Shear Strength Lecture

8/11/2019 Shear Strength Lecture

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of Soils


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Shear failureSoils generally fail in shear

embankment

strip footing

failure surface mobilised shear

resistance

At failure, shear stress along the failure surfacereac es e s ear s reng .


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Shear failure

The soil grains slide over

failure surface

failure surface.

No crushing ofindividual grains.

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Shear failure

At failure, shear stress along the failure surface

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reac es e s ear s reng f .


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Mohr-Coulomb Failure Criterion

tan cf

c

cohesionfriction angle

f

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f is the maximum shear stress the soil can take

without failure, under normal stress of .


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Mohr-Coulomb Failure Criterion

Shear strength consists of two

components: cohesive and frictional.

tanc

f tan frictionalcomponent

f

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c and are measures of shear stren th.

Higher the values, higher the shear strength.


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Mohr Circles & Failure Envelope

Y

X

Y Soil elements at

X

different locationsX ~ failure


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Mohr Circles & Failure Envelope

The soil element does not fail if

the Mohr circle is contained

GL

c

Y cc c+

Initially, Mohr circle is a point


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Mohr Circles & Failure EnvelopeAs loading progresses, Mohr

circle becomes larger

GL

c

Y cc

.. and finally failure occurs

when Mohr circle touches the

envelope


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Orientation of Failure Plane

Failure plane

oriented at 45 + /2Y

GL

to horizontal

45 + /2

c

Y cc c+

90+


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Mohr circles in terms of &

v v u

X X Xh h u= +

effective stresses

total stresses

vhvhu


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Envelopes in terms of & Identical specimens

initially subjected to

different isotropic stresses

and then loaded

f

axially to failure

c

c

c

c

Initially Failure

f

c,

in terms of ,

3 = c; 1 = c+ f

= u ; = - u

c,


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1-3 Relation at Failure

X 3

1

X

3

2

anan31 c2 13


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SIVA Copyright2001


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Soil strength

Soils are essentially frictional materials

the strength depends on the applied stress

Strength is controlled by effective stresses

Soil strength depends on drainage different strengths will be measured for a given soil that

(a) deforms at constant volume (undrained) and

pressures (drained)


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Mohr-Coulomb failure criterion

n

The limiting shear stress (soil strength) is given by

= c + n tan =

= friction angle


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Mohr-Coulomb failure criterion

The parameters c, are in general not soil constants. Theydepend on

d

the type of loading (drained or undrained)

The Mohr-Coulomb criterion is an empirical criterion, and the

failure locus is only locally linear. Extrapolation outside therange o norma s resses or w c as een e erm ne s

likely to be unreliable.


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Effective stress failure criterion

I t e so s at a ure t e e ect ve stress a ure cr ter on w

always be satisfied.

c n' tan '

cand are known as the effective (or drained) strengtharameters.


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Effective stress failure criterion

I t e so s at a ure t e e ect ve stress a ure cr ter on w

always be satisfied.

c n' tan '

cand are known as the effective (or drained) strengtharameters.

effective strength parameters are the fundamental strength

parameters. But they are not necessarily soil constants.


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Total stress failure criterion

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 n utan

cu and u are known as the undrained strength parameters


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cu n utan


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

moisture content of the soil.


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cu n utan


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 soilsthat in the short term remain undrained. Note that as the pore

failure criterion cannot be used.


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Tests to measure soil strength

.

Normal load

Load cell to

op p a en

Motor

drive

measure

Shear Force

Soil

Porous plates

Rollers

Measure relative horizontal displacement, dx

vertical displacement of top platen, dy


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Shear box test

Usually only relatively slow drained tests are performed in shear

box apparatus. For clays rate of shearing must be chosen to

.

gravels tests can be performed quickly

Tests on sands and ravels are usuall erformed dr . Water

does not significantly affect the (drained) strength.

If there are no excess pore pressures and as the pore pressure

identical.

The failure stresses thus define an effective stress failure

envelope from which the effective (drained) strength parametersc, can be determined.


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Typical drained shear box results

Load

(F)

Normal

load

Shea

Horizontal displacement (dx)


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Typical drained shear box results

= F/APeak

Ultimate

= N/AN1 N2


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Figure 11.6 Plot of

shear stress and

ooks/Cole,adivisionofThoms

change in height of

specimen against shear

20

01Br

and dense dry sand

(direct shear test)


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A eak and an ultimate failure locus can be obtained from the

Interpretation of shear box tests

results each with different c and values.

All soils are essentially frictional and continued shearing results

.

Normally consolidated clays (OCR=1) and loose sands do not

show se arate eak and ultimate failure loci and for soils in

these states c = 0.

