25011451 shear strength of soil

7/25/2019 25011451 Shear Strength of Soil

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1

Shear Strength

of Soils

N. Sivakugan

Duration: 17 min: 04 sec



Shear failure

Soils generally fail in shear

strip footing

embankment

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

failure surface mobilised shear

resistance



SIVA Copyright©20013

Shear failure

The soil grains slideover each other alongthe failure surface.

No crushing ofindividual grains.

failuresurface




Shear failure

σ τ

τ

At failure, shear stress along the failuresurface (τ) reaches the shear strength (τf ).




Mohr-Coulomb Failure Criterion

τ

σ

φ σ τ tan+= c f

c

φ

f a i l u r e

e n v e l o p e

cohesion

frictionangle

τf is the maximum shear stress the soil can take

without failure, under normal stress of σ.

τf

σ




Mohr-Coulomb Failure Criterion

φ σ τ tan f f c +=

Shear strength consists of two

components: cohesive and frictional.

σf

τf

φ

τ

σ

c

σf tan φ

c c o h e s

i v e

c o m p o n

e n t

frictionalcompone

nt



c and φ are measures of shear

strength.

Higher the values, higher the shearstrength.



Mohr Circles & Failure Envelope

X

YSoil elements atdifferent locations

XY

X

Y

~ failure

~ stable

τ

σ




Y

nitially, !ohr circle is a point

σc

σc

σc

∆σ

σc

∆σ∆σ

"he soil element does not fail if

the !ohr circle is containedwithin the envelope

!"




Y

σc

σc

σc

∆σ

!"

#s loading progresses, !ohr

circle becomes larger$

.. and finally failure occurs

when !ohr circle touches the

envelope



Orientation of Failure Plane

Y

σc

σc

σc

∆σ

!"

σc∆σ

%&'φ

φ

() ' φ*+

ailure planeoriented at 45 + /2

to hori-ontal

() ' φ*+

Y



Mohr circles in terms of σ & σ’

X X X

σv

σh

σv

σh

u

u

/ '

total stresseseffective stresses

σvσhσvσh

u



Envelopes in terms of σ & σ’dentical specimens

initially sub0ected to

different isotropic stresses1σc2 and then loaded

axially to failure

σc

σc

σc

σc

∆σf

nitially$ ailure

uf

#t failure,

σ3 = σc; σ1 = σc+ σ f

σ3’ = σ3 – uf ; σ1’ = σ1 - uf

c, φ

c, φ

in terms of σ

in terms of σ’


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Triaxial Test pparatus

porous

stone

impervious

membrane

piston 1to apply deviatoric stress2

34ring

pedestal

perspex cell

cell pressure

back pressurepore pressure or

volume change

water

soil sample at

failure

failure plane



T!pes of Triaxial Tests

Under all-around

cell pressure σc

Shearing (loading

!s "he drainage #al#e open$ !s "he drainage #al#e open$

de#ia"oric s"ress ( σ

%es no %es no

&onsolida"ed

sa'pleUnconsolida"ed

sa'ple

rained

loading

Undrained

loading



T!pes of Triaxial TestsDepending on whether drainage is

allowed or not during

initial isotropic cell pressureapplication, and shearing,

there are three special tpes of tria!ialtests that have practical signi"cances.

The are#

Consolidated Drained (CD) test

Consolidated Undrained (CU) testUnconsolidated Undrained (UU) test



!ranu#ar soi#s ha$e

no cohesion%

c & 0 ' c$& 0

(or norma##y conso#i)ate)c#ays* c$ & 0 ' c & 0%

(or unconso#i)ate)un)raine) test* in

terms of tota#

stresses* φu & 0


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C"# C$ an% $$ Triaxial Tests

no e!cess pore pressure throughoutthe test ver slow shearing to avoid build%up ofpore pressure

&onsolidated Drained (&D) Test

gives c$ and φ$

Can ,e )ays-∴ not )esira,#e

'se c$ and φ$ for analsing full drainedsituations (e.g., long term stabilit,ver slow loading)


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pore pressure develops during shear

faster than &D (∴preferred wa to "nd c$and φ$)

&onsolidated 'ndrained (&') Test

gives c$ and φ$

/easure σ$



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pore pressure develops during shear

ver uic test

'nconsolidated 'ndrained ('') Test

analse in terms of σ gives cu and

φu

ot measure)

∴σ$ unnon

& 0 i%e%* fai#ure en$e#ope

is horionta#

'se cu

and φu

for analsing undrained

situations (e.g., short term stabilit,uic loading)



σ- σ' (elation at Failure

)

soil element at failure

σ3 σ1

X σ3

σ1

2645tan7226457tan231 φ φ σ σ +++= c

245tan2245tan2

13 φ φ σ σ −−−= c




Stress Point

t

s

τ

σσh σ$

σ$8σh2

σ$σh2

stress pointstress point

2

hv s σ σ +

=

2

hvt σ σ −

=

X

σv

σh




Stress Path

t

s

*tress pathis the locusof stresspoints

*tress path

9tress path is a con$enient ay to eep trac of the

progress in #oa)ing ith respect to fai#ure en$e#ope%

During #oa)ing

τ

σ




Failure Envelopes

τ

σ

t

s

c

φ

c cos φ

tan45 1sin φ2

fai#ur

e

During #oa)ing shearing%

stress path



Pore Pressure Parameters

*

∆σ1

∆σ3

∆u & ?

; simp#e ay to estimate the pore

pressure change in un)raine)

#oa)ing* in terms of tota# stress

changes < after 9empton 1.54

[ ]7 313 σ σ σ ∆−∆+∆=∆ A Bu

9empton=s pore pressure parameters ; an) >



Pore Pressure Parameters

(or saturate) soi#s* > ≈ 1%

A-parameter at failure (Af )

(or norma##y conso#i)ate) c#ays ;f ≈ 1%

B-parameter

> & f saturation*%%

;f & f?C@

(or hea$i#y o$erconso#i)ate) c#ays ;f is negati$e%

25011451 shear strength of soil

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