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Overview of FoundationConcepts and FoundationAlternatives
Amit Prashant
Indian Institute of Technology Gandhinagar
Short Course on
Geotechnical Investigations for Structural Engineering
13– 15 November, 2014
IITGN Short Course on Geotechnical Investigations for Structural Engineering
Bearing Capacity
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Terzaghi’s Bearing Capacity Theory
AssumptionL/B ratio is large plain strain problemDf t B
Shear resistance of soil for Df depth is neglected
General shear failure
Shear strength is governed by Mohr-Coulomb Criterion
B
Df
neglected Effective overburden
q = γ’.Df
Strip Footing
f ’ f ’45− f ’/2 45− f ’/2
Shear
Planes
a b
de f
g i
j k
qu
Rough Foundation
Surface
c’- f ’ soilB
I
II IIIII III
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Terzaghi’s Bearing Capacity Theory
. . 0.5 .u c qq c N q N B NγγTerzaghi’s bearing
capacity equation
Terzaghi’s bearing capacity factors
Local Shear Failure:
Modify the strength parameters such as:2
3mc c 1 2tan tan
3mφ φ
Square and circular footing:
1.3 . . 0.4 .u c qq c N q N B Nγγ
1.3 . . 0.3 .u c qq c N q N B Nγγ
For square
For circular
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IITGN Short Course on Geotechnical Investigations for Structural Engineering
Total and Effective Stress Analysis
Total stress parameters
c and φFrom UC or UU test
In bearing capacity equation, use total overburden and
bulk/saturated density.
Effective stress parameters
c’ and φ’
From direct shear test, CU or CD test
In bearing capacity equation, use effective overburden and
bulk/submerged density.
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Terzaghi’s Bearing Capacity Theory
Effect of water table:
B
B
Dw
Df
Limit of influence
Case I: Dw t DfSurcharge, . w f wq D D Dγ γ
Case II: Df t Dw ≤ (Df + B)
Surcharge, . Fq Dγ
In bearing capacity equation
replace γ by-
w fD D
Bγ γ γ γ
Case III: Dw > (Df + B)
No influence of water table.
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IS:6403-1981 Recommendations
Shape
Factors
1 0.2 tan 452
fc
Dd
L
φ
1 0.1 tan 452
fq
Dd d
Lγφ
Inclination
Factors
Depth
Factors
Net Ultimate Bearing capacity: . . . . . 1 . . . 0.5 . . . . .nu c c c c q q q qq c N s d i q N s d i B N s d iγ γ γ γγ
. . . .nu u c c c cq c N s d i 5.14cNFor cohesive soils where,
, ,c qN N Nγ as per Vesic(1973) recommendations
1 0.2c
Bs
L1 0.2q
Bs
L1 0.4
Bs
LγFor rectangle,
1.3cs 1.2qs
0.8 for square, 0.6 for circles sγ γ
For square and circle,
for 10oφ
1qd dγ for 10oφ2
190
o
c qi iβ
2
1iγβφ
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Bearing CapacityCorrelations withSPT-value
Peck, Hansen, andThornburn (1974)
&
IS:6403-1981Recommendation
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Bearing Capacity Correlations with SPT-value
Teng (1962):
2 213 . . 5 100 . .
6nu w f wq N B R N D RFor Strip Footing:
2 21. . 3 100 . .
