lutful i. khan, phd, pe cleveland state university
TRANSCRIPT
Lutful I. Khan, PhD, PE
Cleveland State University
Pile Foundations• Classified as deep foundations
• How deep?
• The 55-story 181 Fremont tower, San Francisco – 264 ft
• Installed in groups
• Other types of deep foundations
• Pier
• Cassions
Load TransferPiles transfer loads:
• To suitable bearing strata through toe resistance (end-bearing piles)
• To strata in which pile is embedded through shaft resistance (friction pile)
• Through a combination of both shaft and toe resistance (most common)
Driven Pile Design• The driven pile design and construction process has aspects that are
unique.
• The driving characteristics are related to pile capacity for most soils, and they can be used to improve the accuracy of the pile capacity estimate.
• In general, the methods of determining pile capacity from dynamic data such as driving resistance with wave equation analysis are considerably more accurate than the static analysis methods based on subsurface exploration information.
• The static analysis based on the subsurface exploration information usually provides an estimate of the pile length prior to field installation.
• The final driving criterion is usually a blow count that is established after the field tests of the individual pile penetrations.
• May vary depending on the soil variability.
• Pile driveability is a very important aspect and must be considered during the design phase.
Ultimate Geotechnical Capacity
Primary factors controlling the ultimate geotechnical capacity of a pile are:
• Pile details (type and length)
• Subsurface data
• Method of installation
• Pile setup
❖ Pile drivability is an important aspect of driven pile design
❖ The failure to evaluate pile driveability is one of the most common deficiencies in driven pile design practice.
Driveability
Controlling Factor• The primary controlling factor on pile
driveability is the pile impedance, which is defined as EA/C, where E is the elastic modulus of pile material, A is the cross-sectional area of the pile and C is the wave propagation velocity of pile material.
• Since E and C are constant for a given type of pile, only increasing the pile cross sectional area, A, will improve the pile driveability.
A pile must satisfy two aspects of driveability:
• The pile must have sufficient stiffness to transmit driving forces large enough to overcome soil resistance.
• The pile must have sufficient structural strength to withstand the driving forces without damage.
Other factors affecting Pile Drivaibility
• Pile material strength
• Characteristics of the driving system such as ram weight, stroke, and speed
• Dynamic soil response
Factors Affecting Driveability
Driven Piles (High Displacement and Low Displacement )
Increase lateral ground stress
• Densify cohesionless soils, remolds and weakens cohesive soils temporarily
• Setup time may be 6 months or more in clays for pile groups
Design Approach
1. Perform thorough subsurface exploration including in-situ and laboratory testing to determine design parameters.
2. Perform Static analysis to estimate pile requirements.
3. Perform wave equation driveability analysis.
4. Use design stage pile load testing on large pile driving projects to determine load capacities (load tests during design stage)
5. Use wave equation analysis coupled with dynamic monitoring for construction control and load capacity evaluation.
6. Use pile load tests on projects to substantiate capacity predictions by wave equation and dynamic monitoring.
Static Analysis of Driven Pile Capacity
Static Analysis
• A large number of static analysis methods exists in the literature with
recommendations on factor of safety.
• These recommended factors of safety have routinely disregarded the
influence of the construction control method used to complement the
static analysis computation.
• Qualitative assessment of the validity of the chosen design analysis
method and the reliability of the geotechnical design parameters is
important.
Pile Capacity: Static Analysis of Ultimate CapacityUltimate total capacity
Qu = Qs+Qp - W
Qs = Skin Friction capacity
Qp = End Bearing capacity
W = weight of pile (usually small)
Qs
Qp
Ignoring W, Total capacity Qu = As fs+ At qt
As = pile surface areafs = unit skin friction At = pile cross-section areaqt = unit tip resistance
Qu
Pile Capacity: Static Analysis
Different equations for sand and claySand
Skin Friction Qs : one method
End Bearing Qp : three methods
Clay
Skin Friction Qs : three methods
End Bearing Qp : one method
Qp =9CuAp
Qs
Qp
Soil Resistance• The pile design load should be
supported by soil resistance developed only in soil layers that contribute to long term load support.
