ASCE Workshop DFSAP Presentation

J. P. Singh J. P. Singh & Associates

Richmond, California

Presented atASCE Geotechnical Workshop

Oakland, CaliforniaOctober 21, 2008

ANALYSIS OF LATERALLY AND AXIALLY ANALYSIS OF LATERALLY AND AXIALLY LOADED PILES AND SHAFTS USING DFSAPLOADED PILES AND SHAFTS USING DFSAP

Complexity of the Soil Structure Interaction ProblemComplexity of the Soil Structure Interaction Problem

The Soil-Foundation-Structure Problem involves Kinematic The Soil-Foundation-Structure Problem involves Kinematic Soil-Foundation Interaction occurring during large (cyclic Soil-Foundation Interaction occurring during large (cyclic and permanent) ground deformations as well as Inertial and permanent) ground deformations as well as Inertial Foundation-Structure Interaction occurring during shaking Foundation-Structure Interaction occurring during shaking all of which take place while the soil and possibly structural all of which take place while the soil and possibly structural properties degrade with time.properties degrade with time.

Soil Structure Interaction (SSI) ProblemSoil Structure Interaction (SSI) Problem

Post Earthquake Damage Recon & StudiesPost Earthquake Damage Recon & Studies Modeling of SSI Effects and their ValidationModeling of SSI Effects and their Validation using Full Scale Field Testsusing Full Scale Field Tests Centrifuge Physical ModelingCentrifuge Physical Modeling

Major Causes of DamageMajor Causes of Damage

Ground ShakingGround ShakingSite ResponseSite ResponseNear Fault EffectsNear Fault Effects

Ground DeformationGround DeformationLiquefaction RelatedLiquefaction Related

Soft Soil Related Soft Soil Related

2001 Bhuj Earthquake

Damage to Floating and End Bearing Piles Damage to Floating and End Bearing Piles 1964 Niigata Earthquake 1964 Niigata Earthquake

Hanshin Expressway Route 5 1995 Kobe Earthquake Permanent Horizontal

Displacement of Bridge Piers vs Distance to Waterfront

Permanent HorizontalDisplacements of Bridge Piers versus Free Field Ground Displacement

Important Factors to be considered inImportant Factors to be considered in Solution of the Complex SSI ProblemSolution of the Complex SSI Problem

Thickness and properties (shear strength and Thickness and properties (shear strength and passive pressure) of soil stratapassive pressure) of soil strata

Geometry and Properties of Foundation Geometry and Properties of Foundation Elements Elements

Restraining stiffness and strength of Structural Restraining stiffness and strength of Structural ElementsElements

Pile Types - Vertical or Batter/End Bearing or Pile Types - Vertical or Batter/End Bearing or FloatingFloating

Limit Equilibrium Evaluation of Land Road Bridge FoundationLimit Equilibrium Evaluation of Land Road Bridge Foundation1987 Edgecumbe, New Zealand Earthquake1987 Edgecumbe, New Zealand Earthquake

Limit Equilibrium Method for Design of Deep Foundation subjected to Lateral Spreading (Japan Road Association, 1996)

NEAR FAULT RESPONSE SPECTRA

Port of Oakland - Berth 37 Port of Oakland - Berth 37 Damage Calibration StudyDamage Calibration Study

using FLAC Analysesusing FLAC Analyses

1989 Loma Prieta Earthquake1989 Loma Prieta Earthquake

Berth 37 - Cross SectionBerth 37 - Cross Section

Berth 37 - Damage Calibration StudyBerth 37 - Damage Calibration Study

Calibration Calibration Target DeformationsTarget Deformations

Permanent Horiz. Deck Displacement = 2 - 4 inchesPermanent Horiz. Deck Displacement = 2 - 4 inchesPermanent Horiz. Soil Deformation = 6 inchesPermanent Horiz. Soil Deformation = 6 inches

Visible Damage to the PilesVisible Damage to the Piles

Damage to the Piles at Depth ?Damage to the Piles at Depth ?

SUMMARY OF PILE TOP DAMAGEBERTH 37 - LOMA PRIETA EARTHQUAKE

0%

5%

10%

15%

20%

25%

30%

35%

40%

35 36 37 38

Berth

% o

f Pile

s Da

mag

ed

A % DamageB % DamageC % DamageD % DamageE % DamageF % DamageTotal Percent

Note: Pile Integrity Testing suggests some E-Row piles may be damaged below the liquefiable layer.

Orbital Plots of Loma Prieta Records - Port of Oakland (Acceleration) (Velocity) (Displacement)

Input Time History to FLAC Model

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.4-0.3-0.2-0.100.10.20.30.4

270 Accel (g)

0 A

ccel

(g)

Recorded MotionApprox Berth Alignment

Loma Prieta, Outer Harbor

-60

-45

-30

-15

0

15

30

45

60

-60-45-30-15015304560

270 Velocity (cm/sec)

0 Ve

loci

ty (c

m/s

ec)


-15

-10

-5

0

5

10

15

-15-10-5051015

270 Displacement (cm)

0 D

ispl

acem

ent (

cm)


-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 5 10 15 20 25 30 35 40

Time (Seconds)

Acce

lera

tion

(g's

)

Photo of Pile Top Damage

FLAC Model of Berth 37

FLAC (Version 3.40)

LEGEND

16-Jan- 1 17:22 step 8720 -2.000E+01 <x< 2.300E+02 -8.000E+01 <y< 5.000E+01

Density 1.553E+00 1.826E+00 2.646E+00 2.866E+00 3.236E+00 3.363E+00 3.366E+00 3.509E+00 3.646E+00 4.037E+00

Beam plotPile plot

-7.000

-5.000

-3.000

-1.000

1.000

3.000

(*10^1)

0.000 0.400 0.800 1.200 1.600 2.000(*10^2)

JOB TITLE :

MTR & ASSOCIATES Lafayette, CA USA

2

4

5

3

6

89

10

11

12

13

7

1

3

ABCDEFG

H

Contours of Horizontal Slope Displacement

FLAC (Version 3.40)