3nu w f wq N B R N D RFor Square and
Circular Footing:
For Df > B, take Df = B
0.5 1 1ww w
f
DR R
D
0.5 1 1w fw w
f
D DR R
D
Water Table Corrections:
B
B
Dw
Df
Limit of influence
IITGN Short Course on Geotechnical Investigations for Structural Engineering
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Bearing Capacity Correlations with CPT-value
0 100 200 300 4000
0.0625
0.1250
0.1675
0. 2500
nuq
qc
B (cm)
1fD
B
0.50
IS:6403-1981 Recommendation:
Cohesionless Soil
1.5B
to
2.0B
B
qc value is
taken as
average for
this zone
Schmertmann (1975):
2
kg in
0.8 cmc
q
qN Nγ
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Bearing Capacity Correlations with CPT-value
IS:6403-1981 Recommendation:
Cohesive Soil
Soil TypePoint Resistance Values
( qc ) kgf/cm2
Range of Undrained
Cohesion (kgf/cm2)
Normally consolidated
claysqc < 20 qc/18 to qc/15
Over consolidated clays qc > 20 qc/26 to qc/22
. . . .nu u c c c cq c N s d i
IITGN Short Course on Geotechnical Investigations for Structural Engineering
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Effective Area Method for Eccentric Loading
B
Df
eyex
L’=L-2ey
B’=B-2ey
AF=B’L’
yx
V
Me
F
xy
V
Me
F
In case of Moment loading
In case of Horizontal Force at
some height but the column is
centered on the foundation
.y Hx FHM F d
.x Hy FHM F d
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Settlement
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Pressure BulbSquare Footing Strip Footing
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Newmark’s Chart
Determine the depth, z, where youwish to calculate the stress increase
Adopt a scale as shown in the figure
Draw the footing to scale and placethe point of interest over the centerof the chart
Count the number of elements thatfall inside the footing, N
Calculate the stress increase as:
Point of
stress
calculation
Depth = z1
Depth = z2
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ApproximateMethods
.
.z
B Lq
B z L zσ
2
2z
Bq
B zσ
z
Bq
B zσ
Rectangular Foundation:
Square/Circular Foundation:
Strip Foundation:
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Settlement
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 pressureinduced by external loading and consequently expulsion of water fromthe soil mass, hence volume change. (Important for Inorganic clays)
Secondary Consolidation: Occurs at constant effective stress withvolume change due to rearrangement of particles. (Important forOrganic soils)
SettlementS = Se + Sc + Ss
ImmediateSettlement
Se
PrimaryConsolidation
Sc
SecondaryConsolidation
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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Elastic settlement of Foundation
0 0
1H H
e z z s x s ys
S dz dzE
ε σ µ σ µ σ
sE Modulus of elasticity
H Thickness of soil layer
sµ Poisson’s ratio of soil
Elastic settlement:
Elastic settlement for Flexible Foundation:
21e s fs
qBS I
Eµ
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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Steinbrenner’s Influence Factors for Settlement of the Corners of
loaded Area LxB on Compressible Stratus of m = 0.5, and Thickness Ht
IITGN Short Course on Geotechnical Investigations for Structural Engineering
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Elastic settlement of FoundationSoil Strata withSemi-infinite depth
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Elastic settlement of Foundation
E in kPa
Several other sets of
correlations available
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Elastic settlement of Foundation
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Strain Influence Factor Method for Sandy Soil: Schmertmannand Hartman (1978)
2
1 20
zz
e fs
IS C C q D z
Eγ
1C Correction factor for foundation depth
1 0.5 f fD q Dγ γ
2C 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
IITGN Short Course on Geotechnical Investigations for Structural Engineering
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Settlement due to Primary Consolidation
log log1 1
s c c c c o avc
o o o c
C H C HS
e e
σ σ σσ σ
log1
s c o avc
o o
C HS
e
σ σσ
log1
c c o avc
o o
C HS
e
σ σσ
For NC clay
For OC clayo av cσ σ σ
For OC clayo c o avσ σ σ σ
c o o avσ σ σ σ
oσ Average effective vertical stress before construction
avσ Average increase in effective vertical stress
cσ Effective pre-consolidation pressure
oe Initial void ratio of the clay layer
cC Compression Index
sC Swelling Index
cH Thickness of the clay layer
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6av t m bσ σ σ σ
tσ
bσ
mσ
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Settlement Due to Secondary Consolidation
2
1
log1
cs
p
C H tS
e tα
pe
Cα Secondary Compression Index
2 1log
e
t t
Time, t (Log scale)
Void
Ratio, e
pe
1t 2teVoid ratio at the end of primary consolidation
cH Thickness of Clay Layer
Secondary consolidation settlement is more important in the case of
organic and highly-compressible inorganic clays
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Total Settlementfrom SPT Datafor Cohesionlesssoil
Multiply the settlementby factor W’
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Total Settlement from CPT Data for Cohesionless soil
3
2c
o
qC
σ
lnt ot
o
HS
C
σ σσ
Depth profile of cone resistancecan be divided in severalsegments of average coneresistance
Average cone resistance canbe used to calculate constant ofcompressibility.
