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HOW TO ESTIMATE CUT AND FILL VOLUMES FOR EARTHWORKS PROJECTS
INTRODUCTION
The example project which will be used in this article. This is a (fctional) platorm being added to Alcatraz Island Island in San rancisco rancisco !a" !a".. The project includes includes cut cut (shaded red) red) and fll (blue) (blue) On construction projects it is often necessary to modify the existing ground levels to create platforms to build on. Accurately calculating the volumes of soil that must be removed (cut) or added (ll) to create the nal ground levels is an essential part of the planning process. In this article we are going to describe how these volumes can be calculated. e will ta!e an example project" and use three of the most common methods to estimate cut and ll volumes. #he three methods that we will go through are$ • • •
#he examples described in this article have been wor!ed wor!ed through through for each of these three method with an excel spreadsheet which is available here. 'ou may wish to download this spreadsheet and and wor! wor! throu through gh the examp examples les yours yourself elf to aid aid unde underst rstand anding ing of the method methods s descr describ ibed. ed. #he #he spreadsheet also contains a number of formulas which automate certain aspects of these methods described below" so you may nd it useful for implementing these methods on your own project.
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Sections are drawn at e#ual inter$als through the project. or each section line the cut area and the fll area is determined. The $olume between two sections is determined as the a$erage area o the two sections multiplied b" the distance between them. !" adding together the $olumes between all o the sections the total cut and fll $olumes are obtained. #he cross section method involves plotting cross sections of the existing and proposed levels at regular intervals across the project site. 0or each of the cross sections" the cut area and the ll area is determined. #he volume between each pair of sections is estimated by multiplying the average cut or ll area of the two sections by the distance between them. Once these volumes have been calculated for each pair of sections the total cut and ll volumes are obtained by adding them all together. An example calculation for the volumes between two sections of the example shown opposite. #his calculation is repeated for all of the sections" and the values are added together to get the total cut and ll volumes. #here are several di1erent methods used to determine the areas of cut and ll once the sections have been plotted. 2erhaps the simplest (but most time consuming) method is to plot the sections on gridded paper and count the grid cells of the cut and ll areas. -ultiplying the cell count by the area represented by each of the grid cells gives the cut or ll area for the section. Other methods include drawing the sections in A/ and exporting areas or calculating areas mathematically using the trape3oidal rule. #he spreadsheet included with this article includes formulae which have automated the process of calculating section areas using the trape3oidal rule. #his can save a great deal of time if you are using the cross section method. #he accuracy of the cross section method depends to a large degree on the distance you choose to set between the sections. loser sections improve the accuracy of the estimate" but ta!e longer to estimate. A balance has to be made between accuracy on the one hand" and speed of generating the estimate on the other. One of the great advantages of this method is that cross sections are generated in the process. #hese provide a useful visual summary of the estimation" which present the cut and ll depths across the project in a very clear way. One of the disadvantages o1 the method is that it can be extremely laborious to extract cross sections from the drawing" and to determine the areas of the sections.
#o use the cross%section method to calculate your cut and ll construction project" do the following$ 4.
5ay your plan out on a smooth level service" and with a #%s6uare" divide your plan with a number of e6ually spaced hori3ontal lines. 7. On a piece of graph paper" preferably 44 x 489" plot out the existing elevations from the beginning to the end of each cross%section line. #he vertical axis is for elevations and the hori3ontal axis is for the distance along the cross%section. :. #hen for each cross%section" plot out the proposed elevations from the beginning to the end of each cross%section line on the same graph as the existing. ;. 0or each cross%section" count the number of s6uares where the existing line is above the proposed line. #his is your cut area for that cross%section. <. 0or each cross%section" cout the number of s6uares where the existing line is below the proposed line. #his is your ll area for that cross%section. =. 0or each adjacent pair of cross%sections" average the cut area between the two and multiply it by the distance between the two cross%sections to calculate your cut volume. 8. 0or each adjacent pair of cross%sections" average the ll area between the two and multiply by the distance between the two cross%sections to calculate your ll volume >. ,ow add up all of your cut volumes and divide them by 78 to get the total cut volume for your site in cubic yards. ?. Add up all of your ll volumes and divide them by 78 to get the total ll volume for your site in cubic yards. 4@. #o determine the export for your site" subtract the ll volume from the cut volume. If this is a positive number" then you have more cut than ll so youll need to export material from your site. If the numbers negative you have more ll than cut" and you will need to import material onto your building site.
