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3 Surveys and Earthwork Operations Construction Surveys Construction Stakes The Mass Diagram SURVEYS AND OPERATIONS FM 5-430-00-1/AFPAM 32-8013, Vol 1 EARTHWORK Construction surveys are initiated when new construction is necessary. These surveys reveal the kinds of stakes to be used: provide data for earthwork estimation, including which method of estimation to use; and provide information for use on the mass diagram. The finished survey books should be filed with the construction project records of the Operations and Training Officer (US Army) (S3). Earthwork operations are one of the most important construction aspects in road and airfield construction. Earthwork reqires the greatest amount of engineering effort from the standpoint of personnel and equipment. Therefore, the planning, scheduling, and supervision of earthwork operations are important in ob- taining an efficiently operated construction project. CONSTRUCTION SURVEYS Construction surveying is the orderly process of obtaining data for various phases of construction activity. It includes the fol- lowing surveys: reconnaissance, prelimi- nary, final location, and construction lay- out. The reconnaissance and preliminary surveys are used to determine the best loca- tion. The remaining surveys are conducted after a location has been established. The purpose of construction surveys is to control construction activities. The number and extent of surveys conducted is governed by the time available, the stand- ard of construction desired, and the il bilit f l d t il I ducted for a deliberate project in the com- munications zone. The quality and efficien- cy of construction is directly proportional to the number and extent of surveys and other preplanning activities. The principles and techniques of field surveying are discussed in detail in technical manual (TM) 5-232 and FM 5-233. After completing a thorough construction survey, transfer the design information from paper to the field by construction stakes. These stakes are the guides and reference markers for earthwork operations. M k th tk th t th t ti
  • 3Surveys and Earthwork Operations

    Construction Surveys

    Construction Stakes

    The Mass Diagram


    FM 5-430-00-1/AFPAM 32-8013, Vol 1


    Construction surveys are initiated when new construction isnecessary. These surveys reveal the kinds of stakes to be used:provide data for earthwork estimation, including which methodof estimation to use; and provide information for use on themass diagram. The finished survey books should be filed withthe construction project records of the Operations and TrainingOfficer (US Army) (S3).

    Earthwork operations are one of the most important constructionaspects in road and airfield construction. Earthwork reqiresthe greatest amount of engineering effort from the standpoint ofpersonnel and equipment. Therefore, the planning, scheduling,and supervision of earthwork operations are important in ob-taining an efficiently operated construction project.

    CONSTRUCTION SURVEYSConstruction surveying is the orderlyprocess of obtaining data for various phasesof construction activity. It includes the fol-lowing surveys: reconnaissance, prelimi-nary, final location, and construction lay-out. The reconnaissance and preliminarysurveys are used to determine the best loca-tion. The remaining surveys are conductedafter a location has been established.

    The purpose of construction surveys is tocontrol construction activities. The numberand extent of surveys conducted isgoverned by the time available, the stand-ard of construction desired, and the

    il bilit f l d t i l I

    ducted for a deliberate project in the com-munications zone. The quality and efficien-cy of construction is directly proportional tothe number and extent of surveys and otherpreplanning activities. The principles andtechniques of field surveying are discussedin detail in technical manual (TM) 5-232and FM 5-233.

    After completing a thorough constructionsurvey, transfer the design information frompaper to the field by construction stakes.These stakes are the guides and referencemarkers for earthwork operations.

    M k th t k th t th t ti

  • FM 5-430-00-1/AFPAM 32-8013, Vol 1

    RECONNAISSANCE SURVEYThe reconnaissance survey provides thebasis for selecting acceptable sites androutes and furnishes information for use onsubsequent surveys. If the location cannotbe selected on the basis of this work, itmust be determined by the preliminary sur-vey.

    PRELIMINARY SURVEYThe preliminary survey is a detailed studyof a location tentatively selected on thebasis of reconnaissance, survey informa-tion, and recommendations. It consists ofrunning a traverse along a proposed route,recording topography, and plotting results.For roads, it may be necessary to conductseveral preliminary surveys if the reconnais-sance party has investigated more than onesuitable route. Establish, station, andprofile the route centerline with horizontaland vertical control points set. Take cross-section readings to allow rough calculationsof the earthwork involved. (Sometimescross sections may be taken during thereconnaissance survey if the conditions war-rant.) If the best available route has notbeen chosen, select it at this time.

    The airfield survey consists of establishingcontrols, noting terrain features, measuringglide-angle clearance, making soil profiles,and investigating drainage patterns and ap-proaches. Accurately establish the finalcenterline during the survey.

    FINAL LOCATION SURVEYWhen time permits, conduct a final locationsurvey. Establish permanent bench marksfor vertical control and well-marked pointsfor horizon tal control. These points arccalled hubs because of the short, squarestake used. On most surveys, the hub isdriven flush with the ground, and a tack inits top marks the exact point for angularand linear measurements. The hub loca-tion is indicated by a flat guard stake ex-tended above the ground and driven at aslope so its top is over the hub. Hubs are

    2 inches by 2 inches and the guards areflat stakes, about 3/4 inch by 3 inches.

    Horizontal Control

    The purpose of horizontal control is to ac-curately determine points for the variousfacilities of an engineering project. Estab-lish permanent, well-marked points forhorizontal control and reference them at thesite before construction begins. On a largefacility, establish a grid network and use itfor this control. Tie the network into themilitary grid system in the particular area,if such a system has been established. Onan airfield, place control points beyond theclear zone. These points define the center-line of the runway and other important sec-tions of the airfield.

    As the taxiways and other facilities are laidout, establish and reference new controlpoints. In laying out the centerline, placetarget boards at each end of the runway sothe instrument person can make frequentchecks on alignment while the line is beingstaked out. Target boards may be set upon any line that requires precision align-ment. Reference control stakes to ensurereplacement, if they are disturbed or lost.Locate the target board just beyond the out-ermost control-point stake.

    Vertical Control

    Vertical control methods determine the dif-ference in elevation between points. If avail-able, establish a level reference surface ordatum from a known bench mark. Differen-ces in elevation, with corrections, are sub-tracted from or added to this assignedvalue, resulting in the elevation of thepoints. Take the datum of the bench marksystem from a known elevation orbarometer reading or make an arbitrary as-sumption.

    CONSTRUCTION LAYOUT SURVEYThe construction layout survey is the finalpreconstruction operation. It provides align-ments, grades, and locations that guide con -struction operations. The survey includesdetermining exact placement of the

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  • FM 5-430-00-1/AFPAM

    centerline; laying out curves; setting all culvert sites; and performingremaining stakes, grades, and shoulders; quired to begin construction.

    32-8013, Vol 1

    other work re-Continue this

    staking out necessary structures; laying out survey until construction is completed.