LEGEND

28-Jan- 1 9:22 step 1337044 -2.000E+01 <x< 2.300E+02 -8.000E+01 <y< 5.000E+01

X-displacement contours 0.00E+00 1.00E-01 2.00E-01 3.00E-01 4.00E-01 5.00E-01

Contour interval= 1.00E-01Beam plotPile plot

-7.000

-5.000

-3.000

-1.000

1.000

3.000

(*10^1)

0.000 0.400 0.800 1.200 1.600 2.000(*10^2)

JOB TITLE :


HG F E D C B A

Contours of Vertical Slope Displacement

FLAC (Version 3.40)

LEGEND

28-Jan- 1 9:22 step 1337044 -2.000E+01 <x< 2.300E+02 -8.000E+01 <y< 5.000E+01

Y-displacement contours -5.00E-01 -4.00E-01 -3.00E-01 -2.00E-01 -1.00E-01 0.00E+00 1.00E-01

Contour interval= 1.00E-01Beam plotPile plot

-7.000

-5.000

-3.000

-1.000

1.000

3.000

(*10^1)

0.000 0.400 0.800 1.200 1.600 2.000(*10^2)

JOB TITLE :


HG F E D C B A

FLAC (Version 3.40)

LEGEND

28-Aug- 1 16:33 step 1073877 4.000E+01 <x< 2.200E+02 -1.300E+02 <y< 5.000E+01

Boundary plot

0 5E 1

Beam plotPile plotStructural DisplacementMax Value = 4.695E-01

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

(*10^2)

0.500 0.700 0.900 1.100 1.300 1.500 1.700 1.900 2.100(*10^2)

JOB TITLE :

MTR & Associates Lafayette, California USA

Pile Displacement Vector DiagramPermanent Horizontal Deck Displacement = 0.30 feet

(feet)

Berth 37(Pre-Loma Prieta Condition)

Loma Prieta, Sr = 400 PSF

FLAC (Version 3.40)

LEGEND

29-Aug- 1 10:18 step 1627 0.000E+00 <x< 2.200E+02 -1.700E+02 <y< 5.000E+01

Density 1.553E+00 1.826E+00 2.646E+00 2.866E+00 3.236E+00 3.363E+00 3.366E+00 3.509E+00 3.646E+00 4.037E+00

Beam plotPile plot

-1.400

-1.000

-0.600

-0.200

0.200

(*10^2)

0.200 0.600 1.000 1.400 1.800(*10^2)

JOB TITLE :


12 3 4

Pore Pressure Monitoring Locations

Loma Prieta, Sr = 400 PSFBerth 37(Pre-Loma Prieta Condition)

BDEFGH AC

FLAC (Version 3.40)

LEGEND

29-Aug- 1 18:36 step 824879 HISTORY PLOT Y-axis : sd_pore_pres ( 25, 23) UDPsd_pore_pres ( 36, 20) UDPsd_pore_pres ( 42, 19) UDPsd_pore_pres ( 55, 18) UDP X-axis :Dynamic timeInput Time

4 8 12 16 20

0.000

0.200

0.400

0.600

0.800

1.000

JOB TITLE :


Pore Pressure Ratios

Time (Seconds)

Berth 37


(Pre-Loma Prieta Condition)

Pore

Pre

ssur

e R

atio

4

3

1

2

Soil Deformation Time History Near Top of Batter Pile

FLAC (Version 3.40)

LEGEND

28-Jan- 1 19:04 step 1779831 HISTORY PLOT Y-axis :X displacement( 45, 28) X-axis :Dynamic time

5 10 15 20 25 30 35

0.000

1.000

2.000

3.000

4.000

5.000

(10 )-01

JOB TITLE :

MTR & Associates Lafayette, CA USA

Liquefaction triggered, soil deformation occurs

Cyclic motions,no liq.

Pile Top Shear Time History - Waterside Batter Pile

FLAC (Version 3.40)

LEGEND

28-Jan- 1 19:04 step 1779831 HISTORY PLOT Y-axis :Shear Force (El 90) X-axis :Dynamic time

5 10 15 20 25 30 35

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

(10 )+03

JOB TITLE :

MTR & Associates Lafayette, CA USA

Inertia Loading

Kinematic Loading

FLAC (Version 3.40)

LEGEND

28-Aug- 1 16:33 step 1073877 HISTORY PLOT Y-axis :Axial Force (El 105) X-axis :Dynamic time

4 8 12 16 20

-3.000

-2.000

-1.000

0.000

1.000

2.000

3.000

(10 )+04

JOB TITLE :


Berth 37



Time (Seconds)

Axial Force at Pile/Deck Connection, Pile Row H

-336 kip

Axi

al F

orce

per

foot

pile

spa

cing

(lb)

480 kip

FLAC (Version 3.40)

LEGEND

29-Aug- 1 18:36 step 824879 HISTORY PLOT Y-axis :Moment 1 (El 105) X-axis :Dynamic time

4 8 12 16 20

-3.000

-2.000

-1.000

0.000

1.000

2.000

3.000

(10 )+03

JOB TITLE :


Bending Moment at Pile/Deck Connection, Pile Row H

60 ft-kip

Mp = 60 ft-kip

Berth 37



Time (Seconds)

Mom

ent p

er fo

ot p

ile s

paci

ng (f

t/lb)

FLAC (Version 3.40)

LEGEND

28-Aug- 1 16:33 step 1073877 HISTORY PLOT Y-axis :X displacement( 45, 28) X-axis :Dynamic time

5 10 15 20 25

-0.500

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

(10 )-01

JOB TITLE :


Time (Seconds)

Horizontal Deck Displacement Time History

Dis

plac

emen

t (Fe

et)

Berth 37



3.6 inches

4.4 inches

Moment Diagram, Sr=400 psf

Pile Row E

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

-200

-100

0 100 200

Moment (ft-kip)

Elev

atio

n (ft

)

Pile Row F

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

-200 -100 0 100 200

Moment (ft-kip)

Elev

atio

n (f

t)

Pile Row G

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

-200 -100 0 100 200

Moment (ft-kip)

Elev

atio

n (f

t)

