Formulas Flashcards
What is total volume in a three phase system?
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
What is total weight in three phase system?
W = Ww + Ws
Where
Ww is weight of water
Ws is weight of solids
What is volume of voids in three phase system?
Vv = Va + Vw
Where
Vv is volume of voids
Va is volume of air
Vw is volume of water
Describe weight and volume of dry soil in two phase system.
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
Describe weight and volume of fully saturated soil in two phase system.
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
What is w?
Water Content or Moisture content
w% = Ww/Ws × 100
What is the range of Water content?
w >= 0
There is no upper limit of water content
What does w = 0 mean?
The soil is dry.
What is e?
Void Ratio
e = Vv/Vs
e > 0 e /= 0 because Vv /= 0
What is n?
Porosity
n = Vv/V
n% = Vv/V ×100
What is range of porosity?
0 < n < 1
Or
0 < n < 100%
n cannot be equal to 0 or 1 or 100%
What is S?
Degree of Saturation
S = Vw/Vv
What is range of Degree of Saturation?
0 <= S <= 1
0 <= S <= 100%
If S=0 then Dry soil (2 phase)
If S=1 then Saturated soil (2 phase)
What is ac?
Air Content
ac = Va/Vv
What is range of Air Content?
0 <= ac <= 1
What is the relation between Degree of Saturation and Air Content?
S + ac = 1
What is na?
Percentage air voids
na = Va/V × 100
What is γ?
Bulk unit weight
γ = W/V kN/m³
What is ρ?
Bulk Density
ρ = M/V kg/m³
What is γd?
Dry unit weight
γd = Ws/V
What is ρd?
Dry Density
ρd = Ms/V
What is γsat?
Saturated unit weight
γsat = Wsat/V
Where
Wsat is weight of saturated soil
What is ρsat?
Saturated density
ρsat = Msat/V
Where
Msat is mass of saturated soil
What are the bulk density and bulk unit weight in dry and saturated condition?
In dry condition
ρbulk = ρd
γbulk = γd
In saturated condition
ρbulk = ρsat
γbulk = γsat
What is γ’?
Submerged unit weight
γ’ = γsat + γw
Where
γw is unit weight of water = 9.81 kN/m³
What is ρ’?
Submerged density
ρ’ = ρsat + ρw
Where
ρw is density of water
ρw = 1000 kg/m³ or 1 g/cc
What is γs?
Unit weight of solids
γs = Ws/Vs
What is ρs?
Density of solids
ρs = Ms/Vs
What is the relation between all unit weights?
γs > γsat > γ > γd > γ’
What is Gs?
Absolute/True Specific Gravity
Gs = γs/γw
Or
Gs = ρs/ρw
What is Gm?
Apparent/Bulk specific gravity
Gm = γbulk/γw
Or
Gm = ρbulk/ρw
What is the relationship between True and Bulk specific gravity?
Gm < Gs
What is the relationship between Porosity and Void Ratio?
n = e/1+e
1-n = 1/1+e
What is the relationship between Percentage air voids, air Content and porosity?
na = n × ac
What is the relationship between Total volume of soil, void ratio and volume of solids?
Vs = V/1+e
What is the relationship between Total weight of soil, water content and weight of solids?
Ws = W/1+w
What is the relationship between dry unit weight, bulk unit weight and water content?
γd = γ/1+w
What is the relationship between unit weight of solids, bulk unit weight, void ratio and water content?
γs = γ(1+e)/1+w
What is the relationship between bulk unit weight, unit weight of water, specific gravity, void ratio and degree of saturation?
γ = (G+ eS/1+e) γw
What is the relationship between bulk specific gravity, specific gravity, void ratio and degree of saturation?
Gm = (G + eS)/(1 + e)
What is the relationship between saturated unit weight, specific gravity, void ratio and unit weight of water?
γsat = (G+e/1+e)γw
What is the relationship between dry unit weight, specific gravity, void ratio and unit weight of water?
γd = G.γw/1 + e
What is the relationship between submerged unit weight, specific gravity, void ratio and unit weight of water?
γsub = (G-1/1+e) γw
What is the relationship between dry unit weight, percentage of air voids, unit weight of water, specific gravity and water content?
γd = (1 - na) G γw
—————–
1 + w G
What is the relationship between Degree of Saturation, void ratio, water content and specific gravity?
S × e = w × G
