elastic settlement in soil
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1CE-632Foundation Analysis and Design
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Design
Settlement of FoundationSettlement of Foundation
Foundation Analysis and Design: Dr. Amit Prashant
SettlementSettlementSettlement
S = Se + Sc + Ss
ImmediateSettlement
Se
PrimaryConsolidation
Sc
SecondaryConsolidation
Ss
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Immediate Settlement: Occurs immediately after the construction. This is computed using elasticity theory (Important for Granular soil)
Primary Consolidation: Due to gradual dissipation of pore pressure induced by external loading 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 due to rearrangement of particles. (Important for Organic soils)
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
Foundation Analysis and Design: Dr. Amit Prashant
ElasticityElasticity
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2Foundation Analysis and Design: Dr. Amit Prashant
Stress Distribution: Concentrated load Stress Distribution: Concentrated load Boussinesq Analysis
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Foundation Analysis and Design: Dr. Amit Prashant
Stress Distribution: Concentrated load Stress Distribution: Concentrated load Boussinesq Analysis
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Where,
Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Concentrated loadVertical Stress: Concentrated load
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Influence Factor for General solution of vertical stress
2z BP Iz
=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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3Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Uniformly Distributed Circular LoadVertical Stress: Uniformly Distributed Circular Load
Uniformly Distributed Circular Load
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Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Uniformly Distributed Circular LoadVertical Stress: Uniformly Distributed Circular Load
Rigid Plate on half Space
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Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Rectangular AreaVertical Stress: Rectangular Area
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4Foundation Analysis and Design: Dr. Amit Prashant
Vertical Stress: Rectangular AreaVertical Stress: Rectangular Area
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Foundation Analysis and Design: Dr. Amit PrashantPressure BulbPressure BulbSquare Footing Strip Footing
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Foundation Analysis and Design: Dr. Amit Prashant
Pressure Pressure Bulb for Bulb for Square Square FoundationFoundation
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5Foundation Analysis and Design: Dr. Amit Prashant
Pressure Pressure Bulb for Bulb for CircularCircularFoundationFoundation
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Foundation Analysis and Design: Dr. Amit Prashant
NewmarksNewmarks ChartChart
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Influence Value
This Model is good for normally-consolidated, lightly overconsolidated clays, and variable deposits
Foundation Analysis and Design: Dr. Amit Prashant
Newmarks ChartNewmarks ChartPoint of stress calculation
Depth = z2
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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:
Depth = z1
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6Foundation Analysis and Design: Dr. Amit Prashant
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 thickness but infinite rigidity, that allow only vertical movement but prevent the mass as a whole from undergoing any lateral
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p g g ystrain.
( )32
22 2
12zPz C r z
= + ( )
1 22 1
C =
This Model is specially good for pre-compressed or overconsolidated clays
Foundation Analysis and Design: Dr. Amit Prashant
WestergaardsWestergaards influence Chartinfluence Chart
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Foundation Analysis and Design: Dr. Amit Prashant
FrFrhlichhlich Chart with Chart with concentration factor concentration factor m = 4m = 4
( )0.005 .z n q =
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This Model is specially good for Sands
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7Foundation Analysis and Design: Dr. Amit Prashant
Simplified Methods (Simplified Methods (Poulos and Davis, 1974)Poulos and Davis, 1974)
1.52
1 1 ( )2z zDB qz
= +
Circular Foundation:
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Square Foundation:
1.762
1 1 ( )2z zDf
B qz
= +
Foundation Analysis and Design: Dr. Amit Prashant
Simplified Methods (Simplified Methods (Poulos and Davis, 1974)Poulos and Davis, 1974)
Strip Foundation:
2.602
1 1 ( )2z zDf
B qz
= +
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Rectangular Foundation:
( )2.60 0.84 /1.38 0.62 /1 1 ( )
2
B LB L
z zDf
B qz
+ = +
Foundation Analysis and Design: Dr. Amit Prashant
Approximate Approximate MethodsMethods
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( ) ( )..z
B LqB z L z
= + +
( )2
2zBq
B z = +
( )zBq
B z = +
Rectangular Foundation:
Square/Circular Foundation:
Strip Foundation:
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8Foundation Analysis and Design: Dr. Amit Prashant
Contact Pressure and Settlement distributionContact Pressure and Settlement distribution
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Cohesive Soil - Flexible Footing
Cohesive Soil - Rigid Footing
Granular Soil Flexible Footing
Granular Soil - Rigid Footing
Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of FoundationElastic settlement of Foundation
( )0 0
1H He z z s x s y
s
S dz dzE
= = sE = Modulus of elasticity
H = Thickness of soil layers = Poissons ratio of soil
Elastic settlement:
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sElastic settlement for Flexible Foundation:
( )21e s fs
qBS IE
=
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
Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of FoundationElastic settlement of Foundation
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9Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of FoundationElastic settlement of Foundation
E in kPa
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Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of FoundationElastic settlement of Foundation
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Foundation Analysis and Design: Dr. Amit Prashant
Elastic settlement of FoundationElastic settlement of FoundationSoil Strata with Semi-infinite depth
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Foundation Analysis and Design: Dr. Amit Prashant
Steinbrenners Influence Factors for Settlement of the Corners of Steinbrenners Influence Factors for Settlement of the Corners of loaded Area loaded Area LxBLxB on Compressible Stratus of on Compressible Stratus of = 0.5= 0.5, and Thickness , and Thickness HHtt
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Foundation Analysis and Design: Dr. Amit Prashant
Strain Influence Factor Method for Sandy Soil: Strain Influence Factor Method for Sandy Soil: SchmertmannSchmertmannand Hartman (1978)and Hartman (1978)
( ) 21 20
zz
e fs
IS C C q D zE
= 1C = Correction factor for foundation depth( ){ }1 0.5 f fD q D 2C = Correction factor for creep effects
q For square and circular foundation:
( )1 0.2 log time in years 0.1 +
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q
For foundation with L/B >10:
Interpolate the values for 1 < L/B < 10
Foundation Analysis and Design: Dr. Amit Prashant
ExampleExample
( ) 21 20
zz
e fs
IS C C q D zE
= 231.39fD kN m =
For square and circular foundations
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3.5s cE q
2.5s cE qFor rectangular
foundations
800 in kPasE N Correlation with SPT data:
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Foundation Analysis and Design: Dr. Amit Prashant
Burland and Burbidges Method for Sandy SoilsBurland and Burbidges Method for Sandy Soils
Depth of Stress Influence (z'):
( )0.751.04 ,where B is in metersz B =If N60' is constant or increasing with depth, then If N60' is decreasing with depth, use smaller of
( ) 21 25 L B Elastic Settlement (Se): where B is in meters2 and Thickness of soft layer below foundationz B z z = = =
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( )( )1 2 3
1.250.25e
L BS Bq
L B = +
where B is in meters and is in kPaq
1 = 0.0047 for NC sand0.0016 for OC sand with qna po0.0047 for OC sand with qna po
( )( )
1.42
1.4
1.71
0.57
N
N
==
Compressibility Index: for NC sand
for OC sand
3 2 1z zz z
= for NC sand and for OC sand with qna po
for OC sand with qna po0.67na oq q p = naq q =
Foundation Analysis and Design: Dr. Amit Prashant
Settlement due to Primary ConsolidationSettlement due to Primary Consolidation
log log1 1
s c c c c o avc
o o o c
C H C HSe e
+ = + + +
log1
s c o avc
o o
C HSe
+ = +
log1
c c o avc
o o
C HSe
+ = + For NC clay
For OC clay ( )o av c +
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