Pile Row H

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

-200 -100 0 100 200

Moment (ft-kip)

Elev

atio

n (f

t)

SIMPLE ENGINEERING METHODS

• Traditional p-y Method • Strain Wedge Method (SWM)

CURRENT PRACTICE

• The p-y approach represents the most common method in the current practice for lateral load analyses of piles. It is employed in:

• LPILE• GROUP• COM624• BEAM-COLUMN• FLORIDA-PIER • ALLPILE

p-y curve used in these programs is a function of soil properties and pile width

Traditional empirical p-y curves were developed usingdata from full-scale load tests performed on slender (long) piles as function of soil properties and pile width

• for sand - Mustang Island Test (2-ft diameter steel pipe pile in medium dense sand)

• for soft clay - Sabine River Test (10.75-in diameter steel pipe pile in soft clay)

• for stiff clay - Houston Test (2.5-ft diameter RC pile in med. Stiff clay)

CURRENT PRACTICE

Computer Program DFSAP Deep Foundation System Analysis Program

developed using Strain Wedge Method

for

Washington State Department of Transportation

for

Analysis of Laterally and Axially Loaded Group of Shafts and Piles

1. Assessment of the lateral response (deflection, shear force and bending moment) for

• Isolated piles• Large Diameter shafts • Pile group with/without pile cap

STRAIN WEDGE METHOD (SWM) AND ITS CAPABILITIES FOR ANALYSIS OF LATERALLY LOADED PILES/SHAFTS

2. Analysis of laterally loaded piles in layered soils•Sand• Clay • C- soil• Weak rock

3. Assessment of the laterally load piles/pile groups considering • Soil liquefaction• Lateral soil spread

THE CAPAPILTIES OF THE SWM PROGRAMFOR LATERALLY LOADED PILES/SHAFTS

4. Consideration of the pile/shaft type (short, intermediate & long) effect on the pile lateral response and resulting p-y curve

5. Evaluation of the bridge foundation stiffnesses,• Vertical displacement stiffness • Lateral displacement stiffness• Rotational stiffness• Torsional stiffness

6. Assessment of p-y and t-z curves based on soil and pile properties

7. Assessment of the piles/shafts behavior under axial loads • Pile load - settlement • Axial Load distribution along the pile• Pile’s skin and tip resistance

What are the differences between the SWM approach and the p-y method?

p-y curves in SWM Approach accounts for the following:

• Pile Bending Stiffness (EI)• Pile Head Conditions (Free/Fixed)• Pile Cross-Section Shape (Square/Circular/H-Shape)• Pile-Head Embedment Below Ground• Soil Profile Continuity (Winkler Springs)• Long/Intermediate/Short Piles • Soil Liquefaction and Lateral Soil Spread• Pile Group• Vertical Side Shear Resistance (Large Diameter Shaft))

P-Y CURVES IN STRAIN WEDGE APPROACH

y

p(Es)1

(Es)3

(Es)4

(Es)2p

p

p

y

y

y

(Es)5

p

y

MoPo

Pv

Laterally Loaded Pile as a Beam on Elastic Foundation (BEF)

LARGE DIAMETER SHAFT

z

T

y

p

Soil-Shaft Horizontal Resistance

Soil-Shaft Shear Resistance

Neglected with Long Shafts

PoMo

PvPoo

Moo

Pvy

FP

v

Mt

Fv

FP

FP

Fv

Fv

VtFt

The p-y method provides a unique p-y curve for the equal diameter piles in the same soil regardless of the pile’s EI

S tif f P ile F lex ib le P ile

p -y C u rv e a t a D ep th o f 1 .2 2 m

D en se S an d

L o o se S a n d

E f f ec t o f P ile B e n d in g S tif f n e ss o n th e p -y C u rv e in S an d

0 4 0 8 0 1 2 0P ile D e f lec tio n , y , m m

0

1 0 0

2 0 0

3 0 0

4 0 0So

il-Pi

le R

eact

ion,

p, k

N /

m EI & D = 1 ft0.1 EI & D = 1 ft

q per unit area

B

CL

q

0.5q

Kr =

Kr = 0

Rigid Footing, Kr = Flexible Footing, Kr = 0

Footing H

(1-2s) EP H3

6 (1-2P) Es B3

Kr =

Variation of soil reaction with the change of the footing stiffness (EI) as presented by Terzaghi (1955) and Vesic (1961)

F re e-H e a d P ileF ix ed -H ea d P ile

E ffec t o f P ile -H ea d C o n d itio n s on th e p -y C u rv e in S a n d

p -y C u rv e s a t 1 .2 2 -m D e p th

D en se S a n d

L o o se S a n d

0 40 80 120P ile D eflec tio n , y , m m

0

200

400

600

Soil-

Pile

Rea

ctio

n, p

, kN

/ m

SW Model Analysis

The p-y method provides a unique p-y curve for the equal diameter piles in the same soil for piles with free- or fixed-head conditions

Load Test by Kim et al. (ASCE J., 2004)to Show the Effect of Pile-Head Fixity on the p-y curve

y

p(Es)1

P o

(Es)3

(Es)4

(Es)2p

p

p

y

y

y

(Es)5

p

y

Laterally Loaded Pile as a Beam on Elastic Foundation (BEF)

P P

K1 K2

4 ft4 ft

Effect of Structural Element Cross-Sectional Shape

on Soil Reaction

SAND

CLAY

C-

Weak ROCK

The SW model is based on,

The Basic Strain Wedge Model in Uniform Soil

• Stress-strain behavior of the soil as assessed in the triaxial test,

• Soil effective stress analysis

• Plane stress problem (Norris 1986 and Ashour et al. 1998)

• Beam on Elastic Foundation

Pile

Pile head load Po

Successive mobilizedwedges

m

m

Mobilized zones asassessed experimentally

Horizontal and Vertical Growth in the Soil Passive Wedge Pile

Simplified SW Model Po

Soil Strain = y/d , From Triaxial Test Concept , and Stress-Strain Curve, d = h , Stress Level= SL & Mobilized friction angle = m

dy x

Yo

h

m

m

m

Pile

Real stressed zone

F1

F1

Triaxial testprinciple stresses

A

Side shear ()

p = CD * h + Pile Side Shear

(b) Force equilibrium in a slice of the wedge at depth x

p

Plane taken to simplify analysis (i.e. F1’s cancel)