• The soil resistance from soils subject to scour, or from soil layers above soft compressible soils should not be included.
Pile Capacity: Static Analysis in Sand
Skin Friction
Qs = surface area x f
Qs = SpDL f
unit skin friction f = Ks0’ tand
End Bearing Qp
Three methods• Meyerhof• Vesic• Janbu
Qs
Qp
15D
f
TOTAL PILE CAPACITY Qu = Qp +QsQu
p
= 2000 psf
0'0 9060
Use : Soft clay 600, Sand 900
Pile Capacity: Static Analysis in Clay
Skin Friction Qs = S pDL fs
= pL fs (for straight piles)
Unit Skin Friction fs : three methods1. a method f = aCu
2. l method fav = l(so’ + 2Cu)3. b method f = b so’
End Bearing Qp : one method
Qp =9CuAp
Qs
Qp
QuTOTAL PILE CAPACITY Qu = Qp +QsTOTAL PILE CAPACITY Qu = Qp +Qs
• Total stress analysis
• Ultimate capacity is calculated from the
undrained shear strength Cu of the soil
• Assumes that the shaft resistance is
independent of the effective overburden
pressure and that the unit shaft resistance can
be expressed in terms of an empirical adhesion
factor a times the undrained shear strength.
Frictional Resistance of Pile in Clays : a - method
Qs = S pDL fs
❑ The adhesion factor, α, is a function of the soil stratigraphy and pile embedment
❑ Three common cases are as follows:
• Case 1: Piles driven into stiff clays through overlying sands or sandy gravels• Case 2: Piles driven into stiff clays through overlying soft clays• Case 3: Piles driven into stiff clays without overlying different strata
Tomlinson, 1980
Frictional Resistance of Pile in Clays : a - method
• For a soil profile consisting of clay layers of significantly different consistencies adhesion factors should be determined for each individual clay layer.
• In clays with large shrink-swell potential, static capacity calculations should ignore the shaft resistance from the adhesion in the shrink-swell zone.
• In the case of H piles in cohesive soils, the shaft resistance should not be calculated from the surface area of the pile, but rather from the perimeter area of the four sides.
Tomlinson, 1980
Frictional Resistance of Pile in Clays : a - method
Frictional Resistance of Piles in Clay: l method
• Proposed by Vijayvergia & Focht (1972)
• Values are weighted averages along the embedded length
• Over predicts capacity if the embedment length is less than 50 ft.
• Static capacity calculations in cohesionless, cohesive, and layered soils can also be performed by using effective stress.
• Effective stress based methods were developed to model the long term drained shear strength conditions.
• The effective soil friction angle, φ', should be used in parameter selection.
Frictional Resistance of Piles based on effective stress: b method
According to Fellenius (1991) β depends on soil
composition including the grain size distribution,
• angularity
• mineralogical origin of the soil grains,
• the orginal soil density
• density due to the pile installation,
• the soil strength, as well as other factors.
Even so, β coefficients are generally within the
ranges provided and seldom exceed 1.0.
Frictional Resistance of Pile in Clays : b - method
The unit toe resistance is calculated from:
qt = Nt pt
where: Nt = toe bearing capacity coefficient.
pt = effective overburden pressure at the
pile toe in ksf (kPa).
Frictional Resistance of Pile in Clays : b - method
Ultimate Capacity of Single Piles in Cohesionless Soil
Nordlund method(1963)
• Based on field observations• Considers pile taper and soil
displacement in calculating the shaft resistance.
• Accounts for the differences in soil-pile coefficient of friction for different pile materials.
• The method is based on the results of several load tests in cohesionless soils.
where:
d = depth.
D = embedded length of the pile.
Kδ = coefficient of lateral earth pressure at depth d.
CF = correction factor for Kδ when δ ≠ φ.
Pd = effective overburden pressure at the center of depth
increment Δd.
δ = interface friction angle between pile and soil.
ω = angle of pile taper from vertical.
φ = soil friction angle.
Cd = pile perimeter at depth d.
Δd = length of pile segment.
αt = dimensionless factor dependent on pile depth-width
relationship.
N'q = bearing capacity factor.
At = pile toe area.
