Shear-Strength-of-Soil.pdf

8/13/2019 Shear-Strength-of-Soil.pdf

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CEL 610 Foundation Engineering


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Strength of different

materials

Steel Concrete Soil

Tensile Compressive Shear

Presence of pore waterComplex


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Shear failure of soils

Soils generally fail in shear

Embankment

Strip footing

Failure surface

Mobilized shear

resistance

At failure, shear stress along the failure surface

(mobilized shear resistance) reaches the shear strength.


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Retaining

wall


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Retaining

wall

Mobilized

shear

resistance

Failure

surface

At failure, shear stress along the failure surface

(mobilized shear resistance) reaches the shear strength.


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failure surface

The soil grains slideover each other alongthe failure surface.

ruindividual grains.


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At failure, shear stress along the failure surface ()reaches the shear stren th .


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Mohr-Coulomb Failure Criterion

in terms oftotal stresses

tancf

Cohesion Friction angle

cf

f failure, under normal stress of .


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in terms ofeffective stresses

'tan'' cf

u

=

Effectivecohesion Effective

pressure

cr c on ang ef

f failure, under normal effective stress of .


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Shear strength consists of two

com onents: cohesive and frictional.

''' ff f frictional

c c

component

f '


11/84

.

, .


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Mohr Circle of stress

1

33

Soil element

1

'

3

'

1

,

2''''

'

'

3

'

1

'

3

'

1'2

22os


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1

11

Soil element

33

Soil elementSoil element

33 33

1

11

'

3

'

1

'

3

'

1'2

2

'

3

'

1

2

'

3

'

1 '

3'

1


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1

11

Soil element

33

Soil elementSoil element

33 33

1

11

, '

3

'

1

'

3

'

1'2

2

'

3

'

1

2

'

3

'

1 '

3'

1

PD = Pole w.r.t. plane


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Mohr Circles & Failure Envelo e

Failure surface

'tan'' c

X XY

Y

Soil elements at different locations

Y ~ stable


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Mohr Circles & Failure Envelo e

The soil element does not fail if

within the envelope

Y

cc

c

Initially, Mohr circle is a point

c+


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Mohr Circles & Failure Envelo eAs loading progresses, Mohr

circle becomes larger

Yc

cc

.. and finally failure occurs

when Mohr circle touches the


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Orientation of Failure Plane

11 Failure envelope

, f33

33

1

1

'3

'

1 '

3'

1

2

PD = Pole w.r.t. plane

Therefore, =


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Mohr circles in terms of total & effective stresses

v uv

= Xh

Xu

+Xh

effective stresses

total stresses

oru


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Failure envelopes in terms of total & effective

v uv

= Xh

Xu

+Xh

If X is onfailure

Failure envelope interms of total stressesFailure envelope in terms

of effective stresses

effective stressestotal stresses

orccu


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Mohr Coulomb failure criterion with Mohr circle

v = 1 Failure envelope in termsof effective stresses

X

h = 3

effective stresses

c X is on failure 13

Therefore,

2

'2

'' 3131

SinCotc


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Mohr Coulomb failure criterion with Mohr circle

'''

'

3

'

1

'

3

'

1

22

'''' ''2'3131 oscin

'''' '' 31

''

'1'' CosSin '1'131 SinSin

''

'2''

2231


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Determination of shear strength parameters of ,