C

D

A

h

dHorizontal Slice

(c) Forces at the face of the soil passive wedge (Section elevation A-A)

ds

dx

h

h * CD* dx = * CD * ds sin m

VO

m

KVO

Yo

h

x

Hi iSublayer i+1

Sublayer 1

Vertical Slice

y

p(Es)1

P o

(Es)3

(Es)4

(Es)2p

p

p

y

y

y

(Es)5

p

y

Bea

m o

n E

last

ic F

ound

atio

n

6

h =

0 .69

Xo

Xo

Zero Crossing

Deflec

tion P

attern

Lineari

zed D

eflec

tion

Yo

Long ShaftL/T 4

Xo >

h >

0. 6

9 X

o

Xo

Zero Crossing

Yo

Line

arize

d Defl

ectio

n

Intermediate Shaft4 > L/T > 2

Zero Crossing

h =

Xo

Yo

Defle

ction

Patt

ern

Short ShaftL/T 2

L = SHAFT LENGTHT = (EI/f )0.2

f = Coefficient. of Modulus of Subgrade Reaction

Varying Deflection Patterns Based on Shaft Type

Different Pile/Shaft Cross-Sections Consideredin The SWM Program

Stre

ss

Strain

fs

s

y

Yield Stress (f )y

soE

Uniaxial Elastic-Perfectly PlasticNumerical Steel Model

E sE s E s

Stress-Strain Model for ConfinedConcrete in Compression

f ccEc

Ecc

cc cuCompressive Strain, c

Com

pres

sive

stre

ss, f

c

Pile/Shaft Material Nonlinear Modeling

SWM Validation Example

Single Shaft

Shaft W idth

Reinforced Concrete D rilled Shaft

x x

Longitudinal S tee l

UCLA/CALTRANS TEST

0

50000

100000

150000

200000

250000

300000

350000

0 5 10 15 20

Lateral Deflection, inches

Load

, lbs

Experiment SWM

Measured and Predicted Shaft Response of the Las Vegas Test (8-ft Diameter and 32-ft long Shaft)

Po

0 2 4 6 8S haft-H ead La te ra l D e flection, Y o, in .

0

200

400

600

800

1000

Sha

ft-H

ead

Late

ral L

oad,

Po,

Kip

s

M easuredD F S A PF LP IE R /C O M 624PCOM624P

0 1 2 3 4 5

S haft-H ead Latera l D eflection , Y o , in .

0

100

200

300

400

Sha

ft-H

ead

Late

ral L

oad,

Po,

Kip

s

M easuredD FSAPFLPIER /CO M 624P

Po

15 ft

4 ft

Stiff ClaySu = 5500 psiR/C Shaft

Soil layer

Soil type Thickness (ft)

(pcf)

(deg.) Su (psf) 50**

Layer 1 Clay 22 130 0 5500 0.0095

Measured and Predicted Shaft Response of the Southern California Test (Pier 1)

Pile/Shaft Group

PILE GROUP

P-multiplier (fm) concept for pile group

y

ppsingle

pgroup = fm psingle

Pile in a group

Single pile

fm is assumed:• to be dependent only on the front pile

spacing regardless of the value of the transverse spacing

• does not consider the soil type or layers

• to be constant in a given soil layer• to be constant regardless of level of

loading, and level of deformation

PoPv

S S

?

?

Po

4

Current Practice

• P-multiplier used in the current practice (p-y method) is a reduction factor

Interaction Among the Piles in a Group (Pile Group Analysis)

Different Sets of the P-multiplier from Different Research Sources (Rollins et al. 2006)

y

ppgroup = Pmult x psingle

psingle

Pile in a group

Single pile

(Pmult.)1 =

(Pmult.)2 =

(Pmult.)3 =

The Overlapping of Passive Soil Wedges and the Interaction among the Piles in a Group at any Step of Lateral Loading

6

Pile Group Analysis in SWM Model

No P-multiplier)

Horizontal Passive Wedge Interference in Pile Group Response

Pile Pile

Overlap of stresses based on elastic theory (and nonuniform shaped deflection at pile face)

Overlap employed in SW model based on uniform stress and pile face deflection

(Po)g (Po)gUniform pile face movement

Horizontal (Lateral and Frontal) Interaction for a Particular Pile in a Pile Group at a Given Depth

Applied Load

B

Spacing

Row3 or higher

Row2Row1

Applied Load

Row3 or higher

Row2Row1

Spacing

Row 1

Applied Load

5B or less

Applied Load

B

SpacingSpacing

Row3 or higher

Row2Row1

Applied Load

Row3 or higher

Row2Row1

Spacing

Row 1

Applied Load

5B or less

8

• No p-multiplier is needed. • Interaction among the piles in the Group is Based on

Longitudinal and Transverse Pile-Spacing, Level of Loading, and Soil and Pile Properties.

• The Piles in the Group are Analyzed According to Their Location in the Pile Group.

• The analysis of the pile cap is part of the pile foundation system and is affected by the pile-head stiffness.

