Weight Volume Relationship

Soil mechanics is a branch of engineering mechanics that describes the behavior of soils. It differs from fluid mechanics

and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and water) and particles (usually Clay, Silt, Sand, and Gravel) but soil may also contain organic solids, liquids, and gasses and other

matter. Along with Rock mechanics, soil mechanics provides the theoretical basis for analysis in Geotechnical engineering, a sub discipline of Civil engineering. Soil mechanics is used to

analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of

soil. Examples applications are building and bridge foundations, retaining walls, and dams. Principles of soil mechanics are also used in related disciplines such as Geophysical engineering, Engineering geology, Coastal

engineering, Agricultural engineering, Hydrology and Soil physics.

Weight-Volume Relationship

ObjectivesTo compute the masses (or weights) and

volumes of the three different phases.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

NotationM = mass or weightV = volumes = soil grainsw = watera = airv = voidst = total

DefinitionsWater content (w) is a measure of

the water present in the soil.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

S

W

M

Mw

Expressed as percentage.

Range = 0 – 100+%.

X 100%

DefinitionsVoid ratio (e) is a measure of the

void volume.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

S

V

V

Ve

DefinitionsPorosity (n) is also a measure of the void

volume, expressed as a percentage.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

T

V

V

Vn X 100%

Theoretical range: 0 – 100%

DefinitionsDegree of saturation (S) is the percentage

of the void volume filled by water.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

V

W

V

VS

Range: 0 – 100%

X 100%

DrySaturated

A Simple Example

water

air

soil

In this illustration,

e = 1

n = 50%

S = 50%

DefinitionsBulk density (m) is the density of the soil

in the current state.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

T

Tm V

M

Units: t/m3, g/ml, kg/m3

Definitions

Saturated density (sat) is the density of the soil when the voids are filled with water.

Submerged density (’) is the effective density of the soil when it is submerged. ’ = sat - w

DefinitionsDry density (d) is the density of the soil in

dry state.

soil

air

water

Vs

Va Ma=0

Ms

Mw

Mt

Vw

Vv

Vt

Phase Diagram

T

Sd V

M

Units: t/m3, g/ml, kg/m3

DefinitionsBulk, saturated, dry and submerged unit

weights () are defined in a similar manner.

= g

Here, use weight (kN) instead of mass (kg).

Specific gravity of the soil grains (Gs) typically varies between 2.6 and 2.8.

kg/m3N/m3 m/s2

Weight- Volume Relationship

Consider a fraction of the soil where Vs = 1.

soil

air

water

1 Gsw

SewSe

e

Phase Diagram

The other volumes can be obtained from the previous definitions.

Mass = Density x Volume

volumes masses

The masses can be obtained from:


From the previous definitions,

soil

air

water

1 Gsw

SewSe

e

Phase Diagram

SS

W

G

Se

M

Mw

e

e

V

Vn

T

V

1


soil

air

water

1 Gsw

SewSe

e

Phase Diagram

WS

T

Tm e

SeG

V

M

1

WS

T

Tsat e

eG

V

M

1

WS

T

Sd e

G

V

M

1

Summary of Formula:

Summary of Formula:

Try not to memorise the equations. Understand the definitions, and develop the relations from the phase diagram with VS = 1;

Assume GS (2.6-2.8) when not given;

Do not mix densities and unit weights;Soil grains are incompressible. Their mass and volume remain the same at any void ratio.

A Suggestion..

If you can remember one thing in phase relations, that should be ..

1Gsw

SewSe

e

soil

air

water

Documents

Weight Volume Relationship