01 lecture notes -week 3- a slide per page -gray

8/13/2019 01 Lecture Notes -Week 3- A Slide Per Page -Gray

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Elastic settlement in soilsElastic settlement in soils

ENB371: Geotechnical Engineering 2ENB371: Geotechnical Engineering 2Chaminda GallageChaminda Gallage


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4/53

Subsurface vertical stress increment inhomogeneous and isotropic soils due followingloading conditions on the surface was discussed

Subsurface vertical stress increment inhomogeneous and isotropic soils due followingloading conditions on the surface was discussed

Review Week 2 (1)Review Week 2 (1)

Uniformly loaded infinite area

Uniformly loaded circular area

Strip loading

Uniformly loaded rectangular area

Loading through flexible foundation was assumedLoading through flexible foundation was assumed


5/53

Uniformly loaded infinite areaUniformly loaded infinite areaThe vertical subsurface stress increment at any depth belowthe infinitely loaded area is considered to be the same as thesurface stress due to external load (filling material)

h

hq =


q=== 21

1z

2z

1

2

1z

2z

11 +

22 +


6/53

Subsurface stress increment due to a point loadSubsurface stress increment due to a point load

r


pIz

P2=

2/5

2)/(1

1

2

3

+= zrIp

Influence factor, Ip

z


7/53

Subsurface stress increment due to uniformlyloaded circular areaSubsurface stress increment due to uniformlyloaded circular area


c

Iq0

=


8/53

Vertical stress increment due to strip areacarrying uniform pressure

Vertical stress increment due to strip areacarrying uniform pressure

qB

q

B

X


z

z

X

{ })2cos(sin

++= q

z

z

X

1R

2R

=

2sin2

1

B

Xqz


9/53

rIq0=

BL

DefineDefine m = B/zm = B/zandand n = L/zn = L/z

Vertical stress increment due to uniformly loaded

rectangular area

Vertical stress increment due to uniformly loaded

rectangular area



10/53

Influence chart for vertical stress increaseInfluence chart for vertical stress increase

Newmark (1942) influence chart , based on the Boussinesq solution todetermine the vertical stress increase at any point below an area of anyshape carrying uniform pressure (q0).

Chart consists of influence areas which

has a influence value of 0.005 per unitpressure

The loaded area is drawn on tracing


the scale line on the chart is equal to thedepth z

Position the loaded area on the chartsuch that the point at which the vertical

stress required is at the centre of thechart.

The count the number of influenceareas covered by the scaled drawing, N

Then, vertical stress increase at z depth, = 0.005 qoN


11/53

Approximate method to determine the stresssubsurface stress increment (600 approximation)

Approximate method to determine the stresssubsurface stress increment (600 approximation)


According to this method, the increase in stress at depth z is

))((

0

zLzB

LBq

++

=


12/53

Contours of equal vertical pressure in the vicinity of

(a) a strip area carrying a uniform pressure(b) a square area carrying a uniform pressure

Contours of equal vertical pressure in the vicinity of

(a) a strip area carrying a uniform pressure(b) a square area carrying a uniform pressure

The zone lying inside the vertical stress contour of value0.2q is described as the bulb of pressure

B width of the foundation


13/53

Large DistributedLarge DistributedWeightWeight

Very Large ConcentratedVery Large ConcentratedWeightWeight

Loading on the surface causes deformation/settlement in sub-soilsLoading on the surface causes deformation/settlement in sub-soils

Introduction (1)Introduction (1)

WeightWeight

WeakWeakSoilSoil

Weak RockWeak Rock Strong RockStrong Rock


14/53

Introduction (2): Settlement in soilsIntroduction (2): Settlement in soils

structure embankment

profile

These loads produce corresponding increases in the

vertical effective stress, v Settlement refers to the compression that soils undergo as

a response of placing loads on the surface


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Introduction (3): SignificanceIntroduction (3): Significance

If the settlement is not kept to tolerable limit, the desireduse of the structure may be impaired and the design life of

the structure may be reduced

It is therefore important to have a mean of predicting theamount of soil com ression or settlement


