# basis physical property

**Topics:**Density, Fundamental physics concepts, Relative density

**Pages:**15 (716 words)

**Published:**November 3, 2014

SOIL COMPOSITION

SOIL COMPOSITION

Generally soil can be divided to three components in

natural occurrence

This separation know as three phase systems or three

phase diagram

It consists of soil solids, water and air

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Soil components in natural occurrence

Volume-Weight relationships

As a result from 3 phase diagram several relationship

were produce

This relationship known as volume weight

relationships.

Refer to 3 phase diagram

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Relationship equations

V = Vs +Vv

( eq. 1)

= Vs + Vw + Va

where

Vs =

volume of soil solids

Vv =

volume of voids

Vw =

volume of water in the

voids

Va =

volume of air in voids

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Relationship equations

W = Ws + Ww

where,

Ws =

Ww=

Wa =

( eq. 2)

weight of soil solid

weight of water

zero (negligible)

Water content@ Moisture content

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Void ratio

The ratio of the volume of voids Vv to the volume of

soil solid Vs

Porosity

The ratio of the volume of voids, Vv to total

volume, V expressed as either a decimal or a

percentage.

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Relationship between void ratio and

porosity

e = Vv = Vv

= (Vv/V ) = n

Vs

V – Vv 1 – (Vv/V)

1- n

n=

e

1+e

Degree of saturation

The ratio of the volume of water, Vw to the volume of

voids, Vv. It’s commonly in percentage

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Unit weight

The weight of soil per unit volume

Moist unit weight

Dry unit weight

Relationship between dry unit and bulk unit weight

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Derivation –cont’d

So what is the different between unit weight and

density?

Unit Weight is influence by gravity forces while mass

isn’t (Unit Weight=Weight/ Volume while Density=

Mass/Volume)- Weight = Mass x Gravity acceleration

So we can use the similar equations on related

calculation if there is only density

Specific Gravity

Specific gravity can be determined as a ratio of the unit weight of the soil material to the unit weight of water (9.81 kN/m3 or density 1000 kg/m3)

Most of the specific gravity of soil fall within a range of 2.6 – 2.9

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Relationships between Unit weight, Void ratio, Moisture Content and Specific gravity

let us consider a volume of soil in

which the volume of the soil solids is one

Derivation of equations

Therefore Gs will be substituted as

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Derivation –cont’d

γ = W = WS +WW =GS γ W + wGs γ W = (1+w) Gs γ w

V

V

1+e

1+e

γ d= Ws = Gs γw

V

1+e

Therefore

Vw = Ww = wGs γ w =wGs

γw

γw

How Vw become

wGS???

So if S = 1

(100%)

S= Vw = wGs

Vv

e

Se = wGs

Derivation –cont’d

e = wGs

γ sat = W = WS +WW = Gs γ w + e γ w = (Gs+e) γ w

V

V

1+ e

1+e

Beside bulk unit weight,

dry unit weight and

saturated unit weight

there is another type of

unit weight that is

submerge unit weight, γ’=

γ sat- γ w

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Relationships between Unit weight, Porosity, Moisture Content and Specific gravity

Relationships between Unit weight, Porosity, Moisture Content and Specific gravity

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Relationships between Unit weight, Porosity, Moisture Content and Specific gravity (Saturated Case)

Relationships between Unit weight, Porosity, Moisture Content and Specific gravity

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Air Content

The air content, A can be expressed as

A = e- wGs / 1+ e

or A = e/ 1+e ( 1- wGs/e)

Since n = e/1+e

Therefore, A = n (1-Sr)

Beside using symbol A as air content sometimes

authors use Na

Relative Density

Dr = relative density (%)

e = in situ void ratio of the soil

emax = void ratio of the soil in the loosest state

emin = void ratio of the soil in the densest state

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Relative Density

Dr = relative density (%)

ρd = in situ dry unit weight of the soil

ρd(max) = void ratio of the soil in the loosest state

ρd(min) = void ratio of the soil in the densest state

Relative Density

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Relative...

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