• Pile response under axial loads (Must be part of the pile group analysis under lateral load)

Evaluation of Interaction Among Various Piles in a Group

Treasure Island 3 x 3 Pile Group Test (Rollins et al., ASCE J., No. 1, 2005)

SWM Validation Example

• Isolated Shaft and Shaft Group with Cap

• Effect of Vertical Shear Side Resistance on Large Diameter Shafts

Taiwan Test by Brown et. al. 2001

-0 .5 m0.0 m

3.0 m

8.0 m

12.0 m

17.0 m

25.0 m

32.0 m

= 35 o

= 19 kN /m 3

= 35 o

= 9.2 kN /m 3

= 34o

= 9.4 kN /m 3

= 34o

= 9.2 kN /m 3

S u=121.3 kN /m 2

= 9.2 kN /m 3

5 0 = 0.005

S u=115 kN /m 2

= 9.2 kN /m 3

50= 0.005

S u=60 kN /m 2

= 9.2 kN /m 3

50= 0.007

Sand

S and

Sand

Sand

C lay

C lay

C lay

Free head shaft

a) O rig inal so il p rofile

4.5 m

Loading D irection

b) S ix 1 .5-m -D iam eter Shaft G roup (F ixed H ead)

Shaft B1

Shaft B2

The Taiwan Test by Brown et al. 2001

Traditional p-y curves were modified using LPILE to match the measured p-y data

(Brown et al. 2001)

0 40 80 120 160 200Pile Head Deflection, Yo, mm

0

1000

2000

3000

4000

Pile

He a

d Lo

ad, P

o, kN

Measured (Brown et al. 2001)Predicted (SW Model)No V. Side ShearWith V. Side Shear

Single 1.5-m-Diameter Shaft (B1)

Free-head

0 10 20 30 40C ap D eflection, Y g, m m

0

4000

8000

12000

Pile

Gro

up L

ater

al L

oad,

kN

Measured (Brown et al. 2001)Predicted (SW Model)

Latera l R esponse of a (3 x2) P ile G roup

Fixed head

Pile Cap Effectand

Pile Deflection Patterns

yCap Passive Wedge

Pile Passive Wedges

Pile/Shaft Group with Cap

SWM Example of Pile Group

• 3 x 3 Pile Group

• Various Pile Types within Group • Pile Cap Contribution• Pile-head Effect - Free and Fixed

Loading Direction

P ile in Q u estio n

H o rizo n ta l (la te ra l an d fro n ta l) in te rac tio n fo r a p r ticu la r p ile in a p ile g ro u p a t a g iv en d ep th

P ile T y p e 1

P ile T y p e 2

L o ad in g D irec tio n

L ea d in g R ow

T ra ilin g R ow

T ra ilin g R ow

SP 1S P 1

P ile T y p e 3

P ile T y p e 4

B y P o sit io n

SP 2

SP 2

3 x 3 SHAFT GROUP

FREE-HEAD

0 2 4 6 8S haft D eflection, Y o, in

0

100

200

300

400

Sha

ft-H

ead

Load

, Po,

kips

Pile Type 1Pile Type 2Pile Type 3Pile Type 4

Isolated Shaft

0 2 4 6 8Shaft D eflection , Y o, in

0

100

200

300

400

Sha

ft-H

ead

Load

, Po,

kips Isolated Shaft

Average Shaft

0 0.4 0.8 1.2 1.6S haft D eflection, Y o, in

0

100

200

300

400

500

Sha

ft-H

ead

Load

, Po,

kip

s

Pile Type 1Pile Type 2Pile Type 3Pile Type 4

Iso la ted S haft

0 0.4 0.8 1.2 1.6Shaft D eflection, Y o, in

0

100

200

300

400

500

Sha

ft-H

ead

Load

, Po,

kips Isolated Shaft

Average Shaft

3 x 3 SHAFT GROUP

FIXED-HEAD

Piles + Cap

Piles

Cap

0 2 4 6 8Shaft D eflection , Y o, in

0

400

800

1200

1600

2000

Sha

ft-H

ead

Load

, Po,

kips

FR EE H EAD

0 0.4 0.8 1.2 1.6Shaft D eflection, Y o, in

0

400

800

1200

1600

2000

Sha

ft-H

ead

Load

, Po,

kips

320

Piles + Cap

Piles

Cap410

Free-Head Fixed-Head

Effect of Pile-Head Conditions on Cap Resistance at the Same Deflection Value in DFSAP

Piles/Shafts in Sloping Ground

Piles/Shafts in Sloping Ground

mtanm

m

D

D

h

m

m C

B

x

m

(h-x) tan

h-x

Lateral Load

Different Failure Planes

Sloping Ground

10 Degree Sloping Ground0 Degree Sloping Ground

Effect of Ground Slope on Pile/Shaft Lateral Response

0 4 8 12S haft D eflection, Y o, in

0

100

200

300

400

500

Sha

ft-H

ead

Load

, Po,

kips

Ground Slope20 Degree Downhill20 Degree Uphill0 Degree

Soil Liquefactionand

p-y curves for liquefied soils

Current Available Procedures That Assess the Pile/Shaft Behavior in Liquefied Soils (Using the Traditional P-y Curve):

1. Construction of the p-y curve of soft clay based on the residual strength of liquefied sand presented by Seed and Harder (1990)

2. Reduce the unit weight of liquefied sand with the amount of Ru (Earthquake effect in the free-field ) and then build the traditional p-y curve of sand based on the new value of the sand unit weight.

Pile Deflection, y

Soil-

Pile

Rea

ctio

n, p

Upper Limit of Sr using soft clay p-y curve

Lower Limit of Sr

API Procedure

0 4 8 12 16 20 24Equivalent Clean Sand SPT Blowcount, (N1)60-CS

0

400

800

1200

1600

2000

Res

idua

l Und

rain

ed S

hear

Str

engt

h, S

r (ps

f)

E arthq u ak e -In d u ced L iq u e fac tion an d S lid in g C ase H isto rie s W h ereS P T D ata & R es id u a l S tren g th P a ra m e te rs H ave bee n M easu red

E a rthq u ak e -In d u ced L iq u e fac tion an d S lid in g C ase H isto rie s W h ereS P T D ata & R es id u a l S tren g th P a ra m e te rs H ave bee n E stim ated

C o n stru c tio n -In d u ced L iq u efa tio n an d S lid ing C ase H is to ries

L ow er S a n F er n an d o D a m

Corrected blowcount vs. residual strength, Sr (Seed and Harder, 1990)

Treasure Island Test Result (Rollins and Ashford)

P-Y Curve of Completely Liquefied Soil

Post-liquefaction stress-strain behavior of completely liquefied sand (uc = 3c and Ru =1)

Axial Strain,

Dev

iato

r Stre

ss,

d

Post-liquefaction stress-strain behavior of partially liquefied sand (uc < 3c and. Ru <1)

xo

d = 2 Sr

Post-liquefaction undrained stress-strain behavior of partially or completely liquefied sand