specimens taken from

representative undisturbedsamples

os common a ora ory es s

to determine the shear strengthparameters are,

. ane s ear es

2. Torvane

3. Pocket penetrometer

1.Direct shear test

2.Triaxial shear test

4. Fall cone

5. Pressuremeter

6. Static cone enetrometer

Other laboratory tests include,

Direct simple shear test, torsional

7. Standard penetration test

r ng s ear es , p ane s ra n r ax a

test, laboratory vane shear test,laboratory fall cone test


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Laboratory tests

Field conditions

A re resentative

zvc

soil samplez

vc +

hc hchc

vc vc

Before construction er an ur ng

construction


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Laboratory testsvc +

Simulating field conditionsin the laboratory

hchc

vc0 vc +

hchc00vc

vc0

Step 1Representative vc

Set the specimen in

the apparatus andtaken from the

site

ep

Apply theapp y e n a

stress conditioncorresponding field

stress conditions


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Direct shear test

c ema c agram o e rec s ear appara us


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Direct shear test

rec s ear es s mos su a e or conso a e ra ne es s

specially on granular soils (e.g.: sand) or stiff clays

plates

Components of the shear box Preparation of a sand specimen


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Direct shear test

Preparation of a sand specimen Pressure plate

eve ng t e top sur ace

of specimenSpecimen preparation

completed


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Direct shear test

Test procedure

Pressure plate

ee aP

Porous

plates

S

Proving ring

o measure

shear force

Step 1: Apply a vertical load to the specimen and wait for consolidation


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Direct shear test

PTest procedure

Pressure plate

ee a

Porous

plates

S

Proving ring

o measure

shear force

Step 1: Apply a vertical load to the specimen and wait for consolidation

Step 2: Lower box is subjected to a horizontal displacement at a constant rate


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Direct shear test

Shear box

Dial gauge tomeasure vertical

Proving ringto measure

Loadin frame to Dial au e to

shear force

apply vertical load measure horizontaldisplacement

Di t h t t


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Direct shear test

Analysis of test results

(P)forceNormal

stressNormal

sampletheofsectioncrossofArea

sur aces ngat t eeve operes stanceearstressShear

Note: Cross-sectional area of the sample changes with the horizontal

dis lacement

Direct shear tests on sands


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Direct shear tests on sandsStress-strain relationshi

ss,

Dense sand/

ea

rstr c ayf

Loose sand/

Sh NC clayf

Shear displacement

on

Dense sand/OC Clayh

eight

p

leExpans

Loose sand/NC Claangein

thesa

ssion Shear displacement

C of

Com

pre

Di t h t t d


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,

=arstres

Normal stress = 2Normal stress = 3

f1

Sh f2f3

Shear displacement

re,f

atfailu

Mohr Coulomb failure envelope

rstres

S

he

Normal stress,

Di t h t t d


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Sand is cohesionless

hence c = 0drained and pore water

pressures are,

Therefore,

= and c = c = 0

Di t h t t l


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Direct shear tests on clays

In case of clay, horizontal displacement should be applied at a veryslow rate to allow dissipation of pore water pressure (therefore, one

Failure envelopes for clay from drained direct shear tests

,f Overconsolidated clay (c 0)

tfailu

r

Normally consolidated clay (c = 0)

s

tress

Shear

Normal force,

I t f t t di t h t


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Interface tests on direct shear apparatus

n many oun a on es gn pro ems an re a n ng wa pro ems,

is required to determine the angle of internal friction between soil

and the structural material (concrete, steel or wood)

PP

Soil SSoil S

Foundation materialFoundation material

tan'c Where,ca = a es on,

= angle of internal friction

S


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Triaxial Shear Test

Piston (to apply deviatoric stress)

Failure planeO-ring

impervious

membrane

at failure PorousstonePerspex

sample

cell

Water

pedestal

Cell pressure

Back pressure Pore pressure or

volume change

T i i l Sh T t


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Triaxial Shear Test

Specimen preparation (undisturbed sample)

Sampling tubes

Sample extruder

T i i l Sh T t


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Triaxial Shear Test


Edges of the sample

are carefull trimmed

Setting up the sample

in the triaxial cell

T i i l Sh T t


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Triaxial Shear Test


Sample is coveredCell is com letel

membrane and sealed

filled with water

Tria ial Shear Test


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Triaxial Shear Test


Provin rin to

measure the

deviator load

Dial gauge to

measure vertical

displacement

Types of Triaxial Tests d i t i t


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Types of Triaxial Tests deviatoric stress =cStep 1 Step 2

cc c c

+Under all-around cell pressure c

cShearing (loading)

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

yes no yes no

samplenconsolidated

sample

ra ne

loading

n ra ne

loading

Types of Triaxial Tests


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Types of Triaxial Tests

Step 1 Step 2

- u u c ear ng oa ng

Is the drainage valve open?

yes no

Is the drainage valve open?

