Surveying BEC102 7 - Earthwork Volume

8/13/2019 Surveying BEC102 7 - Earthwork Volume

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EARTHWORKEARTHWORK

COMPUTATIONSCOMPUTATIONS

SrSr SITISITI NUR ALIAA ROSLANNUR ALIAA ROSLAN

KLIUCKLIUC


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IntroductionIntroduction

Estimation of areas and volumes is basic to mostEstimation of areas and volumes is basic to mostengineering schemes, e.g. Roads, tunnels andengineering schemes, e.g. Roads, tunnels andreservoirs.reservoirs.

The excavation and hauling of material on suchThe excavation and hauling of material on suchschemes is the most significant and costly aspectschemes is the most significant and costly aspectof the work.of the work.

Area are required in connection of purchase orArea are required in connection of purchase orsale of land or subdivision of land.sale of land or subdivision of land.

Earthwork volumes enable route alignment to beEarthwork volumes enable route alignment to belocated at such lines and levels that cut and filllocated at such lines and levels that cut and fillare balances as far as practicable.are balances as far as practicable.


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AREASAREAS

Computation of areas may be based on dataComputation of areas may be based on datascaled from plans or drawings, or direct from thescaled from plans or drawings, or direct from thesurvey field data.survey field data.

The most common method of measuring areasThe most common method of measuring areasfrom plan is to use a planimeter.from plan is to use a planimeter.


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Triangular EquationTriangular Equation

i)i) Area =Area = [S(S[S(S--a)(Sa)(S--b)(Sb)(S--c)]c)]

where; S = (a+b+c)where; S = (a+b+c)

ii) Area = (height x width)ii) Area = (height x width)


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Irregular AreasIrregular Areas

A sheet of gridded tracing material maybeA sheet of gridded tracing material maybesuperimposed over it and the number of squaressuperimposed over it and the number of squarescan be counted. The proportions of the squarescan be counted. The proportions of the squares

cut by the irregular boundaries can be estimated.cut by the irregular boundaries can be estimated. When the areas is irregular, boundaries can beWhen the areas is irregular, boundaries can be

reduced to straight lines using givereduced to straight lines using give--andand--taketakelines. The areas taken from the total arealines. The areas taken from the total areabalance out with extra areas given.balance out with extra areas given.


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Area of a Trapezoid

Area = h/2 * (b1 + b2)

b1

b2

h


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Note:

1. This rule assumes a curved boundary.

2. Therefore more accurate than the trapezoidal rule.

3. If the boundary was a parabola, the formula would be exact.

4. The equation requires an odd number of ordinates and even number of

ordinates.


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Area ABCD = Area BBCC + Area CCDD Area BBAArea ADD

= A1 + A2 A3A4

A1 =(XB-XA+XC-XA)(YB-YC)

=(XB+XC-2XA)(YB-YC)

=(XBYB-XBYC+XCYB-XCYC-2XAYB+2XAYC)

A2=(XC-X

A+X

D-X

A)(Y

C-Y

D)

=(XC+XD-2XA)(YC-YD)

=(XCYC-XCYD+XDYC-XDYD-2XAYC+2XAYD)

A1+A2=(-2XAYB-XBYC-XCYD-XDYD+YBXC+YBXB+YCXD+2YDXA)

A3=(XB-XA)(YB-YA) =(XBYB-XBYA-XAYB+XAYA)A4=(XD-XA)(YA-YD) =(XDYA-XDYD-XAYA+XAYD)

A3+A4=(-XAYB+XBYB-XBYA+XDYA-XDYD+XAYD )

Area ABCD=(-XAYB-XBYC-XCYD-XDYA+YAXB+YBXC+YCXD+YDXA )

Area Calculation using Coordinates

X

Y

A

B

C

D

B

D

C


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Area Calculation using Coordinates

A

B

C

D

Area ABCD=(-XA

YB-X

BY

C-X

CY

D-X

DY

A+Y

AX

B+Y

BX

C+Y

CX

D+Y

DX

A)

2xArea =[-XAYB-XBYC-XCYD-XDYA

+YAXB+YBXC+YCXD+YDXA]

A XA YA

B XB YB

C XC YC

D XD YD

A XA YA

Negative Terms

Posit ive Terms


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Area by CoordinatesArea by Coordinates


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Exercise.Exercise.


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VOLUMEVOLUME

CALCULATIONSCALCULATIONS


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VOLUME CALCULATIONSVOLUME CALCULATIONS

Excavation, removal and dumping of earthExcavation, removal and dumping of earthis a frequent work in Civil Engineeringis a frequent work in Civil Engineeringworks.works.

In each case, payments for labor and planIn each case, payments for labor and plan

are based on the volume of materialare based on the volume of materialhandled.handled.

Therefore engineers in charge should beTherefore engineers in charge should beable to make good estimates of volumesable to make good estimates of volumesof earthworks.of earthworks.

There are three general methods forThere are three general methods forcalculating earthworks.calculating earthworks. By crossBy cross--sectionssections By contoursBy contours By spotBy spot--heightheight


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Volumes from CrossVolumes from Cross--SectionsSections

CrossCross--sections are taken at right angles to somesections are taken at right angles to someline runs longitudinally through the earthwork.line runs longitudinally through the earthwork.

Commonly used for long narrow works such asCommonly used for long narrow works such as

roads, railways, canals,embankments and piperoads, railways, canals,embankments and pipeexcavations.excavations.

Depth at center line (or height in

case of embankment) = h units

Formation width = b units.

