9. Earthwork and Mass-Haul Diagram

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Earthwork

EarthworkActivities involve:1. Excavating2. Loading3. Hauling4. Placing5. Compacting6. Grading 7. Finishing

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Earthwork Earthworks of highways. Earthworks of highways.

Earthwork activities.Earthwork quantities and calculations.

Area of cross sections. Determination of volume of earthworks by appropriate methods.

The mass haul diagram The mass‐haul diagram. Determination of the planned movement of materials. Calculation of the mean haul distance and the corresponding cost.

Earthwork Highways involve considerable amount of earthwork.g yEarthwork is simply the quantity of material to be moved or put in place to convert the natural condition and configuration within the ROW of the road to the section and grades described in the plans.

Classification of earthwork operationsClearing and grubbingExcavation

Roadway and drainage excavationExcavation for structuresBorrow excavation

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Earthwork Clearing and grubbingClearing and grubbing

The first operation to be undertaken in road projects.Definition: the removal of trees, stumps, roots, down timber, rotten wood, rubbish and other objectionable materials form an area marked on the plans.

Clearing refers to the removal of materials above existing ground surface and ground surface, and Grubbing means the removal of roots, stumps and similar objects to a nominal depth below the surface.

Clearing and grubbing constitute a single contact item that includes the removal of topsoil to a shallow depth.

Earthwork Excavation: the process of loosening and removing earth or

k f i i i l i i i d i i rock from its original position in a cut and transporting it to a fill section or to a waste deposit.

Roadway and Drainage Excavation.the excavation and grading of the roadway and ditches, including the removal and disposal of all excavated material and all work needed for the construction and completion of the cuts, embankments, slopes, ditches, approaches, intersections and similar portions of the work.

Excavation for structures.the excavation of material in order to permit the construction of pipe culverts, concrete box culverts, foundations for bridges, retaining walls, and practically all other structures that may be required in a particular job.

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Earthwork Excavation: the process of loosening and removing earth or p g grock from its original position in a cut and transporting it to a fill or to a waste deposit.

Borrow excavation.when sufficient material for the formation of embankments and other elements of the roadway structure is not available from excavation performed with in the limits of the right‐of‐way, additional suitable material is generally taken from borrow pits.additional suitable material is generally taken from borrow pits.

.

Earthwork Classification of Excavation

Rock excavationmaterial that cannot be excavated without blasting or the use of rippers and all boulders or other detached stones.

Common excavationexcavation and disposal of all materials of whatever character encountered in the work, which are not classified as rock, borrow.

Borrow excavationexcavation of approved material required for construction of pp qembankments.

Unsuitable excavationthe removal and disposal of deposits of saturated or unsaturated mixtures of soil and organic matter not suitable for embankment material.

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Earthwork Haul and Overhaul

Free Haul: when material is excavated it will be moved over a certain di t f f h NB O l th ti t i id t th distance free of charge. NB: Only the excavation cost is paid, not the transportation cost of the material.

Free Haul Distance (FHD): Distance over which excavated material is moved free of charge (usually 300 – 500 m, but ranges 150 – 900 m).

Overhaul: is defined as the distance over which the excavated material must be hauled less the free haul distance. NB: there is extra payment for transporting material in addition to excavation cost.

Overhaul distance (OHD): Distance over which excavated material is transported beyond the free‐hall distance. OHD = HD ‐ FHD

Economic Overhaul (EOH): Economic overhaul is a distance beyond which it is not economic to overhaul.

Limit of Economic Overhaul (LEH) ‐ is the distance beyond which it is uneconomic to overhaul plus the free haul distance. LEH = EOH + FHD

Earthwork Haul and Overhaul

Haul – is equal to the sum of the products of each volume of material and the distance through which it is moved.

Waste – is the volume of material, which must be exported from a section of the road due to a surplus or unsuitability.

Borrow – is that volume of material, which must be imported in to section of the road due to a deficiency of (suitable) material.

LCC eohexc ⋅+= fill tomove &cut from material excavated of m 1 ofCost 3

.EOH FHDLEH

CCEOH

EOHLCCLCC

CC

oh

bor

eborexceohexc

borexc

+=⇒≤

=+=⋅+

+=

distance, haul economic Total

]:NB[:hauling-over oflength economical Maximum

fill toplace & borrow waste,material, excavated of m 1 ofCost 3

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Earthwork

FILL (Embankment)Estimation of Earthwork Quantities

The estimation of the quantity of material which must be excavated (cut), and the

CUT (Excavation)

CUT and FILL

quantity of material required to raise the elevation of the existing ground (fill), is very useful in the development of a cost estimate for road projects.

Earthwork

FILL (Embankment)Estimation of Earthwork Quantities

The estimation of the quantity of material which must be excavated (cut), and the

CUT (Excavation)

CUT and FILL

quantity of material required to raise the elevation of the existing ground (fill), is very useful in the development of a cost estimate for road projects.