Pt = effective overburden pressure at the pile toe.
Pile Capacity: Static Analysis - Factor of Safety FS
Allowable Capacity Qa = Qu / FS
Qs
Qp
FS primarily depends on:
• The level of confidence in the input parameters.
• The level of confidence is a function of • The type and extent of the subsurface
exploration and laboratory testing of soil and rock materials.
• Variability of the soil and rock. • Method of static analysis. • Effects of and consistency of the proposed pile
installation method. • Level of construction control (static load test,
dynamic analysis, wave equation analysis, Gates dynamic formula).
Pile Capacity: Static Analysis FS Factor of Safety
FS = Qu /Qa
• Range of static analysis factors of safety in the past was from 2 to 4• Most static analysis methods recommended a factor of safety of 3• As foundation design loads increased over time, the use of higher
factors of safety often resulted in pile installation problems.• Experience has shown that construction control methods have a
significant influence on pile capacity. • The factor of safety used in a static analysis calculation should be
based on the construction control method specified.
Pile Capacity: Static Analysis FSFactor of Safety
FS = Qu /Qa
Construction Control Method Factor of Safety1. Static load test with wave equation analysis 2.002. Dynamic testing with wave equation analysis 2.253. Indicator piles with wave equation analysis 2.504. Wave equation analysis 2.755. Gates dynamic formula 3.50
FHWA NHI-06-089 9 – Deep Foundations Soils and Foundations – Volume II
Pile Setup
Pile Capacity Change with TimePile Setup
• Capacity increases with time
• Occurs frequently in clay soils.
• Skov & Denver method (1988)
• Qt = axial capacity of the pile after time t of driving,
• Q0 = initial axial capacity at time t0 ( 1 day) after driving,
• A = constant dependent on soil type and subsurface condition. Requires evaluation at the site after pile installation.
Pile Relaxation
• Capacity decreases with time after the driving has been completed
• Occurs rarely in dense saturated fine sands, dense silts, or weak laminated rocks such as shale
)].[log(100 t
tA
Q
Qt +=
Pile Set-up in Ohio Soils
Twenty three small diameter steel pipe piles driven in silt-
clay soils were investigated.
Relaxations were observed in two piles.
Set-up occurred in twenty one piles, i.e. 91 % cases
0
100
200
300
400
500
600
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Pile
Lo
ad (
Kip
)
Pile number
Intial Capacity Total (kips)
Restrike Capacity Total (kips)
Pile Set-up in Ohio Soils
0
50
100
150
200
250
300
350
400
450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Pile
Lo
ad (
Kip
)
Pile number
Intial Shaft capacity (kips)
Restrike Capacity Shaft (kips)
0
50
100
150
200
250
300
350
400
450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Pile
Lo
ad (
Kip
)
Pile number
Tip Capacity Initial
Tip Capacity Restrike
Drivability Evaluation• Candidate pile types should be evaluated for driveability.
• Can the candidate pile type and/or section be driven to the required capacity and penetration depth at a reasonable pile penetration resistance (blow count) without exceeding allowable driving stresses for the pile material?
• Analysis is performed by using the wave equation theory.
• Possible hammers must be identified to make sure that the pile is driveable to the capacity and depth required.
• For H-piles and pipe piles, it may be possible to increase the pile section without increasing the soil resistance to driving.
• For concrete piles an increase in section usually means a larger pile size. Therefore, an increase in soil resistance must also be overcome
FHWA NHI-06-089 9 – Deep Foundations
Soils and Foundations – Volume II
Pile Group Design
Pressure Isobars of Group of closely spaced piles
• Governed by the sum of the ultimate capacities of the individual piles, with some reduction due to overlapping zones of shear deformation in the surrounding soil
• Holds In the absence of negative shaft resistance in cohesive soil
• Reduction in group capacity is done by multiplying the aggregate capacity of the individual piles with group efficiency
Pile Group Design
Minimum Spacing between Piles• Stipulated in building codes
• Straight uniform diameter piles – 2d to 6 d
• Friction piles – 3d
• For end bearing piles • passing through relatively compressible strata, the spacing of piles shall not be less than 2.5d• For end bearing piles passing through compressible strata and resting in stiff clay - 3.5d
• For compaction piles - 2d.