Consolidatedsam le

Unconsolidated Drained Undrainedoa ng

CD test UU test

Consolidated- drained test (CD Test)


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( )

Step 1: At the end of consolidation

, ,

=

hC 0 hC =Step 2: During axial stress increase

hC

VC +

V = VC + =1hC 0 h = hC = 3Drainage

VC + f Vf= VC + f=1f

hC 0

hf

= hC

=3fDrainage



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=

3 = hC

Deviator stress (q or d) = 13



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Volume chan e of sam le durin consolidation

f

the

p

ansion

hange E

Time

olum

e

ample

sion

Compre



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Stress-strain relationshi durin shearin

,d

Dense sand

r

stres

d)fLoose sand

eviato or NC Clayd)f

Axial strainon

Dense sand

or OC claange

ple

Expans

lumec

thesa

ssion Axial strain

oose san

or NC clay

V of

Com

pre

CD tests How to determine strength parameters c and


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ess,

Confining stress = 3c1 3 d f

iatorst

Confining stress = 3ad)fbon n ng s ress = 3b

3De

Axial strain d fa

ss,

Mohr Coulomb

arstr

Sh

or 3c 1c3a 1a(d)fa3b 1b

(d)fb

CD tests


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reng parame ers c an o a ne rom es s

Since u = 0 in CD

=Therefore, c = c

and = , cd and d are usedto denote them

CD tests Failure envelopes


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For sand and NC Clay, cd = 0

,

d

stres

o r ou om

failure envelope

hea

r

or3a 1ad fa

Therefore one CD test would be sufficient to determine of sand or NC clay

CD tests Failure envelopes


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For OC Clay, cd 0

or3 1

c

Some practical applications of CD analysis for


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p pp y

1. Embankment constructed very slowly, in layers over a soft clay

deposit

Soft clay

= in situ drainedshear strength



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p pp y

2. Earth dam with steady state seepage

Core

= drained shear



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p pp y

3. Excavation or natural slope in clay

= In situ drained shear strengthNote: CD test simulates the long term condition in the field.

Thus, cd and d should be used to evaluate the longterm behavior of soils

Consolidated- Undrained test (CU Test)


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Step 1: At the end of consolidation

, ,

=

hC 0 hC =Step 2: During axial stress increase

hC

VC + No

V VC 1

hC udrainage h = hC u = 3

VC + f Vf= VC + fuf=1fhCodrainage uf hf= hC uf=3f




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fthe

p

ansion

hange E

Time

olum

e

amp

le

sion

Compre

Stress strain relationshi durin shearin



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Stress-strain relationshi durin shearin

,d

Dense sand

r

stres

d)fLoose sand

eviato or NC Clayd)f

Axial strain

Loose sand

/NC Clay

+

u-

Axial strain

or OC clay

CU tests How to determine strength parameters c and


59/84

= ess,

Confining stress = 3b

iatorst

3

3a

De

Axial strain Total stresses at failure

d fa

tres

s, cuMohr Coulomb

failure envelope in

terms of total stresses

h

ear

S

or ccu 3b 1b3a 1a

(d)fa

CU tests How to determine strength parameters c and 1 = 3 + (d)f - uf


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1 3 ( d)f uf

Mohr Coulomb failure

envelo e in terms of

=3 - ufuf

s,

Mohr Coulombeffective stresses

Effective stresses at failure

rstre cua ure enve ope nterms of total stresses

She

or ccu 3b 1bC ufa

ufb

(d)fa3b 1b3a 1a

(d)fa 3a 1a

CU tests


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reng parame ers c an o a ne rom es s

Shear strength

parameters in terms

parameters in terms

of effective stressesof total stresses are

ccu andcuare c and

c = c and =

CU tests Failure envelopes


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or san an ay, ccu an c =

Mohr Coulomb failure

Mohr Coulomb enve ope n erms o

effective stresses

ress, cufailure envelope in

terms of total stresses

ear

st

S or3a

(d)fa,

cu and = d) of sand or NC clay

Some practical applications of CU analysis for


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1. Embankment constructed rapidly over a soft clay deposit

Soft clay

= in situ undrainedshear strength



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2. Rapid drawdown behind an earth dam

Core

= Undrained shear



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3. Rapid construction of an embankment on a natural slope

Note: Total stress arameters from CU test c and can be used for

= In situ undrained shear strengthstability problems where,

Soil have become fully consolidated and are at equilibrium with

the existing stress state; Then for some reason additional

stresses are applied quickly with no drainage occurring

Unconsolidated- Undrained test (UU Test)


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Initial specimen conditionSpecimen conditionduring shearing

C = 3 =

No 3 + dNo 3

Initial volume of the sample = A0 H0

Volume of the sample during shearing = A H

Since the test is conducted under undrained condition,

=

A (H0H) = A0 H0A

A 0

A (1 H/H0

) = A0

z



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0

Step 2: After application of hydrostatic cell pressureC = 3 =

3 = 3 -uc

No

c 3 3 c

c 3Increase of cell pressure

increase of cell pressureSkemptons pore water

pressure parameter, B

Note: If soil is fully saturated, then B = 1 (hence, uc

= 3

)


