Quantity Calculation
Calculation models
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The quantity or the soil calculation is a statement of
the soil masses that should be:

Digged up

Moved

Removed

Built-in
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The quantities are used in the project design for:

To create balance between removed and
build-in quantities

The basis for the tender for the relation
between owner and contractor

Regulation of the tender price (in case
the real quantities are different in
relation to the invitation for bids)
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The quantities are used in the project design for:



Planning of the price calculation,
including mashine calculation (size and
working capacity)
Ressource controlling. The right
ressources at the right times
During the working process to control
that the Under arbejdets udførelse at
kontrollere at der omsættes de mængder
der skal
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The quantities are used in the project design for:

Calculation basis between contractor and
the contract worker teams

Bill demands for down payment from
owner to contractor
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
Following mathematicals methods are shown:

The prism method

The ramp formula

The square grid method

Truncated pyramid
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The prism method
New road in terrain
Section in
excavation
area
Section in
excavation
area
If equivalent sections with distance ”a” is inserted the
total volume are:
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The prism method
”F” means the surface area
Ill. with figure:
Ill. with figure:
a= 5m
F1=10 m2
F2=12 m2
F3=16 m2
F4=14 m2
F5=9 m2
V = (10/2+12+16+14+9/2)x5
V = 258 m3
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The ramp formula
There is some confusion when
a gradient of a slope is stated.
An easy mnemonic rule is to think
in fractions.
1:2 means therefore ”1 above 2”
or converted 0,5.
”everything belowe 1 is not steep”
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The ramp formula
Is used among other things for determination
of soil quantities in relation to up- and down
ramps in building excavations.
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
Ramp formula
Ill. with figure:
m=2
(the gradient of the ramp)
n =1
(the gradient of the slope of the platform)
n1 = 1
(the gradient of the slope of the ramp)
a = 3 m (the width of the ramp)
h = 4 m (the hight of the platform)
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
Ramp formula
Ill. with figure:
2
V 
 3 3  2 1 4 2  1   ( 2  1)


6
2 
4
V = 35 m3
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The square grid method
Should a bigger area be reprofiled the known
square grid method from the plane
topographical levelling is used.
Originally terrain
New terrain
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The square grid method
Princip:
A square grid with the side lenght of ”a” is inserted.
In the corner points the high difference between the originally terrain
and the new terrain are readed.
h is calculated negative for back filling and positive for excavation soil.
Originally terrain
New terrain
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The square grid method
The volume of the soil for each grid can then be
determinated by:
Ill. with figure:
a = 5 m (sidelængden på nettet)
h1 = 2,5 m
h2 = 1,8 m
h3 = 1,0 m
h4 = 1,4 m
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
The square grid method
Ill. with figure:
V = 52x((2,5+1,8+1,0+1,4)/4)
V = 42 m3
Copyright 2006 © Nicolai Green Hansen
Quantity Calculation
Truncated pyramid
Ill. with figure:
Depth of excavation: h = 3 m
Top area G = 200 m2
Bottom area g = 100 m2
3
V   ( 200  100  200 100)
3
V  441m
3
Copyright 2006 © Nicolai Green Hansen