Side width = w

Horizontal projection for every

single unit vertical rise = m units.

Area of cross section

= [ 2 ( b/2 + mh) + b ] h

= h(b + mh)


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1.1. Sections with crossSections with cross--fallfall

In this case the existing ground has a cross fall orIn this case the existing ground has a cross fall or

transverse gradient relative to the centre line andtransverse gradient relative to the centre line andthe side width are not equal because the sectionthe side width are not equal because the sectionis not symmetrical about the centre line.is not symmetrical about the centre line.

Area = 1/2m [(b/2 + mh)(w1 + w2)Area = 1/2m [(b/2 + mh)(w1 + w2) b2/2]b2/2]


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2.2. Sections part in cut and partSections part in cut and part

in fillin fill


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3.3. Cross sections of three levelCross sections of three level

sectionssections


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4.4. Irregular cross sectionsIrregular cross sections


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Computation of volumesComputation of volumes

After computing crossAfter computing cross--sectionalsectionalareas at different sections along theareas at different sections along thelongitudinal line, volumes can belongitudinal line, volumes can becomputed using one the followingcomputed using one the followingmethods.methods.

a)a) Mean areasMean areas

b)b) End areasEnd areasc)c) Prismoidal formula (more accurate)Prismoidal formula (more accurate)


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(a) Volumes by Mean Areas(a) Volumes by Mean Areas

The volume is determined by multiplyingThe volume is determined by multiplyingthe mean of the crossthe mean of the cross--sectional areas bysectional areas bythe distance between the end sections.the distance between the end sections.

If the areas are AIf the areas are A11, A, A22, A, A33, , A, , Ann--11, A, Annand the distance between sections Aand the distance between sections A11 andandAAnn is L, thenis L, then

This method is not very accurate.This method is not very accurate.

x


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Volumes from Contour LinesVolumes from Contour Lines

Volumes are calculated for horizontalVolumes are calculated for horizontalareas enclosed by contour lines.areas enclosed by contour lines.

Due to high cost of contouring large areas,Due to high cost of contouring large areas,

the method is not commonly used.the method is not commonly used. Where accurate contours are available,Where accurate contours are available,

e.g. Reservoir sites, they can bee.g. Reservoir sites, they can beconveniently used.conveniently used.

A planimeter can be used to obtain theA planimeter can be used to obtain theareas enclosed by contour lines (from theareas enclosed by contour lines (from theplan).plan).

Volumes can be calculated using the endVolumes can be calculated using the end--areas formula or prismoidal formula.areas formula or prismoidal formula.


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Volumes from Spot LevelsVolumes from Spot Levels This method is used for large open excavationsThis method is used for large open excavations

for tanks, basements etc and for ground levellingfor tanks, basements etc and for ground levellingoperations such as playing fields and buildingoperations such as playing fields and buildingsites.sites.

First the area should be divided into squares orFirst the area should be divided into squares orrectangles and then the levels should be taken atrectangles and then the levels should be taken ateach of these corner points.each of these corner points.

Volume within each square = plan area x averageVolume within each square = plan area x averageof the depth of excavation or fill.of the depth of excavation or fill.

The volume of cut under the first square =

d2/4 (ha + hb + hc + hd)

where,

Length of side of square = d

OR

d x l . (ha + hb + hc + hd)/4where,

d and l are the side dimensions


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ExerciseExercise


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ANSWERANSWER

VolumeVolume = A= A22/4 [/4 [(h x n)](h x n)]

= (10 x 10)/4 [= (10 x 10)/4 [(h x n)](h x n)]

= (100)/4 (58.44)= (100)/4 (58.44)

= 25 (58.44)= 25 (58.44)

= 1461 m3= 1461 m3


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MASS HAUL DIAGRAMMASS HAUL DIAGRAM

MassMass--haul diagram is useful in planning andhaul diagram is useful in planning andconstruction of railways and roads where largeconstruction of railways and roads where largevolumes of earthwork have to be handled.volumes of earthwork have to be handled.

Aggregate volumes in cubic metres are plottedAggregate volumes in cubic metres are plotted

along the longitudinal section.along the longitudinal section. When evaluating the aggregate volumes, cuttingsWhen evaluating the aggregate volumes, cuttings

are taken as positive and fills are taken asare taken as positive and fills are taken asnegative.negative.

In plotting the massIn plotting the mass--haul curve, positive volumeshaul curve, positive volumes

are plotted above the base line and total negativeare plotted above the base line and total negativebelow it.below it.


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After excavation most materials increaseAfter excavation most materials increasein volumein volume BulkingBulking

After reAfter re--compacted by roller or othercompacted by roller or othermeans, soils occupy less volume thanmeans, soils occupy less volume than

original volumeoriginal volume ShrinkageShrinkage


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HaulHaul

Free haulFree haul In the bill of quantities, unitIn the bill of quantities, unitprice for excavation will include forprice for excavation will include fortransporting the material a certaintransporting the material a certain

specified distance (say 0.5km). Thisspecified distance (say 0.5km). Thisdistance is known as the free haul.distance is known as the free haul.

OverhaulOverhaul If the material has to beIf the material has to bemoved a greater distance than the freemoved a greater distance than the freehall, the extra distance is known ashall, the extra distance is known as

overhaul.overhaul. HaulHaul Volume of cut multiplied by theVolume of cut multiplied by the

distance between centroids of cutting anddistance between centroids of cutting andthe embankment it forms.the embankment it forms.

Surveying BEC102 7 - Earthwork Volume

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