16/53

Total settlement in soil due to loadingTotal settlement in soil due to loading

Deformation of soil and

rock grains Compression of air and

water in voids

Deformation of soil and

rock grains Compression of air and

water in voids

Elastic Deformation(Immediate

settlement) (Se)

Elastic Deformation(Immediate

settlement) (Se)


ra nage o wa er anair from voids allowing

compression of soil

skeleton

Creep movements plastic adjustment of soilfabric under a constanteffective stress

ra nage o wa er anair from voids allowing

compression of soil

skeleton

Creep movements plastic adjustment of soilfabric under a constanteffective stress

+ PrimaryConsolidation (Sp)

+ PrimaryConsolidation (Sp)

+ SecondaryCompression (Ss)

+ SecondaryCompression (Ss)

Se+Sp+Ss= Total SettlementSe+Sp+Ss= Total Settlement


17/53

TimingTimingtimetimelog timelog time

elasticelastic -- immediateimmediate -- fully recoverablefully recoverable

1 week to several years1 week to several years


settlement

settlement

primary consolidationprimary consolidation

due to removal of waterdue to removal of waterinelasticinelastictimetime--dependentdependentpartial recovery onlypartial recovery only

secondary compressionsecondary compressioncreep of particlescreep of particlesinelasticinelastictimetime--dependentdependent

unrecoverableunrecoverable

0.5yr0.5yr 5yr 5yr 50yr50yr


18/53

Elastic (immediate) settlement of soil (Se)Elastic (immediate) settlement of soil (Se)


Caused by the elastic deformation of soil particles whenthe effective stress is increasedFully recoverable

Not time dependent (occur within very short time)Calculations generally based on equations derived fromtheory of elasticity

AA

HH

FFFF

FFFF

uniformuniformaxialaxialstress,stress,

== HH// EE

= F= F // AA

= / = / = / = / = / = / = / = /

= = = = = = = = EE

F

or

or

F

or

or


19/53

Flexible vs Rigid FoundationFlexible vs Rigid Foundation


Flexible foundation: uniform contact pressure, non-uniform

deformation

Rigid foundation: non-uniform contact pressure, uniformdeformation


20/53

Flexible vs Rigid Foundation(contact pressure and settlement in clay)

Flexible vs Rigid Foundation(contact pressure and settlement in clay)

(a) Flexible foundation in clay


(b) Rigid foundation in clay


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Flexible vs Rigid Foundation(contact pressure and settlement in sand)

Flexible vs Rigid Foundation(contact pressure and settlement in sand)

(a) Flexible foundation in sand


(b) Rigid foundation in sand


22/53

Elastic properties (E Youngsmodulus) of clay and sand

Elastic properties (E Youngsmodulus) of clay and sand

In the case of an extensive, homogeneous deposit of saturated clay, it is a reasonable approximation to assume

that E is constant throughout the deposit


In the case of sand, however, the value of E varies with

confining pressure and, therefore, will increase with depth

and varies across the width of the loaded area


23/53

Elastic settlement of sandy soil under flexible foundation(Equation based on theory of elasticity) - 1


fs

s

se II

EBqS

2

0

1)'(

=

Bowels (1987)Bowels (1987)

'

0

soilofratiosPoisson

foundationtheonpressureappliednetq

s =

=

)1948,(

)1934,(

2/'

40fromelasticityofmodulusAverage

FoxfactordepthI

erSteinbrennfactorshapeI

foundationofcornerforB

foundationofcentretheforBB

BzabouttozE

f

s

s

=

=

=

=

==

=

fundationofcornertheat

foundationofcentretheat

,1

,4

=

=

levelfoundationfromrocktheDepth to

foundationtheofDepthD

foundationtheofLengthL

foundationtheofWidth

f

=

=

=

=

H

B


24/53

Is= shape factorIs= shape factor

2121 FFI ss

+=



fs

s

se II

EBqS

2

01)'( =

sF1 and F2can be obtained from tables using m and n or can

be calculatedF1 and F2can be obtained from tables using m and n or can

be calculated

)2/('' B

HnB

Lm

foundationtheofcentretheat

settlementthecalculateTo

==BHn

BLm

foundationtheofcorneraat

settlementthecalculateTo

== ''


