Dr.HusseinM.AshourAl.Khuzaie;[email protected] 1
FoundationEngineering,2018-2019
Dr.HusseinM.AshourAl.KhuzaieProfessor,CivilEngineering,CollegeofEngineering,Al-MuthannaUniversity
Syllabus of Foundation DesignSite Investigation, Bearing capacity of Soil, Settlement,
Foundation Design, Piles, Lateral Earth Pressure, slope Stability.
1st Lecture:ReviewofShearStrengthofSoils
ShearStrengthofSoils
Dr.HusseinM.AshourAl.Khuzaie;[email protected] 2
Date:10/1/2018
Foundation Engineering
Shearfailure
Soilsgenerallyfailinshear
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strip footing
embankment
At failure, shear stress along the failure surface reaches the shear strength.
failure surface mobilised shear resistance
Shearfailure
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The soil grains slide over each other along the failure surface.
No crushing of individual grains.
failure surface
Shearfailure
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At failure, shear stress along the failure surface (t) reaches the shear strength (tf).
Mohr-CoulombFailureCriterion
Dr.HusseinM.AshourAl.Khuzaie;[email protected]
t
s
fst tan+= cf
c
f
cohesion friction angle
tf is the maximum shear stress the soil can take without failure, under normal stress of s.
tf
s
Mohr-CoulombFailureCriterion
Dr.HusseinM.AshourAl.Khuzaie;[email protected] 7
fst tanff c +=
Shear strength consists of two components: cohesive and frictional.
sf
tf
f
t
s
c
sf tan f
c
frictional component
c and f are measures of shear strength.
Higher the values, higher the shear strength.
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Mohr Circles & Failure Envelope
X
Y Soil elements at
different locations
XY
X
Y
~ failure
~ stable
t
s
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Mohr Circles & Failure Envelope
Y
Initially, Mohr circle is a point
sc
sc
sc
Ds
sc+DsDs
The soil element does not fail if the Mohr circle is contained within the envelope
GL
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Mohr Circles & Failure Envelope
Y
sc
sc
sc
Ds
GL
As loading progresses, Mohr circle becomes larger…
.. and finally failure occurs when Mohr circle touches the envelope
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Orientation of Failure Plane
Y
sc
sc
sc
Ds
GL
sc+Ds
90+ff
45 + f/2
Failure plane oriented at 45 + f/2to horizontal
45 + f/2
Y
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Mohr circles in terms of s & s’
X X X
sv
sh
sv’
sh’
u
u= +
total stresseseffective stresses
svshsv’sh’u
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Envelopes in terms of s & s’Identical specimens initially subjected to different isotropic stresses (sc) and then loaded axially to failure
sc
sc
sc
sc
Dsf
Initially… Failureuf
At failure,
s3 = sc; s1 = sc+Dsf
s3’= s3 – uf ; s1’ = s1 - uf
c, f
c’, f’
in terms of s
in terms of s’
Dr.HusseinM.AshourAl.Khuzaie;[email protected]
TriaxialTestApparatus
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porous stone
impervious membrane
piston (to apply deviatoric stress)
O-ring
pedestal
perspex cell
cell pressure
back pressurepore pressure or
volume change
water
soil sample at failure
failure plane
TypesofTriaxialTests
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Under all-around cell pressure sc
Shearing (loading)
Is the drainage valve open? Is the drainage valve open?
deviatoric stress (Ds)
yes no yes no
Consolidatedsample
Unconsolidatedsample
Drained loading
Undrainedloading
TypesofTriaxialTests
Dr.HusseinM.AshourAl.Khuzaie;[email protected] 17
Depending on whether drainage is allowed or not during
v initial isotropic cell pressure application, andv shearing,
there are three special types of triaxial tests that have practical significances. They are:
Consolidated Drained (CD)testConsolidated Undrained (CU)testUnconsolidatedUndrained (UU)test
Forunconsolidatedundrainedtest,intermsoftotalstresses,fu =0
1
Fornormallyconsolidatedclays,c’ =0&c=0.
3
Granularsoilshavenocohesion.c=0&c’=0
2
ForReview
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CD,CU andUU TriaxialTests
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v no excess pore pressure throughout the testv very slow shearing to avoid build-up of pore
pressure
Consolidated Drained (CD) Test
v gives c’ and f’
Canbedays!\ notdesirable
Use c’ and f’ for analysing fully drainedsituations (e.g., long term stability, very slow loading)
CD,CU andUU TriaxialTests
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v pore pressure develops during shear
v faster than CD (\preferred way to find c’ and f’)
Consolidated Undrained (CU) Test
v gives c’ and f’
Measureè s’
CD,CU andUU TriaxialTests
Dr.HusseinM.AshourAl.Khuzaie;[email protected] 21
v pore pressure develops during shear
v very quick test
Unconsolidated Undrained (UU) Test
v analyse in terms of s è gives cu and fu
Notmeasured\s’ unknown
=0;i.e.,failureenvelopeishorizontal
Use cu and fu for analysing undrainedsituations (e.g., short term stability, quick loading)
s1- s3 Relation at Failure
X
soil element at failure
s3 s1
X s3
s1
)2/45tan(2)2/45(tan231 ffss +++= c
)2/45tan(2)2/45(tan213 ffss ---= cDr.HusseinM.AshourAl.Khuzaie;[email protected] 22
StressPoint
Dr.HusseinM.AshourAl.Khuzaie;[email protected]
t
s
t
ssh sv
(sv-sh)/2
(sv+sh)/2
stress point stress point
2hvs ss +
=2
hvt ss -=
X
sv
sh
StressPath
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t
s
Stress path is the locus of stress points
Stress path
Stresspathisaconvenientwaytokeeptrackoftheprogressinloadingwithrespecttofailureenvelope.
During loading…
t
s
FailureEnvelopes
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t
s
t
s
c
f
c cos f
tan-1 (sin f)
failure
During loading (shearing)….
stress path
PorePressureParameters
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Y
Ds1
Ds3
Du = ?
A simple way to estimate the pore pressure change in undrained loading, in terms of total stresschanges ~ after Skempton (1954)
[ ])( 313 sss D-D+D=D ABu
Skempton’s pore pressure parameters A and B
PorePressureParameters
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For saturated soils, B » 1.
A-parameter at failure (Af)
For normally consolidated clays Af » 1.
B-parameter
B = f (saturation,..)
Af = f(OCR)
For heavily overconsolidated clays Af is negative.