    CONSTRUCTION STAKESUse construction stakes for centerline,slope, offset, shoulder, grade, reference,ditch, culvert, and intermediate slakes andfor temporary bench marks. The stakesshould be approximately 1 inch by 3 inchesby 2 feet. Use finished lumber when pos-sible. If it is not possible to usc finishedlumber, usc small trees or branches blazedon both sides and cut to length. Finishedgrade stakes and temporary bench marksare 2 inches by 2 inches by 12 inches.Place stakes using a three- to five-personcrew equipped wtth transit, level, rod, tape,ax, sledgehammer, and machete.

    The primary functions of constructionstakes are to indicate facility alignment con-trol elevations, guide equipment operators,and eliminate unnecessary work. They alsodetermine the width of clearing required byindicating the limits of the cut and fill atright angles to the centerline of a road.

    Mark and place construction stakes to con-form to the planned line and grade of theproposed facility. Use colored markingcrayons to mark the stakes. Use a uniformsystem so the information on the stakescan be properly interpreted by the construc-tion crew.

    Construction stakes indicate-

    The stationing or location of any part ofthe facility in relation to its startingpoint. If the stake is located at a criti-cal point such as a point of curvature(PC), point of intersection (PI), or pointof tangency (PT) of a curve, note this onthe stake.

    The height of cut or fill from the existingground surface to the top of the sub-grade for centerline stakes or to theshoulder grade for shoulder or slopestakes.

    The horizontal distance from the center-line to the stake location.

    The side-slope ratio used on slopestakes.

    The number and location of stakes used dif-fer between roads and airfields. A typicalset of construction stakes consists of acenterline stake and two slope stakes andis referred to as a three-point system.Point one is the centerline of the facility.Points two and three are the constructionlimits of the cut and fill at right angles tothe centerline.

    CENTERLINE OR ALIGNMENT STAKESThe centerline or alignment (hub) stakes,shown in Figure 3-1, are placed on thecenterline of a road or air field and indicateits alignment, location, and direction. Theyare the first stakes placed and must be lo-cated accurately. These stakes are used asreference points in locating the remainingstakes. Centerline stakes are placed at 100-foot (or 30-meter) intervals. On roughground or sharp horizontal and vertical

    Figure 3-1. Centerline stakes

    Surveys and Earthwork Operations 3-3

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    curves, place the stakes closer together.On horizontal curves, also stake the PC, PI,and PT. On vertical curves, also stake thepoint of vertical curvature (PVC), the pointof vertical intersection (PVI), the point of ver-tical tangency (PVT), and the low point (LP)or high point (HP) of the curve.

    Place centerline stakes with the broad sidesperpendicular to the centerline. The side ofthe stake that faces the starting point isthe front. Mark the front of the stake witha for centerline and, if applicable, PC, PI,or PT. Also mark on the front the distancefrom zero or the starting point in 1 00-footstations and the fractional part of a station,if used, For example, marked ona stake indicates it is 654.22 feet from theorigin of the facility and is known as thestation of this point. Stations are used inlocating sections of construction and inpreparing reports.

    PIace the amount of cut or fill required atthe station on the reverse side of the stake.A cut is marked C; a fill, F. A centerlinestake, placed at station 78 + 00 and requir-ing a fill of 6.0 feet to bring this station upto the final grade line, would be placed andshown as indicated in Figure 3-1, page 3-3.

    The amount of cut or fill indicates the dif-ference between the final grade line and theground line where the stake is emplaced. Apoint on the stake is seldom used as theline of reference to the final grade.

    To prevent misinterpretation of the amountof cut or fill, mark decimal parts of a foot,as shown in Figure 3-1. The decimal partis written smaller, raised, and underlined.Facing the direction of increasing stations,the centerline forms the dividing line be-tween the right and left sides of the area tobe graded. When facing either side of thecenterline, it is customary to refer to theareas as the right or left side.

    SLOPE STAKESSlope stakes, shown in Figure 3-2, definethe limits of grading work. When used inread work, they can be used as guides in

    Figure 3-2. Marking and placement of slopestakes

    determining the width of clearing necessary.The area to be cleared usually extends 6feet beyond the slope stakes. Set slopestakes on lines perpendicular to the center-line (one on each side), at points where thecut and fill slopes intersect the naturalground surface. Stakes at points of zerocut or fill are placed sloping outward fromthe centerline.

    Sloping the stakes outward allows the equip-ment to work to the stake without removingit. The slope indicates the direction of thecenterline of the road and enables the equip-ment operators to read the stakes more easi-ly. Place slope stakes at 100-foot intervalson tangents and at 50-foot intervals onhorizontal or vertical curves, Whenever asharp break in the original ground profileoccurs, it should be staked.

    The front of a slope stake is the side facingthe centerline. On this side of the stake,mark the difference in elevation betweenthe natural ground elevation at this pointand the finished grade at the edge of the

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  • shoulders. Under this figure, place anotherfigure that indicates the horizontal distancefrom the centerline of the road to the slopestake. Place the station number on theother side of this stake. Below the stationnumber, indicate the appropriate sloperatio. Figure 3-2 shows the proper mark-ings for a slope stake in a typical situation.

    OFFSET STAKESEquipment used on a cut or fill section maydestroy or remove many of the grade (center-line, shoulder, or slope) stakes. To preventloss of man-hours and repetition of surveywork, caution construction crews to protectgrade stakes whenever possible. Place off-set stakes beyond construction limits toavoid resurveying portions of the road torelocate these stakes. Figure 3-3 shows off-set stakes used to relocate the originalstakes.

    Place offset stakes on a line at right anglesto the centerline of the facility. Fromthese, the slope stakes can easily be lo-cated. After relocating a slope stake, relo-cate the centerline stake by measuringtoward the centerline of the road thehorizontal distance indicated on the slopestake and placing the new centerline stakethere.

    An offset stake contains all the informationgiven on the original slope stake plus thedifference in elevation and horizontal dis-tance from the original slope stake to theoffset stake. Mark the offset distance onthe front of the stake and circle it to indi-cate it is an offset reference. If the offsetstake is at a different elevation from theslope stake, the cut or fill value must be in-creased or decreased by the difference inelevation. An offset stake placed a horizon-tal distance of 10 feet from and 1 footabove the right slope stake would be placedand marked as shown in Figure 3-3. Coor-dination between the surveyor and grade su-pervisor concerning the meaning of themarkings is most important regardless ofthe type of marking used.

    FM 5-430-00-1/AFPAM 32-8013, Vol 1

    Figure 3-3. Marking and placement of offsetstakes

    FINISH-GRADE STAKESUse wooden stakes, 2 inches by 2 inches,with tops colored red or blue, for finish-grade stakes. Blue or red tops, as they arecalled, indicate the actual finished elevationof the final grade to which the completedfacility is to be constructed. They are usedwhen the grade is within a short distanceof the final elevation. Do not use thesestakes in combat road construction exceptin areas with steep slopes. This type ofstake normally requires a guard stake toprotect it and indicate its location. Onlarge projects, it may be impractical to useguards with each stake.

