Soil-Pile Interaction in FB-MultiPier

Developed by: Florida Bridge Software Institute

Dr. Mike McVay, Dr. Marc Hoit, Dr. Mark Williams

Dr. J. Brian Anderson, P.E.

Session Outline

• Identify and Discuss Soil-Pile Interaction Models– Precast & Cast Insitu Axial T-Z & Q-Z Models– Torsional - Models– Lateral P-Y Models– Nonlinear Pile Structural Models

• FB-MultiPier Input and Output– Example #1 Single Pile

Session Outline

• Identify and Discuss Soil-Pile Interaction Models– Precast & Cast Insitu Axial T-Z & Q-Z Models– Torsional - Models– Lateral P-Y Models– Nonlinear Pile Structural Models

• FB-MultiPier Input and Output– Example #1 Single Pile

Soil-Structure Interaction

Vertical Nonlinear SpringVertical Nonlinear Spring

Lateral Nonlinear SpringLateral Nonlinear Spring

Torsional Nonlinear Spring

Nonlinear Tip SpringNonlinear Tip Spring

Driven Piles - Axial Side Model

z

r

z

r

r + r / r r

z

r

r

+ / r r

r

roo

(Randolph &

Wroth)

Driven Piles - Axial Side Model

zZ

r

rd

zd

r

zG

Also:

Substitute: Grd

zd

Rearrange: drG

dz

Previous r

roo

Substitute: drGr

rdz o 0

rm

r0

Also:

2

fi 1

GG

Substitute:

m

0

r

r2

fi

0

1

dr

Gr

rz o

Driven Piles - Axial Side Model

f

0 0

0m

0m

0

m

i

00 ,lnz

r

rr

rr

r

r

G

r

T-Z (Along Pile)

0

200

400

600

800

1000

1200

0 0.5 1 1.5

z - Displacement (inches)

Tau

0 (

psf) f = 1000psf

Gi = 3 ksi

Driven Piles - Axial Tip Model

2

fi0 P

P1Gr4

-1Pz

Where:

P = Mobilized Base LoadPf = Failure Tip Loadro = effective pile radius = Poisson ratio of SoilGi = Shear Modulus of SoilT-Z (At Tip)

0

50

100

150

200

250

300

0 1 2 3 4 5

z - Displacement (inches)

Tip

Loa

d (k

ips) Pf = 250 kips

Gi = 10 ksi = 0.3r0 = 12 inches

(Kraft, Wroth, etc.)

Driven Piles - Axial Properties

• Ultimate Skin Friction (stress), Tauf , along side of pile (input in layers).

• Ultimate Tip Resistance (Force), Pf , at pile tip .

• Compressibility of individual soil layers, I.e. Shear Modulus, Gi , and Poisson’s ratio, .

Driven Piles - Axial Properties

• From Insitu Data:– Using SPT “N” Values run SPT97, DRIVEN,

UNIPILE, etc. to Obtain: Tauf , and Pf

– Using Electric Cone Data run PL-AID, LPC, FHWA etc. to Obtain: Tauf , and Pf

– Determine G or E from SPT correlations, i.e. Mayne, O’Neill, etc.

Florida: SPT 97 Concrete Piles

Skin Friction, f (TSF)

• Plastic Clay: f= 2N(110-N)/4006

• Sand, Silt Clay Mix: f = 2N(110-N)/4583

• Clean Sand: f = 0.019N

• Soft Limestone f = 0.01N

Ultimate Tip, Pf/Area(tsf)

• Plastic Clay:– q = 0.7 N

• Sand, Silt Clay Mix:– q = 1.6 N

• Clean Sand:– q = 3.2 N

• Soft Limestone– q = 3.6 N

Cast Insitu Axial Side and Tip Models

• For soil (sands and clays) – Follow FHWA Drilled Shaft Manual For Sands

and Clays to Obtain Tauf and Pf ( and cu)

– Shape of T-Z cuve is given by FHWA’s Trend Lines.