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Earthwork Estimation of Earthwork Quantities

Soil Volume ChangesSoil Volume ChangesExcavated in‐situ material used in embankments or fills may swell or shrink. It is important to determine the properties of a material in order to evaluate how these properties will affect the earthwork volume estimates. Swell / bulking

Shrinkage

Natural or In‐situ state

Disturbed state Compacted state

1.0 1.25 0.90

Bank Loose Compacted


Soil Volume ChangesSoil Volume Changes• Material volume increases during excavation• Decreases during compaction• Varies with

• Soil type • Fill depth

hi h fill %

Swell:• Excavated rock 5 – 25%

• high fill: 10 – 15 %• shallow fill: 20 – 25 %

A1A2

A3Shrinkage:• Light soil

• Ordinary soil 10 – 20% • Swampy soil 20 – 40%

• Heavy soil upto 10%

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Earthwork Soil Volume Changes

1001densityBank(%)S ll ⎟⎞

⎜⎛

swell11

densityBank density LooseFactor Load

100density Compacted

densityBank 1(%) Shrinkage

1001density LoosedensityBank (%) Swell

+==

×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

Factor Shrinkage VolumeBank Volume Compacted

Factor Load Volume LooseVolumeBank

Shrinkage1density Compacted

densityBank Factor n)(Compactio Shrinkage

×=

×=

−==


Estimation of the area of cross‐section as a cut and fill.The distance between these areas, l (or L)Volume of earthwork

Cut volume andFill volume.

Area of cross sectionArea of cross sectionCoordinate methodTrapezoidal ruleSimpson’s rule

A1A2

A3

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Earthwork Calculation of cross‐sectional areasCalculation of cross sectional areas

Coordinate method:With the coordinates of all the corners of a cross‐section known, the area may be computed by means of the coordinate method.The point of intersection of the center of formation with the centerline of the road (c) is used as the origin.

The cut above the formation are written as plus (+) and those below as minus (‐). The distances to the right are written as plus (+) and those to the left as minus (‐).


Coordinate method:

The products along the marked diagonals are all positive and the product along the unmarked diagonals are all negative

1

1

6

6

5

5

4

4

3

3

2

2

1

1

XY

XY

XY

XY

XY

XY

XY

the product along the unmarked diagonals are all negative. The difference gives double area of the section.

Area, A

( ) ( )[ ]nnnn YXYXYXYXXYXYXYXYA 1433221143322121 −− ++++−++++= LL

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Trapezoidal rule:assumes that if the uniform interval (b) between the offsets is small, the boundary can be approximated to a straight line between the offsets.

211 )(21 ⋅+= bhhA

( )[ ]1321

322

211

22

)(21)(21

−+++++=

⋅+=+

nn hhhhhbA

bhhAbhhA

L

h1 hnh2 ……

b


Simpson’s rule:assumes that instead of being made up of a series of straight lines the boundary consists of a series of parabolic arcs.

54342

32121

)4(3

)4(3

++=+

++=+

hhhbAA

hhhbAAh1 hnh2 ……

( ) ( )[ ]1422531

54342

423

)(

−− +++++++++= nnn hhhhhhhhbA LL

… and n is an odd number

b

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Earthwork Computation of Volumes

Average end‐area methodbased on the volume of a right prism whose volume is equal to the average end area multiplied by the length.

Prismoidal methoda prismoid is a solid whose ends are parallel and whose sides are plane surfaces.

.A1

A2

A2

Computing VolumesA2A d th d

L

A1

Average end areas method

V = ½ (A1 + A2)L

Where• A A : end cross section areas

( )[ ]1321 22 −+++++= nn AAAAALV L

• A1, A2: end cross-section areas• L: distance between cross-sections

ExampleA0 = 39.2 m2 A1 = 36.5 m2 L = 20 mV = ½ (39.2 m2 + 36.5 m2)(20 m) = 757 m3

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Computing VolumesP i id l th d APrismoidal method

V = L/6 (A1 + 4M + A2)

L

A1

A2M

( ) ( )[ ]1422531 262 −− +++++++++= nnn AAAAAAAALV LL

and n is an odd number Where• A1, A2: cross-section areas• M: area of middle section• L: distance between cross-

sections

… and n is an odd number

EarthworkTabulation of earthwork quantitiesTabulation of earthwork quantities

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Earthwork Mass‐Haul Diagrams

A Mass Haul Diagram is a continuous curve representing the cumulative volume of earthwork along the linear profile of a roadway or airfieldMass diagrams are extremely useful in determining the most economical distribution of material

Horizontal stationing is plotted along the x‐axisNet earthwork values are plotted along the y‐axisp g y

cumulative earthwork from the origin to that Pointupward sloping curves (rising left to right) indicate a cutdownward sloping curves (falling left to right) occur in a fill sectionpeaks indicate a change from cut to fill and valleys occur when the earthwork changes from fill to cut

