Mechanic of Soils

7/30/2019 Mechanic of Soils

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2/18/2013 Mechanics of Soils 1

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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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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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


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


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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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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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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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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Mechanic of Soils