25/53

Variation of F1

Variation of F1


26/53

Variation of F2

Variation of F2


27/53

Is( shape factor ) can be calculatedIs( shape factor ) can be calculated21

1

21FFI

s

ss

+=



)2/(''

B

Hn

B

Lm

foundationtheofcentretheatsettlementthecalculateTo

==B

Hn

B

Lm

foundationtheofcorneraatsettlementthecalculateTo

== ''

2

1

2

101

tan

2

'

)(1

An

F

AAF

=

+=

)1'''

'

1'''

'1)1''(ln

)1''1('

'')1'1(ln'

222

22

22

1

22

222

0

++=

+++

+++=

+++

+++=

nmn

m

A

nmm

nmmA

nmm

nmmmA


28/53

If= depth factorIf= depth factor

LDf



fs

s

se II

EBqS

2

01)'( =

BB sf ,,

If can be obtained from charts using Df/B,s and L/BIf can be obtained from charts using Df/B,s and L/B

I b bt i d f h t i D /B d L/BI b bt i d f h t i D /B d L/B


29/53


I can be obtained from charts using D /B and L/BI can be obtained from charts using D /B and L/B


30/53


El ti ttl t f d il d fl ibl f d tiEl ti ttl t f d il d fl ibl f d ti


31/53

Due to the heterogeneous nature of soil deposits, the

magnitude of Esmay vary with depth. For that reason, Bowles(1987) recommended using average of Es

Due to the heterogeneous nature of soil deposits, the

magnitude of Esmay vary with depth. For that reason, Bowles(1987) recommended using average of Es

fs

s

se II

EBqS

2

0

1)'(

=



z

zEE is

s

=

)(

smalleriswhicheverBorHz

zdepthawithinelasticityofulussoilE is

,5

mod)(

=

=

E l 1 1E l 1 1


32/53

Example 1 - 1Example 1 - 1

A flexible shallow foundation 1 m X 2 m is shown below.Calculate the elastic settlement at the centre of thefoundation.

A flexible shallow foundation 1 m X 2 m is shown below.Calculate the elastic settlement at the centre of thefoundation.

fs

s

se II

EBqS

2

01)'( =

E l 1 2E l 1 2


33/53


fs

s

se II

EBqS

2

01)'( =

zE

B = 1 m, L = 2 mB = 1 m, L = 2 m Bmz 55 ==

zs =

kPaEs 400,105

)2000,12()1000,8()2000,10(=

++=

For centre of foundationFor centre of foundation

105.0

5

)2/(',2

1

2',4 =======

B

Hn

B

Lm

5.02

1

2' ===

B

B

Example 1 3Example 1 3


34/53


10',2' == nm From tables, F1 = 0.641 F2= 0.031From tables, F1 = 0.641 F2= 0.031

659.0031.0

3.01

3.021641.0

1

2121 =

+=

+= FFI

s

ss

21f LD

mmIIE

BqS fss

se 27.1201227.0709.0659.0

400,10

)3.01(5.04150

1)'(

22

0 ==

=

=

.,.,

1

,

1 fS

BB


35/53

Improved equation for Elastic Settlement of

sandy soil-1


sandy soil-1Mayne and Poulos (1999) presented an improved formula forcalculating the elastic settlement of soil (sand) under

foundation load taking into account:

Rigidity of the foundation

Mayne and Poulos (1999) presented an improved formula forcalculating the elastic settlement of soil (sand) under

foundation load taking into account:

Rigidity of the foundation

Depth of embedment of the foundation

Increase in elastic modulus of the soil with depth

Location of rigid layers at limited depth

Depth of embedment of the foundation

Increase in elastic modulus of the soil with depth

Location of rigid layers at limited depth

I d i f El i S l fI d i f El i S l f


36/53

oundationoulusElasticE

layersoillecompressibofulusElasticE

foundationofdiameterEquivalentBfoundationof

centrethebelowsettlementelasticTheS

S

e

e

=

=

=

=

mod

mod


sandy soil-2


sandy soil-2

( )20

0 1 sEFGe

eE

IIIBqS =

foundationofthicknesst

factorcorrectionembedmentFoundationI

factorcorrectionrigidityFoundationI

depthwithEof

iationtheforfactorInfluenceI

depthFoundationDsoilratiosPoisson

E

F

s

G

f

s

=

=

=

=

=

=

var

'

levelfoundationfromrocktheDepth to=H

Improved equation for Elastic Settlement ofImproved equation for Elastic Settlement of