    There are no markings on finish-gradestakes other than the color on the top.These stakes may be set for use with thetop of the stake exactly at the finishedgrade or with the top of the stake above thefinished grade, as decided upon by the sur-veyor and construction foreman.

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    With the stakes set and marked at apredetermined distance above the finishedgrade, stretch a string between two stakesacross the work and use a graduated ruleror stick to check the elevation. On an air-field layout, place these stakes along thecenterline, edge of pavement, intermediatelines, shoulder lines, and ditch slopes. Forroad work, place stakes along the centerlineand the edge of the shoulder; they may ormay not be placed on the slopes.

    REFERENCE STAKESMany hubs marking the location of high-ways and airfields are uprooted or coveredduring construction. They must bereplaced, often more than once, before con-struction is completed. AS an aid in relocat-ing a point which may become hidden byvegetation, or as a means of replacingpoints which may have been destroyed,measurements are made to nearby per-manent or semipermanent objects. Thisprocess is known as referenceing or witness-ing a point. On many surveys, permanentobjects may not be available as witnesses.In such cases, additional stakes may bedriven. These stakes usually are ap-proximately 2 inches by 2 inches by 18 in-ches.

    There are no markings on a reference stake.A point can be referenced by a known dis-tance and a known angle or by two knowndistances. A transit must be used in thefirst case and may be used to advantage inthe second, The method of using twoknown distances can be used, however,when a transit is not available. Place twopoints at measured distances from the pointto be referenced. Use two tapes to relocatethe original point or stake. Hold the zeroend of one tape on one reference point andthe zero end of the other tape on the otherreference point. The point of intersection ofthe two tapes at the respective distancesgives the location of the point in question.

    To be of most value in replacing a missingstation or point, the reference stakes or wit-nesses will be less than 100 feet from thepoint and, if possible, the arcs should inter-

    sect at approximately right angles. Placethem outside the construction limits, and in-dicate their location by blazing trees or addi-tional stakes. Normally, the location of thereference stakes can be obtained from thesurveyors notebook.

    CULVERT STAKESCulvert stakes are located on a line parallelto and offset a few feet from the centerline.The information required on the culvertstakes includes the distance from the staketo the centerline, the vertical distance to theinvert, and the station number. Once thesurvey crew has finished staking out the cul-vert, the construction supervisor can placethe pipe accurately by using batter boards.

    BENCH MARKSVertical control of a road or airfield must bemaintained during construction. To do this,points of known elevation must be estab-lished. Obtain elevations from permanentmonuments, known as bench marks, estab-lished by geodetic surveys. From thesebench marks, run a line of levels and settemporary bench marks (TBMs). On smallprojects the TBMs frequently are set by run-ning the levels from a point of assumedelevation. This is especially true of construc-tion in combat areas.

    Usually, TBMs are placed at 500- to 1,000-foot (or 150- to 300-meter) intervals and areplaced off the limits of construction. Stakes2 inches by 2 inches, solidly emplaced inthe ground, may be used for this purpose.However, a nail driven into a tree, a man-hole cover, or a pipe driven into the groundmay also be used. Frequently, referencepoints serve as TBMs. The TBMs are setbefore setting the centerline stakes becausevertical control must be established beforeconstruction begins.

    EARTHWORK ESTIMATIONEarthwork computations involve the calcula-tion of earthwork volumes, the determina-tion of final grades, the balancing of cuts

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    and fills, and the planning of the mosteconomical haul of material. The exactnesswith which earthwork computations aremade depends upon the extent and ac-curacy of field measurements, which inturn arc controlled by the time availableand the type of construction involved. Toplan a schedule, the quantity of earthworkand the soil and haul conditions must beknown so the most eficient type and quan-tity of earthmoving equipment can bechosen and the appropriate time allotted.

    When time is critical, the earthwork quan-tities are estimated either very roughly ornot at all. When time is not critical, higherconstruction standards are possible andearthwork quantities are estimated and controlled by more precise methods.


    The volume of a rectangular object may bedetermined by multiplying the area of oneend by the length of the object, Thisrelationship can be applied to the deter-mination of earthwork by considering roadcross sections at the stations along theroad as the end areas and the horizontaldistance between cross sections as thelengths. The end areas of the cross sec-tions must be computed before volumes canbe calculated.


    When the centerline of the construction hasbeen located, measurements are taken inthe field from which the required quantitiesof cut or fill can be computed. A cross-sectional view of the land is plotted fromthese measurements. The cross sectionsare taken on vertical planes at right anglesto the centerline. Where the ground sur-face is regular, cross sections are taken atevery full station (100 feet), Where theground is irregular, they must be taken atintermediate points as determined by thesurveyor. A typical cross section is shownin Figure 3-4.

    Figure 3-4. Typical fill cross section

    Plot ground elevations from the surveyorsnotes. Make a sectional template of thesubgrade that shows the finished subgradeand slopes plotted to the same scale as thecross sections. Superimpose the templateon the cross section and adjust it to the cor-rect centerline elevation. Trace the tem-plate and extend the side slopes to intersectthe original ground. If the section involvesboth cut and fill, draw only the appropriatelines of each template. When the sectionsare completed, begin the end-area measure-ments, then determine the volume. Of theseveral satisfactory methods of measuringthe end areas, only the trapezoidal, strip-per, double-meridian (triangular), andplanimeter methods will be described inthis manual. The method chosen willdepend upon the time available, the ac-curacy desired, the aids at hand, and theengineers preference.

    Trapezoidal Method

    The trapezoidal method is widely used todetermine end areas. The computations aretedious, but the results are accurate. Inusing the trapezoidal method, the area ofany cross section is obtained by dividingthe cross section into triangles andtrapezoids, computing the area of each partseparately, and taking the total area of theverticals to the ground line (Figure 3-5,page 3-8) in order to divide the cross sec-tion into two triangles and two trapezoids.Make the assumption that the ground isperfectly straight between these selectedpoints on the ground line. While this isnot usually correct, the assumption iswithin the accuracy normally required.

