1 Soil Mechanics Revision-1

8/11/2019 1 Soil Mechanics Revision-1

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Applied Geotechnics Soil Mechanics Review 1


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Applied Geotechnics

Hossein TaiebatRoom CE 502

E-mail: [email protected]


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Soil Behaviour

A look at how weve got at this point:

Origin of soils and rocks (Geology)

Phase relationships

Stress in soil, effective stress concept

Seepage and flow of water in soil

Consolidation settlement, rate of consolidation

Shear strength of soils


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7/77Applied Geotechnics Soil Mechanics Review 7

Clay

Three main minerals:Kaolinite (weathered tropical soil)

Strong bond

A particle may have 100 stacks

Resists water penetration and ions

SiAl

Hydrogen bond +

Van der waals forces

Does not absorb

water, thus little

swell on wetting

Silica

Gibbsite

Clay minerals:

Complex aluminium silicates: Two basic units:

Silica tetrahedron (SiO4)

Alumina octahedron (Al (OH)3)



Clay Clay minerals:

Complex aluminium silicates: Two basic units:

Silica tetrahedron (SiO4)

Alumina octahedron (Al (OH)3)

Three main minerals:

Kaolinite (weathered tropical soil)

Illite (moderate rainfall areas)

Moderate water absorbent

Silica

Gibbsite

SiAlSi

K ions -> minor affinity

with water, fixed ions


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PHASE RELATIONSHPS


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Definitions

Soil grain

Air

Water

It is not the actual volumes that are important but rather the

ratios between the volumes of the different phases.

Va

Vw

Vs

Vv

Void ratio (e)s

v

V

Ve

Degree of saturation (Sr

)

v

W

r V

VS

Moisture content:s

w

W

Wm

s

r

G

S.e

m

s

w

M

M

For saturated soil, Sr=100%

s

G

em m65.2e


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Major Soil Types Based on grain size:

Coarse grained (granular) soils: Visible to naked eyes: sands, gravels.

Fine grained soils:

Silts, clays, and organic soils.

Based on major properties:

Cohesive soils

Clays

Cohesionless soils Silts, Sands, Gravels

Grain size (mm)

0.060.002Silt

0.002-Clay

20.06Sand602Gravel

MaxMinSoil type



Particle size (mm)

Finer%

100

90

80

70

60

50

40

30

20

10

0

Grain Size Distribution

Clay Silt Sand Gravel Cobbles0.0001 0.001 0.01 0.1 1 10 100

W

P

U

C

F

SieveHydrometer


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STRESS IN SOIL



t=0

Stresses in Dry Soil

zW

sv

W = gdz AW = sv A

sv= gdz

q

+q

shsh= Kosv

Ko= Coefficient of lateral earth pressure

at rest


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Stresses in Saturated Soil

Effective stress concept:

Vw

F`


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sv= sv- u

Effectivestress

Totalstress

Pore waterpressure =gwzw

sh

= Ko

sv

Coefficient of earth pressure at rest

sh= sh + u


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u

u

u

uss

s

s

s


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Pressure (kPa)

e1.0

0.9

0.8

0.7

0.61 10 100 1000

Ideal Soil Behaviour

Normally consolidated

(on the line)

Over-consolidated

Soil is normally consolidated if

the current stress in the soil is the

maximum ever experienced by

the soil.

Soil is over-consolidated if it has

been subjected to a larger stress

than the current stress.


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Coefficient of Volume ChangeDefines the rate of volume change around a specific

stress range:

In one dimensional settlement problems:

'

H/Hm ov

s

Or:

'

)e1/(em ov

s

Unit: (kPa-1)

mvdepends on stress level.

It is not a constant property of soil.

'

V/Vmv

s


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Settlement Calculation

Two methods to estimate the consolidation

settlement:

Using the slopes of the bilinear e-logsplot

Using the coefficient of volume change, mv:

'

H/Hm ov

s

H = mvsoHo

Stf=H oo

He1

e

)

'

'log(Ce

i

fr

s

sFor over-consolidated soils

)'

'log(Ce

i

fc

s

sFor normally consolidated soils

Can use average conditions at mid-layer.

Can divide the layer into sub-layers:

tftf

SS


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Rate of Settlement Settlement of granular soils is instantaneous.

Settlement of fine grained soils occur over a longtime.

Sandq

s

q

s

t

s, u, s

Clayq s

s

t

s, u, s

u

u

C lid i M d l


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Consolidation Model

water

Tap, as soil

permeability

Spring, as

soil skeleton

q

C lid ti


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Consolidation Conditions at the beginning and the end of

consolidation can be calculated.

qus

What is the conditions during the process of

consolidation?

Consolidation process may take a long time.

Effective stress and settlement need to be determined

during the consolidation process.

