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Shear Strength of Soils

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Shear Strength of Soils

failure surface

mobilised shear resistance

Soils generally fail in shear

embankment

strip footing

At failure, shear stress along the failure surface reaches the shear strength.

failure surface

The soil grains slide over each other along the failure surface.

No crushing of individual grains.

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

f

failure envelope

friction angle

cohesion

c

f is the maximum shear stress the soil can take without failure, under normal stress of .

f

f tan

frictional component

cohesive component

c

c

f

Shear strength consists of two components: cohesive and frictional.

c and are measures of shear strength.

Higher the values, higher the shear strength.

Y

X

Mohr Circles & Failure Envelope

X

Y

Soil elements at

different locations

X

~ failure

Y

~ stable

c

c

Mohr Circles & Failure Envelope

The soil element does not fail if the Mohr circle is contained within the envelope

GL

Y

c

c+

Initially, Mohr circle is a point

c

c

Mohr Circles & Failure Envelope

As loading progresses, Mohr circle becomes larger…

GL

Y

c

.. and finally failure occurs when Mohr circle touches the envelope

Y

45 + /2

45 + /2

c

c

Orientation of Failure Plane

Failure plane oriented at 45 + /2 to horizontal

GL

90+

Y

c

c+

v

v’

u

h

h’

u

X

X

X

effective stresses

total stresses

u

Mohr circles in terms of & ’

=

+

h’

v’

h

v

c

c

c

c

Envelopes in terms of & ’

Identical specimens initially subjected to different isotropic stresses (c) and then loaded axially to failure

f

uf

Initially…

Failure

c,

in terms of

At failure,

3= c; 1 = c+f

3’= 3 – uf ; 1’ = 1 - uf

c’, ’

in terms of ’

failure plane

O-ring

impervious membrane

soil sample at failure

porous stone

water

piston (to apply deviatoric stress)

perspex cell

cell pressure

pore pressure or

volume change

back pressure

pedestal

deviatoric stress ()

Under all-around cell pressure c

Shearing (loading)

Is the drainage valve open?

Is the drainage valve open?

no

yes

yes

no

Consolidated sample

Undrained loading

Drained loading

Unconsolidated sample

Depending on whether drainage is allowed or not during

- initial isotropic cell pressure application, and

- shearing,

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

ConsolidatedDrained (CD) test

Consolidated Undrained (CU) test

Unconsolidated Undrained (UU) test

For unconsolidated undrained test, in terms of total stresses, u = 0

For normally consolidated clays, c’ = 0 & c = 0.

Granular soils have no cohesion.

c = 0 & c’= 0

Consolidated Drained (CD) Test

- no excess pore pressure throughout the test

- very slow shearing to avoid build-up of pore pressure

Can be days!

not desirable

- gives c’ and ’

Use c’ and ’ for analysing fully drained

situations (e.g., long term stability,

very slow loading)

Consolidated Undrained (CU) Test

- pore pressure develops during shear

Measure ’

- gives c’ and ’

- faster than CD (preferred way to find c’ and ’)

Unconsolidated Undrained (UU) Test

- pore pressure develops during shear

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

Not measured

’ unknown

- analyse in terms of gives cu and u

- very quick test

Use cu and u for analysing undrained

situations (e.g., short term stability,

quick loading)

1

X

3

X

soil element at failure

1

3

1- 3 Relation at Failure

v

h

X

t

stress point

(v-h)/2

s

(v+h)/2

stress point

v

h

t

s

During loading…

Stress path is the locus of stress points

Stress path

Stress path is a convenient way to keep track of the

progress in loading with respect to failure envelope.

t

s

c

failure

tan-1 (sin )

stress path

c cos

During loading (shearing)….

1

3

Y

u = ?

A simple way to estimate the pore pressure change in undrained loading, in terms of total stress changes ~ after Skempton (1954)

Skempton’s pore pressure parameters A and B

B-parameter

B = f (saturation,..)

For saturated soils, B 1.

A-parameter at failure (Af)

Af = f(OCR)

For normally consolidated clays Af 1.

For heavily overconsolidated clays Af is negative.