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    Figure 3-5. Cross section in cut withverticals drawn at critical points

    Basic Formulas. Before the area of thecross section can be computed, the basicformulas for the computation of the areasof triangles and trapezoids must be under-stood. If a line is drawn, as shown in Fig-ure 3-6, from one of the vertices of a tri-angle perpendicular to the side or base (b)opposite this vertex, the line formed repre-sents the altitude (h) of the triangle. Thearea of any triangle can be expressed asthe product of one-half the base multipliedby the altitude. This relationship is ex-pressed by the formula:

    Figure 3-6. Triangle base and heightdimension locations

    A trapezoid is a four-sided figure havingtwo sides parallel but not equal in length,as shown in Figure 3-7. If the two parallel

    sides of the bases are crossedby a line perpendicular to each, the dis-tance between the two bases along this per-pendicular line is the altitude of thetrapezoid. The area of any trapezoid can beexpressed as the average length of thebases multiplied by the altitude. Thisrelationship can be expressed by the for-mula:

    Figure 3-7. Trapezoid base and heightdimension locations

    Computation of Areas. The first step in com-puting areas by the trapezoidal method isto break the cross-sectional area into tri-angles and trapezoids by drawing verticals,as shown in Figure 3-5. Then determinethe area of these small figures by the ap-propriate formula.

    To determine the appropriate dimensions,the notes taken by the surveyors must beknown. The cross-section notes taken inthe field are in fractional form. The figurebelow the line indicates the horizontal dis-tance from the centerline to that point onthe ground. The figure above the line indi-cates the ground elevation of that point.Points on the grade line of the proposedroad are written in a similar manner andare obtained by computations from the finalgrade line to be established, as shown inFigure 3-8. Thus, the note 32.0/21 indi-cates a point that is at elevation 32.0 and21 feet from the centerline of the road. If

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    the cross section is divided into triangles Stripper Methodand trapezoids by erecting verticals, obtain The stripper method is a variation of thenotes for the centerline, shoulders, and end trapezoidal method. To use this method,of slopes to solve for the area. consider a section such as that shown in

    Figure 3-9.

    Figure 3-8. Cross-section cut showingdistances and elevations

    To solve the triangles and trapezoidsformed, consider the bases of these figuresto be vertical and the altitudes to behorizontal. All vertical bases are found bysubtracting elevations, and all horizontal al-titudes are found by subtracting horizontaldistances from the closest vertical in thedirection of the centerline.


    Referring to Figure 3-8, area a], and sub-stituting in the formula for the area of a tri-angle:

    Referring to Figure 3-8, area and sub-stituting in the formula for the area of atrapezoid:

    Find the areas of the remaining trapezoidand triangle in the same way.

    Figure 3-9. Fill cross section arranged toshow the stripper method


    If vertical lines are drawn at equal distan-ces apart, then by the trapezoidal formula,the end area, A, will be given by the follow-ing computation:

    Factor in and combine terms:

    First, measure (graphically) each length (b)and multiply the sum by the width (w) (con-stant). The distance between vertical lines,w, may be any value, but it must be con-stant throughout the cross-section area. Inrough terrain the vertical lines should becloser together to ensure greater accuracy.

    One of the easiest and most convenientways to measure the vertical lines (b) iswith a strip of paper or plastic. Lay thestrip along each vertical line in such a man-ner as to add each in turn to the total.The strip will show the sum of all verticallines in the same scale that the cross sec-tion is plotted. This figure, multiplied bythe value of w, will give the area of thecross section.

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    Inaccuracies result when either a triangleor trapezoid falls within the limits of w orwhen the area is curved. However, themethod is rapid, and the accuracy is ade-quate under urgent conditions. Figure 3-10shows a typical cross section with a strip-per marked to show the total length of allvertical lines and the value of w. The strip-per indicates that the sum of all verticallines is 21.7 feet: w is given as 10 feet. Ap-plying these figures to the formula, then-

    Figure 3-10. Cross section with the sum of allvertical lines added on the stripper

    Double-Meridian Triangle Method

    The double-meridian method explained inChapter 13 of TM 5-232 gives a moreprecise value for a cross-section area thanthe stripper method. However, it involvesmore time.

    With this method, shown in Figure 3-11,the area is subdivided into two series oftrapezoids using the elevations of adjacentpoints and their projections on the center-line (the distances). These trapezoids havebases equal to the horizontal distance ofthe respective points from the centerline,and heights equal to their differences inelevation. Where the difference in elevationis plus, the area of the trapezoid is plus;where the difference is minus, the area ofthe trapezoid is minus. The componentareas are added algebraically. Because thisprocedure uses the sum of the bases of thetrapezoid, the area obtained is double thetrue area and must be divided by 2. Thecomputation is simple arithmetic: subtractadjoining elevations, multiply by the dis-tance from the centerline, add the multi-plied results and list plus and minus quan-tities, add these quantities, and divide by 2.

    Figure 3-11. Cross-section area by the double-meridian method

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    The steps for completing the procedure forthe double-meridian triangle method follow(refer to Figure 3-11).

    1. Start at the centerline ground or gradeelevation, whichever is lower (A). Workfrom the centerline in a clockwise directionto the left (A), (B), (C), (D), (E), (F); andcounterclockwise to the right (A), (G), (H),(I), (F), to the centerline ground or gradeelevation, whichever is higher (F).

    2. Working from point to point, multiplythe difference in elevation between each ad-jacent pair of points by the sum of their dis-

    tance from the centerline. Point (F) topoint (A) is not considered because the sumof their distances from the centerline iszero. Going from a lower to a higher eleva-tion gives a plus quantity, while going froma higher to a lower elevation gives a minusquantity. Place plus quantities in onecolumn and minus quantities in another.

    3. Divide the algebraic sum of the plusand minus quantities by 2 to obtain thearea of the cross section in square feet (sqft). In sections having both cut and fill,treat each part as a separate section.

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    Planimeter Method

    A polar planimeter is an instrument used tomeasure the area of a plotted figure by trac-ing its perimeter. The planimeter, shown inFigure 3-12, touches the paper at threepoints: the anchor point, P; the tracingpoint, T; and the roller, R. The adjustablearm, A, is graduated to permit adjustmentto the scale of the plot. This adjustmentprovides a direct ratio between the areatraced by the tracing point and the revolu-tions of the roller. As the tracing point ismoved over the paper, the drum, D, and thedisk, F, revolve. The disk records therevolutions of the roller in units of tenths;the drum, in hundredths; and the vernier,V, in thousandths.

    NOTE: Always measure cut and fill areasseparately.

    Check the accuracy of the planimeter as ameasuring device to avoid errors fromtemperature changes and other noncompen-sating factors. A simple method of testingits consistency is to trace an area of 1square inch with the arm set for a 1:1ratio. The disk, drum, and vernier com-bined should read 1.000 for this area.

    Before measuring a specific area, determinethe scale of the plot and set the adjustablearm of the planimeter according to thechart in the planimeter case. Check the set-ting by carefully tracing a known area,such as five large squares on the cross-section paper, and verifying the reading onthe disk, drum, and vernier. If the readingis inconsistent with the known area, read-just the arm settings until a satisfactoryreading is obtained.