Effect of Cyclic Loading upon Subsequent Undrained Stress-Strain Relationship for Sacramento River Sand (Dr = 40%) (Seed 1979)

0 1 0 2 0 3 0 4 0 5 0A x ial S tr a in , 1, %

0

2

4

6

8

10D

evia

tor S

tres

s, d

, kg/

cm2

0 1 0 2 0 3 0 4 0 5 0

- 2

- 1

0

1

Cha

nge

in P

orew

ater

Pre

ssur

e

u x

s, n

f, kg

/cm

2

0 1 0 2 0 3 0 4 0 5 0

A x ia l S tra in , 1 , %

Initia l S tatic Loading

A fter 9 C yclesC SR of 0 .18 P roduced ru = 1

In itia l S ta tic Loading

100% R esidua l Porew ater P ressure A fter 9 C ycles,C SR of 0.18

Initia l E ffective C onfin ingPressure = 1 kg/cm 2

SWM Example of Pile in Liquefiable Soil Profile

• Pile Head Response• p-y curves for liquified soil

Treasure Island Liquefaction Test (TILT)

TABLE I. SOIL PROPERTIES EMPLOYED IN THE SWM ANALYSIS FOR TREASURE ISLANDTEST

Soil LayerThick. (m)

Soil Type Unit Weight, (kN/m3)

(N1)60 φ(degree)

ε50%

*SukN/m2

0.5 Brown, loose sand (SP) 18.0 16 33 0.45

4.0 Brown, loose sand (SP) 8.0 11 31 0.6

3.7 Gray clay (CL) 7.0 4 1.5 20

4.5 Gray, loose sand (SP) 7.0 5 28 1.0

5.5 Gray clay (CL) 7.0 4 1.5 20

* Undrained shear strength

Peak Ground Acceleration (amax) = 0.1 gEarthquake Magnitude = 6.5 Induced Porewater Pressure Ratio (ru) = 0.9 - 1.0

Soil Profile and Properties at the Treasure Island Test

Shaft Width

x x

Longitudinal Steel

Steel ShellSo

il-Pi

le R

eact

ion,

p

Pile Deflection, y

Treasure Island Test Result (Rollins and Ashford)

Upper Limit of Sr using soft clay p-y curve

Lower Limit of Sr API Procedure

0 100 200 300 400Pile-Head Deflection, Yo, mm

0

100

200

300

400

500Pi

le- H

ead

L oad

, Po,

kN

CISS, 0.61 mEI = 448320 kN-m2

ObservedPredicted (SWM)Predicted (Com624)

No-L

ique

facti

on

Post-Liquefaction (uxs, ff + uxs, nf)

0 4 0 80 12 0 1 60 2 000

40

80

120

160

200

Pile-H

ead Lo

ad, Po

, kN

0

100

200

300

400

500

Pile

-Hea

d L

oad,

Po,

kN

Pile-Head Response (Yo vs. Po) for 0.61-m Diameter CISS at Treasure Island Test

0 40 80 120 160P ile Latera l Deflection, y (m m )

0

20

40

60

80p

(kN

/m)

M easured Pred icted (SW M odel)

0.2 m Below Ground

0 40 80 120P ile Latera l D eflection , y (m m )

0

10

20

30

40

50

p (k

N/m

)


1.5 m Below Ground

0 40 80 120P ile La tera l Deflection, y (m m )

0

10

20

30

40

50

p (k

N/m

)


3.2 m Below Ground p-y Curve of 0.61-m Diameter CISS in Liquefied Soil (Treasure Island, After Rollins et al. 2005)

p-y Curve Empirical Formula in Liquefied Sandby Rollins et al. 2005

p(d=324 mm) = A(By)C for Dr = 50%

where: A = 3 x 10-7 (z+1)6.05, B = 2.8 (z+1)0.11

C = 2.85(z+1)-0.41 z is depth in (m)y is lateral deflection (mm)

pmultiplier = 3.81 ln d + 5.6

p = p (d=324 mm) x pmultiplier

p-y Curves for loose and dense sand for M=6.5 and amax=0.35g

0 0.1 0.2 0.3 0.4 0.5P ile-H ead D eflection, Yo, in .

0

20

40

60

80

Pile

-Hea

d La

tera

l Loa

d, P

o, K

ip

Loose S and (Profile 1)M ed. D ense Sand (Pro f ile 2)

p cfN 1 6 0 = 22

L o ose S an dp cfN 1 6 0 = 6

p cfN 1 6 0 = 3 5

Soil P rof ile 1

p cfN 1 60 = 2 2

ed D en sep cfN 1 6 0 = 2 0

p cfN 1 6 0 = 3 5

Soil P rof ile 2

M = 6.5 am ax = 0.35g

10 ft

40 ft

40 ft

7 ft

0 0.5 1 1.5 2 2.5D eflection, y, in

0

400

800

1200

1600

2000

Soi

l-Pile

Rea

ctio

n, p

, lb/

in

Soil Profile 1Soil Profile 2LPILE for any Soil Profile

0 0.5 1 1.5 2 2.5Def lection, y, in

0

0.2

0.4

0.6

0.8

1

Soi

l-Pile

Rea

ctio

n, p

, lb/

in

p-y Curves at 6 ft below Pile Headfor Different Seismic Events Zoom ed p-y Curve at 6 ft below Pile

Head for M = 6.5 and am ax= 0.35g

M = 6.5 am ax = 0.35g

Loose Sand Profile for Three Levels of EarthquakeM=4.5, amax=0.15g; M=5.0, amax=0.25g; M=6.5, amax=0.35g

0 0.5 1 1.5 2 2.5P ile-H ead Deflection, Yo, in .