CAPACITY OF PILE GROUP
Group capacity in Sand• Feld’s Rule
• Reduces the capacity of each pile by 1/16 for each adjacent pile
• Converse-Labarre Formula
Group capacity in clay• Failure Modes
Individual failure – spacing about 8d
Block failure - spacing less than 3d
Block failure of pile groups is generally a design consideration only for pile groups in softcohesive soils or in cohesionlesssoils underlain by a weak cohesive layer.
GROUP CAPACITY IN SAND CONVERSE-LABARRE FORMULA
( ) ( )mn
nmmng
90
111
−+−−=
g = pile group efficiencym = number of columns of piles in a group,n = number of rows,θ = tan-1( d/s) in degrees,d = diameter of pile,s = spacing of piles center to center.
= uggu QQ
GROUP EFFICIENCY IN CLAY
(d = pile diameter)
TWO Failure Modes• Individual pile failure : spacing about 8d• Block pile failure : spacing less than 3d
= PILE EFFICIENCYQ1 = ULTIMATE LOAD CAPACITY OF SINGLE PILEQB = ULTIMATE LOAD CAPACITY OF BLOCKn = number of piles
𝑛
𝑃𝑖𝑙𝑒𝑔𝑟𝑜𝑢𝑝𝑢𝑙𝑡𝑖𝑚
𝑎𝑡𝑒𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦
5 10 15
1
𝜂2= 1 +
𝑛2 𝑄12
𝑄𝑔2
GROUP EFFICIENCY IS SMALLER OF THE TWO:1. Q1 X n2. QB
Pile Group Block Failure
cLLBAcNQ rrgcgu )(2 ++=
c = cohesion beneath the pile group,
L = length of pile,
2(Br+Lr) = perimeter of pile group,
A g= sectional area of group,
Nc = bearing capacity factor which ~ 9 for deep foundations.
NOTE: ONLY HAPPENS IN CLAY
SETTLEMENT OF PILE GROUPS
Settlement of a group is affected by • Shape and size of the group • Length of piles • Method of installation of piles and possibly many other factors.
Total Settlement
Elastic Settlement
Consolidation Settlement
Settlement of Pile Groups in Cohesionless Soils• Meyerhof (1976) recommended
the settlement of a pile group in a homogeneous sand deposit not underlain by a compressible soil be conservatively estimated by the following expressions in FPS units. s = estimated total settlement in inches
pf = design foundation pressure in ksf = group design load divided by group areaB = width of pile group in ftN' = average corrected SPT N60 value within a depth B below pile toeIf = influence factor for group embedment = 1 - [ D / 8B ] ≥ 0.5D = pile embedment depth in ft
Semi-Empirical Formulas and Curves
• Vesic (1977) – single pile, extended to pile group
S = total settlement,
Sp = settlement of the pile tip,
Sf = settlement due to the deformation of the pile shaft.
Settlement of Pile Groups in Cohesionless Soils
Pile settlement : sand
• Qp= point load,
• d = diameter of the pile at the base,
• q pu - ultimate point resistance per unit area,
• Dr = relative density of the sand,
• Cw = settlement coefficient, = 0.04 for driven piles= 0.05 for jacked piles= 0.18 for bored piles,
• Qf = friction load,
• L = pile length,
• A = cross-sectional area of the pile,
• E = modulus of deformation of the pile shaft,
• α = coefficient which depends on the distribution of skin friction along the shaft and can be taken equal to 0.6.
Pile Group Settlement : Vesic method(1967)
Fg = group settlement factor
Sg = settlement of group,
S = settlement of a single pile.
Curve showing the relationship between group settlement ratio and relative widths of pile
groups in sand (Vesic, 1967)
Settlement of Pile Group: Cohesive Soil
( ) ( ).
.z
B Lq
B z L zsD =
+ +
( )1
46
av t m bs s s s D = D + D + D
Consolidation Settlement equation
log log1 1
s c c c c o avc
o o o c
C H C HS
e e
s s s
s s
+ D= +
+ +
Settlement of Pile Group: Cohesive Soil
CASE 1
• The soil is homogeneous clay.