    To measure an area, set the anchor point ofthe adjusted planimeter at a convenientposition outside the plotted area. Place thetracing point on a selected point on theperimeter of the cross section. Take an ini-tial reading from the disk, drum, and ver-nier. Continue by tracing the perimeterclockwise, keeping the tracing point careful-ly on the lines being followed. When thetracing point closes on the initial point,take a reading again from the disk, drum,and vernier. The difference between the ini-tial reading and the final reading gives avalue proportional to the area beingmeasured.

    Figure 3-12. Polar planimeter in use

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    Make two independent measurements to en-sure accurate results. The first is per-formed as discussed above. The secondmeasurement is made with the anchorpoint again placed outside the area beingmeasured but on the opposite side of thearea from its position in the first measure-ment. This procedure gives two compensat-ing readings the mean of which is more ac-curate than either.

    To measure plotted areas larger than thecapacity of the planimeter, divide the areainto sections and measure each sectionseparately, as outlined above.

    Computer-Aided Design (CAD)

    Very accurate measurements can be made ifcross sections arc digitized using CAD.Cross sections can be placed on a digitizingpad, points plotted into the computer and,with one command, the area calculated,

    METHODS OF VOLUME DETERMINATIONAn engineer can accomplish the necessaryearthwork computations by using the follow-ing methods: average- end-area, prismoidalformula, average-depth -of-cut-or-fill, grid,or contour.


    Average-End-Area Method

    The average-cnd-area method is most com-monly used to determine the volume bound-ing two cross sections or end areas. usethe formula:


    V is the volume, in cubic yards (cy) (1 cy =27 cubic feet (cf)), of the prismoid betweencross sections having areas in square feetof A1 and A2, separated by a distance of Lfeet .

    If cross sections are taken at full 100-footstations, the volume in cubic yards betweensuccessive cross sections in squarefeet, may be found by the formula:

    In either form, the formula is only accuratewhen A1 and A2 are approximately thesame shape. The greater the difference inshape between the two end sections, thegreater the possibility of error. However,the method is consistent with field methodsin general. In most cases, the time re-quired for a more accurate method is notjustified.

    Prismoidal-Formula Method

    The prismoidal method is used where eitherthe end areas differ widely in shape or amore exact method of computing volume isneeded. Its use is very limited because itrequires more time than the average-end-area method and gives greater accuracythan is required for most road and airfieldconstruction.

    The prismoidal formula is

    Determine by averaging the correspond-ing linear dimensions of andthen determining its area, rather thanaveraging the areas of

    Average-Depth-of-Cut-or-Fill Method

    With only the centerline profile and finalgrade established, earthwork can be es-timated with the average-depth-of-cut-or-fillmethod. Estimate the average depth of cutor fill between 100-foot stations and obtainthe volume of material from Table 3-1, page3-14, The accuracy of this method dependson the care given to establishing thecenterline profile, the instruments used,and the accuracy of field reconnaissance.

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    Table 3-1. Earthwork average cut or fill

    This table shows the number of cubic yards of earthwork that are in a 100-foot-long section of cut or fill havinga known average depth. To use this table you must know the following:

    1. Width.

    a. Cut section - the width of the base of the cut, including ditches.

    b. Fill section - the width of the top of the fill.

    2. Average amount of cut or fill.

    3. Slope ratio. Column 2 gives the correct amount of earthwork when the side slopes are 1:1. When theslope ratio is other than 1:1, an adjustment must be made (see column 4).NOTE: The final answer obtained from the table is for a section 100 feet long. If the actual length ofthe cut or fill is not 100 feet, an adjustment must be made. (For an 85-foot section, multiply by 0.85;for a 50-foot section, multiply by 0.50, and so on.)

    However, the volumes obtained by thismethod are generally adequate for mostmilitary construction.

    The centerline profile of a road is typical ofthe entire transverse section because of thenarrow widths. Because of the greaterwidth required on an airfield runway, thecen terline profile may be misleading as tothe typical conditions across the entiretransverse width at that point. Therefore,

    earthwork quantities for airfields should beestimated mainly from cross sections. How-ever, in the absence of sufficient time, theaverage-cut-or -fill method is better thannone at all.

    Determine the following before using Table3-1:

    Average amount of cut or fill.

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    Width of the base of the cut or the topof the fill in 2-foot increments between26 feet and 44 feet.

    Quantity to be added to the figure incolumn 2, if the width of the base or topof the fill is an odd number of feet.

    Quantity to be added if the slope ratioon both sides is 1.5:1 or 2:1.

    NOTE: The table is based upon a lengthof 100 feet between cross sections and aslope ratio of 1:1.

    Follow these steps to use the table:

    1. Enter column 1 and read down to theaverage amount of cut or fill for the lengthconcerned.

    2. Read horizontally to the right and ob-tain the figure under the appropriate baseof the cut or top of the fill in column 2.

    3. Make corrections to this figure fromcolumns 3 and 4, if they apply.

    4. If the length is not 100 feet between thepoints considered, adjust the answer propor-tionately,

    Grid Method

    When the quantity of material within thelimits of the cut sections is not enough tobalance the fill sections, material must beborrowed. The most convenient method isto widen the cuts adjacent to the fills wherethe material is needed. Compute thevolume by extending the cross sections.However, where this is not possible, locateborrow pits at some other area. The gridmethod is a convenient method of comput-ing the borrow material available in a givenborrow pit.

    In this method, first stake out over the areaa system of squares referenced to pointsoutside the limits of work. The dimensionsof these squares depend on the roughnessof the original terrain, the anticipated rough-ness of the final surface, and the accuracydesired. Rougher terrain requires smallerdimensions to get accurate results. The

    squares must be of such size that no sig-nificant breaks, either in the originalground surface or in the pit floor, exist be-tween the corners of the square or betweenthe edges of the excavation and the nearestinterior corner.

    By taking elevation readings at the stakesbefore and after excavation, data is ob-tained to compute the volume of borrowtaken from the pit. Figure 3-13 shows aborrow pit over which 25 squares werestaked, To identify the various intersectingpoints, label lines in one direction by num-bers and in the other direction by letters.Thus the intersection of lines C and 3would be labeled C3.

    Outline squares falling completely withinthe excavation with a heavy line, Withinthat line, determine the volume of excava-tion for each square in the following man-ner:

    1. Label the points on one square, asshown in Figure 3-14, page 3-16,

    Figure 3-13. Computation grid system for aborrow pit

    2. Points a, b, c, and d are on the originalground line, while and are onthe final ground line. The volume of the

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    an hq. (Refer to Figure 3-13, page 3-15and Figure 3-14.) The total borrow-pitquantity also includes the wedge-shapedvolumes lying between the complete solidsand the limits of excavation. For thesevolumes, use proportional surface areas,Use the formula:

    A grid is illustrated in Figure 3-15. Thelength of the sides of each square is 50feet. Therefore, given

    Figure 3-14. Excavation volume for one square

    resulting form is the product of the rightcross-sectional area A and the average ofthe four corner heights and in cubic yards.