Overconsolidated clays and dense sands have peak strengthsw c .

Note that dense sands do not possess any true cohesion

bonds the a arent cohesion results from the tendenc of soil

to expand when sheared.


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Shear box test - advantages

Easy and quick test for sands and gravels

Lar e deformations can be achieved b reversin shear

direction. This is useful for determining the residual strength of a

soil

Large samples may be tested in large shear boxes. Small

samples may give misleading results due to imperfections

fractures and fissures or the lack of them.

Samples may be sheared along predetermined planes. This is

planes are required.

Sh b di d


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Shear box test - disadvantages

- .stress-strain behaviour cannot be determined. The estimated

stresses may not be those acting on the shear plane.

There is no means of estimating pore pressures so effectivestresses cannot be determined from undrained tests

Undrained strengths are unreliable because it is impossible to

prevent localised drainage without high shearing rates

In practice shear box tests are used to get quick and crude

estimates of failure parameters

T t t il t th


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Tests to measure soil strength

2. The Triaxial TestDeviator load

Confining

cylinder

Rubber

membrane

-

seals

Porous filterSoil

Celldisc

pressure

and volume

change


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Triaxial Test A aratuspiston (to apply deviatoric stress)

O-ring

failure plane

porous

membrane

soil sample at

failure

stoneperspex cell

water

cell pressure

back pressurepore pressure or

volume chan e


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T es of Triaxial Testsdeviatoric stress ()

n er a -aroun

cell pressure c

ear ng oa ng

Is the draina e valve o en? Is the draina e valve o en?

yes no yes no

samplenconsolidated

sample

ra ne

loading loading


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T es 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

Unconsolidated Undrained (UU) test


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For unconsolidated

undrained test in

terms of total

stresses, u = 0

Granular soils have

no cohesion.

For normally consolidated

clays, c = 0 & c = 0.c = 0 & c= 0


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CD, CU and UU Triaxial Tests

Consolidated Drained (CD) Test

very slow shearing to avoid build-up of pore

Can be days!

not desirable

situations (e.g., long term stability,very slow loading)


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Consolidated Undrained (CU) Test

pore pressure eve ops ur ng s ear

Measure

gives c and

faster than CD (preferred way to find c and )


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Unconsolidated Undrained (UU) Test

pore pressure eve ops ur ng s ear

Not measured

unknown= 0; i.e., failure envelope is

horizontal

analyse in terms of gives cu and u

Use cu and u for analysing undrained

situations (e.g., short term stability,quick loading)


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1-3 Relation at Failure

X 3

1

X

3

2

anan31 c2 13


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Stress PointvXh

q stress point stress point

-

p

or

h v

v

p(

v

+h

)/2

2

hvq

2

hvp


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Stress Path

During loading

q

is the locusof stressoints

Stress path

p

or

p

Stress path is a convenient way to keep track of the

ro ress in loadin with res ect to failure envelo e.


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Failure Envelo es

q failure

tan-1 (sin )

p

During loading (shearing).


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Pore Pressure Parameters

A simple way to estimate the pore

pressure change in undrained

loading, in terms of total stresschan es ~ after Skem ton 1954

1 )( 313 ABuY 3

u = ? Skemptons pore pressure

parameters A and B


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=

If soil is saturated B=1, therefore,

u = 3 + A (1 -3)

3 ,

A = u / (1 - 3)


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Pore Pressure Parameters

B-parameter

For saturated soils, B 1.

,..

A-parameter at failure (Af)

For normally consolidated clays Af 1.

f

For heavily overconsolidated clays Af is negative.

Stresses in triaxial specimens


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=r

=r r

pressure)

a

= x a s ress



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p

=r

=r r

pressure)

a

= x a s ress

Fa r

Arom equ r um we ave



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p

,

q a r ( ) ( ) 1 3

The axial and radial stresses are principal stresses

If q = 0 increasing cell pressure will result in

volumetric compression if the soil is free to drain. The

effective stresses will increase and so will the strength increasing pore water pressure if soil volume is constant

(that is, undrained). As the effective stresses cannot change

o ows a u = r

Increasing q is required to cause failure

Strains in triaxial specimens


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p

, ,volume dV we can determine

dh

Volume strain

ah0

VdV

where h0 is the initial height and V0 is the initial volume

0

Strains in triaxial specimens


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p

, ,volume dV we can determine

dh

Volume strain

ah0

VdV

where h0 is the initial height and V0 is the initial volume

0

It is assumed that the specimens deform as right circular cylinders.