Earthwork Mass‐Haul Diagramsg

Any horizontal line which joins points on the curve where balance is achieved is called a balance line. The FHD and/or the limit of economic overhaul are established and plotted on the mass haul diagram. A vertical break between any two balance lines indicates an area where balance does not occur. At these breaks a shortfall (borrow ) or excess (waste ) material exists. A positive value at the end of the curve indicates that a waste operation will be the net resultA negative value at the end of the curve indicates that borrow is required to complete the fill

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EarthworkMass‐Haul Diagram Any horizontal line on mass diagram is a

balance line – within balance line cut = fill

Fill areas Cut areas

Profile

Ele

vatio

n

Mass diagram

Volu

me

EarthworkMass‐Haul Diagram Borrow

Free haul

Waste

Overhaul

Profile

Ele

vatio

n Grade line

Mass diagram

Volu

me

Free Haul

Free HaulLEH LEH

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Earthwork Calculation of Mass‐haul diagrams manually

Compute the net earthwork values for each station, applying the appropriate shrink factorNet cuts have a positive value, net fills have a negative valueThe value (earthwork quantity) at the first station (origin) = 0Plot the value of each succeeding station which equals the cumulative value to that pointIdentify the resulting balanced sections, which are bounded by points that intersect the x‐axish l l h f h l l h fThe scale length of a horizontal line connecting the centre of gravity

of the cut and fill sections is the average length of haul within that balanced sectionDetermine earthwork volumes within each balanced sectionDetermine whether there is an overall balance, waste or if borrow is required

Mass‐Haul Diagram

Between Stations 0 + 00 and 0 + 132, cut and fill equal each other, d l hdistance is less than FHD of 200 m

Note: Figure NOT to scale!

Source: Wright, 1996

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Mass‐Haul DiagramBetween Stations 0 + 132 and 0 + 907, cut and fill equal each other, but distance is greater than either FHD of 200 m or LPH of 725 m

Distance = [0 + 907] – [0 + 132] = 775 m


Mass‐Haul Diagram

Between Stations 0 + 179 and 0 + 379, cut and fill equal each other, di t FHD f distance = FHD of 200 m Treated as freehaul


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Mass‐Haul Diagram

Between Stations 0 + 142 and 0 + 867, cut and fill equal each other, distance = LPH of 725 m


Mass‐Haul Diagram

Material between Stations 0 + 132 and 0 + 142 becomes waste and material between stations 0 + 867 and 0 +907 becomes borrow


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Mass‐Haul Diagram

Between Stations 0 + 970 and 1 + 170, cut and fill equal each other, distance = FHD of 200 m


Mass‐Haul Diagram

Between Stations 0 + 960 and 1 + 250, cut and fill equal each other, distance is less than LPH of 725 m


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Mass‐Haul Diagram

Project ends at Station 1 + 250, an additional 1200 m3 of borrow is required


EarthworkUse of Mass‐Haul Diagramg

If mass haul is drawn for each trial grade line it can be used for selecting the most economical gradient which balance the cut and fill.Once the formation level is designed, it can be used to indicate the most economical method of moving the earth around the project and a good estimate of the overall cost of h h i b l l dthe earth moving can be calculated.The required volumes of material are known before construction begins enabling suitable plant and machinery to be chosen and sites for spoil heaps and borrows pits to be located and direction of haul to be established.

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EarthworkExample:

Th t b l t d d t i b l i The tabulated data given below is the volume of cut and fill for a given road bed preparation.

Costs:Excavation Ce = 3.00 Birr /m3

Borrow Cb = 4.00 Birr /m3

Overhaul Coh = 1.35 Birr /m3– station [1‐station = 100 m][ ]

FHD = 300 m

a) Draw the mass curve and the profile

b) Find out the total estimate of cost of the project

0 0

1.0

2.0

3.0

4.0

me (x10

3 )

Earthwork

Profile

‐3.0

‐2.0

‐1.0

0.0

0 200 400 600 800 1000 1200 1400 1600 1800

Volum

Station

Mass‐Haul 3.0

4.0

5.0

103 )

Mass‐Hauldiagram

‐4.0

‐3.0

‐2.0

‐1.0

0.0

1.0

2.0

0 200 400 600 800 1000 1200 1400 1600 1800

Cumm. Volum

e (x1

Station

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Mass‐Haul Diagram

1 0

0.0

1.0

2.0

3.0

4.0

0 200 400 600 800 1000 1200 1400 1600 1800Volume (x10

3 )280.2 m 186.4 m

Borrow

1 0

2.0

3.0

4.0

5.0

me (x10

3 )