37/53

For rectangular foundationFor rectangular foundation

BLBe =

4

Improved equation for Elastic Settlement ofsandy soil-3

Improved equation for Elastic Settlement ofsandy soil-3

( )20

0 1 sEFGe

eE

IIIBqS =

foundationoflengthL

oun a onow

=

=

For circular foundationFor circular foundation

foundationofdiameterB

BBe

=

=kzEEs += 0

zwithuluselasticsoilinincreaseofratekfoundationofbottomthefromdepthz

depthfoundationatsoilofelasticityE

mod

0

=

=

=



38/53

Influence factor for the variation of Eswith depthInfluence factor for the variation of Eswith depth

),( 0GHE

fI ==

Improved equation for Elastic Settlement ofsandy soil- 4


( )2

0

0

1 sEFGe

e E

IIIBq

S =

ee



39/53

Foundation rigidity

correction factor

Foundation rigidity

correction factor



( )2

0

0 1 sEFGeeE

IIIBqS =

3

0

2

2

106.4

1

4

+

+

+=

ee

f

F

B

t

kB

E

E

I



40/53

Foundation embedmentcorrection factorFoundation embedmentcorrection factor

( )

2

0

0

1 sEFGe

e E

IIIBq

S =



( )

+

=

6.14.022.1exp5.31

f

e

E

D

BI

Elastic settlement of sandy soil using strainElastic settlement of sandy soil using strain


41/53

Elastic settlement of sandy soil using straininfluence factor - 1


The settlement of granular soils can also be evaluated by theuse of semiemperical strain influence factor proposed by

Schmertmann (1978).

The settlement of granular soils can also be evaluated by theuse of semiemperical strain influence factor proposed by

Schmertmann (1978).

Iz2

zEqq se

=

021

f

z

Dq

foundationtheofleveltheatstressq

soilincreepforaccounttofactorcorrectionaC

embedmentfoundationofdepththeforfactorcorrectionaC

I

=

=

=

=

=

2

1

factorinfluenceStrain



42/53



z

E

IqqCCS

z

s

ze =

2

0

21 )(

Correction factor for depth (C1) and correction factor for creep (C2) areCorrection factor for depth (C1) and correction factor for creep (C2) are

+=

=

1.0log2.01

5.01

2

1

yearsintimeC

qq

qC



43/53



zE

IqqCCSz

s

ze =

2

0

21 )(

The strain influence factor Izfor square (L/B=1) or circular foundations and

foundations with L/B10 is shown here. Izdiagrams for foundations with 1


44/53



Procedure for calculation of Se using the strain influence factorProcedure for calculation of Se using the strain influence factor

Step1: Plot the variation of Izwith depth

Step2: Plot the actual variation of Es

ofsoil with depth. Escan be calculatedfrom SPT or CPT results

Step1: Plot the variation of Izwith depth

Step2: Plot the actual variation of Es

ofsoil with depth. Escan be calculatedfrom SPT or CPT results

of Es in to number of layers of soilhaving constant Es

Step4: Divide the soil layer from z=0 toz=z2into number of layers which will

depend on breaking in continuity in Izand Esdiagrams

Step5: Prepare a table to obtain

Step6: Calculate C1 and C2

of Es in to number of layers of soilhaving constant Es

Step4: Divide the soil layer from z=0 toz=z2into number of layers which will

depend on breaking in continuity in Izand Esdiagrams

Step5: Prepare a table to obtain

Step6: Calculate C1 and C2

zE

I

s

z

E l 2 1E l 2 1


45/53

Example 2 -1Example 2 -1

A 3 m wide strip foundation on adeposit of sand layer is shown alongwith the variation of modulus ofelasticity of the soil (Es). The unitweight of sand is 18 kN/m3.

