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Mechanics of Soils
Prof.Derin N. URAL
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Lecture 1
SECTION 1
Soil Formation
Particle Size Distribution
Soil Classification
SECTION 2
Soil Composition
3-phase material
Soil Characterization (particle size, soilplasticity)
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Soil Mechanics
Soil mechanics is the branch of science that deals with the
study of physical properties of soil and the behavior of soil
masses subjected to various types of forces.
Classify soils and rocks
Establish engineering properties
Ascertain the compressibility
Ascertain the shear strength
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According to Terzaghi (1948):
Soil Mechanics is the application of laws of
mechanics and hyd raul ics to engineer ing problemsdeal ing w ith sediments and other unconsol idated
accumulations o f sol id partic les produced by the
mechanical and chemical dis integrat ion of ro cks
regardless of whether or not th ey contain an
admixture of organic constituent.
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Soil Formation
Parent Rock
Residual soil Transported soil
~ in situ weathering (by
physical & chemical
agents) of parent rock
~ weathered andtransported far away
by wind, water and ice.
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Soil Formation
~ formed by one of these three different processes
igneous sedimentary metamorphic
formed by cooling of
molten magma (lava)
formed by gradual
deposition, and in layers
formed by alteration
of igneous &sedimentary rocks by
pressure/temperaturee.g., limestone, shale
e.g., marble
e.g., granite
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3-Phase Material
Solid
WaterAir
By P. Jayawickrama, Texas Tech U
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The Mineral Skeleton
Volume
Solid Particles
Voids (air or water)
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Three Phase Diagram
Solid
Air
Water
Mineral Skeleton Idealization:
Three Phase Diagram
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Fully Saturated Soils
Fully Saturated
Water
Solid
Mineral Skeleton
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Dry Soils
Mineral Skeleton Dry Soil
Air
Solid
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Partly Saturated Soils
Solid
Air
Water
Mineral Skeleton Partly Saturated Soils
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Phase Diagram
Volume Weight
Solid
Air
WaterWT
Ws
Ww
Wa~0
Vs
Va
Vw
Vv
VT
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15
Objectives of a Phase Diagram
To compute the weights (or masses) and volumes of
the three different phases.
NotationM = mass or weight
V = volumes = soil grains
w = water
a = air
v = voids
t = total
Vs
Va Wa=0
Ws
Ww
Wt
VwVv
Vt
Phase Diagram
Solid
Air
Water
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Volume Relationships
Void ratio (e): is a measure of the void volume.
S
V
V
Ve
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
Phase Diagram
Solid
Air
Water
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Volume Relationships
Porosity (n): is also a measure of the void volume,
expressed as a percentage.
T
V
V
Vn X 100%
Theoretical range: 0 100% Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt
Phase Diagram
Solid
Air
Water
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Volume Relationships
Degree of saturation (S): is the percentage of the void
volume filled by water.
V
W
VVS
Range: 0 100%
X 100%
DrySaturated
Vs
Va Wa=0
Ws
Ww
Wt
Vw
Vv
Vt
Phase Diagram
Solid
Air
Water
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Weight Relationships
Water content (w): is a measure of the water
present in the soil.
S
W
WWw
Expressed as percentage.
Range = 0 100%.
X 100%
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
Phase Diagram
Solid
Air
Water
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Unit Weight Relationships
Natural Unit Weight (): is thedensity of the soil in the
current state.
Dry Unit Weight (d): is the unit
weight of the soil in dry state.
T
Sd
V
W
T
T
V
W
Vs
Va Wa=0
Ws
WwWt
Vw
Vv
Vt
Phase Diagram
Solid
Air
Water
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Unit Weight Relationships
Saturated Unit Weight (sat): is theunit weight of the soil when thevoids are filled with water.
Submerged Unit Weight (sub):isthe effective unit weight of the soilwhen it is submerged.
T
vs
V
VWsat
w*
Vs
Va Wa=0
Ws
Ww Wt
Vw
Vv
Vt
Phase Diagram
Solid
Air
Water
wsatsub
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Phase Relations
Consider a fraction of the soil whereVs = 1.
