ce 632 settlement2009
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CE-632
Foundation Analysis and
Design
Settlement of FoundationSettlement of Foundation
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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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Elastic settlement of FoundationElastic settlement of Foundation
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Elastic settlement of FoundationElastic settlement of Foundation
E in kPa
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Elastic settlement of FoundationElastic settlement of Foundation
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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:
F d ti A l i d D i D A it P h t
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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 = = =
F d ti A l i d D i D A it P h t
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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 +