• User has Option of inputting custom T-z / Q-z curves

Cast Insitu - Sand (FHWA):

Qs = D L v’

DL

L/2v’ = L/2

L/2) 0.5 1.2>

Qt = 0.6 NSPT D 2 / 4 NSPT < 75

Cast Insitu - Clay (FHWA):

DLQs = 0.55 Cu D (L-5’-D)

Qt = 6 [1+0.2(L/D) ] Cu (D 2 / 4)

Cast Insitu trend line for Sand

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8 10

Settlement / Diameter (%)

Mo

bili

zed

Str

ess

/ Ult

imat

e S

tres

s

End Bearing

Side Friction

Cast Insitu trend line for Clay

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8 10

Settlement / Diameter (%)

Mo

bili

zed

Str

ess

/ Ult

imat

e S

tres

s

End Bearing

Side Friction

Session Outline

• Identify and Discuss Soil-Pile Interaction Models– Precast & Cast Insitu Axial T-Z & Q-Z Models– Torsional - Models– Lateral P-Y Models– Nonlinear Pile Structural Models

• FB-MultiPier Input and Output– Example #1 Single Pile

Torsional Model (Pile/Shaft)

• Hyperbolic Model– G and Tauf

• Custom T-

Torsional Model (Pile/Shaft)

(rad)

T (F-L)

Tult =1/b

(dT/d(dT/d)=1/a )=1/a G Gii

Tult = = 22 r r22LLultult

T = T = a + b a + b

Tult = f Asurf r

ult = Ultimate Axial Skin Friction (stress)

Session Outline

• Identify and Discuss Soil-Pile Interaction Models– Precast & Cast Insitu Axial T-Z & Q-Z Models– Torsional - Models– Lateral P-Y Models– Nonlinear Pile Structural Models

• FB-MultiPier Input and Output– Example #1 Single Pile

Lateral Soil-Structure Interaction

Passive State

Active State

Y

Near Field: Lateral (Piles/Shafts)

r

y

X

P r dF

Lr

0

2

P r dF

Lr

0

2

r

Y=5”

r

r

Y=0

P = 0 P

Y

Pu

P rStiffClay

Sand &Soft Clay

PPPP

P-y Curves - Reese’s Sand

k

m

b/60 3b/80

x = 0

x = x1

x = x2

x = x3

x = x4

u

pk

yk

ym

yupm

pu

m

y

P

ks x

Pu is a function of, , and b

Y is a function of b (pile diameter)

0.0

0.5

1.0

PPU

yy50

1.0 8.0

p

p0.5

y

yu 50

1 / 3

Matlock’s Soft Clay

Pu is a function ofCu, , and b

Y is a function of

y50 (50)

Reese’s Stiff Clay Below Water

Deflection, y (in.)

Soi

l Res

ista

nce

, p (

lb/in

.)

18Asy506Asy50y50Asy50

Esi = ksx

0.5Pc

0

P Pcy

y0 5

50

0 5. ( ) .

P poffset cy A y

A ys

s 0 055 50

50

1 25. ( ) .

STATIC

Essp

yc 0 0625

50

.

Pc is a function ofC, , ks and b

Y is a function of

y50 (50)

O’Neill’s Integrated Clay

0.0

0.5

1.0

RATIO OF DEFLECTION,

RA

TIO

OF

SO

IL R

ESI

STA

NC

E, P

/ P U

201

PP

YYU C

0 5 0 387. ( ) .

Y

YC

P P FOR X XU Cr

PP S S

XXU Cr

F F ( )1

6

Pu is a function ofc, and b

Fs is a function of 100

Yc is a function of b and 50

Soil Properties for Standard Curves

• Sand:– Angle of internal friction, – Total unit weight, – Modulus of Subgrade Reaction, k

• Clay or Rock:– Undrained Strength, Cu– Total Unit Weight, – Strain at 50% of Failure Stress, 50

– Optional: k, and 100

Soil InformationHelp Menu EPRI (Kulhawy & Mayne)

P-y Curves from Insitu Tests

• Cone Pressuremeter

• Marchetti Dilatometer

Insitu PMT & DMT Testing

Cone Pressuremeter

Cone Pressuremeter

(Robertson, Briaud, etc.)