Settlement of each layer iscalculated separately due tofoundation loading and thenadded together
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Fox’s Depth CorrectionFactor for RectangularFootings of (L)x(B) atDepth (D)
Depth factorc Embedded
c Surface
S
S
Rigidity Factor as perIS:8009-1976
Total settlement of
rigid foundation
Total settlement at the center
of flexible foundation
Rigidity factor 0.8
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IITGN Short Course on Geotechnical Investigations for Structural Engineering
ShallowFoundation Design
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Common Types of Footing
Strip footing
Spread Footing
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Common Types of Footing
Combined Footing
Raft or Mat footing
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Location and depth of Foundation
IS:1904-1986: Minimum depth of foundation = 0.50 m.
Foundation shall be placed below the zone ofExcessive volume change due to moisture variation (usually
exists within 1.5 to 3.5 m depth)
Topsoil or organic material
Unconsolidated material such as waste dump
Foundations adjacent to flowing water (flood water,
rivers, etc.) shall be protected against scouring.
A raised water table may cause damage to the
foundation byFloating the structure
Reducing the effective stress beneath the foundation
Water logging around the building: proper drainage system
around the foundation may be required so that water does not
accumulate.
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Location and depth of Foundation
Footings on surface rock or sloping rock faces
Shallow rock beds: foundation on the rock surface after chipping
Rock bed with slope: provide dowel bars of minimum 16 mm
diameter and 225 mm embedment into the rock at 1 m spacing.
Footings adjacent to existing structures
Minimum horizontal distance between the foundations shall not be
less than the width of larger footing. Otherwise, the principal of
2H:1V distribution be used to minimize influence to old structure
Proper care is needed during excavation phase of foundation
construction beyond merely depending on the 2H:1V criteria.
Excavation may cause settlement to old foundation due to lateral
bulging in the excavation and/or shear failure due to reduction in
overburden stress in the surrounding of old foundation
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Plate Load Test – IS:1888-1982
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Plate Load Test: Bearing Capacity
uf f
up p
q B
q B
For cohesioless soil
uf upq q
For cohesive soil
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Modulus ofSub-gradeReaction
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Differential Settlement
Caused by variations in soil profile and structural loads
Consider construction tolerances
Consider best case/worst case scenarios
Use D/ ratios
d D
DD
L
δ = maximum settlement
D= differential settlement
D/ d = angular distortion
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Total and Differential Settlement for Clays
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Total and Differential Settlement for Sands
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Design values of δD/δ Ratios
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How Accurateare our
SettlementPredictions?
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Allowable Bearing Pressure
Maximum bearing pressure that can be applied on thesoil satisfying two fundamental requirements
Bearing capacity with adequate factor of safety– net safe bearing capacity
Settlement within permissible limits (critical in most cases)– net safe bearing pressure
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Allowable Bearing Pressure
Teng’s (1962) Correlation:
depth correction factor 1 2fD
DC
B
Sa in mm and all other
dimensions in meter.
.cor NN C N
1.75 for 0 1.05
0.7N o ao a
C PP
σσ
3.5 for 1.05 2.8
0.7N o ao a
C PP
σσ
oσ Effective Overburden stress
20.3
1.4 32n cor w D a
Bq N R C S
Bρ
Net safe bearing pressure
2kN m
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Allowable Bearing Pressure
Meyerhof’s (1974) Correlation:
210.49 for 1.2 mn D aq N R S kN m Bρ
1 depth correction factor
1 0.2 1.2
D
f
R
D
B
22
2
0.30.32 for 1.2 mn D a
Bq N R S kN m B
Bρ
Net safe bearing pressure
2 depth correction factor
1 0.33 1.33
D
f
R
D
B
Bowel’s (1982) Correlation:
210.73 for 1.2 mn D aq N R S kN m Bρ
22
2
0.30.48 for 1.2 mn D a
Bq N R S kN m B
Bρ
N-value corrected for overburden using bazaraa’s equation, but
the N-value must not exceed field value
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Allowable Bearing Pressure
IS Code recommendation: Use total settlement correlations with SPT
data to determine safe bearing pressure.
Correlations for raft foundations:
Rafts are mostly safe in bearing capacity and they do not show much
differential settlements as compared to isolated foundations.
20.7 3n w D aq N R C S kN mρTeng’s Correlation:
Peck, Hanson, and Thornburn (1974):20.88a net w aq C N S kN m
Correlations using CPT data:
Meyerhof’s correlations may be used by substituting qc/2 for N,
where qc is in kg/cm2.
