Formulas

Question 1

What is total volume in a three phase system?

Answer 1

V = Va + Vw + Vs

Where
V is total volume of soil
Va is volume of air
Vw is volume of water
Vs is volume of solid

Question 2

What is total weight in three phase system?

Answer 2

W = Ww + Ws

Where
Ww is weight of water
Ws is weight of solids

Question 3

What is volume of voids in three phase system?

Answer 3

Vv = Va + Vw

Where
Vv is volume of voids
Va is volume of air
Vw is volume of water

Question 4

Describe weight and volume of dry soil in two phase system.

Answer 4

W = Ws
V = Va + Vs

Where
W is total weight of soil
Ws is weight of solids
V is total volume of soil
Va is volume of air
Vs is volume of solids

Question 5

Describe weight and volume of fully saturated soil in two phase system.

Answer 5

W = Ww + Ws
V = Vw + Vs

Where
W is total weight of soil
Ww is weight of water
Ws is weight of solids
V is total volume of soil
Vw is volume of water
Vs is volume of solids

Question 6

What is w?

Answer 6

Water Content or Moisture content

w% = Ww/Ws × 100

Question 7

What is the range of Water content?

Answer 7

w >= 0
There is no upper limit of water content

Question 8

What does w = 0 mean?

Answer 8

The soil is dry.

Question 9

What is e?

Answer 9

Void Ratio

e = Vv/Vs

e > 0 e /= 0 because Vv /= 0

Question 10

What is n?

Answer 10

Porosity

n = Vv/V

n% = Vv/V ×100

Question 11

What is range of porosity?

Answer 11

0 < n < 1
Or
0 < n < 100%

n cannot be equal to 0 or 1 or 100%

Question 12

What is S?

Answer 12

Degree of Saturation

S = Vw/Vv

Question 13

What is range of Degree of Saturation?

Answer 13

0 <= S <= 1
0 <= S <= 100%

If S=0 then Dry soil (2 phase)
If S=1 then Saturated soil (2 phase)

Question 14

What is ac?

Answer 14

Air Content

ac = Va/Vv

Question 15

What is range of Air Content?

Answer 15

0 <= ac <= 1

Question 16

What is the relation between Degree of Saturation and Air Content?

Answer 16

S + ac = 1

Question 17

What is na?

Answer 17

Percentage air voids

na = Va/V × 100

Question 18

What is γ?

Answer 18

Bulk unit weight

γ = W/V kN/m³

Question 19

What is ρ?

Answer 19

Bulk Density

ρ = M/V kg/m³

Question 20

What is γd?

Answer 20

Dry unit weight

γd = Ws/V

Question 21

What is ρd?

Answer 21

Dry Density

ρd = Ms/V

Question 22

What is γsat?

Answer 22

Saturated unit weight

γsat = Wsat/V

Where
Wsat is weight of saturated soil

Question 23

What is ρsat?

Answer 23

Saturated density

ρsat = Msat/V

Where
Msat is mass of saturated soil

Question 24

What are the bulk density and bulk unit weight in dry and saturated condition?

Answer 24

In dry condition
ρbulk = ρd
γbulk = γd
In saturated condition
ρbulk = ρsat
γbulk = γsat

Question 25

What is γ'?

Answer 25

Submerged unit weight γ' = γsat + γw Where γw is unit weight of water = 9.81 kN/m³

Question 26

What is ρ'?

Answer 26

Submerged density ρ' = ρsat + ρw Where ρw is density of water ρw = 1000 kg/m³ or 1 g/cc

Question 27

What is γs?

Answer 27

Unit weight of solids γs = Ws/Vs

Question 28

What is ρs?

Answer 28

Density of solids ρs = Ms/Vs

Question 29

What is the relation between all unit weights?

Answer 29

γs > γsat > γ > γd > γ'

Question 30

What is Gs?

Answer 30

Absolute/True Specific Gravity Gs = γs/γw Or Gs = ρs/ρw

Question 31

What is Gm?

Answer 31

Apparent/Bulk specific gravity Gm = γbulk/γw Or Gm = ρbulk/ρw

Question 32

What is the relationship between True and Bulk specific gravity?

Answer 32

Gm < Gs

Question 33

What is the relationship between Porosity and Void Ratio?

Answer 33

n = e/1+e 1-n = 1/1+e

Question 34

What is the relationship between Percentage air voids, air Content and porosity?

Answer 34

na = n × ac

Question 35

What is the relationship between Total volume of soil, void ratio and volume of solids?

Answer 35

Vs = V/1+e

Question 36

What is the relationship between Total weight of soil, water content and weight of solids?

Answer 36

Ws = W/1+w

Question 37

What is the relationship between dry unit weight, bulk unit weight and water content?

Answer 37

γd = γ/1+w

Question 38

What is the relationship between unit weight of solids, bulk unit weight, void ratio and water content?

Answer 38

γs = γ(1+e)/1+w

Question 39

What is the relationship between bulk unit weight, unit weight of water, specific gravity, void ratio and degree of saturation?

Answer 39

γ = (G+ eS/1+e) γw

Question 40

What is the relationship between bulk specific gravity, specific gravity, void ratio and degree of saturation?

Answer 40

Gm = (G + eS)/(1 + e)

Question 41

What is the relationship between saturated unit weight, specific gravity, void ratio and unit weight of water?

Answer 41

γsat = (G+e/1+e)γw

Question 42

What is the relationship between dry unit weight, specific gravity, void ratio and unit weight of water?

Answer 42

γd = G.γw/1 + e

Question 43

What is the relationship between submerged unit weight, specific gravity, void ratio and unit weight of water?

Answer 43

γsub = (G-1/1+e) γw

Question 44

What is the relationship between dry unit weight, percentage of air voids, unit weight of water, specific gravity and water content?

Answer 44

γd = (1 - na) G γw ----------------- 1 + w G

Question 45

What is the relationship between Degree of Saturation, void ratio, water content and specific gravity?

Answer 45

S × e = w × G