‐3.0

‐2.0

‐1.0 0 00 00 600 800 000 00 00 600 800V

LEH

FHD Waste

‐4.0

‐3.0

‐2.0

‐1.0

0.0

1.0

0 200 400 600 800 1000 1200 1400 1600 1800

Cumm. V

olum

Station

Waste Borrow

FHD

Alternative 1

:loop1m 600 m 300 m 300

m 300 stations 3sta-birr/m35.1

birr/m0.4

st

3

3

=+=+=

=====

FHDEOHLEHCCEOHL

oh

bore

EF][linem300FHDdistance,haulFree

:loop 2stations) (1.7 m 170 300 - 470 AOHD distance, haul-over Average

m 470 stations 4.7 AEHD distance, hauling economic AverageCD] [linem 600 LEH haul, ecoomic ofLimit AB] [linem 300 FHD distance, haul Free

:loop 1

nd

=

====

==

distance. haul free than theless is line balance The -

station) 3 ( haul freein with is loop whole thebecause haulingover No -:loop 3station) (0.4 m 40 300 - 340 AOHD distance, haul-over Average

m 340 stations 3.4 AEHD distance, hauling economic AverageGH] [linem 380 LEH haul, ecoomic ofLimit EF][linem300 FHD distance, haul Free

rd <

====

=

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300, 4.0400, 4.2

500, 3.53.5

4.0

4.5

Mass‐Haul Diagram

FHD = 300 m0 1A B

Qty Dist QxD1.0 550 550

100, 2.0

200, 3.2

600, 2.0

1 0

1.5

2.0

2.5

3.0

Cumm. Volum

e (x10

3 )

550 m

410 m

310 m

1.0

1.2

0.1A B

C D

1.0 550 5501.2 410 4920.1 310 312.3 1073

c.g. = 466.5 m4.7 stations

0, 0.0 700, 0.00.0

0.5

1.0

0 100 200 300 400 500 600 700 800

Station

LEH = 600 m

Waste Borrow

600, 2.0 1200, 2.0

1.0

2.0

3.0

3 )

Mass‐Haul Diagram

D

500mG' H'

700, 0.0

800, ‐1.8

1000, ‐1.4

1100, 0.4

‐2.0

‐1.0

0.0

0 200 400 600 800 1000 1200 1400

Cumm. Volum

e (x10 Borrow

E F

G H0.9

AEHD = 340 m

380 m

FHD = 300 m

Alternative 2

900, ‐3.4

‐4.0

‐3.0

Station

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EarthworkCost summary

Excavation costExcavation cost

Borrow cost

( )Birr650,40

Birr/m00.3m100.40.24.315.4 333

=××+++=

Birr0004Birr/m00.4m100.1 333

=××=

Total Cost= 40,650 + 4,000 + 5,765= 50, 415 Birr

Overhaul cost

Birr000,4

( ) ( )[ ]Birr765,5

StaBirr/m35.1Stam1009.05.00.13.37.1 333

=−×−×−+−=

Alternative 2

AB] [linem 300 FHD distance, haul Free

:loop 1st

=

400t ti4 0AEHDdi th liiA]H'G' [linem 500 LEH haul, ecoomic ofLimit

EF] [linem 300 FHD distance, haul Free

:loop 2stations) (1.7 m 170 300 - 470 AOHD distance, haul-over Average

m 470 stations 4.7 AEHD distance, hauling economic AverageCD][linem600LEH haul, ecoomicofLimit

nd

==

====

=

distance. haul free than theless is line balance The -

station) 3 ( haul freein with is loop whole thebecause haulingover No -:loop 3station) (1.0 m 100 300 - 400 AOHD distance, haul-over Average

m400stations4.0AEHDdistance,hauling economicAverage

rd <

====

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Mass‐Haul Diagram

1 0

0.0

1.0

2.0

3.0

4.0

0 200 400 600 800 1000 1200 1400 1600 1800Volume (x10

3 )280.2 m 186.4 m

No Borrow

1 0

2.0

3.0

4.0

5.0

me (x10

3 )

‐3.0

‐2.0

‐1.0 0 00 00 600 800 000 00 00 600 800V

LEH

FHD

LEH Waste

‐4.0

‐3.0

‐2.0

‐1.0

0.0

1.0

0 200 400 600 800 1000 1200 1400 1600 1800

Cumm. V

olum

Station

Waste Borrow

FHD

W

EarthworkCost summary (Alternative 2)

Excavation costExcavation cost

Borrow cost

( )Birr650,40

Birr/m00.3m100.40.24.315.4 333

=××+++=

( )Borrow No0=

Total Cost= 40,650 + 0 + 7,844= 48,494 Birr

Overhaul cost( ) ( )[ ]

Birr844,7StaBirr/m35.1Stam10)9.0(0.10.10.13.37.1 333

=−×−×−−+−=

Documents

9. Earthwork and Mass-Haul Diagram