Calculate the elastic settlement offoundation after 10 years using the

A 3 m wide strip foundation on adeposit of sand layer is shown alongwith the variation of modulus ofelasticity of the soil (Es). The unitweight of sand is 18 kN/m3.

Calculate the elastic settlement offoundation after 10 years using the

1.5m

kPaq 2000 =

3 m

2

)(MPaEs

6 Mpa

. .

Depth (m)

15

7.5

12 Mpa

10 Mpa

3/18 mkN=

zE

IqqCCS

z

s

ze =

2

0

21 )(

Example 2 -2Example 2 -2 1003 LBL


46/53


kPaq 2000 =

)(MPaEs

3/18 mkN=

2.0=zI

5.0=I

zI

z

z 1.02.0

30

+=

100.3, ==B

BL

z

)3(9/5.05.0

123

=

zI

z

z

9/)3(*5.05.0 = zIz

E l 3 3E l 3 3


47/53


Layer No z [m] Es[kPa]

Z to themiddle oflayer

Izat themiddle oflayer

1 2.0 6000 1.0 0.3 0.0001

]/[ 3 kNmzE

I

s

z

3 4.5 12000 5.25 0.375 0.000141

4 4.5 10000 9.75 0.125 0.0000563

kNmkNmzEI

s

z /000334.0]/[ 33 =



48/53


4.110

log2.01log2.01

922.027200

27

5.015.01

2

1

=

+=

+=

==

=

yearsintimeC

qq

q

C

kPaDqkPaq

f 275.118200

===

=

mmmzE

IqqCCS

z

s

ze 75075.0000334.0)27200(4.1922.0)(

2

0

21 ====

..

kNmkNmzE

I

s

z /000334.0]/[ 33 =

Elastic settlement of foundation onElastic settlement of foundation on


49/53

Saturated ClaySaturated ClayJanbu (1956) proposed an equation for evaluating the average settlement offlexible foundation on saturated clay soilsJanbu (1956) proposed an equation for evaluating the average settlement offlexible foundation on saturated clay soils

eE

BqAAS 021=

A1 is a function of H/B and L/BA2is a function of Df/BA1 is a function of H/B and L/BA2is a function of Df/B

foundationon thepressureappliedNetq

clayofelasticityofModulusE

levelfoundationfromrocktheDepth to

foundationtheofDepthDfoundationtheofLengthL

foundationtheofWidth

0

s

f

=

=

=

=

=

=

H

B

Elastic settlement of sandy soilElastic settlement of sandy soil


50/53

under rigid foundationunder rigid foundationLoadLoad

stressstress

LoadLoad

stressstress

),()( 93.0 centreflexibleerigide SS

deflectiondeflection deflectiondeflection


51/53

Elastic Modulus, E(MPa)Elastic Modulus, E(MPa)

(210k)

(210k)

cret

cret(20

k

(20

k--40k)

40k)

wood

wood(5

k

(5

k

--20k)

20k)

Clay

Clay

Clay

Clay

seSand

seSand

eSand

eSand))

iteite(50k

(50k--100k)

100k)

ston

ston

(200

(200--8k)

8k)

ston

ston

(3

k

(3

k--20k)

20k)

ston

ston

(200

(200--8k)

8k)

1,000

1,000

200,000

200,000

100,000

100,000

10,000

10,000

100100101011

Ste

Ste

Con

Con

Har

Har

SoilSoilRockRock

H

ar

H

ar

Soft

Soft

D

e

D

e

Loo

Loo

G

ra

G

ra

M

u

M

u

San

San

XWXW

HWHW

MWMW

SWSWFF

CWCW

M

u

M

u


52/53

Elastic parametersElastic parameters -- clayclayElastic parametersElastic parameters -- clayclay

EE

Soft clay

Medium cla

4.1 20.7 MPa

20.7 41.4 MPa

Stiff Clay

All saturated clays

41.1 96.6 MPa

0.5 (no vol. change)


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