A sample of mica flakes has a dry mass of 145 grams. The Gs for the sample is 2.
ID: 1920979 • Letter: A
Question
A sample of mica flakes has a dry mass of 145 grams. The Gs for the sample is 2.82. In the loose state, the sample had a volume of 1000 cm^3. After vibration, the volume of the sample was reduced to 400 cm^3, and finally after vibrating the sample with a load placed on the mica flakes, the volume was reduced to 200 cm^3.
a. For the 3 conditions described (loose, vibrated, loaded) calculate the void ratio and porosity for each.
b. For the 3 conditions, calculate the dry density, saturated density, and submerged density for each (9 different values)
c. Calculate the unit weight for the dry density, saturated density, and submerged density for each of the 3 conditions using lb/ft^3.
Explanation / Answer
specific gravity Gs = 2.82
Dry mass = 145 g
a) loose condition, soil having volume V = 1000 cm3 , calculation of void ratio e and porosity n
dry unit weight yd = Wd/V
= (145/1000) x 9.81
= 1.42 KN/m3
void ratio e = (Gyw/ yd )-1
unit weight of water yw = 9.81
e = (2.82 x 9.81/1.42) - 1
= 18.48
Porosity n = e/1+e
= 18.48/1+18.48
= 0.98
Vibrated condition V = 400 cm3
yd =( Wd/V ) x 9.81
= (145/400) x 9.81
= 3.55 KN/m3
e = (Gyw/yd) - 1
= ( 2.82 x 9.81/3.55) - 1
= 6.79
n = e/1+e
= 6.79/1+6.79
= 0.87
loaded condition V = 200 cm3
yd = (145/200) x 9.81
= 7.11 KN/m3
e = (Gyw/yd) - 1
= (2.82 x 9.81/7.11) - 1
= 2.89
n = e/1+e
= 2.89/1+2.89
= 0.74
b) calculation of dry density, saturated density and submerged density
loose condition V = 1000 cm3
dry density = dry density/volume
= 145/1000
= 0.145 g/cm3
saturated density is 0, because the soil is dry and in loose state and not saturated
submerged density is 0, because the soil is dry and in loose state and not submerged
Vibrated condition, V = 400 cm3
dry density = dry density /volume
= 145/400
= 0.36 g/cm3
saturated density is 0, because the soil mass is dry and in loose state and not saturated
submerged density is 0, because the soil mass is dry and in loose state and not submerged
loaded condition, V = 200 cm3
dry density = 145/200
= 0.725 g/cm3
saturated density is 0, because the soil mass is dry and in loose state
submerged density is 0, becuase the soil mass is dry and in loose state
c) Calculation on unit weight of dry density, saturated density and submerged density
as saturated density and submerged density is 0, unit weight of only dry density is calculated
loose condition, V = 1000 cm3
unit weight fro dry density = (145/1000) x 9.81
= 1.42 KN/m3
= 0.088 lb/ft3
Vibrated condition, V = 400 cm3
unit weight for dry density = (145/400) x 9.81
= 3.55 KN/m3
= 0.22 lb/ft3
loaded condition, V = 200 cm3
unit weight for dry density = (145/200) x 9.81
= 7.11 KN/m3
= 0.44 lb/ft3
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