The other volumes canbe obtained from theprevious definitions.
Weights = Unit Weights x Volume
The weights can beobtained from:
1 Gsw
SewSe
e
Phase Diagramvolumes weights
Solid
Air
Water
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Phase RelationsFrom the previous definitions,
SS
W
G
Se
W
Ww
ee
VVnT
V
11 Gsw
SewSe
e
Phase Diagramvolumes weights
Solid
Air
Water
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Phase Relations
WS
T
T
e
SeG
V
W
1
WS
T
Tsat
e
eG
V
W
1
WS
T
Sd
e
G
V
W
1
1 Gsw
Sew
Se
e
Phase Diagramvolumes weights
Solid
Air
Water
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Definitions
Bulk (natural), saturated, dry and submerged
densities () are defined in a similar manner.
Here, you can also use mass (kg) instead of weight (kN).
/ g = = M/V
kg/m3
N/m3 m/s2
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Specific Gravity
Unit weight of Water,w w = 1.0 g/cm
3 (strictly accurate at 4 C)
w = 9.81 kN/m3
WaterofVolumeEqualanofWeightceSubsaofWeightGS tan
WaterofWeightUnitceSubsaofWeightUnitGS tan
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In Terms of Density
i. Density of water : w= 1000kg/m3
ii. Dry density of soil :
iii. Bulk density of unsaturated or saturated soil:
iv. Air content (A) :
WS
T
Sd
e
G
V
M
1
WS
T
T
e
SeG
V
M
1
e
wGe
V
VA S
T
a
1
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Relationship between parameters
These definitions can be used to determine any desired
relationships between above quantities, and
hence to determine void ratio, degree of saturation, etc.
That cannot be measured directly by laboratory tests.Some relationships are as follows:
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Relationship between parameters
Forunsaturated soils:
Forsaturated soils: S = 1 then;
Bulk density;
Dry density;
Degree of Saturation;
SS
W
G
Se
W
Ww [1]
S
wGe S
wGe S
WS
T
T
e
SeG
V
M
1 e
wG
e
GwG wSw
SS
1
)1(
1
)(
WS
T
Sd
e
G
V
M
1
)1( wd
wS
S
Gw
wGS
)1(
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REMEMBER:
Try not to memorize the equations. Understand
the definitions, and develop the relations from thephase 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 andvolume remain the same at any void ratio.
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Determination of Particle Size
Distribution
Mechanical analysis is used in the determination of the
size range of particles present in a soil, expressed as a
percentage of the total dry weight.
There are two methods that are utilized to determine the
particle size distribution of soil:
Sieve Analysis (for particle sizes > 0.075mm in diameter) Hydrometer Analysis ( < 0.075mm )
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Sieve Analysis
It is performed by shaking
the soil sample through a
set of sieves having
progressively smaller
openings.
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Hydrometer Analysis
It is based on the principle of sedimentation of soil grains
in water.
By David Airey, The University of Sydney
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Hydrometer Analysis
Also called SedimentationAnalysis
Stokes Law
18
)(2 Lsw GGDv
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Particle Size Distributions and Soil
Particle Characteristics
Particle size distribution curve is a representation in graphical or
tabular form of the various (diameter) grain sizes in a soil,
determined through sieving and sedimentation.
The particle diameters are plotted in log scale, and the
corresponding percent finer in arithmetic scale.
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SILT & CLAY SAND GRAVEL
Particle Size Distribution Curve
0.075
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Some commonly used measures are:
a) Effective size :
It is the diameter in the particle size distribution curve
corresponding to 10% finer. (maximum size of the smallest 10%
of the soil)
b) Uniformity Coefficient:
It is the ratio of the maximum diameter of the smallest 60% to
the effective size.
