Quantity Calculation Calculation models Copyright 2006 © Nicolai Green Hansen.

Quantity CalculationQuantity Calculation

Calculation modelsCalculation models

Copyright 2006 © Nicolai Green Hansen

Quantity CalculationQuantity CalculationThe quantity or the soil calculation is a The quantity or the soil calculation is a statement of the soil masses that should be:statement of the soil masses that should be:

Digged upDigged up

MovedMoved

RemovedRemoved

Built-inBuilt-in


Quantity CalculationQuantity CalculationThe quantities are used in the project design for:The quantities are used in the project design for:

To create balance between To create balance between removed and build-in quantitiesremoved and build-in quantities

The basis for the tender for the The basis for the tender for the relation between owner and relation between owner and contractorcontractor

Regulation of the tender price (in Regulation of the tender price (in case the real quantities are different case the real quantities are different in relation to the invitation for bids)in relation to the invitation for bids)



Planning of the price calculation, Planning of the price calculation, including mashine calculation (size including mashine calculation (size and working capacity)and working capacity)

Ressource controlling. The right Ressource controlling. The right ressources at the right timesressources at the right times

During the working process to During the working process to control that the Under arbejdets control that the Under arbejdets udførelse at kontrollere at der udførelse at kontrollere at der omsættes de mængder der skalomsættes de mængder der skal



Calculation basis between Calculation basis between contractor and the contract worker contractor and the contract worker teamsteams

Bill demands for down payment Bill demands for down payment from owner to contractorfrom owner to contractor


Quantity CalculationQuantity CalculationFollowing mathematicals methods are shown:Following mathematicals methods are shown:

The prism methodThe prism method

The ramp formulaThe ramp formula

The square grid methodThe square grid method


Truncated pyramidTruncated pyramid

Quantity CalculationQuantity CalculationThe prism methodThe prism method


Section in excavation area

Section in excavation area

New road in terrain

If equivalent sections with distance ”a” is inserted the total volume are:

Quantity CalculationQuantity CalculationThe prism methodThe prism method

””F” means the surface F” means the surface areaarea

Ill. with Ill. with figure:figure:

a= 5ma= 5mFF11=10 m=10 m22

FF22=12 m=12 m22

FF33=16 m=16 m22

FF44=14 m=14 m22

FF55=9 m=9 m22

Ill. with figure:Ill. with figure:

V = V = (10/2+12+16+14+9/2)x(10/2+12+16+14+9/2)x55

V = 258 mV = 258 m33


Quantity CalculationQuantity CalculationThe ramp formulaThe ramp formula

There is some confusion There is some confusion when a gradient of a slope when a gradient of a slope is stated.is stated.


An easy mnemonic rule is to An easy mnemonic rule is to think in fractions.think in fractions.1:2 means therefore ”1 above 1:2 means therefore ”1 above 2” or converted 0,5.2” or converted 0,5.”everything belowe 1 is not ”everything belowe 1 is not steep”steep”

Quantity CalculationQuantity CalculationThe ramp formulaThe ramp formula

Is used among other things for Is used among other things for determination of soil quantities in determination of soil quantities in relation to up- and down ramps in relation to up- and down ramps in building excavations.building excavations.


Quantity CalculationQuantity CalculationRamp formulaRamp formula

Ill. with figure:Ill. with figure:m = 2 (the gradient of the ramp)m = 2 (the gradient of the ramp)n = 1 (the gradient of the slope of the n = 1 (the gradient of the slope of the platform)platform)nn11 = 1 (the gradient of the slope of the = 1 (the gradient of the slope of the ramp)ramp)a = 3 m (the width of the ramp)a = 3 m (the width of the ramp)h = 4 m (the hight of the platform)h = 4 m (the hight of the platform)


Quantity CalculationQuantity CalculationRamp formulaRamp formula

Ill. with Ill. with figure:figure:


V42

63 3 2 1 4

2 12

2 1( )

V = 35 mV = 35 m33

Quantity CalculationQuantity CalculationThe square grid methodThe square grid method


Should a bigger area be reprofiled the Should a bigger area be reprofiled the known square grid method from the known square grid method from the plane topographical levelling is used.plane topographical levelling is used.

Originally terrain

New terrain



Princip:Princip:A square grid with the side lenght of ”a” is inserted.A square grid with the side lenght of ”a” is inserted.

In the corner points the high difference between the originally In the corner points the high difference between the originally terrain and the new terrain are readed.terrain and the new terrain are readed.

h is calculated negative for back filling and positive for h is calculated negative for back filling and positive for excavation soil.excavation soil.

Originally terrain

New terrain



The volume of the soil for each grid can The volume of the soil for each grid can then be determinated by:then be determinated by:


a = 5 m (sidelængden på nettet)a = 5 m (sidelængden på nettet)hh11 = 2,5 m = 2,5 mhh22 = 1,8 m = 1,8 mhh33 = 1,0 m = 1,0 mhh44 = 1,4 m = 1,4 m




V = V = 5522x((2,5+1,8+1,0+1,4)/4)x((2,5+1,8+1,0+1,4)/4)

V = 42 mV = 42 m33

Quantity CalculationQuantity CalculationTruncated pyramidTruncated pyramid



Depth of excavation: h = 3 Depth of excavation: h = 3 mmTop area G = 200 mTop area G = 200 m22

Bottom area g = 100 mBottom area g = 100 m22

3441

)100200100200(3

3

mV

V

Quantity Calculation Calculation models Copyright 2006 © Nicolai Green Hansen.

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