Marchetti Dilatometer

Pressuremeter P-y Curves Auburn, Alabama

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5 10 15 20 25 30 35 40

y (mm)

P (

kN/m

m)

1 m2 m3 m4 m6 m8 m10 m

PMT P-y Curves - Auburn

Dilatometer P-y Curves Auburn, Alabama

0

500

1000

1500

2000

2500

0 50 100 150 200 250 300 350

y (mm)

P(k

N/m

)

0.6 m2.1 m3 m4.2 m6.3 m7.2 m

DMT P-y Curves - Auburn

Actual and Predicted Lateral Top of Shaft DeflectionsAuburn, Alabama

0

100

200

300

400

500

600

700

800

900

1000

0.0 10.0 20.0 30.0 40.0 50.0 60.0

Lateral Deflection (mm)

La

tera

l L

oad

(kN

)

PMTDMTCPTShaft 1Shaft 2Shaft 3Shaft 6

Auburn Predictions

P-y Curves for PMT1Pascagoula, Mississippi

0

1

2

3

4

5

6

0 20 40 60 80 100 120 140 160 180 200

y (mm)

P (

kN/m

m)

9.7

10.7

11.7

12.7

13.8

14.8

15.8

16.8

17.8

18.8

PMT P-y Curves Pascagoula

P-Y Curves from DMT 1Pascagoula, Mississippi

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60

p (mm)

y (k

N/m

m)

9.610.811.712.616.016.917.8

DMT P-y Curves Pascagoula

Pascagoula Predictions

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 10 20 30 40 50

Deflection (mm)

Lo

ad (

kN) DMT

PMT

Actual

Instrumentation & Measurements

• Strain gages– Measure strain– Calculate bending moment, M = ε(EI/c), if EI

of section known– “high tech”

• Slope inclinometer– Measures slope– Relatively “low tech”

Theoretical Pile Behavior

PM

Pile

Y(z)

Deflection

Y’(z)

Slope

M(z)

Moment

M’(z)

Shear

P(z)

Soil Reaction

Strain Gages Bending Moment

Bending Moment versus Depth

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200

Bending Moment (kN*m)

Dep

th (

m) 36

62

93

121

153

182

211

258

LateralLoad in Kilonewtons

Bending Moment vs. Depth

PM

Pile

Y(z)

Deflection

Y’(z)

Slope

M(z)

Moment

M’(z)

Shear

P(z)

Soil Reaction

Two Integrals to Deflection

PM

Pile

Y(z)

Deflection

Y’(z)

Slope

M(z)

Moment

M’(z)

Shear

P(z)

Soil Reaction

Two Derivatives to Load

PM

Pile

Y(z)

Deflection

Y’(z)

Slope

M(z)

Moment

M’(z)

Shear

P(z)

Soil Reaction

z

z

Non-linear Concrete ModelTest Pile T1

0.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

0.0E+00 2.0E-03 4.0E-03 6.0E-03 8.0E-03 1.0E-02Curvature, (1/m)

EI (

kN-m

2 )

P-y Curves from Strain Gages

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35

Displacement, y (mm)

p (k

N/m

)

1.0

2.0

3.0

4.1

D. to G.S.(m)

Slope Inclinometer Slope

Deflection versus Depth

-2

0

2

4

6

8

10

-0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Horizontal Displacement (m)

De

pth

(m

)

36

62

90

122

153

183

208

243

Lateral Load in Kilonewtons

Slope Inclinometer → Slope vs. Depth

PM

Pile

Y(z)

Deflection

Y’(z)

Slope

M(z)

Moment

M’(z)

Shear

P(z)

Soil Reaction

One Integral to Deflection

PM

Pile

Y(z)

Deflection

Y’(z)

Slope

M(z)

Moment

M’(z)

Shear

P(z)

Soil Reaction

Three Derivatives to Load

PM

Pile

Y(z)

Deflection

Y’(z)

Slope

M(z)

Moment

M’(z)

Shear

P(z)

Soil Reaction

z

z

z

P-y Curves from Slope Inclinometer

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35

Displacement, y (mm)

p (k

N/m

)