A well graded soil will have
1060 /DDCu
)( 10D
sandsfor6C
gravelsfor4
u
u
C
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Some commonly used measures are:
c) Coefficient of Curvature:
:Diameter corresponding the 30% finer
d) Clay Fraction: (CF)
It is the percentage by dry mass of particles smaller than
0.002mm (2m), and is an index property frequently quoted
relation to fine grained soils (soils with 50% or more finer than
63m). It has a strong influence on the engineering propertiesof fine grained soils.
)D*(D/)(D 1060230c C
30D
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Definitions
e) Well-Graded Material Contains particles of a wide range of
sizes. The smaller particles fill the spaces left between the larger
particles; therefore the soil has greater strength than a poorly
graded soil, and lower permeability.
f) Poorly Graded Material Contains a large portion of uniformly
sized particles. This particular soil has larger voids in its structure
and poor strength along with high permeability.
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Soil A: ?
Soil B: ?
Soil C: ?
By D. Airey, The University of Sydney
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Soil A: Well Graded
Soil B: Poorly Graded
Soil C: Uniform
By D. Airey, The University of Sydney
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Soil Plasticity & Consistency Limits
In the early 1900s a Swedish scientist Atterberg developed amethod to describe the consistency offine grained soils with
varying degree of moisture content.
If a soil is gradually dried from a slurry, it passes from state of
viscous liquid to a plastic state; then to a semi-solid, and finally intoa solid state. The moisture contents at which the soil passes from
one state to the next are known as consistency limits (also called
Atterberg Limits)
Consistency limits are utilized to compare soils from differentlocations and different depths.
There are 4 basic states
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Consistency of fine-grained soil varies in proportion to the water content
Atterberg Limits
Shrinkage limit
Plastic limit
Liquid limit
solid
semi-solid
plastic
liquid
PlasticityIndex
(cheese)
(pea soup)
(peanut butter)
(hard candy)
By P. Jayawickrama, Texas Tech U
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Consistency Limits
Moisture Content (%)
Volume
LLSL PLSolid
Semi-
Solid
Plastic
Viscous
Liquid
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Definitions
a) Liquid Limit (LL) : is the minimum moisture content at which thesoil will flow under its own weight. The moisture content (in %)
required to close a distance of 12.7mm along the bottom of the
groove after 25 blows is the LL.
b) Plastic Limit (PL): is the moisture content (in %) at which the soil
when rolled into threads of 3.2mm in diameter, crumbles. PL is
the lower limit of the plastic stage of the soil. The test is simple
and performed by repeated rollings of ellipsoidal size soil mass by
hand on a ground glass plate.
c) Shrinkage Limit (SL): is the moisture content (in %) at which the
volume change of the soil mass ceases.
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Definitions
d) Plasticity Index (PI): is a measure of the range of the moisture
contents over which a soil is plastic.
e) Liquidity Index (LI):The relative consistency of a cohesive soilin a natural state can be defined by the ratio called LI.
f) Activity :is the ratio of PI to the clay fraction (% by dry weight of
particles < 2m)
PL-LLPI
PL)-(LL/PL)-(wLI
fraction%)(Clay/PIA
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CLASSIFICATION OF SOILS
The sizes of particles that make up soil may vary widely
depending on the predominant size of particles. Soils are
classified as :
1) Gravel
2) Sand
3) Silt
4) Clay
Unified Soil Classification System (USCS) : most
comprehensive
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USCS
This system classifies soils under two broad
categories: Coarse Grained Soils -are gravelly and sandy in
nature with
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USCS
The standard system used worldwide for most major
construction projects is known as the Unified Soil
Classification System (USCS).
This is based on an original system devised by
Casagrande. Soils are identified by symbols determined
from
Sieve analysis and
Atterberg Limit tests.
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USCS Table
Give typical names: indicate ap-proximat e percent ages of sa ndand gravel: maximum size:angularity, surface condition,and hardness of the coarsegrains: local or geological nameand other pertinent descriptiveinformation and symbol in
parenthes es.
For undisturbed soils add infor-mation on stratification, degreeof compactness, cementation,moisture conditions and drain-age characteristics.