    3. The volume represented by each squaremight be computed by the precedingmethod and all volumes added. However,when a number of such volumes adjoin oneanother, it is quicker to use the followingrelation which gives the total volume, repre-sented by all complete squares:

    This could be approximated by adding allcorner cuts and multiplying by A, or

    In the preceding formula, A is the rightcross-sectional area of one rectangularsolid, is a corner height found in onesolid, is a corner height common to twosolids, is a corner height common tothree solids, and is a corner height com-mon to four solids. As an example, is

    An alternative method is to compute thetotal of all cuts at each corner (123 feet),compute the average cut across all squares(123/25 = 4.92), and then multiply by thelength of the sides of the figure.

    Figure 3-15. Sample grid-system work sheet

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    On many projects, one objective of thepaper location study is to design the gradeline so the total cut within the limits of thework equals the total fill. The uncertainchange of volume of the material make thisdifficult. It is usually more economical tohaul excavated material to the embankmentsections, thereby eliminating borrow andwaste.


    Shrinkage has occurred when 1 cubic yardof earth, as measured in place before ex-cavation, occupies less than 1 cubic yard ofspace when excavated, hauled to an em-bankment, and compacted. This differenceis due to the combined effects of the loss ofmaterial during hauling and compaction toa greater-than-original density by the heavyequipment used in making the embankment.

    Shrinkage is small in granular materialssuch as sand and gravel, and is large in or-dinary earth containing appreciable percent-ages of silt, loam, or clay.

    Shrinkage is very high (possibly 70 percent)for shallow cuts containing humus, whichis discarded as unsuitable for embankments.These shallow cuts (usually 4 to 8 inchesdeep) arc called stripping.

    Loose and swell refer to a condition whichis the reverse of shrinkage. The earth as-sumes a larger volume than its naturalstate when stockpiled or loaded into atruck. This factor ranges from 10 to 40 per-cent swell and is usually uniform for agiven material.

    Shrinkage, however, varies with changes inthe soil constituents and with changes inmoisture content and the type of equipmentused. Consequently, a percentage al-lowance assumed in design may eventuallyprove to be 5 percent or more in error. Acommon shrinkage allowance is 10 to 30percent for ordinary earth.

    Settlement refers to subsidence of the com-pleted embankment. It is due to slow addi-tional compaction under traffic and togradual plastic flow of the foundationmaterial beneath the embankment.

    Net Volume Calculation

    Compute the volume of cut and fill and thenet volume between any two points on theconstruction project. The net volume is thedifference between the volume of cut andthe volume of fill between any two specifiedstations. The net volume may apply to theentire project or to a few stations. Netvolume may be described in a compacted,place, or loose state. Table 3-2 providesconversion factors used to find the netvolume. All calculations are recorded on

    Table 3-2. Soil conversion factors


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    the earthwork volume sheet shown in Table3-3.

    Earthwork Volume Sheet

    The earthwork volume sheets allow you tosystematically record this information andmake the neccessary calculations. They pro-vide a means of tabulating earthwork quan-tities for use in the mass diagram dis-cussed later in this chapter. The earthworkvolume calculation sheet, shown in Table3-3, is divided into columns for recordingand calculating information.

    Stations (column 1). List in column 1 allstations at which cross-sectional areas havebeen plotted. Normally, these areas aretaken at all full stations and at inter-mediate stations that are required to fullyrepresent the actual ground conditions andearthwork involved.

    Area of Cut (column 2). Record in column 2the computed cross-sectional areas of cutat each station. These areas may be com-puted by one of the commonly usedmethods, depending on the degree of ac-curacy required.

    Area of Fill (column 3), Complete column 3in the same manner as column 2, exceptshow cross-sectional areas of fill.

    Volume of Cut (column 4). Complete thevolume of cut material between adjacent sta-tions and record it in column 4. The mostcommon method for computing volumes isthe average-end-area method (or theearthwork table based on this method).

    This volume represents only the volume ofcut between the stations and the volumesreflected as in-place yardage.

    Volume of Fill (column 5). Complete column5 in the same manner as column 4, exceptshow fill volumes. Fill volumes reflect com-

    This layer varies in depth but is usually 4to 6 inches deep. This material must bewasted because it is not satisfactory toplace in an embankment, Indicate incolumn 6 the volume between stations ofthis humus material over sections of cut.

    Stripping Volume in Fill (column 7). Beforean embankment can be constructed, thesame layer of humus must be removed andthe volume replaced with satisfactorymaterial. Indicate in column 7 the volumeof this material between stations over sec-tions of fill.

    Net Volume of Cut (column 8). Indicate incolumn 8 the volume of cut material be-tween stations that is available for embank-ment. Column 8 is column 4 minuscolumn 6, because the total cut must bedecreased by the amount of material wastedin stripping, including the organic material.

    Adjusted Volume of Cut (column 9). Onecubic yard of material in its natural, undis-turbed state occupies approximately 1.25cubic yards when removed and placed in atruck or stockpile. The same 1 cubic yard,when placed in an embankment section andcompacted, occupies a volume of ap-proximately 0.9 cubic yards. In planningoperations, convert these various volumesto the same state so the comparisons canbe made, Changes in volume of earthworkare discussed in this chapter, and Table3-1, page 3-14, provides the necessary con-version factors. Column 9 is column 8 mul-tiplied by the appropriate conversion factor(in this case, 0.9) to convert it from in-place yardage to compacted yardage.

    Total Volume of Fill (column 10). Indicate incolumn 10 the amount of compactedmaterial required between stations to com-plete needed embankments, Column 10 iscolumn 5 plus column 7, plus the amountnecessary to replace the quantity removedby stripping. This figure represents the fill

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    Table 3-3. Earthwork volume calculation sheet

    material that is available (plus) or required tion 0 + 00. While passing through a(negative) within the station increment after stretch where cutting predominates, thisthe intrastation balancing has been done. column increases in value. While passing

    Mass Ordinate (column 12). Column 12 indi-through a stretch where embankment is re-quired, this column decreases.

    cates the total of column 11 starting at sta-

    THE MASS DIAGRAMThe first step in planning earthmoving plans for economical and efficient comple-operations is the estimation of earthwork tion of the earthmoving mission.quantities involved in a project. This canbe done accurately by one of several The mass diagram is one method of analyz-methods, depending upon the standard of ing earthmoving operations. This diagramconstruction preferred. With these es- can tell the engineer where to use certaintimates, the engineer can prepare detailed types of equipment, the quantities of

    materials needed, the average haul

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    distanccs and, when combined with aground profile, the average slope for eachoperation. This permits the preparation ofdetailed management plans for the entireproject. The mass diagram is not the com-plete answer to job planning, and it haslimitations that restrict its effectiveness forcertain typres of projects. However, it is oneof the most effective engineer tools and iseasily and rapidly prepared.


