Interrelationship Between the Properties of Soil | Properties of Soil | Soil Mechanics

  Interrelationship Between the Properties of Soil  

1. s·e=w·G
2. \(γ=\frac{(G+e·s)γ_w}{1+e}\)
3. \(γ_{dry}=\frac{G·γ_w}{1+e}\)
4. \(γ_{sat}=\frac{(G+e)·γ_w}{1+e}\)
5. \(γ′=\frac{(G-1)·γ_w}{1+e}\)
6. \(γ′=γ_{dry}\)+(η-1)\(γ_w\)
7. \(γ_{dry}\)=\(\frac{γ}{1+w}\)
8. \(γ_d=\frac{G(1-η_a)·γ_w}{1+w·G}\) 
9. \(η=\frac{1}{1+e}\) 
10. \(Ws=\frac{Wt}{1+w}\) 
11. \(Vs=\frac{Vt}{1+e}\) 
12. (Vs)mix=Vs1+Vs2,(Ws)mix=Ws1+Ws2 In the problem of mixing, excavation, transportation of soil Weight of solid, volume of solid not change. 

1. Interrelationship Between Voids ratio (e), Water Content (w), Specific Gravity (G), Degree of Saturation(s)

We know that:

\(\mathrm{e}=\frac{V v}{Vs}=\left(\frac{V v}{V s}\right)\left(\frac{V w}{V s}\right)\) Multiply by Vw in Numerator Denominator.

\(e=\frac{1·Vw}{s·Vs}\)        {\(Vw=\frac{Ww}{γ_w}\)}

\(e=\frac{Ww}{s·Vs·γ_w}\)

{\(G=\frac{γ_s}{γ_w}=\frac{Ws}{Vsγ_w}\)}

\(e=\frac{Ww·G·γ_w}{s·γ_w·Ws}\) \(e=\frac{wG}{s}\)

s·e=w·G

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2. Interrelationship Between Voids ratio (e), Unit Weight (γ), Specific Gravity (G), Degree of Saturation(s), Unit Weight of Water(\(γ_w\))

We know that

\(γ=\frac{W}{V}\) \(γ=\frac{Ws+Ww}{Vv+Vs}\)

(G=ϒs/ϒw)& (ϒs=Ws/Vs)

\(γ=\frac{VsGγ_w+Vwγ_w}{Vs(1+\frac{Vv}{Vs})}\) \(γ=\frac{Vsγ_w(G+Vw/Vs)}{Vs(e+1)}\) \(\frac{Vw}{Vs}=\frac{Vw·Vv}{Vs·Vv}=e·s\)

\(γ=\frac{(G+e·s)γ_w}{1+e}\)

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3. Interrelationship Between Voids ratio (e),Dry Unit Weight (\(γ_{dry}\)), Specific Gravity (G), Unit Weight of Water(\(γ_w\))

We know that:

For dry soil, s=0,γ=\(γ_{dry}\)

\(γ_{dry}=\frac{G·γ_w}{1+e}\)

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4. Interrelationship Between Voids ratio (e), Saturated Unit Weight (\(γ_{sat}\)), Specific Gravity (G),Unit Weight of Water(\(γ_w\))

We know that:

For saturated soil, s=1,γ=\(γ_{sat}\)

\(γ_{sat}=\frac{(G+e·1)·γ_w}{1+e}\)

\(γ_{sat}=\frac{(G+e)·γ_w}{1+e}\)

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5. Interrelationship Between Voids ratio (e), Submerged Unit Weight γ’, Specific Gravity (G),Unit Weight of Water (\(γ_w\))

We know that:

γ’=\(γ_{sat}\)–(\(γ_w\))

γ’=\(\frac{(G+e)·γ_w}{1+e}\)–(\(γ_w\))

γ’=\(\frac{(G+e)·γ_w-γ_w(1+e)}{1+e}\)

\(γ′=\frac{(G-1)·γ_w}{1+e}\)

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6. Interrelationship Between Submerged Unit Weight γ’, Porosity(η), Dry Unit Weight (\(γ_{dry}\)), Unit Weight of Water(\(γ_w\)) 

We know that:

γ’=\(\frac{(G-1)·γ_w}{1+e}\)

γ’=\(\frac{G·γ_w}{1+e}\frac{γ_w}{1+e}\)

e=\(\frac{η}{1-η}\)

1+e=\(\frac{η}{1-η}\)+1

1+e=\(\frac{1}{1-η}\)

\(\frac{1}{1+e}\)=1-η

γ’=\(γ_{dry}\)-(1-η)\(γ_w\)

\(γ′=γ_{dry}\)+(η-1)\(γ_w\)

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7. Interrelationship Between Dry Unit Weight (\(γ_{dry}\)), Water Content (w), Unit Weight(γ) 

\(γ_{dry}\)=\(\frac{Wd}{V}=\frac{Ws}{V}=\frac{W}{V(1+w)}\)

\(γ_{dry}\)=\(\frac{γ}{1+w}\)

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8. Interrelationship Between Dry Unit Weight (\(γ_{dry}\)), Specific Gravity (G), Unit Weight of Water(\(γ_w\)), Water Content(w), Percentage Air Voids (ηa) 

V=Vv+Vs= Va+Vw+Vs

Divided by V both side.

\(\frac{V}{V}=\frac{Va}{V}+\frac{Vw}{V}+\frac{Vs}{V}\)

\(1=η_a+\frac{Ww}{V·γ_w}+\frac{Ws}{G·γ_w·V}\)

\(1-η_a=\frac{w·Ws}{V·γ_w}+\frac{Ws}{G·γ_w·V}\)

\(1-η_a=\frac{w·Wd}{V·γ_w}+\frac{Wd}{G·γ_w·V}\)

\(1-η_a=\frac{w·γ_d}{γ_w}+\frac{γ_d}{G·γ_w·}\)

\(1-η_a=\frac{γ_d}{γ_w}(w+\frac{1}{G}\)

\(γ_d=\frac{G(1-η_a)·γ_w}{1+w·G}\) 

“This relationship is also significant to understand the compactness of soil”

\(γ_d=\frac{G(1-η_a)·γ_w}{1+w·G}\)

 

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Subject	Soil Mechanics
Unit	Soil Formation & Properties of Soil
Topic	Interrelationship Between the Properties of Soil
Next Topic	Test of Specific Gravity
Previous Topic	Relative Compaction

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