) T = thickness of strata or even cut (feet)
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:
 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)
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:
 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)
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:
 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)

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:

 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

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:

 V = T * A * (1/27) Where, V = volume (cubic yards) A = surficial slope area (square feet) T = thickness of strata or even cut (feet)

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:

 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)

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:

 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)

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:

 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)

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:

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.

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.

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.”

Add Grading & Excavation Contractor Weekly to  your newsletter preferences and keep up with the latest articles on grading and excavation: construction equipment, insurance, materials, safety, software, and trucks and trailers.

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.