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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:
Weight- Volume Relationship
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
Weight- Volume Relationship
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