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: BA wa or Abs 100% A GSSD B BC GASTM A BC GAPPARENT A AC 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 BAC 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%