Example:
Well graded gravels, gravel-sand mixtures, little or nofines
Poorly graded gravels, gravel-sand mixtures, little or nofines
Silty gravels, poorlygraded gravel-sand-silt mixtures
Clayey gravels, poorly gradedgravel-sand-clay mixtures
Well graded sands, gravellysands, little or no fines
Poorly graded sands, gravellysands, little or no fines
Silty sands, poorly gradedsand-silt mixtures
Clayey sands, poorly gradedsand-clay mixtures
GW
GP
GM
GC
SW
SP
SM
SC
Wide range of grain size and substantialamounts of all intermediate particlesizesPredominantly one size or a range ofsizes with some intermediate sizesmissing
Non-plastic fines (f or ident ificationprocedures see ML be low)
Plastic fines (for identification pro-cedures see CL below)
Wide range in grain sizes and sub-stantial amounts of all i ntermediate
particle sizesPredominantely one size or a range ofsizes with some intermediate sizes missing
Non-plastic fines (f or ident ification p ro-cedures, see ML below)
Plastic fines (for identification pro-cedures, see CL below)
ML
CL,CI
OL
MH
CH
OH
Pt
Dry strengthcrushing
character-istics
None to
slight
Medium tohigh
Slight tomedium
Slight tomedium
High to veryhigh
Medium tohigh
Readily identified by colour, odourspongy feel and frequently by fibroustexture
Dilatency(reaction
to shaking)
Quick to
slow
None to ver yslow
Slow
Slow tonone
None
None to ver yhigh
Toughness(consistencynear plastic
limit)
None
Medium
Slight
Slight tomedium
High
Slight tomedium
Inorganic silts and very fine sands,rock flour, silty or clayeyfine sands with slight plasticityInorganic clays of low to m edium
plasticit y, gravell y clays, sa ndyclays, silty clays, lean clays
Organic silts and organic silt-clays of low plasticity
inorganic silts, micaceous ordictomaceous fine sandy orsilty soils, elastic silts
Inorganic clays of highplasticit y, fat cla ys
Organic clays of medium tohigh plasticity
Peat and other highly organic soils
Give typical name; indicate degree
and character of plasticity,amount and maximum size ofcoarse grains: colour in wet con-dition, odour if any, local orgeological name, and other pert-inent descriptive information, andsymbol in parentheses
For undisturbed soils add infor-mation on structure, stratif-ication, consistency and undis-turbed and remoulded states,moisture and drainage conditions
ExampleClayey silt, brown: slightly plastic:small percentage of fine sand:numerous vertical root holes: firmand dry in places; loess; (ML)
Field identification procedures(Excluding particles larger than 75mm and basing fractions on
estimated weights)
Groupsymbols
1Typical names
Information required fordescribing soils
Laboratory classificationcriteria
C = G re ate r t ha n 4D
D----60
10U
C = Between 1 and 3(D )
D x D----------------------30
10c
2
60
Not meet ing all gra dation req uireme nts for GW
Atterberg limits below"A" line or PI less than 4
Atterberg limits above "A"line with PI greater than 7
Above "A" line withPI between 4 and 7are borderline casesrequiring use of dualsymbols
Not meet ing all gra dation requ irements for SW
C = G re ate r t ha n 6D
D---- 60
10
U
C = Between 1 and 3(D )
D x D----------------------30
10c
2
60
Atterberg limits below"A" line or PI less than 4
Atterberg limits above "A"line with PI greater than 7
Above "A" line withPI between 4 and 7are borderline casesrequiring use of dualsymbolsD
eterm
inepercentagesof
gravelan
dsan
dfromgra
insizecurve
Usegra
in
sizecurve
inidentifyingthe
fractionsasg
ivenun
der
fiel
didentification
Depen
dingonpercentageso
ffines
(fract
ionsmal
lerthan.0
75mm
sievesize
)coarsegra
ined
soilsareclassi
fiedas
follows
Lessthan5%
Morethan
12%
5%to12%
GW,G
P,SW,S
P
GM,G
C,S
M,
SC
Bor
del
inecaserequ
iringuseo
fdualsym
bo
ls
The.0
75m
msievesize
isaboutthesmal
lestparticlev
isible
