Note11_ShearStrengthOfSoil

8/10/2019 Note11_ShearStrengthOfSoil

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Shear Strength of Soils

ChihChih--Ping LinPing LinNationalNational ChiaoChiaoTungTungUniv.Univ.

[email protected]@mail.nctu.edu.tw

Soil Mechanics

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Outline

Shear FailureShear Failure

Soil StrengthSoil Strength

MohrMohr--Coulomb Failure CriterionCoulomb Failure Criterion

Laboratory Shear Strength TestLaboratory Shear Strength Test

Direct shearDirect shear

TriaxialTriaxial

Stress PathStress Path

Pore Pressure ParametersPore Pressure Parameters


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Shear failure

Soils generally fail inSoils generally fail in shearshear

strip footing

embankment

At failure, shear stress along the failure surfacereaches the shear strength.

failure surface mobilised shear

resistance

Shear Failure

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Shear failure

The soil grains slide overeach other along thefailure surface.

No crushing ofindividual grains.

failure surface

Shear Failure


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Shear failure

At failure, shear stress along the failure surface() reaches the shear strength (f).

Shear Failure

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Soil (Shear) Strength

Soils are essentiallySoils are essentially frictional materialsfrictional materials

the strength depends on the applied stressthe strength depends on the applied stress

Strength is controlled byStrength is controlled by effective stresseseffective stresses

water pressures are requiredwater pressures are required

Soil strength depends onSoil strength depends on drainagedrainage

different strengths will be measured for a given soildifferent strengths will be measured for a given soil

a)a) deforms at constant volume (deforms at constant volume (undrainedundrained) and) and

b)b) deforms without developing excess pore pressuresdeforms without developing excess pore pressures(drained)(drained)

Soil Strength


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Mohr-Coulomb Failure Criterion

'tan'' += cf

c

failure

envel

ope

cohesionfriction angle

f is the maximum shear stress the soil can take

without failure, under normal stress of .

f

Mohr-Coulomb

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Mohr-Coulomb Failure Criterion

'tan'' ff c +=

Shear strength consists of two

components: cohesive and frictional.

f

f

c

f tan

c cohesiveco

mpone

nt frictionalcomponent

Mohr-Coulomb


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c and are measures of shear strength.

Higher the values, higher the shear strength.

The parameters c, depend on

Soil composition

Stress state of the soil (OCR)

The MohrThe Mohr--Coulomb criterion is an empirical criterion,Coulomb criterion is an empirical criterion,

and the failure locus is only locally linear.and the failure locus is only locally linear.

Extrapolation outside the range of normal stressesExtrapolation outside the range of normal stresses

for which it has been determined is likely to be unreliable.for which it has been determined is likely to be unreliable.

Mohr-Coulomb

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Mohr Circles & Failure Envelope

Y

Initially, Mohr circle is a point

c

c

c

c+

The soil element does not fail if

the Mohr circle is contained

within the envelope

GL

Mohr-Coulomb


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Mohr Circles & Failure Envelope

Y

c

c

c

GL

As loading progresses, Mohr

circle becomes larger

.. and finally failure occurs

when Mohr circle touches the

envelope

Mohr-Coulomb

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Orientation of Failure Plane

Y

c

c

c

GL

c+

90+

45 + /2

Failure plane

oriented at 45 + /2

to horizontal (1)

45 + /2

Y

Mohr-Coulomb


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Mohr circles in terms of &

X X X

v

h

v

h

u

u

= +

total stresseseffective stresses

vhvhu

Mohr-Coulomb

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Envelopes in terms of &

Identical specimens

initially subjected to

different isotropic stresses

(c) and then loaded

axially to failure

c

c

c

c

f

Initially Failure

uf

At failure,

3 = c; 1 = c+ f

3 = 3 uf ; 1 = 1 - uf

c,

c,

in terms of

in terms of

Mohr-Coulomb


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Effective stress failure criterion

tan +=c

cand are known as the effective (or drained) strength

parameters.

Soil behaviour is controlled by effective stresses, and the

effective strength parameters are the fundamental strength

parameters. But they are not necessarily soil constants.

If the soil is at failure the effective stress failure criterion will

always be satisfied.

Mohr-Coulomb

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Total stress failure criterion

uuc tan+=

If the soil is taken to failure at constant volume (undrained) then the

failure criterion can be written in terms of total stress as

cu and u are known as the undrained strength parameters

These parameters are not soil constants, they depend strongly on the

moisture content of the soil.

The undrained strength is only relevant in practice to clayey soils

that in the short term remain undrained. Note that as the porepressures are unknown for undrained loading the effective stress

failure criterion cannot be used.

Mohr-Coulomb


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Laboratory Tests for Shear Strength Parameters

Direct shear testDirect shear test

TriaxialTriaxial testtest

Direct simple shear testDirect simple shear test

Plane strainPlane strain triaxialtriaxial testtest

TorsionalTorsional ring shear testring shear test

Shear Strength Test

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Direct Shear Test

Motor

drive

Load cell tomeasure

Shear Force

Normal load

Rollers

Soil

Porous plates

Top platen

Measure relative horizontal displacement, dx

vertical displacement of top platen, dy

Direct Shear


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Sand

Direct Shear

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Clay

Direct Shear


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Types of Triaxial Tests

Under all-around

cell pressure c

Shearing

(loading)

Is the drainage valve open? Is the drainage valve open?

deviatoric stress ()

yes no yes no

Consolidatedsample

Unconsolidatedsample

Drainedloading

Undrainedloading

Triaxial

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Types of Triaxial TestsDepending on whether drainage is allowedor not during

initial isotropic cell pressure application, and

shearing,

there are three special types of triaxial teststhat have practical significances. They are:

Consolidated Drained (CD) test

Consolidated Undrained (CU) test

Unconsolidated Undrained (UU) test

Triaxial


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Granular soils have

no cohesion.

c = 0 & c= 0

For normally consolidated

clays, c= 0 & c = 0.

For unconsolidated

undrained test, in

terms of total

stresses, u = 0

Triaxial

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CD, CU and UU Triaxial Tests

no excess pore pressure throughout the test

very slow shearing to avoid build-up of porepressure

Consolidated Drained (CD) Test

gives c and

Can be days!

not desirable

Use c and for analysing fully drainedsituations (e.g., long term stability,very slow loading)

Triaxial


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1 and 3 at Failure

Triaxial

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Stress Point

t

s

h v

(v-h)/2

(v+h)/2

stress point stress point

2

hvs +

=

2hvt

=

X

v

h

Stress Path


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Stress Path

t

s

Stress path is

the locus ofstress points

Stress path

Stress path is a convenient way to keep track of the

progress in loading with respect to failure envelope.

During loading

Stress Path

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Failure Envelopes

t

s

c

c cos

tan-1 (sin )

failure

During loading (shearing).

stress path

Stress Path


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Pore Pressure Parameters

Y

1

3

u = ?

A simple way to estimate the pore

pressure change in undrained

loading, in terms of total stress

changes ~ after Skempton (1954)

[ ])( 313 += ABu

Skemptons pore pressure

parameters A and B



For saturated soils, B 1.

A-parameter at failure (Af)

For normally consolidated clays Af 1.

B-parameter

B = f (saturation,..)

Af= f(OCR)

For heavily overconsolidated clays Afis negative.


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Note11_ShearStrengthOfSoil