25011451 Shear Strength of Soil
-
Upload
anonymous-xqnx0v7d -
Category
Documents
-
view
222 -
download
5
Transcript of 25011451 Shear Strength of Soil
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 1/26
1
Shear Strength
of Soils
N. Sivakugan
Duration: 17 min: 04 sec
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 2/26
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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 3/26
SIVA Copyright©20013
Shear failure
The soil grains slideover each other alongthe failure surface.
No crushing ofindividual grains.
failuresurface
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 4/26
SIVA Copyright©20014
Shear failure
σ τ
τ
At failure, shear stress along the failuresurface (τ) reaches the shear strength (τf ).
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 5/26
SIVA Copyright©20015
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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 6/26
SIVA Copyright©20016
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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 7/26
c and φ are measures of shear
strength.
Higher the values, higher the shearstrength.
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 8/26
Mohr Circles & Failure Envelope
X
YSoil elements atdifferent locations
XY
X
Y
~ failure
~ stable
τ
σ
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 9/26
Mohr Circles & Failure Envelope
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
!"
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 10/26
Mohr Circles & Failure Envelope
Y
σc
σc
σc
∆σ
!"
#s loading progresses, !ohr
circle becomes larger$
.. and finally failure occurs
when !ohr circle touches the
envelope
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 11/26
Orientation of Failure Plane
Y
σc
σc
σc
∆σ
!"
σc∆σ
%&'φ
φ
() ' φ*+
ailure planeoriented at 45 + /2
to hori-ontal
() ' φ*+
Y
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 12/26
Mohr circles in terms of σ & σ’
X X X
σv
σh
σv
σh
u
u
/ '
total stresseseffective stresses
σvσhσvσh
u
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 13/26
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’
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 14/26SIVA Copyright©2001 14
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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 15/26SIVA Copyright©2001 15
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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 16/26SIVA Copyright©2001 16
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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 17/26
!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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 18/26SIVA Copyright©2001 1+
C"# C$ an% $$ Triaxial Tests
no e!cess pore pressure throughoutthe test ver slow shearing to avoid build%up ofpore pressure
&onsolidated Drained (&D) Test
gives c$ and φ$
Can ,e )ays-∴ not )esira,#e
'se c$ and φ$ for analsing full drainedsituations (e.g., long term stabilit,ver slow loading)
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 19/26SIVA Copyright©2001 1.
C"# C$ an% $$ Triaxial Tests
pore pressure develops during shear
faster than &D (∴preferred wa to "nd c$and φ$)
&onsolidated 'ndrained (&') Test
gives c$ and φ$
/easure σ$
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 20/26
SIVA Copyright©2001 20
C"# C$ an% $$ Triaxial Tests
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$e#ope
is horionta#
'se cu
and φu
for analsing undrained
situations (e.g., short term stabilit,uic loading)
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 21/26
σ- σ' (elation at Failure
)
soil element at failure
σ3 σ1
X σ3
σ1
2645tan7226457tan231 φ φ σ σ +++= c
245tan2245tan2
13 φ φ σ σ −−−= c
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 22/26
SIVA Copyright©2001 22
Stress Point
t
s
τ
σσh σ$
σ$8σh2
σ$σh2
stress pointstress point
2
hv s σ σ +
=
2
hvt σ σ −
=
X
σv
σh
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 23/26
SIVA Copyright©2001 23
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
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 24/26
SIVA Copyright©2001 24
Failure Envelopes
τ
σ
t
s
c
φ
c cos φ
tan45 1sin φ2
fai#ur
e
During #oa)ing shearing%
stress path
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 25/26
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) >
7/25/2019 25011451 Shear Strength of Soil
http://slidepdf.com/reader/full/25011451-shear-strength-of-soil 26/26
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%