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The a$erage cut or fll depths are determined or each cell in the grid. rom these depths the $olumes o each grid cell can be calculated% and b" adding the cell $olumes together the total cut and fll $olumes are obtained
#he grid method involves drawing a uniform grid onto a plan of the earthwor!s project" and ta!ing o1 the existing and proposed ground levels at each node of the grid. ith these values the average depth of cut or ll re6uired on each cell of the grid is calculated" and the volume for each cell is obtained by multiplying the depth by the cell area. Cy adding the volumes for each cell together the total cut and ll volumes for the project can be estimated. #he cut or ll depth for each cell is found by subtracting the average existing level of the cell from the average proposed level. If the resultant depth is positive then this is a ll cell" while a negative value indicates a cut cell. In either case" the volume is calculated by multiplying the cut of ll depth by the area of the grid cell.
An example calculation o the $olume or one o the grid cells in the example on the right Once the volume has been calculated for each grid cell" all of the cut cells are added together to obtain the total cut volume. #he same is done for the ll cells to get the total ll volume. As with the cross%section method" the accuracy of the grid method depends upon the si3e of grid cell which is used. A compromise has to be made between the accuracy which is re6uired" and the time which will be ta!en to produce the estimate. An advantage of the grid method are that the basis of the estimate can be fully summarised on the site drawings" which presents a very clear summary of the calculations for others to chec!. One of the disadvantages are no graphical summary is generated for the estimation. Also" li!e the section method" the grid method is time%consuming and tedious to implement.
#o use the grid method to calculate your cut and ll construction projects" do the following steps$ 4. 7. :.
5ay your plan out on the Dat surface. #hen with a large #%s6uare" draw set of e6ually spaced hori3ontal and vertical lines across your plan. At each intersection of the hori3ontal and vertical lines" determine the existing and the proposed elevation 0or each intersection subtract the existing elevation from the proposed elevation. 2ositive numbers are ll. ,egative numbers are cut.
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0or each cell" add the four cut and ll numbers together and divide them by ;.@ to calculate the average cut or ll depth for that cell. -ultiply the average cut or ll depth by the number of s6uare feet in the grid cell to get the cut or ll volume in cubic feet. Add all of the cut volumes up and divide that number by 78 to get the total cut for the site in cubic yards. Add all of the ll volumes up and divide that number by 78 to get the total ll for the site in cubic yards. #o calculate the import or export" subtract the ll volume from the cut volume. If the result is a positive number" you have more cut than ll and you will need export material from your site. If the numbers negative" you will need to import dirt onto the building site.
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A screen shot from Eubla ubed" which is software for estimating earthwor!s volumes. As well as calculating volumes automatically" the cut and ll depths are shaded. -odern computer software allows earthwor!s volumes to be calculated 6uic!er and more accurately than either of the two manual methods described above. #here are a number of software products available for this purpose. #hese products vary greatly in terms of complexity and price. #he rst stage of producing an estimate using software is to import the existing terrain. Once this is done the proposed terrain is drawn" and the software automatically calculates the cut and ll volumes re6uired.
/i1erent software products use di1erent methods to generate the estimate. *ome will essentially apply the grid method described above on a ne%resolution grid" whereas others use a triangulation of the terrain to calculate volumes directly. In any case" the processing power of modern computers means that a high level of accuracy can be achieved in a fraction of the time it would ta!e to produce a manual estimate. #here are many advantages to using software to calculate earthwor!s volumes" and most companies which estimate earthwor!s on a regular basis will use software to do so. 2erhaps the principal advantage of software is that it is much 6uic!er to produce a more accurate estimate when compared with the manual methods described above. Another major advantage is that most modern software products of this type will have useful display options which can be exported for presentations. *hading cut and ll depths across the project is a particularly useful facility. ightly or wrongly" people tend to be more impressed by computer%generated images than they are by hand calculations" and trust them more. #his is particularly important when presenting your estimates to a client as part of a tender. #he primary disadvantage of using software to produce estimates is the cost of the software licence" which varies between around F7@@ to several F4@@@s. hile this cost should be o1set against the time saved by using the software as well as the improved chance of winning bids with computer visualisations" it can nevertheless be a cause of concern for a company that does not need to produce many earthwor!s estimates.
*&--A' #here are a number of methods available for estimating cut and ll 6uantities" three of which are described here. #he best method for a particular organi3ation will depend on a number of factors" including$
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#he #he #he #he
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#he money you have available to buy software licences
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number and complexity of the projects which you need to estimate presentational re6uirements for the estimation level of accuracy re6uired time you have available to produce the estimate