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Soil Mechanics > Formulas > Flashcards

Formulas Flashcards

1
Q

What is total volume in a three phase system?

A

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

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2
Q

What is total weight in three phase system?

A

W = Ww + Ws

Where
Ww is weight of water
Ws is weight of solids

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3
Q

What is volume of voids in three phase system?

A

Vv = Va + Vw

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

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4
Q

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

A

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

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5
Q

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

A

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

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6
Q

What is w?

A

Water Content or Moisture content

w% = Ww/Ws × 100

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7
Q

What is the range of Water content?

A

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

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8
Q

What does w = 0 mean?

A

The soil is dry.

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9
Q

What is e?

A

Void Ratio

e = Vv/Vs

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

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10
Q

What is n?

A

Porosity

n = Vv/V

n% = Vv/V ×100

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11
Q

What is range of porosity?

A

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

n cannot be equal to 0 or 1 or 100%

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12
Q

What is S?

A

Degree of Saturation

S = Vw/Vv

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13
Q

What is range of Degree of Saturation?

A

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

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

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14
Q

What is ac?

A

Air Content

ac = Va/Vv

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15
Q

What is range of Air Content?

A

0 <= ac <= 1

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16
Q

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

A

S + ac = 1

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17
Q

What is na?

A

Percentage air voids

na = Va/V × 100

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18
Q

What is γ?

A

Bulk unit weight

γ = W/V kN/m³

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19
Q

What is ρ?

A

Bulk Density

ρ = M/V kg/m³

20
Q

What is γd?

A

Dry unit weight

γd = Ws/V

21
Q

What is ρd?

A

Dry Density

ρd = Ms/V

22
Q

What is γsat?

A

Saturated unit weight

γsat = Wsat/V

Where
Wsat is weight of saturated soil

23
Q

What is ρsat?

A

Saturated density

ρsat = Msat/V

Where
Msat is mass of saturated soil

24
Q

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

A

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

25
Q

What is γ’?

A

Submerged unit weight
γ’ = γsat + γw

Where
γw is unit weight of water = 9.81 kN/m³

26
Q

What is ρ’?

A

Submerged density

ρ’ = ρsat + ρw

Where
ρw is density of water
ρw = 1000 kg/m³ or 1 g/cc

27
Q

What is γs?

A

Unit weight of solids

γs = Ws/Vs

28
Q

What is ρs?

A

Density of solids

ρs = Ms/Vs

29
Q

What is the relation between all unit weights?

A

γs > γsat > γ > γd > γ’

30
Q

What is Gs?

A

Absolute/True Specific Gravity

Gs = γs/γw
Or
Gs = ρs/ρw

31
Q

What is Gm?

A

Apparent/Bulk specific gravity

Gm = γbulk/γw
Or
Gm = ρbulk/ρw

32
Q

What is the relationship between True and Bulk specific gravity?

A

Gm < Gs

33
Q

What is the relationship between Porosity and Void Ratio?

A

n = e/1+e

1-n = 1/1+e

34
Q

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

A

na = n × ac

35
Q

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

A

Vs = V/1+e

36
Q

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

A

Ws = W/1+w

37
Q

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

A

γd = γ/1+w

38
Q

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

A

γs = γ(1+e)/1+w

39
Q

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

A

γ = (G+ eS/1+e) γw

40
Q

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

A

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

41
Q

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

A

γsat = (G+e/1+e)γw

42
Q

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

A

γd = G.γw/1 + e

43
Q

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

A

γsub = (G-1/1+e) γw

44
Q

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

A

γd = (1 - na) G γw
—————–
1 + w G

45
Q

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

A

S × e = w × G

Soil Mechanics (1 decks)

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