St 3 D i li ti f i l l d


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Step 3: During application of axial load

+ 1 = 3 + d -uc ud3

drainage 3 = 3 -uc ud= +uc ud

ud = ABdIncrease of pwp due to

increase of deviator stressIncrease of deviator

stress

Skemptons pore water

pressure parameter, A


C bi i t 2 d 3


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Combining steps 2 and 3,

uc = B 3 ud = ABdTotal pore water pressure increment at any stage, u

u = uc + udu = B [3 + Ad]

Skemptons pore

water pressureu = B [3 + A(13]equa on


, ,


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Step 1: Immediately after sampling

0V0 = ur

0 -ur h0 = ur C

C -ur uc = -ur cNo

drainage

VC C r -C rh = ur

(Sr= 100% ; B = 1)

Step 3: During application of axial load

V = C + + ur -c uC C

No

drainage-ur c u h = C + ur -c u

Step 3: At failure Vf= C + f+ ur -c uf= 1fC + fhf= C + ur -c uf

= 3f-u

r

cu

f

C

drainage


, ,


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Step 3: At failure Vf= C + f+ ur -c uf= 1f + hf= C + ur -c uf

= 3f -ur c ufC

drainage

Mohr circle in terms of effective stresses do not depend on the cell

pressure.

Therefore, we get only one Mohr circle in terms of effective stress for

different cell pressures

3 1f


, ,


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Step 3: At failure Vf= C + f+ ur -c uf= 1f + hf= C + ur -c uf

= 3f -ur c ufC

drainage

Mohr circles in terms of total stresses

Failure envelope, u = 0

uaub

cu

3b 1b3a 1af

3 1 or


Effect of degree of saturation on failure envelope


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Effect of degree of saturation on failure envelope

S < 100% S > 100%

3b b3a a3c c

Some practical applications of UU analysis for


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1. Embankment constructed rapidly over a soft clay deposit

Soft clay

= in situ undrainedshear strength



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2. Large earth dam constructed rapidly with

no change in water content of soft clay

Core

= Undrained shear



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3. Footing placed rapidly on clay deposit

= In situ undrained shear strength

Note: UU test simulates the short term condition in the field.

, ubehavior of soils

Unconfined Compression Test (UC Test)


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1 = VC +

= 0

Unconfined Compression Test (UC Test)


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1 = VC + fs,

arstre

3 = 0Sh

qu

Normal stress,

f= 1/2 = qu/2 = cu

Various correlations for shear strength


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For NC clays, the undrained shear strength (cu) increases with theeffective overburden pressure,0

)(0037.011.0'

PIcu

Skempton (1957)

Plasticity Index as a %

For OC clays, the following relationship is approximately true

8.0

'

0

'

0

)(OCR

edConsolidatNormally

u

idatedOverconsol

u

Ladd (1977)

For NC clays, the effective friction angle () is related to PI as follows

)log(234.0814.0' IPSin Kenny (1959)

Shear strength of partially saturated soils


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In the previous sections, we were discussing the shear strength of saturated soils. However, in most of the cases, we will encounter

WaterPore water

pressure, u

Air pressure, ua

Effective

ore wa er

pressure, uw

stress, Effectivestress,

Saturated soils Unsaturated soils

Pore water pressure can be negative in unsaturated soils


Bishop (1959) proposed shear strength equation for unsaturated soils as


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Bishop (1959) proposed shear strength equation for unsaturated soils as

follows

'tan)()(' waanf uuuc Where,

n ua = Net normal stress

u u = Matric suction

= a parameter depending on the degree of saturation

( = 1 for fully saturated soils and 0 for dry soils)

Fredlund et al (1978) modified the above relationship as follows

b

waanf uuuc tan)('tan)(' ,

tanb = Rate of increase of shear strength with matric suction



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bwaanf uuuc tan)('tan)('

Same as saturated soils Apparent cohesion

Therefore, strength of unsaturated soils is much higher than the strength

- ua

How it become possible


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b'' waanf

Same as saturated soils Apparent cohesion

due to matric suction

Apparent - uacohesion


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Shear-Strength-of-Soil.pdf