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Net vs. Gross Allowable Bearing Pressure
2 2g c c c f cQ Q B D B D Dγ γ
Gross load
2 2
g cg f c c
Q Qq D D
B Bγ γ γ
2c
n g f c c
Qq q D D
Bγ γ γ
cγ γ is small, so it may be neglected
2c
n
B
Soil Soil
cD
fD
2c
a net
B
2c
g c c c
Qq D t
Bγ γ
t
2c
n g f c c f
Qq q D D t D
Bγ γ γ
Usually Dc+t is much smaller than Df
2c
n f
Qq D
Bγ
2c
a net f
Qq D
Bγ
2c
a gross
B
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SUMMARY of Terminology
Net Loading IntensityPressure at the level of foundation causing actual
settlement due to stress increase. This includes
the weight of superstructure and foundation only.
Ultimate Bearing capacity:
Maximum gross intensity of loading that the
soil can support against shear failure is
called ultimate bearing capacity.
Net Ultimate Bearing Capacity:
Maximum net intensity of loading that the
soil can support at the level of foundation.
Gross Loading IntensityTotal pressure at the level of foundation
including the weight of superstructure,
foundation, and the soil above foundation.
superstructure Foundation soil
Foundationg
Q Q Qq
A
n g fq q Dγ
from
Bearing capacity calculationuq
nu u fq q Dγ
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SUMMARY of Terminology
Gross Safe Bearing capacity:
Maximum gross intensity of loading that the soil
can safely support without the risk of shear failure.
Safe Bearing Pressure:
Maximum net intensity of loading that can be
allowed on the soil without settlement
exceeding the permissible limit.
Allowable Bearing Pressure:
Maximum net intensity of loading that can
be allowed on the soil with no possibility of
shear failure or settlement exceeding the
permissible limit.
Net Safe Bearing capacity:
Maximum net intensity of loading that the soil can
safely support without the risk of shear failure.nu
ns
FOS
gs ns fq q Dγ
from settlement analysissqρ
Minimum of
bearing capacity and
settlement analysis
a netq
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Loads on Foundation
Permanent Load: This is actual service load/sustained loads of astructure which give rise stresses and deformations in the soil belowthe foundation causing its settlement.
Transient Load: This momentary or sudden load imparted to astructure due to wind or seismic vibrations. Due to its transitorynature, the stresses in the soil below the foundation carried by suchloads are allowed certain percentage increase over the allowablesafe values.
Dead Load: It includes the weight of the column/wall, footings,foundations, the overlaying fill but excludes the weight of thedisplaced soil
Live Load: This is taken as per the specifications of IS:875 (pt-2) –1987.
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Loads for Proportioning and Design of FoundationIS:1904 - 1986
Following combinations shall be used
Dead load + Live load
Dead Load + Live load + Wind/Seismic load
For cohesive soils only 50% of actual live load is consideredfor design (Due to settlement being time dependent)
For wind/seismic load < 25% of Dead + Live load
Wind/seismic load is neglected and first combination is used tocompare with safe bearing load to satisfy allowable bearing pressure
For wind/seismic load ≥ 25% of Dead + Live load
It becomes necessary to ensure that pressure due to secondcombination of load does not exceed the safe bearing capacity bymore than 25%. When seismic forces are considered, the safebearing capacity shall be increased as specified in IS: 1893 (Part-1)-2002 (see next slide). In non-cohesive soils, analysis for liquefactionand settlement under earthquake shall also be made.
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Other considerations for Shallow Foundation Design
For economical design, it is preferred to have square footing for
vertical loads and rectangular footing for the columns carrying
moment
Allowable bearing pressure should not be very high in comparison
to the net loading intensity leading to an uneconomical design.
It is preferred to use SPT or Plate load test for cohesionless soils
and undrained shear strength test for cohesive soils.
In case of lateral loads or moments, the foundation should also be
checked to be safe against sliding and overturning. The FOS shall
not be less than 1.75 against sliding and 2.0 against overturning.
When wind/seismic loads are considered the FOS is taken as 1.5
for both the cases.
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Combined Footings
Combined footing is preferred whenThe columns are spaced too closely that if isolated footing isprovided the soil beneath may have a part of common influencezone.
The bearing capacity of soil is such that isolated footing designwill require extent of the column foundation to go beyond theproperty line.
