Foundation Engineering, 2018- 2019...2018/11/01 · Shear failure Soils generally fail in shear Dr. Hussein M. Ashour Al.Khuzaie; [email protected] 3 strip footing embankment At failure,

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


Date:10/1/2018

Foundation Engineering

Shearfailure

Soilsgenerallyfailinshear


strip footing

embankment

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

failure surface mobilised shear resistance

Shearfailure


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

No crushing of individual grains.

failure surface

Shearfailure


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


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.


Mohr Circles & Failure Envelope

X

Y Soil elements at

different locations

XY

X

Y

~ failure

~ stable

t

s



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



Y

sc

sc

sc

Ds

GL

As loading progresses, Mohr circle becomes larger…

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


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


Mohr circles in terms of s & s’

X X X

sv

sh

sv’

sh’

u

u= +

total stresseseffective stresses

svshsv’sh’u


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’


TriaxialTestApparatus


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


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


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


CD,CU andUU TriaxialTests


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)



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’



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


t

s

t

ssh sv

(sv-sh)/2

(sv+sh)/2

stress point stress point

2hvs ss +

=2

hvt ss -=

X

sv

sh

StressPath


t

s

Stress path is the locus of stress points

Stress path

Stresspathisaconvenientwaytokeeptrackoftheprogressinloadingwithrespecttofailureenvelope.

During loading…

t

s

FailureEnvelopes


t

s

t

s

c

f

c cos f

tan-1 (sin f)

failure

During loading (shearing)….

stress path

PorePressureParameters


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


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.

Documents

Foundation Engineering, 2018- 2019...2018/11/01 · Shear failure Soils generally fail in shear Dr. Hussein M. Ashour Al.Khuzaie; [email protected] 3 strip footing embankment At failure,