CE 632 Settlement2009

8/6/2019 CE 632 Settlement2009

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CE-632

Foundation Analysis and

Design

Settlement of FoundationSettlement of Foundation


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Foundation Analysis and Design: Dr. Amit Prashant

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SettlementSettlement

Immediate Settlement: Occurs immediately after the construction. This is computedusing elasticity theory (Important for Granular soil)

Primary Consolidation: Due to gradual dissipation of pore pressure induced by externalloading and consequently expulsion of water from the soil mass, hence volume change.(Important for Inorganic clays)

Secondary Consolidation: Occurs at constant effective stress with volume change dueto rearrangement of particles. (Important for Organic soils)

Settlement

S = Se + Sc + Ss

Immediate

Settlement

Se

Primary

Consolidation

Sc

Secondary

Consolidation

Ss

For any of the above mentioned settlement calculations, we first need vertical stress

increase in soil mass due to net load applied on the foundation


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ElasticityElasticity


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Stress Distribution: Concentrated loadStress Distribution: Concentrated load

Boussinesq Analysis


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Stress Distribution: Concentrated loadStress Distribution: Concentrated load

Where,

Boussinesq Analysis


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Vertical Stress: Concentrated loadVertical Stress: Concentrated load

Influence Factor for

General solution of vertical stress

2z B

PI

z =

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

BI

r z


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Vertical Stress: Uniformly Distributed Circular LoadVertical Stress: Uniformly Distributed Circular Load

Uniformly Distributed Circular Load


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Vertical Stress: Uniformly Distributed Circular LoadVertical Stress: Uniformly Distributed Circular Load

Rigid Plate on half Space


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Vertical Stress: Rectangular AreaVertical Stress: Rectangular Area


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Vertical Stress: Rectangular AreaVertical Stress: Rectangular Area


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Pressure BulbPressure BulbSquare Footing Strip Footing


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PressurePressure

Bulb forBulb for

SquareSquareFoundationFoundation


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PressurePressure

Bulb for CircularBulb for CircularFoundationFoundation


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Newmarks ChartNewmarks Chart

Influence Value

This Model is good for normally-consolidated, lightly overconsolidated

clays, and variable deposits


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Newmarks ChartNewmarks Chart

Determine the depth, z, where you

wish to calculate the stress increase

Adopt a scale as shown in the figure

Draw the footing to scale and place

the point of interest over the center

of the chart

Count the number of elements that

fall inside the footing, N

Calculate the stress increase as:

Point of

stress

calculation

Depth = z1

Depth = z2


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Westergaards MethodWestergaards Method

Provided solution for layered soils Point Loads Assumption:

Elastic soil mass is laterally reinfrced by numorous,closely spaced, horizontal sheets of negligible thicknessbut infinite rigidity, that allow only vertical movement butprevent the mass as a whole from undergoing any lateralstrain.

This Model is specially good for pre-compressed or overconsolidated clays


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Westergaards influence ChartWestergaards influence Chart


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FrFrhlich Chart withhlich Chart with

concentration factorconcentration factor

m = 4m = 4

( )0.005 .z n q =

This Model is specially good for

Sands


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Simplified Methods (Simplified Methods (Poulos and Davis, 1974)Poulos and Davis, 1974)

1.52

1 1 ( )2

z zD

Bq

z

= +

Circular Foundation:

Square Foundation:

1.762

1 1 ( )2

z zD

f

B qz

= +


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Simplified Methods (Simplified Methods (Poulos and Davis, 1974)Poulos and Davis, 1974)

Strip Foundation:

Rectangular Foundation:

2.602

1 1 ( )2

z zD

f

Bq

z

= +

( )2.60 0.84 /1.38 0.62 /

1 1 ( )2

B LB L

z

f

Bq

z

+

= +


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ApproximateApproximate

MethodsMethods

( ) ( )

.

.z

B Lq

B z L z =

+ +

( )

2

2zBq

B z =

+

( )z

Bq

B z

=+

Rectangular Foundation:

Square/Circular Foundation:

Strip Foundation:


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Contact Pressure and Settlement distributionContact Pressure and Settlement distribution

Cohesive Soil - Flexible Footing

Cohesive Soil - Rigid Footing

Granular Soil Flexible Footing

Granular Soil - Rigid Footing


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Elastic settlement of FoundationElastic settlement of Foundation

( )0 0

1

H H

e z z s x s y

s

S dz dzE

= = sE = Modulus of elasticity

H = Thickness of soil layer

s = Poissons ratio of soil

Elastic settlement:

Elastic settlement for Flexible Foundation:

( )

21e s f

s

qBS I

E

=

fI = influence factor: depends on the rigidity and shape of the foundation

sE = Avg elasticity modulus of the soil for (4B) depth below foundn level


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E in kPa


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Elastic settlement of FoundationElastic settlement of FoundationSoil Strata with

Semi-infinite depth


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Steinbrenners Influence Factors for Settlement of the Corners ofSteinbrenners Influence Factors for Settlement of the Corners of

loaded Arealoaded Area LxBLxB on Compressible Stratus ofon Compressible Stratus of = 0.5= 0.5, and Thickness, and Thickness HHtt


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Strain Influence Factor Method for Sandy Soil: SchmertmannStrain Influence Factor Method for Sandy Soil: Schmertmann

and Hartman (1978)and Hartman (1978)

( )2

1 2

0

z

ze f

s

IS C C q D z E

= 1

C = Correction factor for foundation depth

( ){ }1 0.5 f f D q D 2

C = Correction factor for creep effects

q For square and circular foundation:

For foundation with L/B >10:

Interpolate the values for 1 < L/B < 10

( )1 0.2log time in years 0.1 +

F d ti A l i d D i D A it P h t


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ExampleExample

( )2

1 2

0

z

ze f

s

IS C C q D z E

=

3.5s cE q

231.39f D kN m =

2.5s cE q

For square and

circular foundations

For rectangular

foundations

800 in kPasE NCorrelation with SPT data:



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Burland and Burbidges Method for Sandy SoilsBurland and Burbidges Method for Sandy Soils

Depth of Stress Influence (z'):

( )0.75

1.04 ,where B is in metersz B =If N60 ' is constant or increasing with depth, thenIf N60 ' is decreasing with depth, use smaller of

( )

( )

2

1 2 3

1.25

0.25e

L BS Bq

L B

= +

Elastic Settlement (Se):

where B is in meters

and is in kPaq

1 = 0.0047 for NC sand0.0016 for OC sand with qna po

0.0047 for OC sand with qna po

( )

( )

1.4

2

1.4

1.71

0.57

N

N

=

=

Compressibility Index: for NC sand

for OC sand

3 2 1z z

z z

=

for NC sand and for OC sand with qna po

for OC sand with qna po0.67na oq q p = naq q =

2 and Thickness of soft layer below foundation z B z z = = =



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Settlement due to Primary ConsolidationSettlement due to Primary Consolidation

log log

1 1

s c c c c o avc

o o o c

C H C H S

e e

+ = +

+ +

log1

s c o avc

o o

C HS

e

+ = +

log1

c c o avc

o o

C HS e

+ = +

For NC clay

For OC clay ( )o av c +

Documents

CE 632 Settlement2009