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

Contents

## 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

### 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)

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

$$γ=\frac{(G+e·s)γ_w}{1+e}$$

### 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=$$γ_{dry}$$

$$γ_{dry}=\frac{G·γ_w}{1+e}$$

### 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=$$γ_{sat}$$

$$γ_{sat}=\frac{(G+e·1)·γ_w}{1+e}$$

$$γ_{sat}=\frac{(G+e)·γ_w}{1+e}$$

### 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’=$$\frac{(G+e)·γ_w-γ_w(1+e)}{1+e}$$

$$γ′=\frac{(G-1)·γ_w}{1+e}$$

### 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)$$γ_w$$

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

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

$$γ_{dry}$$=$$\frac{γ}{1+w}$$

### 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”

$$γ_d=\frac{G(1-η_a)·γ_w}{1+w·G}$$

 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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