0

200

400

600

800

Soi

l-Pile

Rea

ctio

n, p

, lb/

in

M = 4.5, am ax= 0.15 gM = 5 .0, am ax= 0.25 gM = 6 .5, am ax= 0.35 gLP ILE fo r any Seism c Event

0 0.5 1 1.5 2 2.5D eflection, y, in

0

0.2

0.4

0.6

0.8

1

Soi

l-Pile

Rea

ctio

n, p

, lb/

in

p-y Curves at 6 ft below Pile Headfor Different Seismic Events Zoom ed p-y Curve at 6 ft below Pile

Head for M = 6.5 and amax= 0.35g

0 0.1 0.2 0 .3 0.4 0.5P ile-H ead D eflection, Yo, in .

0

20

40

60

80

Pile

-Hea

d La

tera

l Loa

d, P

o, K

ip

M = 4 .5, am ax= 0.15 gM = 5 .0, am ax= 0.25 gM = 6 .5, am ax= 0.35 g

Lateral Soil SpreadLateral Soil Spread

Bartlett and Youd, 1995 (Current Practice)

LATERAL SOIL SPREADING PROBLEM

• Mobilized Driving Lateral Forces Acting on Piles and Generated by Crust Layer(s)

• Varying Strength of Liquefied Soil(s)

• Amount of Soil Lateral Displacement

Stress-Strain Behavior of Fully Liquefied SandAxial Strain,

Dev

iato

r Stre

ss, d

xo

Soil Lateral Displacement (Xo)in DFSAPShaft Cross Section Liquefied Soil

Soil Flow Around

(Ishihara)

Clay

Po

Axial Load

MoMoMo

Shaft Diameter

Phase I

Clay

Liquefiable Soil“Full”

y

p

P-y Curve for Fully Liquefied Soil

y

p

P-y Curve for Partially Liquefied Soil

y

p

P-y Curve for Non- Liquefied Soil

y

p

Lateral Spread Effect

P-y Curve for Crust Layer

Pile-Soil Response Under Lateral Soil Spread

Liquefiable Soil“Partial”

Po

Axia l Load

C rust

Fully L iquefied

P artia lly L iq .

y s1

y s

N on-L iquefied

Phase II

Comparison of Pile Behavior forComparison of Pile Behavior for

- - As Is ConditionAs Is Condition - Liquefaction - Liquefaction

- Liquefaction with Lateral Spread - Liquefaction with Lateral Spread

1 6

1 2

8

4

0

Dep

th (m

)

0 400 800

M om ent (kN -m )

Pile head load = 100 kNPile head moment = 316 kN-m

No-LiquefactionLiquefactionLiquefaction + Lateral Spread

Lateral Spread ProblemPile Cross-Section # 1

Ben

ding

Stif

fnes

s, EI

, kN

-m2

Bending Moment, M, kN-m

0

500000

1000000

1500000

2000000

2500000

3000000

0 500 1000 1500 2000 2500 3000

1 6

1 2

8

4

0

Dep

th (m

)

-20 0 20 40 60 80D eflection (m m )

Pile head load = 100 kNPile head moment = 316 kN-m

No-LiquefactionLiquefactionLiquefaction + Lateral Spread

Dense Sand

Loose Sand

Clay = 6 kN/m3, Dr = 21-35% = 30o, 50= 0.01

= 7 kN/m3, Dr = 69-83% = 36o, 50= 0.004

Cu= 44 kPa = 16 kN/m3

14.39.22.24.60.0511.1723.5

Pile Cap Length (m)

Pile CapWidth (m)

Pile CapHeight (m)

Pile Spacing(m)

Wall Thick.(m)

Diameter(m)

Pile Length(m)

UC Davis, Centrifuge Test(Boulanger et al. 2003, and Brandenberg and Boulanger 2004)

UC Davis, Centrifuge Test on 2 x 3 Fixed-Head Pile Group(After Brandenberg and Boulanger, 2004)

-100 0 100 200 300 400P ile Latera l D eflection, y (m m )

2 5

2 0

1 5

1 0

5

0

Dep

th (m

)

M easured C om puted

Pile Displacement

-12000 -8000 -4000 0 4000 8000 12000M om ent, kN -m

2 5

2 0

1 5

1 0

5

0

Dep

th (m

)

M easured C om puted

Bending Moment

amax = 0.67 g Magnitude = 6.5

Niigata Court House Bld.0.35-m-Diam. RC Pile,1964 Niigata EQ, Yoshida and Hamada, 1991

Soil Layer # 1(N onliquefied)

Soil Layer # 2(L iquefiable Soil)

290 kN

2 m

6 m

1 mFirm Soil

Niigata Court House Bld. 1964 Niigata EQ 0.35-m-Diam. RC Pile (Yoshida and Hamada, 1991)

0 40 80 120 160

D E FLEC TIO N , y (m m )

1 0

8

6

4

2

0

DE

PTH

, m

-200 -100 0 100 200

M om ent, M (kN -m )

1 0

8

6

4

2

0

DE

PTH

, m

SWM AnalysisBased on Shaft Length

h =

0 .69

X

o Xo

Zero Crossing

Xo >

h >

0.6

9 X

o

Xo Zero Crossing

Zero Crossing

h =

Xo

Deflec

tion P

attern

Lineari

zed D

eflec

tionYo Yo Yo

Line

arize

d Defl

ectio

n

Defle

ction

Patt

ern

Long ShaftL/T 4

Intermediate Shaft4 > L/T > 2

Short ShaftL/T 2

L = SHAFT LENGTHT = (EI/f )0.2

f = Coefficient. of Modulus of Subgrade Reaction

Varying Deflection Patterns Based on Shaft Type

Yo

b) Passive Wedges Developed with Short Shaft

m

m

Upper Passive Wedge

Lower Passive Wedge

Yo

Strain Wedge(Side View)

