HIGHWAY GEOMETRIC DESIGN6.0. EARTHWORK COMPUTATIONS

6.1. INTRODUCTIONEarthworks are engineering works that result from moving and/or processing of large amounts earth material (soil or rock)Earthworks are done to reshape the topography/existing terrain to achieve required road design levelsInvolve cutting and fillingCutting involves excavating earth material from a given location to achieve desired levels/gradesFilling involves moving excavated material/additional earth material to a given location to achieve desired levels/grades

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6.1. INTRODUCTION**

6.1. INTRODUCTIONApplications of Earthworks :Road worksRailwaysIrrigation projects (dams, canals, etc)etcEarthworks constitute a large & costly item of many road projectsNeed to determine earthwork quantities involved in a given road projectDistance through materials will be moved (haulage distance)Unit of calculation: m3**

6.2. EARTHWORK COMPUTATIONS- AREASAreas are determined firstCalculated area is based on cross-sections which are in turn based on field data collected during detailed survey of proposed route/highway/road

a). Areas from triangle:Area, A = (base, B x height of triangle, H); height of triangle is measured perpendicular to its base

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6.2. EARTHWORK COMPUTATIONS- AREASa). Areas from triangle:OR:

OR:

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6.2. EARTHWORK COMPUTATIONS- AREASb). Cross coordinate method:Standard coordinates of the cross-section are used to compute the area

North coordinates of a given point are multiplied with east coordinates for the next point moving clockwise across the figure, & summation of products done (X1)East coordinates of a given point are multiplied with north coordinates for the next point moving clockwise across the figure, & summation of products done (X2)Difference: X1- X2 = 2 (Area required)2xArea = (N1E2 + N2E3 + N3E4 +........+ NN-1EN+ NNE1) - (E1N2 + E2N3 + E3N4 +........+ EN-1NN+ ENN1)

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6.2. EARTHWORK COMPUTATIONS- AREASb). Cross coordinate method:

Area of ABC = Area of ABQP + Area of BCRQ Area of ACRP

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6.2. EARTHWORK COMPUTATIONS- AREASb). Cross coordinate method:

Area of ABQP:

Area of BCRQ:

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6.2. EARTHWORK COMPUTATIONS- AREASb). Cross coordinate method:

Area of ACRP :

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6.2. EARTHWORK COMPUTATIONS- AREASb). Cross coordinate method:

Area of ABC = Area of ABQP + Area of BCRQ Area of ACRP

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6.2. EARTHWORK COMPUTATIONS- AREASc). Graphical method:Squares & parts of squares covering a given cross section are countedGiven the plan scale, area per square is computed & hence total area can be computedA squared paper is laid over the cross section

d). Trapezoidal ruleAssumption: if interval between offsets is small, the boundary can be estimated to a straight line between offsets

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6.2. EARTHWORK COMPUTATIONS- AREASd). Trapezoidal rule

Generally, area A:

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6.2. EARTHWORK COMPUTATIONS- AREASe). Simpsons ruleAssumption: Boundary consists of series of parabolic arcs instead of straight lines

Offsets are considered in sets of three

Generally, area A =L/3(O1+ON+4even offsets+2 remaining odd offsets), N= number of offsets.

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6.2. EARTHWORK COMPUTATIONS- AREASf). PlanimeterMechanical device for determining areas for irregular plane figuresConsists of a tracing point, measuring/integrating unit & a pole blockArea is obtained when tracing point is moved around perimeter of the figure in a clockwise direction

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PLANIMETER:**

6.3. EARTHWORK COMPUTATIONS- VOLUMESa). End area method (Average end area):Cross sections are taken at fixed interval, LIf areas at the two ends of the length being A1 & A2

Average area:

Volume of earthworks:

If there are n cross sections, then total volume:

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6.3. EARTHWORK COMPUTATIONS- VOLUMESCalculate the area between two end areas, 100 ft apart

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6.3. EARTHWORK COMPUTATIONS- VOLUMESCalculate the area between two end areas, 100 ft apart

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6.3. EARTHWORK COMPUTATIONS- VOLUMESb). Prismoidal formulaVolume between a series of cross sections at fixed interval, L is approximated to a volume of a prismoidPrismoid= a solid figure with plane parallel ends & plane sides

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6.3. EARTHWORK COMPUTATIONS- VOLUMESb). Prismoidal formulaFor 3 cross sections:

If A4, A5 were added then:

Volume for 1 to 5 sections:

In general total volume:

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6.4. MASS HAUL DIAGRAMGraphical representation of amount of earth to be cut & filled along a proposed routeDiagram gives:Balance pointsDirection of movement of earth (haul) & length of haulAmount of earth to be hauled from one location to anotherBulking & shrinkage of materialsSome materials increase in volume when excavated & compacted (bulking)Others (gravel, clay) decrease in volume (shrinkage)Need to adjust volumes for bulking & shrinkageTypical values: Rock 1.3 (bulking); sand, clay- 0.9 (shrinkage)

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6.4. MASS HAUL DIAGRAM

**CutFillBorrow

6.4. MASS HAUL DIAGRAMIn general:Cut volume of excavation for a given cutFill volume of material to be added to an existing terrain to achieve desired levelWaste volume of material that is required to be hauled off siteBorrow volume of material that is required to be brought on site to meet fill deficitWithin a cut, the curve rises from left to rightWhilst within a fill, the curve falls from left to right

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6.4. MASS HAUL DIAGRAM

**CutFillBorrow

6.4. MASS HAUL DIAGRAMA peak on the curve represents a point where the earthwork changes from cut to fillWhen a horizontal line (FG) intersects the curve at two or more points, the accumulated volumes at these points are equal Length of balance line=haulage distance between sections

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6.4. MASS HAUL DIAGRAM**If excess cut:Greater embankment widthGreater embankment heightFlatter side slopesIf deficit of fill:Deeper cuttingWider cuttingImport/borrow material

However, need to consider cost & physical constraints when considering the potential of the above

EARTHWORK COMPUTATIONS- VOLUMESHomeworkCross sections at 30m interval have been drawn at a scale of 1:200 horizontal and 1:20 vertical. The measured areas of cut and fill (in cm2) are shown below. Determine the total amount of cut and fill using the end area method in m3. Ignore any bulking and shrinkage

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Cross section1234567Cut area (cm2)201052Fill area (cm2)---4122030

*-Cross sections = vertical profiles taken at right angles to the survey centreline.-Every cross section is an area formed by the subgrade, the side slopes, and theoriginal ground surface.*-N must be an odd number for the Simpsons rule to apply**********