    Using column 1 (station) and column 12(mass ordinate, cumulative total) of a com-pleted earthwork volume sheet, a massdiagram can be plotted as shown in Figure3-16.

    Plot the mass diagram on scaled graphpaper with the stations indicated horizontal-ly and the mass indices (column 12)denoted vertically. Connect all plottedpoints to complete the mass diagram asshown in Figure 3-16. Positive numbersarc plotted above the zero datum line, nega-tive numbers below.

    PROPERTIES OF THE MASS DIAGRAMFigure 3-17 shows a typical mass diagramwith the actual ground profile and finalgrade line of the project plotted. Note thatboth usc the same horizontal axis (sta-tions). The ground profile is placed abovethe mass diagram to facilitate the calcula-tion of the average grade over which equip-ment will work. The horizontal axis is theonly thing these graphs have in common.

    The mass diagram is a running total of thequantity of earth that is in surplus or defi-cient along the construction profile. If atone station more material is being cut thanfilled, you have a cut operation at that sta-tion. The quantity or volume of surplusmaterial will be increasing as cutting opera-tions continue through the station, produc-ing an ascending mass diagram curve line.Cutting is occurring from stations A to Band stations D to E in Figure 3-17. The

    total volume for the cut at station A to B isobtained by projecting the points on thecurve line at stations A and B to the verti-cal axis and reading the volume

    Conversely, if at one station more materialis being filled than cut, you have a filloperation at that station. The quantity orvolume of deficient material will be increas-ing as filling operations continue throughthe station, producing a descending mass-diagram curve line. Filling is occurringfrom stations B to D in Figure 3-17. Thetotal volume for the fill at stations B to D isobtained by projecting the points on thecurve line at stations B and C to the verti-cal axis and reading and adding thevolumes above and below the zero datumline.

    The maximum or minimum point on themass diagram, where the curve changesfrom rising to falling or vice versa, indicatesa change from cut to fill or vice versa. Thispoint is referred to as a transition point(TP). On the ground profile, the grade linecrosses the ground line at the TP, as il-lustrated at stations B and D.

    When the mass diagram crosses the datumline or zero volume, as at station C, thereis exactly as much material filled as thereis material cut, or zero volume excess ordeficit at that point. The section of themass diagram, from the start of the projectat station A to a point of crossing the zerovolume line, is known as a node. Eachcrossing point on the zero volume line indi-cates another node. The last node may ormay not return to the zero datum line.Nodes are numbered from left to right.

    The final position of the mass diagram line,above or below the datum line, indicateswhether the project was predominately cutor fill. In Figure 3-17, where the massdiagram ends at station E, the operationwas cutting; that is, surplus material wasgenerated by cutting and must be hauledaway (waste operation). Borrow operationsoccur when the final position of the massdiagram is below the zero volume line.

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    Figure 3-16. Plotting the mass diagram

    Figure 3-17. Properties of a mass diagram

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    PROJECT ANALYSISOnce the basic properties of the massdiagram arc understood, the engineer canconduct a detailed analysis 10 determinewhere dozers, scrapers, and clump truckswill operate This is accomplished by usingbalance lines. A balance line is a line ofspecific length drawn horizontally, intersect-ing the mass diagram in two places. Thespecific length of the balance line is therecommended working or maximum hauldistance for different pieces of equipment.The term maximum haul distance is usedbecause opera ting the equipment beyondthis point would not be efficient. The maxi-mum haul distances (balance-line lengths)are

    MaximumEquipment Haul Distance

    Dozer Up to 300 feet

    Scraper 301 to 5,000 feet

    Dump Truck 5,001 feet to severalmiles

    These lengths are measured using thehorizontal scale (stations measured inhundreds of feet). Always use the maxi-mum haul distance (length) of each piece ofequipment, provided the project or node isat least that length. Start excavating eachnode with the dozer followed by the scraperand dump truck.

    Figure 3-18 shows a balance line drawn ona portion of a mass diagram. If this was adozer balance line, the distance between sta-tions A and C would be 300 feet.

    Cut equals fill between the ends of abalance line. The mass line returns to ex-actly the same level, indicating that theinput and the expenditures of earth havebeen equal. In Figure 3-18, this occurs be-tween stations A and C. There has been anexact balance of earthwork.

    In Figure 3-18, the amount of materialmade available by cutting between stationsA and B is measured by the vertical linemarked Q. This is also the amount of em-bankment material required between sta-

    Figure 3-18. Mass diagram with a balance line

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    tions B and C. This is described as thebalanced quantity of earthwork.

    If equipment was used to do the balancedearthwork between stations A and C, themaximum distance that earth would have tobe moved would be the length of thebalance line AC.

    In accomplishing balanced earthwork opera-tion between stations A and C, some of thehaul distance would be short, while somewould approach the maximum haul dis-tance. The average haul distance (AHD) isthe length of the horizontal line placed mid-way between the balance line and the topor bottom point (transition point) of thecurve (Figure 3-18) and is found by dividingthe vertical distance of Q in half.

    If the curve is above a balance line, thedirection of haul is from left to right. Theconverse is true when the curve is below abalance line.

    Figure 3-19 shows a part of a massdiagram on which two balance lines have

    been drawn. The same principles apply forthe area between the lines as with only onebalance line. The quantity balanced is thevertical distance between the balance line,while the horizontal bisector is the averagehaul distance. The longer balance line isthe maximum haul distance, and theshorter balance line is the minimum hauldistance. The haul distance depends uponthe position of the curve with respect to thebalance lines.

    The mass diagram is a useful indicator ofthe amount of work expended on a project.By definition, work is the energy expendedin moving a specified weight a given dis-tance. It is the product of weight times dis-tance. Because the ordinate of the massdiagram is in cubic yards (which representsweight) and the abscissa is in stations ordistance, an area on the mass diagram rep-resents work. In Figure 3-20, page 3-24, ifequipment is used to do the balancedearthwork between the ends of the balancelines as drawn, the work expended is equalto the area between the mass line and thebalance line.

    Figure 3-19. Mass diagram with two balance lines

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    Figure 3-20. Work in earthmoving operations

    Another item calculated from the massdiagram is average grade. This value isused when computing equipment schedul-ing and utilization. Figure 3-21 and Figure3-22, page 3-26, illustrate a portion of themass diagram on which the average gradehas been determined.

    USE OF THE MASS DIAGRAMThe mass diagram is used to find the costof a project in terms of haul distance andyardage, to locate the areas for operationfor various types of equipment, to establishthe requirements for borrow pits and wasteareas, and to provide an overall control ofrequired earthmoving operations. However,the means used to analyze the massdiagram will follow the same principlesregardless of the end result desired. Theanalysis of the mass diagram is based uponthe proper location of balance lines.