1.0

2.0

3.0

4.0

D. to GS(m)

0

20

40

60

80

0 5 10 15 20 25 30 35

Displacement, y (mm)

p (k

N/m

)

SGincPMT/DMTSPT

Comparison of P-y Curves

Prediction of Pile Top Deflection

0

50

100

150

200

250

300

0 20 40 60 80 100

Top Displacement (mm)

Lo

ad

(kN

)

W. line

FLPIER-sg

FLPIER-inc

P-y Curves Available in FB-Pier

• Standard– Sand

• O’Neill

• Reese, Cox, & Koop

– Clay• O’Neill

• Matlock Soft Clay Below Water Table

• Reese Stiff Clay Below Water Table

• Reese & Welch Stiff Clay Above Water Table

P-y Curves Available in FB-Pier

• User Defined– Pressuremeter– Dilatometer– Instrumentation

• Strain Gages

• Slope Inclinometer

Session Outline

• Identify and Discuss Soil-Pile Interaction Models– Precast & Cast Insitu Axial T-Z & Q-Z Models– Torsional - Models– Lateral P-Y Models– Nonlinear Pile Structural Models

• FB-MultiPier Input and Output– Example #1 Single Pile

Pile Discrete Element Modelh h2

h2

X

Z

X

Y

(Top View)

(Side View)

M M

M M

1 3

2 4

U n iv e r s a l J o in t

Rigid center-blocks

Rigid end Block

Spring

Curvature-Strain-Stress-Moment

a) Strain due to

z-axis bendingb) Strain due to

y-axis bendingc) Strain due to

axial thrust

NN

F

,

F

,i

i

1

2

x

y

z

dF

dA

i

i

e) Stress-strain relationshipd) Combined strains

Stress-Strain Curves for Concrete & Steel

Strains -> Stress -> Moments

x

y

z

dF

dA

i

i

d) Combined strains

dFi=i*dAi

n_PointsIntegratio

x ydF*M

Stiffness of Cross-Section: Flexure, Axial

M

x

y

z

dF

dA

i

i

d) Combined strains

n_PointsIntegratio

x ydF*M

Failure Ratio Calculation

My

Mx

P

Mx

o

Myo

Pactua

l

Failure Ratio = Surface

Length

Actual Length

Pile Material Properties

References:• Robertson, P. K., Campanella, R. G., Brown, P. T., Grof, I., and Hughes, J. M., "Design of

Axially and Laterally Loaded Piles Using In Situ Tests: A Case History,“ Canadian Geotechnical Journal, Vol. 22, No. 4, pp.518-527, 1985.

• Robertson, P. K., Davies, M. P., and Campanella, R. G., "Design of Laterally Loaded Driven Piles Using the Flat Dilatometer," Geotechnical Testing Journal, GTJODJ, Vol. 12, No. 1, pp. 30-38, March 1989.

• Reese, L. C., Cox, W. R. and Koop, F. D (1974). "Analysis of Laterally Loaded Piles in Sand," Paper No. OTC 2080, Proceedings, Fifth Annual Offshore Technology Conference, Houston, Texas, (GESA Report No. D-75-9).

• Hoit, M.I, McVay, M., Hays, C., Andrade, P. (1996). “Nonlinear Pile Foundation Analysis Using Florida Pier." Journal of Bridge Engineering. ASCE. Vol. 1, No. 4, pp.135-142.

• Randolph, M. and Wroth, C., 1978, “Analysis of Deformation of Vertically Loaded Piles, ASCE Journal of Geotechnical Engineering, Vol. 104, No. 12, pp. 1465-1488.

• Matlock, H., and Reese, L., 1960, “Generalized Solutions for Laterally Loaded Piles,” ASCE, Journal of Soil Mechanics and Foundations Division, Vol. 86, No. SM5, pp. 63-91.

Session Outline

• Identify and Discuss Soil-Pile Interaction Models– Precast & Cast Insitu Axial T-Z & Q-Z Models– Torsional - Models– Lateral P-Y Models– Nonlinear Pile Structural Models

• FB-MultiPier Input and Output– Example #1 Single Pile