Lower Passive Wedge

Upper Passive Wedge

Xo >

h >

0. 6

9 X

o

Xo

x

h =

L - X

o x

Zero Crossing

h =

L - X

o

Zero Crossing

x

h =

Xo

x

Def

lect

ion

Patte

rn

Def

lect

ion

Pat

tern

b) Passive Wedges Developed with Intermediate Shaft xn

xn+1

xn+2

xn+3

n+1

n+2

Zero Crossing

c) Varying Soil Strain and Deflection Angle in the Lower Passive Wedge

Deflec

tion P

atter

n

yn+3

yn+2

- 1 0 1 2 3 4Shaft deflection, y, in

80

60

40

20

0

Dep

th, X

, ft

0 500 1000 1500 2000 2500M om ent, M , kip-ft

80

60

40

20

0

Dep

th, X

, ft

Po

MoPv

y

75 ft

6 ft

Pv = 100 kipPo = 150 kipMo = 800 kip-ftL/T = 3.1Intermediate Shaft

Soil Profile – S5Short Shaft AnalysisIntermediate Analysis

Short Shaft AnalysisIntermediate Analysis

- 1 0 1 2 3 4 5S haft Deflection, y, in

100

80

60

40

20

0D

epth

, x, f

t

0 1000 2000 3000M om ent, M , k ip-ft

100

80

60

40

20

0

Dep

th, x

, ft

Po

MoPv

y

90 ft

6 ft

Pv = 100 kipPo = 150 kipMo = 800 kip-ftL/T = 4.0 Long Shaft

Soil Profile – S5

Short Shaft AnalysisLong Shaft Analysis

Effect of Soil Liquefaction on Response of Shafts

of Different Lengths

Effect of Shaft Length and Soil Layerson p-y Curve at Certain Depth

Po

MoPv

y

65 ft

6 ft

Pv = 100 kipPo = 800 kipMo = 3000 kip-ftMEQ = 6.0

Soil Profile – S7Liquefaction

- 2 0 2 4 6 8Shaft deflection, y, in

80

60

40

20

0

Dep

th, X

, ft

No Liq. (L/T) = 3.6 am ax= 0.1g (L/T) = 2.9am ax= 0.3g (L/T) = 2.5

0 4000 8000M om ent, M , k ip-ft

80

60

40

20

0

Dep

th, X

, ft

Po

MoPv

y

L

6 ft

Soil Profile – S5

Shaft-Length Effect on the p-y Curve

0 1 2 3 4 5Shaft D eflection, y, in

0

2000

4000

6000

8000Li

ne L

oad,

p, l

b/in

75 ft & (L/T) = 4.2 65 ft & (L/T) = 3.655 ft & (L/T) = 3.0

P-y Curve at 5 ft depth

0 0.4 0.8 1.2Shaft Deflection, y, in

0

1000

2000

3000

Line

Loa

d, p

, lb/

in

75 ft & (L/T) = 4.2 65 ft & (L/T) = 3.655 ft & (L/T) = 3.0

P-y Curve at 20 ft depth

Poo

MoPv

y

90 ft

6 ft

Pv = 100 kipPo = 800 kipMo = 3000 kip-ftMEQ = 6.0

- 2 0 2 4 6 8Shaft de flection , y , in

100

80

60

40

20

0

Dep

th, X

, ft

No Liq. (L/T) = 5.1 amax= 0.1g (L/T) = 3.8amax= 0.3g (L/T) = 2 .1

0 4000 8000M om ent, M , k ip-ft

100

80

60

40

20

0

Dep

th, X

, ft

No Liq. (L/T) = 5.1 amax= 0.1g (L/T) = 3.8amax= 0.3g (L/T) = 2.1


Po

MoPv

y

65 ft

6 ft


Effect of Soil Profile (Liquefaction) on the p-y Curve at the Same Depth

0 2 4 6 8Shaft D eflection, y, in

0

2000

4000

6000

8000

10000Li

ne L

oad,

p, l

b/in


p-y Curve at Depth 5 ft

0 0.4 0.8 1.2 1.6 2Shaft Deflection, y, in

0

1000

2000

3000

Line

Loa

d, p

, lb/

in


p-y Curve at Depth 20 ft

Pile and Pile Group Stiffnesses with/without Pile Cap

Loads and Axis

F1

F2

F3

M1M2

M3 X

Z

Y

F1

F2

F3

M1

M2

M3

X

Z

Y

Linear Stiffness Matrix

K11 0 0 0 0 -K16

0 K22 0 0 0 00 0 K33 K34 0 00 0 K43 K44 0 00 0 0 0 K55 0-K61 0 0 0 0 K66

F1 F2 F3 M1 M2 M3

Linear Stiffness Matrix is based on • Linear p-y curve (Constant Es), not the real case• Linear elastic shaft material (Constant EI), not the

actual behaviorTherefore,P, M = P + M and P, M = P + M

1

2

3

1

2

3

Shaft Deflection, y

Lin

e L

oad,

p

yP, M > yP + yM

yM

yPyP, M

y

p(Es)1

(Es)3

(Es)4

(Es)2p

p

p

y

y

y

(Es)5p

y

MoPo

Pv

Nonlinear p-y curve

As a result, the linear analysis (i.e. the superposition technique ) can not be employed

Actual Scenario

Nonlinear (Equivalent) Stiffness Matrix

K11 0 0 0 0 00 K22 0 0 0 00 0 K33 0 0 00 0 0 K44 0 00 0 0 0 K55 00 0 0 0 0 K66

F1 F2 F3 M1 M2 M3

• Nonlinear Stiffness Matrix is based on • Nonlinear p-y curve • Nonlinear shaft material (Varying EI)

P, M > P + M K11 = Papplied / P, M P, M > P + M K66 = Mapplied / P, M

1

2

3

1

2

3

Pile Load-Stiffness Curve

Linear Analysis

Pile

-Hea

d St

iffne

ss, K

11, K

33, K

44, K

66

Pile-Head Load, Po, M, Pv

P 1, M

1

P 2, M

2

Non-Linear Analysis

PL

Pv

M

(K22)(K11)

(K66) xx

K11 0 0 0 0 00 K22 0 0 0 00 0 K33 0 0 00 0 0 K44 0 00 0 0 0 K55 00 0 0 0 0 K66

1

2

3

1

2

3

(K11) = PL / 1

(K22) = Pv / 2

(K33) = M 3

Group Stiffness Matrix

(pv)M(pv)M

(pv)Pv(pv)Pv

PL

Pv (1)

M

(pL)PL

(Fixed End Moment)

THANK YOU!!!

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