• The load Qg is assumed to act on a fictitious footing at a depth 2/3L from the surface and distributed over the sectional area of the group.
• The load on the pile group acting at this level is assumed to spread out at a 2 Vert : 1 Horiz slope.
CASE 2
• The pile passes through a very weak
layer of depth L1 and the lower
portion of length L2 is embedded in a
strong layer.
• In this case, the load Q is assumed to
act at a depth equal to 2/3 L2 below
the surface of the strong layer and
spreads at a 2 : 1
Settlement of Pile Groups in Cohesive Soil
CASE 3
• The piles are point bearing piles.
• The load in this case is assumed to act at the level of the firm stratum and spreads out at a 2 : 1 slope.
Allowable Load in Groups of Piles
1. Shear failure
2. Settlement
Negative Skin Friction
Occurrence of Negative Skin Friction
• If the fill material is loose cohesionless soil.
• When fill is placed over peat or a soft clay
stratum
• By lowering the ground water which
increases the effective stress causing
consolidation of the soil with resultant
settlement and friction forces being
developed on the pile
Magnitude of Negative Skin Friction• Single pile – Cohesionless Soil
• Single pile – Cohesive Soil
• Ln = length of piles in the compressible material
• s = shear strength of cohesive soils in the fill
• P = perimeter of pile
• K = earth pressure coefficient normally lies between the active and the passive earth pressure coefficients
• δ = angle of wall friction
Negative Skin Friction on Pile Group
L1 = depth of fill,
L2 = depth of compressible natural soil,
s1, s2 = shear strengths of the fill and compressible soils respectively,
γ1, γ2= unit weights of fill and compressible soils respectively,
Fnl = negative friction of a single pile in the fill,
Fn2 = negative friction of a single pile in the compressible soil.
Uplift Capacity
Uplift Capacity• Pul = uplift capacity of pile,
• W p= weight of pile,
• fr = unit resisting force
• As = effective area of the embedded length of pile.
• cu = average undrained shear strength of clay along the pile shaft
• α = adhesion factor
• ca = average adhesion
Cohesive Soil
Uplift Capacity of Pile Group
L = depth of the pile block
B = overall length and width of the pile group
cu = average undrained shear strength of soil around the sides of the group
W = combined weight of the block of soil enclosed by the pile group plus the weight of the piles and the pile cap.
Uplift of a group of closely-spaced piles in cohesive soils
Group Settlement Based on Pile Stress Interaction
Pile Group Settlement: Early EquationsEmpirical Approaches
• Skempton (1953) • Meyerhof (1959)• For driven piles and displacement
caissons in sand
• Square group
Analytical ApproachPoulous & Davis (1980)
Analysis of Pile Group Settlement
Pile Group Capacity and Settlement
a
Interaction Factors a for Floating Piles• Skin friction piles
S
AP
E
REK =
4/2d
AR P
A
=
Average values of K for different solid piles
Multiply by RA for H- piles
Interaction Factor Corrections
• Effect of finite layer• Nh is the correction factor.• Can be used for other L/d and K values
hF Naa =
Other Interaction Factor Corrections• Effect of enlarged pile base
• Effect of Poisson’s Ratio
• Effect of Non uniform Soil Modulus
• Finite Compressibility of Bearing Stratum
• Interaction of Piles of Different Size
Interaction Factors: End Bearing Piles
Pile Group Capacity and Settlement
• For a group of 4 piles equally spaced at s diameters
rG = displacement of pile groupP1 = load on each pile (equally loaded)r1 = displacement of single pile under unit loada1 = interaction factor for spacing s.d
a2 = interaction factor for spacing 2s.d
Group Settlement Analysis of General GroupsSettlement of k-th pile in group
( ) k
n
kjj
kjjk PP 1
1
1 . rarr += =
ALSO The load equilibrium must be satisfied