Types of combined footingsRectangular combined footing
Trapezoidal combined footing
Strap beam combined footing
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Rectangular Combined Footing
If two or more columns are carryingalmost equal loads, rectangularcombined footing is provided
Proportioning of foundation willinvolve the following steps
Area of foundation
Location of the resultant force
For uniform distribution of pressure under the foundation, theresultant load should pass through the center of foundation base.
Length of foundation,
Offset on the other side,
The width of foundation,
1 2
a net
Q QA
q2
1 2
Q Sx
Q Q
12L L S
2 1 0L L S L
B A L
Q1 Q2
Q1+Q2
x
L1 S L2
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Trapezoidal Combined Footing
If one of the columns is carrying muchlarger load than the other one,trapezoidal combined footing is provided
Proportioning of foundation will involvethe following steps if L, and L1 are known
Area of foundation
Location of the resultant force
For uniform distribution of pressure under the foundation, theresultant load should pass through the center of foundation base.This gives the relationship,
Area of the footing,
1 2
a net
Q QA
q2
1 2
Q Sx
Q Q
1 21
1 2
2
3
B B Lx L
B B1 2
2
B BL A
Solution of thesetwo equations
gives B1 and B2
Q1 Q2
Q1+Q2
x
L1 S L2
B1 B2
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Strap Combined Footing
Strap footing is used toconnect an eccentrically loadedcolumn footing to an interiorcolumn so that the moment canbe transferred through thebeam and have uniform stressdistribution beneath both thefoundations.
This type of footing is preferredover the rectangular ortrapezoidal footing if distancebetween the columns isrelatively large.
Some design considerations:
Strap must be rigid: Istrap/Ifooting > 2.
Footings should be proportioned to have approximately equal soil
pressure in order to avoid differential settlement
Strap beam should not have contact with soil to avoid soil reaction to it.
Q1 Q2
M2
IITGN Short Course on Geotechnical Investigations for Structural Engineering
Pile FoundationDesign
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When is it needed
Top layers of soil are highly compressible for it to supportstructural loads through shallow foundations.
Rock level is shallow enough for end bearing pilefoundations provide a more economical design.
Lateral forces are relatively prominent.
In presence of expansive and collapsible soils at the site.
Offshore structures
Strong uplift forces on shallow foundations due to shallowwater table can be partly transmitted to Piles.
For structures near flowing water (Bridge abutments, etc.)to avoid the problems due to erosion.
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Types of Piles Based on Their Function and Effectof Installation
Piles based on their functionEnd Bearing Piles
Friction Piles
Compaction Piles
Anchor Piles
Uplift Piles
Effect of InstallationDisplacement Piles
Non-displacement Piles
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Displacement PilesIn loose cohesionless soils
Densifies the soil upto a distance of 3.5 times the pile diameter(3.5D) which increases the soil’s resistance to shearing
The friction angle varies from the pile surface to the limit ofcompacted soil
In dense cohesionless soilsThe dilatancy effect decreases the friction angle within the zone ofinfluence of displacement pile (3.5D approx.).
Displacement piles are not effective in dense sands due to abovereason.
In cohesive soilsSoil is remolded near the displacement piles (2.0 D approx.) leadingto a decreased value of shearing resistance.
Pore-pressure is generated during installation causing lowereffective stress and consequently lower shearing resistance.
Excess pore-pressure dissipates over the time and soil regains itsstrength.
Example: Driven concrete piles, Timber or Steel piles
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Non-displacement Piles
Due to no displacement during installation, there is no heave inthe ground.
Cast in-situ piles may be cased or uncased (by removingcasing as concreting progresses). They may be provided withreinforcement if economical with their reduced diameter.
Enlarged bottom ends (three times pile diameter) may beprovided in cohesive soils leading to much larger point bearingcapacity.
Soil on the sides may soften due to contact with wet concreteor during boring itself. This may lead to loss of its shearstrength.
Concreting under water may be challenging and may resultingin waisting or necking of concrete in squeezing ground.
