How specific is gravity How specific is gravity anyway?anyway?

aka Relative aka Relative DensityDensity

SPECIFIC GRAVITYSPECIFIC GRAVITY

or How dense are your or How dense are your relatives?relatives?

What is Specific Gravity?What is Specific Gravity?It’s just the density of any It’s just the density of any

material relative to (divided material relative to (divided by) the density of by) the density of waterwater

We measure the volume of We measure the volume of any material by finding its any material by finding its

mass in air and mass in air and waterwater

The density of any material The density of any material is just its mass divided by is just its mass divided by

its volumeits volume

Back in 200 BC in in 200 BC in Greece…Greece…

Archimedes figured out how to Archimedes figured out how to find the volume of any weird-find the volume of any weird-

shaped object…shaped object…

……its volume is equal to the its volume is equal to the volume of water that it volume of water that it

displaces when immersed in displaces when immersed in waterwater

In the lab we can weigh an In the lab we can weigh an object in air and then in object in air and then in

water or use a pycnometerwater or use a pycnometer

For Coarse Aggregate:For Coarse Aggregate:we measure:we measure:

A = Oven dry mass of the sample A = Oven dry mass of the sample (kilograms)(kilograms)

B = Mass of SSD sample in air (kilograms)B = Mass of SSD sample in air (kilograms)C = Mass of SSD sample in water C = Mass of SSD sample in water

(kilograms)(kilograms)

CBB

GSSD

and then and then calculate:calculate:

100%A

ABAbs or wa

CAA

GAPPARENT CB

AGASTM

NOTE:NOTE:

)water(kg/m of Densitykg)displaced( water of Mass

Mass(kg))Volume(m

Mass(kg)Density

3

3

)water(kg/m of Densitykg)displaced( water of Mass

)(m Volume 33

kg)displaced( water of Mass)water(kg/m of DensityMass(kg)

Density3

kg)displaced( water of MassMass(kg)

Gravity Specific

for specific gravity, divide density by the density of for specific gravity, divide density by the density of water...water...

The SSD mass in air is also just...The SSD mass in air is also just...

the oven dried mass in air, the oven dried mass in air, PLUSPLUS

++==

the mass of water in the water permeable the mass of water in the water permeable voidsvoids

BB AA B - AB - A

GGSSDSSD and G and GASTMASTM

This is because the “Bulk” volume This is because the “Bulk” volume of the material is used in the of the material is used in the

calculationcalculationThe “Bulk” volume The “Bulk” volume includes the water includes the water permeable voids:permeable voids:

are “Bulk” Specific Gravitiesare “Bulk” Specific Gravities

B - CB - C

NOTE: the SSD sample does not NOTE: the SSD sample does not absorb any water when its weighed in absorb any water when its weighed in

waterwater

For the “Apparent” Specific For the “Apparent” Specific Gravity, GGravity, GAPPARENTAPPARENT, ,

The volume excludes the The volume excludes the water permeable voids:water permeable voids:

A - CA - C

For Fine Aggregate:For Fine Aggregate:we measure:we measure: 500.0 grams of SSD sample500.0 grams of SSD sample A = Oven dry mass of the sample (grams)A = Oven dry mass of the sample (grams) B = Mass of the pycnometer + water B = Mass of the pycnometer + water (grams)(grams) C = Mass of pycnometer + sample + water C = Mass of pycnometer + sample + water (grams)(grams)

C500B500

GSSD

and then and then calculate:calculate:

100%A

A500.0Abs or wa

CABA

GAPPARENT

C500BA

GASTM

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,

MWABSThe Bulk Volume is the volume of solids VS + the volume of water absorbed VWABS

WABSS

WABSSSSD VV

MMG

WABSS

SASTM VV

MG

S

SAPPARENT V

MG

Bulk VolumeMass of water displaced by SSD sample = B +

500 - C

Mpyc

calibration mark

MS + MWABS

Mwcal Mwexcal

+ -

(500 grams)

B = Mpyc + Mwcal

500 = MS + MWABS

C = Mpyc + Mwexcal

+ MS + MWABS

Since ρw = 1 g/cm3

Therefore, Bulk Volume =+ MwcalMpyc + MS + MWABS - Mpyc - Mwexcal - MS - MWABS

Apparent VolumeMass of water displaced by solids = B + A -

C

B = Mpyc + Mwcal

A = MS C = Mpyc + Mwexcal + MS + MWABS

Therefore, Apparent Volume =+ MwcalMpyc + MS - 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 water-permeable 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.

WABSS

WABSSSSD VV

MMG

WABSS

SASTM VV

MG

S

SAPPARENT V

MG

S

WABSa M

MAbs or w

SaWABS Mw M Then,

If masses are in grams and volumes in cm3,

then

3WABS

WABS g/cm 1M

V WABSWABS MV OR

For example, we can find an expression for GSSD in terms of GAPPARENT and wa:

WABSS

WABSSSSD VV

MMG

S

SAPPARENT V

MG

SaAPPT

S

SaSSSD

MwGM

MwM G

Substituting:APPARENT

SS G

MV

S

WABSa M

M w

SaWABS Mw M

WABSWABS MV

SaWABS MwV

Cancelling Ms’s:

aAPPT

aSSD

wG

1w1

G

and Rearranging:

APPTa

APPTaSSD Gw1

)Gw(1 G

Similar relations can be determined for any of the four parameter in terms of any 2 of

the others.

Also, given any 2 of the parameter values, the other 2 can be determined.

Example: If GASTM =2.605 & GAPPARENT = 2.718, find the GSSD and wa.Basing the calculations on 100 g of oven dried material,

WABSSASTM VV

g 1002.605G

3WABSS cm 38.388

2.605g 100

VV

SAPPT V

g 1002.718G

3S cm 36.792

2.718g 100

V

3WABS cm 1.59636.79238.388V

2.647cm 38.388

g 101.596G 3SSD 1.596%wa