rk = displacement of the k th pile in the groupPj = load on pile jPk= load on pile kr1 = displacement of single pile under unit loadakj = interaction factor for spacing between pile k and j
PG = total group load
Gives n+1 equations for n piles
Analysis of General Groups
• The n+1 equations are solved for either of the two conditions
1. Flexible Pile Cap - Equal Loads on all piles
2. Rigid Pile Cap – Equal Settlement of all Piles
The Results can be expressed
In terms of settlement ratio Rs
𝑅𝑆 =𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑔𝑟𝑜𝑢𝑝 𝑠𝑒𝑡𝑡𝑙𝑒𝑚𝑒𝑛𝑡
𝑆𝑒𝑡𝑡𝑙𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑎 𝑠𝑖𝑛𝑔𝑙𝑒 𝑝𝑖𝑙𝑒 𝑎𝑡 𝑠𝑎𝑚𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑙𝑜𝑎𝑑 𝑎𝑠 𝑎 𝑝𝑖𝑙𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑔𝑟𝑜𝑢𝑝
In terms of group reduction factor RG
𝑅𝐺 =𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑔𝑟𝑜𝑢𝑝 𝑠𝑒𝑡𝑡𝑙𝑒𝑚𝑒𝑛𝑡
𝑆𝑒𝑡𝑡𝑙𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑎 𝑠𝑖𝑛𝑔𝑙𝑒 𝑝𝑖𝑙𝑒 𝑎𝑡 𝑠𝑎𝑚𝑒 𝑡𝑜𝑡𝑎𝑙 𝑙𝑜𝑎𝑑 𝑎𝑠 𝑡ℎ𝑒 𝑔𝑟𝑜𝑢𝑝
Analysis of General Groups
• Also provides loads in individual piles when analyzed for flexible pile cap condition
1rr avSG PR=
1rr GGG PR=
Pav = average load on a pile in the groupPG = total group load
• Once Rs and Rg have been determined, the group settlement rG is given by either of the two equations:
EXAMPLE PROBLEM
A freestanding group of six 12 inch – diameter concrete piles is driven into a deep layer of medium clay, and is to be subjected to a load of 300 tons. A test on a single pile at the site gives a final settlement of 0.60 in. under a load of 50 tons. Determine the final settlement of the six pile group
Summary of Solution• Value of K is about 2000 • Piles 1,3,4 and 6 behave identically – Type A : Load PA
• Piles 2 and 5 will behave identically – Type B : Load PB
• Find interaction factors from Fig. 6.3 for L/d = 25 and K = 2000
tons2.35 tons,4.57
in. 66.1
BA ==
=
PP
Gr
For Rigid Cap
Load Distribution in Piles with Rigid Pile Caps
Analytical Method of Group Settlement
• Soil properties not required
• Field condition is incorporated
• Based on actual pile capacity measured in the field
• Loads on individual piles can be obtained for rigid pile cap condition
Advantages
Disadvantage
• Does not account for pile setup or relaxation
Design StepsDetermine static capacity for a single pile
L, D
Design a pile group
Determine single pile (L, D) settlement under average
group load in the field
Use Analytic Approach to determine group settlement and
load on individual pile
Adjust L, D if settlement exceeds design value
Adjust L, D if group settlement exceeds design value
Closing Notes
• The shaft resistance of piles driven into cohesive soils is frequently as much as 80 to 90% of the total capacity. Therefore, it is important that the shaft resistance of piles in cohesive soils be estimated as accurately as possible.
• It should be remembered that the movement required to mobilize the toe resistance is several times greater than that required to mobilize the shaft resistance.
• At the movement required to fully mobilize the toe resistance, the shaft resistance may have decreased to a residual value.
• Therefore, the contribution of the toe resistance to the ultimate pile capacity in cohesive soils is sometimes ignored except in hard cohesive deposits such as glacial tills.
Closing Notes• The time dependent capacity (setup or relaxation) may
significantly affect the long term capacity of driven piles
• The ability of a pile to be driven to the required depth has become increasingly more important and must be evaluated in the design stage.
• All of the analysis methods are meaningless if the pile cannot be driven to the required design depth without sustaining damage.
• The limit of pile driveability is the maximum soil resistance a pile can be driven either without sustaining damage or a refusal driving resistance with a properly sized driving system.
Ref: FHWA NHI-06-089 9 – Deep Foundations Soils and Foundations – Volume II
Thank you!