    Because the lengths of balance lines on amass diagram are equal to the maximum orminimum haul distances for the balancedearthmoving operation between their endpoints, they should be drawn to conform tothe capabilities of the available equipment.Equipment planned accordingly will operate

    at haul distances that are within its bestrange of efficiency. Figure 3-21 illustratesa portion of a mass diagram on which twobalance lines have been drawn: 300 feet toconform to dozer capabilities and 5,000 feetfor the scraper.

    The following job analysis can be madefrom the diagram in Figure 3-21:

    Use dozers between stations C and E. Themaximum haul distance is 300 feet; theaverage haul distance is the horizontalbisector shown. The amount that will becut between stations C and D and filledbetween stations D and E is the length ofthe indicated vertical lines.

    Use scrapers for cutting from stations A toC and filling from stations E to G. Theminimum and maximum haul distances are301 and 5,000 feet, respectively. Theaverage haul distance is the horizontal linemidway between the balance lines. Theamount of earthwork is indicated by thevertical line.

    To determine the average grade for eitherthe scraper or dozer work area, use the fol-lowing procedure:

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    Figure 3-21. Balance lines for equipment efficiency

    1. Draw on the profile a horizontal linethrough the work area that roughly dividesthe area in half. This is a rough estima-tion. (See Figure 3-22, page 3-26.)

    2. Extend a vertical line from the endpoints of the previously determined averagehaul line up through the project profile.These lines are referred to as the averagehaul vertical. (See Figure 3-23, page 3-26.)

    3. Draw a final line connecting the inter-secting points of the lines drawn in steps 1and 2. This line represents the averagegrade.

    4. Determine the average change in eleva-tion (the vertical distance between the cutand fill).

    5. Calculate the average grade as follows:

    Average Grade % =

    Average change in elevation x 100Average haul distance

    In the example shown in Figure 3-23, theaverage grade for the dozer would be

    Average Grade % =

    18x 100 = -8.87%


    Since this is an operation which movesearth downhill, the grade would be negative,or -8.87% An uphill cut would have a posi-tive grade.

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    Figure 3-22. Determining average grade, step 1

    Figure 3-23. Determining average grade, step 2

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    Placement of Balance Lines to MinimizeWork

    Because the area between the apex of themass diagram and the balance line is ameasure of the work involved in the balanc-ing operation, the size of these areasshould be decreased whenever possible,However, the method used to minimize thearea depends upon the shape of the massdiagram and the number of adjacent nodesthat can be used.

    If two nodes are adjacent, work is mini-mized when two balance lines are drawn asone continuous line, with the balance linesequal in length. Each balance line must bewithin the maximum efficient haul distan-ces for the equipment. The best placementof balance lines on the portion of a massdiagram shown in Figure 3-24 would belines AE and EF, with AE = EF.

    Only one balance line, CH, may be neededif it is within efficient haul distancespecifications. The quantity involved wouldbe Q yards and the work involved would bethe area above CH.

    If this one balance line was replaced by twobalance lines, BD and DG, with BD lessthan DG. the quantity of earthworkbalanced would remain the same. Thework would be decreased by the size of thearea between CH and DG and increased bythe size of the area between BD and C.This would result in a savings because theincrease is less than the decrease for thesame amount of earthwork balanced. Thisdecreasing process will continue by raisingthe lines to the point where one equals theother, or until AE = EF is reached.

    If there is an even number of adjacentnodes, as shown in Figure 3-25, work isreduced when the balance lines are one con-tinuous line and AB + CD + EF = BC + DE+ FG. The length of each balance line mustbe within equipment maximum haulcapabilities as defined earlier.

    Figure 3-25. Minimizing work with an evennumber of nodes

    If there is an odd number of adjacentnodes, as shown in Figure 3-26, work isdecreased when the balance lines are onecontinuous line and AB + CD + EF - (BC +DE) equals the limit of efficient haul, or ap-proximately 1,000 feet. All balance linesmust be within equipment limits.

    Figure 3-26. Minimizing work with an oddnumber of nodes

    Calculation of Earthwork not WithinBalance Lines

    It is usually impossible to place balancelines so that the entire amount ofearthwork on a project can be balanced.Some part of the mass line will be outsidethe balance lines. This material must bewasted or borrowed. If the portion notwithin balance lines is ascending (cutting),there is waste; if it is descending (filling),there is borrow, This is shown in Figure3-27, page 3-28. Concentrate all necessaryborrow and waste operations in one generalarea.

    Figure 3-24. Minimizing work with two nodes

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    Figure 3-27. Waste and borrow on a massdiagram

    Format for Analysis

    The simplest and most practical method ofTabulating the results of a mass diagram isto write all quantities and distances on thediagram, as shown in Figure 3-28. It isalso possible to extract information fromthe mass diagram and put it in a formatthat effectively controls the operation. Onemethod is to prepare a mass diagramanalysis sheet as shown in Figure 3-29.

    The mass diagram has many limitationsthat preclude its use in all earthmovingoperations. At best, it is merely a guide in-dicating the general manner in which theoperations should be controlled. Any at-tempt to get exact quantities and distancesfrom it may be misleading. However, it is agood starting point.

    The mass diagram is most effective whenused to plan operations along an elongatedproject similar to a road, an airfieldrunway, or a taxiway. The haul distancesare along the centerline or parallel to it.However, if the project becomes relativelywide compared to its length, movement ofearth may be transverse as longitudinal,resulting in longer, transverse haul distan-ces and invalidating the mass diagramanalysis.

    The mass diagram is used to analyze onlythe potentiality of balancing within one

    Figure 3-28. Mass diagram showing analysis results

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    phase of a project. For instance, the massdiagram may indicate that the best balanc-ing of a certain portion of a runway will re-quire a haul distance of 2,200 feet alongthe site. However, it may be better tobalance yardage with an adjacent taxiwayin which the haul distance will be only1,200 feet. The mass diagram can dealonly with the runway or the taxiway, notwith both simultaneously.

    The mass diagram assumes that allmaterial excavated in the cut sections is ac-ceptable for use in the embankment sec-

    tions. This is not necessarily true. How-ever, all unacceptable quantities can beeliminated from the earthwork table.

    The mass diagram is applicable to projectsneeding balanced earthwork. Balancingeliminates the double handling of quan-tities. If there is a short distance betweenan acceptable borrow pit and an embank-ment section, it may be more economical touse the borrow pit instead of a long balanc-ing operation, This can be determined by awork or economy. study.

    Figure 3-29. Mass-diagram analysis sheet

    Surveys and Earthwork Operations 3-29