tothena
kedeye
Finegrainedsoils
Morethanhalfofmaterialissmallerthan
.075mmsievesize
Coarsegrainedsoils
Morethanhalfofmaterialislargerthan
.07
5mmsievesize
Siltsandclays
liquidlimit
greaterthan
50
Siltsandclays
liquidlimit
le
ssthan50
Sands
Morethanhalfofcoarse
fractionissmallerthan
2.36mm
Gravels
Morethanhalfofcoarse
fractionislargerthan
2.36mm
Sandswith
fines
(appreciable
amountoffines)
Cleansa
nds
(littleor
no
fines)
Gravelswith
fines
(apreciable
amountoffines)
Cleangravels
(littleorno
fines)
Identification p rocedure on fraction smaller than .425mmsieve size
Highly organic soils
Unified soil classification (including identification and description)
Silty sand, gravelly; about 20%hard angular gravel particles12.5mm maximum size; roundedand subangular sand grainscoarse to fine, about 15% non-
plastic lin es with l ow drystrength; well compacted andmoist in places; alluvial sand;(SM)
0 10 20 30 40 50 60 70 80 90 1 00Liquid limit
0
10
20
30
40
50
60
Plast
icity
index
CH
OH
or
MHOL
MLor
CL
"A" l
ine
Comparing soils at equal l iquid limit
Toughness and dry strength increase
with increasing plasticity index
Plasticity chartfor laboratory classification of fine grained soils
CI
CL-MLCL-ML
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Classification Procedure
Coarse Grained MaterialsIf more than half of the material is coarser than the 75 m sieve,
the soil is classified as coarse. The following steps are then
followed to determine the appropriate 2 letter symbol
Determine the1st letter of the symbol If more than half of the coarse fraction is sand then use prefix S
If more than half of the coarse fraction is gravel then use prefix G
Determine the 2nd letter of symbol
This depends on the uniformity coefficient Cu and the coefficientof curvature Cc obtained from the gradation curve, on thepercentage of fines, and the type of fines.
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Classification Procedure
First determine the percentage of fines, that is the % of materialpassing the 75 m sieve.
Then if % fines is
< 5% use W or P as suffix
> 12% use M or C as suffix between 5% and 12% use dual symbols. Use the prefix from above
with first one of W or P and then with one of M or C.
If W or P are required for the suffix then Cu and Cc must beevaluated
If prefix is G then suffix is W if Cu > 4 and Cc is between 1 & 3otherwise use P
If prefix is S then suffix is W if Cu > 6 and Cc is between 1 & 3
otherwise use P
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Classification Procedure
If M or C are required they have to be determined fromthe procedure used for fine grained materials discussedbelow. Note that M stands for Silt and C for Clay. Thisis determined from whether the soil lies above or belowthe A-line in the plasticity chart.
For a coarse grained soil which is predominantly sand thefollowing symbols are possible :
SW, SP, SM, SC
SW-SM, SW-SC, SP-SM, SP-SC
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Classification Procedure
These are classified solely according to the results fromthe Atterberg Limit Tests. Values of the Plasticity Indexand Liquid Limit are used to determine a point in theplasticity chart. The classification symbol is determined
from the region of the chart in which the point lies.Examples
CH High plasticity clay
CL Low plasticity clay
MH High plasticity silt
ML Low plasticity silt
OH High plasticity organic soil (Rare)
Pt Peat
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Casagrande Plasticity Chart
0 10 20 30 40 50 60 70 80 90 100Liquid limit
0
10
20
30
40
50
60
Plasticity
index
CH
OH
or
MH
CL OL
MLor
CL
ML
"A"
line
Comparing soils at equal liquid limit
Toughness and dry strength increase
with increasing plasticity index
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