Transcript SPECIFIC GRAVITY - spin.mohawkc.on.ca

SPECIFIC GRAVITY
aka Relative Density
How specific is gravity anyway?
or How dense are your
relatives?
What is Specific Gravity?
It’s just the density of any
material
relative
to
(divided
by)
The density of any material is
the
density
of
water
just its mass divided by its
volume
We measure the volume of any
material by finding its mass in
air and water
Archimedes figured out how to find
Back
in 200
BC weird-shaped
in Greece…
the volume
of any
object…
…its volume is equal to the
volume of water that it
displaces when immersed in
water
In the lab we can weigh an
object in air and then in water
or use a pycnometer
For Coarse Aggregate:
we measure:
A = Oven dry mass of the sample (kilograms)
B = Mass of SSD sample in air (kilograms)
C = Mass of SSD sample in water (kilograms)
and then calculate:
BA
wa or Abs 
 100%
A
GSSD
B

BC
GASTM
A

BC
GAPPARENT
A

AC
NOTE:
Mass of water displaced(kg)
Volume (m ) 
Density of water(kg/m3 )
3
Mass(kg)
Mass(kg)
Density 

3
Volume(m ) Mass of water displaced(kg)
Density of water(kg/m3 )
Mass(kg) Density of water(kg/m3 )
Density 
Mass of water displaced(kg)
for specific gravity, divide density by the density of water...
Mass(kg)
SpecificGravity 
Mass of water displaced(kg)
The SSD mass in air is also just...
the oven dried mass in air, PLUS
B
=
A
+
B - A
the mass of water in the water permeable voids
GSSD and GASTM
are “Bulk” Specific Gravities
This is because the “Bulk” volume of
the material is used in the calculation
The “Bulk” volume
includes the water
permeable voids:
NOTE: the SSD sample does not absorb
any water when its weighed in water
B - C
For the “Apparent” Specific
Gravity, GAPPARENT,
The volume excludes the water
permeable voids:
A - C
For Fine Aggregate:
we measure:
500.0 grams of SSD sample
A = Oven dry mass of the sample (grams)
B = Mass of the pycnometer + water (grams)
C = Mass of pycnometer + sample + water (grams)
and then calculate:
500.0  A
wa or Abs 
 100%
A
GSSD
500

B  500  C
GASTM
A

B  500  C
GAPPARENT
A

BAC
Instead of the A, B, C’s let’s use
some meaningful nomenclature:
Let the oven dried mass of the sand or stone
(i.e., mass of solids in air) be MS
The SSD mass of the sand or stone in air is
then MS + the mass of water absorbed, MWABS
The Bulk Volume is the volume of solids VS +
the volume of water absorbed VWABS
G
SSD
MS
MS
MS  MWABS
GASTM 
GAPPARENT 

VS  VWABS
VS
VS  VWABS
Bulk Volume
3
Since
Mass of
ρw =water
1 g/cm
displaced
Therefore,
by SSD Bulk
sample
Volume
= B + =500 - C
Mpyc
+ Mwcal
B = Mpyc + Mwcal
+ MS + MWABS - Mpyc - Mwexcal - MS - MWABS
C = Mpyc + Mwexcal +
500 = MS + MWABS
MS + MWABS
Mpyc
calibration mark
Mwcal
Mwexcal
-
+
MS + MWABS
(500 grams)
Apparent Volume
Mass of water
displaced
by solids
= B= + A - C
Therefore,
Apparent
Volume
Mpyc
+ Mwcal
B = Mpyc + Mwcal
+ MS
A = MS
- Mpyc - Mwexcal - MS - MWABS
C = Mpyc + Mwexcal + MS + MWABS
Mwcal – Mwexcal is the bulk volume of all the sand
particles in the sample
Since this includes the volume of the waterpermeable voids in all the sand particles,
subtracting the MWABS will leave the volume of
the solid parts of the sand particles only
Now we can examine the
relationships among these different
versions of specific gravity and the
absorption capacity.
MWABS
wa or Abs 
MS
Then, MWABS  wa  MS
If masses are in grams
and volumes in cm3, then
VWABS
GSSD
MS  MWABS

VS  VWABS
GASTM
MS

VS  VWABS
GAPPARENT
MWABS

3 OR VWABS  MWABS
1 g/cm
MS

VS
For example, we can find an expression for
GSSD in terms of GAPPARENT and wa:
GSSD
MS  MWABS

VS  VWABS
Substituting:
GSSD
MS  waMS

MS
 waMS
GAPPT
Cancelling Ms’s:
GSSD 
1  wa
1
 wa
GAPPT
MS
GAPPARENT 
VS
MS
VS 
GAPPARENT
MWABS
wa 
MS
MWABS  wa  MS
VWABS  MWABS
VWABS  wa  MS
and Rearranging:
GSSD
(1  wa )GAPPT

1  waGAPPT
Also, given
2 can
of=2.605
the
parameter
values,
Similar
relations
be determined
for
anythe
of
Example:
Ifany
GASTM
& GAPPARENT
= 2.718,
2 can
beterms
determined.
the fourother
parameter
in
any 2 of the
find the
GSSD
and
wof
a.
others.
Basing the calculations on 100 g of oven dried material,
GASTM
100 g
 2.605
VS  VWABS
GAPPT
100 g
 2.718
VS
100 g
3
VS  VWABS 
 38.388cm
2.605
100 g
VS 
 36.792cm3
2.718
VWABS  38.388 36.792 1.596cm
3
 GSSD
101.596g

 2.647
3
38.388cm
wa  1.596%