The cross-sectional area, A, can then be determined from

1 +dV

V 1 - v0

1 +dh

h

1 -

o o

a

0

Advantages of the triaxial test


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pec mens are su ecte to approx mate y un orm stressesand strains

The complete stress-strain-strength behaviour can be

investigated

Drained and undrained tests can be performed

,allowing effective stresses to be determined

applied

Typical triaxial results


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Increasing cell

pressure

a

Interpretation of Laboratory results


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. ra ne s ear oa ng

In laboratory tests the loading rate is chosen so that no excess

water pressures will be generated, and the specimens are free

to drain. Effective stresses can be determined from the applied

total stresses and the known pore water pressure.

relevance to drained tests.

It is possible to construct a series of total stress Mohr circles but

e n erre o a s ress un ra ne s reng parame ers are

meaningless.



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Effective strength parameters are generally used to check thelong term stability (that is when all excess pore pressures have

dissipated) of soil constructions.

For sands and gravels pore pressures dissipate rapidly and theeffective strength parameters can also be used to check the

short term stability.

In rinci le the effective stren th arameters can be used tocheck the stability at any time for any soil type. However, to do

this the pore pressures in the ground must be known and in

general they are only known in the long term.



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In undrained laboratory tests no drainage from the sample must occur,

nor should there be moisture redistribution within the sample.

In the shear box this requires fast shear rates. In triaxial tests slowerloading rates are possible because conditions are uniform and

drainage from the sample is easily prevented.

In a triaxial test with ore ressure measurement the effectivestresses can be determined and the effective strength parameters c,

evaluated. These can be used as discussed previously to evaluatelong term stability.



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undrained) strength parameters cu, u. If these parameters are to berelevant to the ground the moisture content must be the same. This can

be achieved either b erformin UU tests or b usin CIU tests and

consolidating to the in-situ stresses.

The total (undrained) strength parameters are used to assess the short

erm s a y o so cons ruc ons. s mpor an a no ra nage

should occur if this approach is to be valid. For example, a total stress

analysis would not be appropriate for sands and gravels.

For clayey soils a total stress analysis is the only simple way to assess

stability

o e a un ra ne s reng s can e e erm ne or any so , u ey

may not be relevant in practice

Relation between effective and total stress criteria


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triaxial tests. Each sample is subjected to a different cell pressure. No

water can drain at any stage.



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water can drain at any stage. At failure the Mohr circles are found to

e as s own

13



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water can drain at any stage. At failure the Mohr circles are found to

e as s own

13

We find that all the total stress Mohr circles are the same size,and therefore u = 0 and = su = cu = constant



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,stress failure condition must also be satisfied. As all the circles

have the same size there must be only one effective stress Mohr

circle c n' tan '

1313



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,stress failure condition must also be satisfied. As all the circles

have the same size there must be only one effective stress Mohr

circle c n' tan '

1313

1 3 1 3 2 cuWe have the following relations

1 3 = N + 2 c N



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The different total stress Mohr circles with a single effectivestress Mohr circle indicate that the pore pressure is different for

each sample.

As discussed previously increasing the cell pressure withoutallowing drainage has the effect of increasing the pore pressure

by the same amount (u = r) with no change in effectivestress.

The change in pore pressure during shearing is a function of the

initial effective stress and the moisture content. As these are

identical for the three samples an identical strength is obtained.

Significance of undrained strength parameters


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It is often found that a series of undrained tests from a particular

site give a value of u that is not zero (cu not constant). If thisha ens either

the samples are not saturated, or

the samples have different moisture contents

If the samples are not saturated analyses based on undrained

behaviour will not be correct

The undrained strength cu is not a fundamental soil property. If

the moisture content changes so will the undrained strength.

Example


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In an unconsolidated undrained triaxial test the undrainedstrength is measured as 17.5 kPa. Determine the cell pressure

used in the test if the effective stren th arameters are c = 0

= 26o and the pore pressure at failure is 43 kPa.

Example


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Analytical solution

= = 1 3 1 3

. 2 2

Example


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Analytical solution

= = 1 3 1 3

.

Failure criterion 1 3 = N + 2 c N

2 2

Example


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Analytical solution

= = 1 3 1 3

.

Failure criterion 1 3 = N + 2 c N

2 2

Hence = 57.4 kPa, = 22.4 kPa

and cell pressure (total stress) = + u = 65.4 kPa

Graphical solution


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26

17.5

Graphical solution


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26

17.5

13

Graphical solution


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26

17.5

1313


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= + +

Ms

= (dh)cu

x d/2

T = c [( d2h/2) +(d3/4)]

= for triangular mobilization of undrained shear

strength

= or un orm mo zat on o un ra ne s ear

strength

=

strength

Shear Strength Lecture

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