C l l ti f S ttl t


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Calculation of Settlement

0.0 0.2 0.4 0.6 0.8 1.0

U(%)

Dimensionless time, Tv

00

40

60

20

80

100

Approximate equations for degree of consolidation:

)2.0T(T4

U vv

)2.0T(e8

1U v4/T

2v

0.197


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SHEAR STRENGTH OFSOIL

I t d ti


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Introduction Soil strength needs to be evaluated in many problems.

A failure surface can be identified in many cases along

which shear stress reaches the shear strength of soil.

I t d ti


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I t d ti


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M h C l b C it i


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Mohr-Coulomb Criterion

N

F

F

N

A failure : F = mN

m= tan d

F = N tan d

dsn

t

tf

snA failure : t

f

= sn

tan f

Failure plane

A simple model:

Based on friction only

M h C l b C it i


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F

F

A failure : F = Fa

t

tf

A failure : tf

= c

Failure plane

A simple model:

Based on cohesion only

c = soil cohesion

Mohr Co lomb Criterion


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Failure plane


N

F

F

N

A failure : F = mN +Fa

m= tan d

F = N tan d+Fa

dsn

t

tf

snA failure : t

f

= sn

tan f+ c

A simple model:

Based on friction and cohesion

Failure plane

Mohr Coulomb Criterion


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Shear strength of soil has 2 components:

Friction Cohesion


tf= c + sntan ftf = shear strength of soil

sn= normal stress on failure planec = soil cohesion (unit of stress), a soil property

f = friction angle of soil grains, a soil property

Cohesion and friction angle are measures of shear

strength

Higher the values, higher the shear strength.



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Friction Cohesion


tf= c + sntan f Graphical representation:

t

s

f

sn

c

sntan f

tf


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Friction Cohesion


tf= c + sntan f Graphical representation:

t

s

f

t< tfSafe stress state

Impossible stress state



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t

s

f

sn

t

sh

sn

t



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t

s

f

sn

t


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t

s

f

sn

t


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Mohr-Coulomb Criterion In terms of principal stresses:

t

ss3 s1f

(s, t)

2cotc

2sin31

31

ssf

ss

f

ff

ffss

sin1

cosc2sin1

sin131

)2/45tan(c2)2/45(tan231 ffss

ffss Nc2N31

(s1- s3) / 2

)2/45(tanN 2 ff

(s1+ s3) / 2c cotf


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Cohesionless Soils


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Cohesionless Soils Strength criterion

tf= sntan f Always effective normal stress is used, sn. Friction angle, f, can be measured:

In the lab using direct shear test

In the field, usingStandard Penetration Test (SPT)

Cone Penetration Test (CPT)

Direct Shear Test Apparatus


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Direct Shear Test Apparatus


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Cohesive Soils


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Cohesive Soils Strength is related to consolidation process and

loading speed.

Cohesive soils have low permeability.

If load is applied quickly, soil deforms under undrained

conditions.

If load is applied slowly, or long time after loading, soildeforms under drainedconditions.

The strength of soil will continuously change during the

consolidation process.

The undrained and drained strengths are the twoextremes of soil shear strength.

Undrained and drained strength parameters can be

obtained from laboratory tests.

Drained Shear Strength


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Drained Shear Strength Used to assess soil strength a long time after loading

or where the failure is deemed to occur slowly.

Strength criteriontf= c+ sntan f

tf = shear strength of soil

sn= effective normal stress on failure planec = drained soil cohesion

= 0 for normally consolidated clays

f = drained soil friction angle

t

sc

f


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Triaxial Test


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Triaxial tests can be used toobtained all strength

parameters for different soils.

Different radial and axialpressure can be applied. The applied stresses are the

principal stresses.

Pore water pressure inside thesample can be controlled. Drained and undrained behaviour

of the soil can be simulated.

Triaxial Test


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Triaxial Test


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Triaxial Test

Cell pressure

(sr or s3)

Deviator load

Deviator stress

All tests have 2 loading phases:

Application of cell pressureApplication of deviator load

Types of Triaxial Tests


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Types of Triaxial Tests There are many test variations depend on the

drainage condition during the 2 phases of loading:

1stphase: application of cell pressure:

Drainage valve open; soil sample is consolidated (C).

Drainage valve closed; soil sample is unconsolidated (U).

2nd

phase: application of deviator load:Drainage valve open; soil behaves under drained conditions (D).

Drainage valve closed; soil behaves under undrained conditions (U).

Triaxial tests are designated by two letters describing

the drainage conditions of the 2 phases of loading. The most commonly tests are:

UU (Unconsolidated Undrained)

CU (Consolidated undrained)

CD (Consolidated Drained)


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CU Triaxial Test


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CU Triaxial Test The undrained shear strength (cu) is dependent on

the level of effective stress under which the soil has

been consolidated.

It increases as the consolidation stress increases.

Relationship between consolidation stress and undrained

strength for normally consolidated clay is linear.

Consolidation stress

cu

s(kPa)

t (kPa)

cu1

cu2

cu3


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1 Soil Mechanics Revision-1

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