Example: Bored cast in-situ or pre-cast piles
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Load Transfer Mechanism of Piles
The frictional resistanceper unit area at anydepth
Ultimate skin frictionresistance of pile
Ultimate point load
Ultimate load capacityin compression
Ultimate load capacityin tension
.z
sz
S z perimeter of pileS
suQ
.pu pu pQ q A
u pu suQ Q Q
u suQ Q
bearing capacity of soilpuq bearing area of pilepA
upQ usQ
uQ
sQz
z
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IS:2911 Pile Load Capacity in Cohesionless Soils
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IS:2911 Pile Load Capacity in Cohesionless Soils
IITGN Short Course on Geotechnical Investigations for Structural Engineering
ForBoredPiles
ForDrivenPiles
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IS:2911 Pile Load Capacity in Cohesionless Soils
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IS:2911 Pile Load Capacity in Cohesionless Soils
IS code recommends K-value to be chosen between 1 and 2 fordriven piles and 1 and 1.5 for bored piles. However, it is advisableto estimate this value based on the type of construction and fair
estimation of the disturbance to soil around pile. Typical values ofratio between K and Ko are listed below.
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IS:2911 Pile Load Capacity in Cohesive Soils
0.5For 1 0.5 , but 1v vu uc cσ α σ
0.25For 1 0.5 , but 0.5 and 1v vu uc cσ α σ
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IS:2911 Pile Load Capacity in Cohesive Soils
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Meyerhof’s Formula for Driven Piles based on SPT value
For L/D > 10
A limiting value of 1000 t/m2 for point bearing and 6 t/m2 is
suggested
For Sand:
For Non-plastic silt and fine sand:
For Clays:
IITGN Short Course on Geotechnical Investigations for Structural Engineering
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IS:2911 Pile Load Capacity in Non-CohesiveSoils Based on CPT data
The ultimate pointbearing capacity:
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IITGN Short Course on Geotechnical Investigations for Structural Engineering
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IS:2911 Pile Load Capacity in Non-CohesiveSoils Based on CPT data
Correlation of SPT and CPT:
The ultimate skin friction resistance:
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Allowable Pile Capacity
Factor of Safety shall be used by giving due consideration to thefollowing points
Reliability of soil parameters used for calculation
Mode of transfer of load to soil
Importance of structure
Allowable total and differential settlement tolerated by structure
Factor of Safety as per IS 2911:
uall
FSu
all
FS
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Load Tests on Piles
Note: Piles used for initial testing are loaded to failure or at least twice the
design load. Such piles are generally not used in the final construction.
Note: During this test pile should be loaded upto 1.5 times the working
(design) load and the maximum settlement of the test should not exceed
12 mm. These piles may be used in the final construction.
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Vertical Load Test: Maintained Load Test
The test can be initial or routinetest
The load is applied in incrementsof 20% of the estimated safeload. Hence the failure load isreached in 8-10 increments.
Settlement is recorded for eachincrement until the rate ofsettlement is less than 0.1 mm/hr.
The ultimate load is said to havereached when the final settlementis more than 10% of the diameterof pile or the settlement keeps onincreasing at constant load.
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Vertical Load Test: Maintained Load Test
After reaching ultimate load, theload is released in decrements of1/6th of the total load andrecovery is measured until fullrebound is established and nextunload is done.
After final unload the settlementis measured for 24 hrs toestimate full elastic recovery.
Load settlement curve dependson the type of pile
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Vertical Load Test: Maintained Load TestUltimate Load
De Beer (1968):
Load settlement curve is plotted in a
log-log plot and it is assumed to be a
bilinear relationship with its
intersection as failure load
Chin Fung Kee (1977):
Assumes hyperbolic curve.
Relationship between
settlement and its division with
load is taken as to be bilinear
with its intersection as failure
load
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IITGN Short Course on Geotechnical Investigations for Structural Engineering
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Vertical Load Test: Maintained Load Test SafeLoad as per IS: 2911
Safe Load for Single Pile:
Safe Load for Pile Group:
IITGN Short Course on Geotechnical Investigations for Structural Engineering
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Dynamic Pile Formula for Driven Piles:Modified Hiley Formula
. . .
/ 2u
W HQ
S C
α η. . .
/ 2u
W HQ
S C
α η
WH
SuQ
Weight of hammer
Height of fall
Pile resistance or Pile capacity
Pile penetration for the last blow
α Hammer fall efficiency
Efficiency of blowηSum of temporary elastic compressionof pile, dolly, packing, and ground
C
Note: Dynamic pile formula are not used for soft clays due to pore pressure evolution