How specific is gravity anyway? or How dense are your relatives? 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 water The density of any material is just its mass divided by its volume We measure the volume of any material by finding its mass in air and water

Back in 200 BC in Greece… Archimedes figured out how to find the volume of any weird-shaped 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:

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

The SSD mass in air is also just... the oven dried mass in air, PLUS = + A B - A B 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: B - C NOTE: the SSD sample does not absorb any water when its weighed in water

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:

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 

Mass of water displaced by SSD sample = B + 500 - C Bulk Volume Since ρw = 1 g/cm3 Mass of water displaced by SSD sample = B + 500 - C Therefore, Bulk Volume = Mpyc + Mwcal + MS + MWABS - Mpyc - Mwexcal - MS - MWABS C = Mpyc + Mwexcal + MS + MWABS B = Mpyc + Mwcal 500 = MS + MWABS Mpyc calibration mark Mwcal Mwexcal - + MS + MWABS (500 grams)

Mass of water displaced by solids = B + A - C Apparent Volume Mass of water displaced by solids = B + A - C Therefore, Apparent Volume = Mpyc + Mwcal + MS - Mpyc - Mwexcal - MS - MWABS B = Mpyc + Mwcal A = MS 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 water-permeable voids in all the sand particles, subtracting the MWABS will leave the volume of the solid parts of the sand particles only

If masses are in grams and volumes in cm3, then Now we can examine the relationships among these different versions of specific gravity and the absorption capacity. If masses are in grams and volumes in cm3, then OR

For example, we can find an expression for GSSD in terms of GAPPARENT and wa: Substituting: Cancelling Ms’s: and Rearranging:

Example: If GASTM =2.605 & GAPPARENT = 2.718, find the GSSD and wa. Also, given any 2 of the parameter values, the other 2 can be determined. Similar relations can be determined for any of the four parameter in terms of any 2 of the others. Example: If GASTM =2.605 & GAPPARENT = 2.718, find the GSSD and wa. Basing the calculations on 100 g of oven dried material,