Soil-Pile Interaction in
FB-MultiPier
Dr. J. Brian Anderson, P.E.
Developed by: Florida Bridge Software Institute
Dr. Mike McVay, Dr. Marc Hoit, Dr. Mark Williams
Session Outline
• Identify and Discuss Soil-Pile Interaction Models
– Precast & Cast Insitu Axial T-Z & Q-Z Models
– Torsional T- 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 T- Models
– Lateral P-Y Models
– Nonlinear Pile Structural Models
• FB-MultiPier Input and Output
– Example #1 Single Pile
Soil-Structure Interaction
Vertical Nonlinear Spring
Torsional Nonlinear Spring
Lateral Nonlinear Spring
Nonlinear Tip Spring
Driven Piles - Axial Side Model
z
r
t
t
to
t o ro
r
(Randolph &
Wroth)
z
s
s
t + D t/D r  d r
dz
sr
s r + D s r/ D r  d r
t
s
dr
d 
r
Driven Piles - Axial Side Model
r0
rm
Dz d z


Dr d r
DZ
z
Substitute:
Dr
Rearrange: dz 
Substitute: dz 
Substitute: z 
rm

r0
t o r0
rG
t
G
dr
dr
 t 
r Gi 1  
 tf 
2
t
dr
t  G
dz
G
dr
Previous
Also:
t o r0
Also:
t
t o ro
 t 
G  Gi 1  
 tf 
r
2
Driven Piles - Axial Side Model
z
t 0 r0   rm   
 rm  r0  
 
ln 
,
Gi   r0    rm   r0    

r0 t 0
tf
T-Z (Along Pile)
1200
Tau 0 (psf)
1000
tf = 1000psf
800
600
Gi = 3 ksi
400
200
0
0
0.5
1
z - Displacement (inches)
1.5
Driven Piles - Axial Tip Model
z
(Kraft, Wroth, etc.)
P 1 -  
 P
4 r0 G i 1  
 Pf 
Where:
2
P = Mobilized Base Load
Pf = Failure Tip Load
ro = effective pile radius
 = Poisson ratio of Soil
Gi = Shear Modulus of Soil
T-Z (At Tip)
Tip Load (kips)
300
Pf = 250 kips
Gi = 10 ksi
 = 0.3
r0 = 12 inches
250
200
150
100
50
0
0
1
2
3
z - Displacement (inches)
4
5
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,
n.
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, tf (TSF)
• Plastic Clay:
– tf= 2N(110-N)/4006
• Sand, Silt Clay Mix:
– tf = 2N(110-N)/4583
• Clean Sand:
– tf = 0.019N
• Soft Limestone
– tf = 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):
L/2
sv’ =  L/2
L
D
  1.5 .135 L/2) 0.5
1.2>  >0.25
Qs = p D L  sv’
Qt = 0.6 NSPT p D 2 / 4
NSPT < 75
Cast Insitu - Clay (FHWA):
Qs = 0.55 Cu p D (L-5’-D)
L
D
Qt = 6 [1+0.2(L/D) ] Cu (p D 2 / 4)
Mobilized Stress / Ultimate Stress
Cast Insitu trend line for Sand
1.6
1.4
End Bearing
1.2
Side Friction
1.0
0.8
0.6
0.4
0.2
0.0
0
2
4
6
Settlement / Diameter (%)
8
10
Cast Insitu trend line for Clay
Mobilized Stress / Ultimate Stress
1.6
1.4
1.2
End Bearing
1.0
0.8
Side Friction
0.6
0.4
0.2
0.0
0
2
4
6
Settlement / Diameter (%)
8
10
Session Outline
• Identify and Discuss Soil-Pile Interaction Models
– Precast & Cast Insitu Axial T-Z & Q-Z Models
– Torsional T- 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)
T (F-L)
(dT/d)=1/a  Gi
Tult =1/b
Tult = tf Asurf r
Tult = 2p r2 D L tult
tult = Ultimate Axial
Skin Friction
(stress)
T=/a+b
 (rad)
Session Outline
• Identify and Discuss Soil-Pile Interaction Models
– Precast & Cast Insitu Axial T-Z & Q-Z Models
– Torsional T- Models
– Lateral P-Y Models
– Nonlinear Pile Structural Models
• FB-MultiPier Input and Output
– Example #1 Single Pile
Lateral Soil-Structure Interaction
Y
Active State
Passive State
Near Field: Lateral (Piles/Shafts)
y
X
sr
sr
r

P
Y=5”
Y=0
 F  2p
P     sr r d
 L
0
P=0
P

r
 F  2p
P     sr r d
 L
0
Sand &
Soft Clay
Pu
P
Pr
Stiff
Clay
Y
P-y Curves - Reese’s Sand
Pu is a function of
, , and b
P
x = x4
x = x3
x = x2
pu
m
pk
x = x1
m
yu
pm
k
u
ym
yk
Y is a function
of b (pile diameter)
ks x
x=0
3b/80
b/60
y
Matlock’s Soft Clay
1.0
Pu is a function of
Cu, , and b
P
PU
 p 
 y 

  0.5 

pu 
 y 50 
0.5
Y is a function of
y50 (50)
0.0
1.0
8.0
y
y 50
1/ 3
Reese’s Stiff Clay Below Water
Soil Resistance, p (lb/in.)
Pc is a function of
C, , ks and b
S TATIC
y
P  0 .5 P c ( y ) 0 . 5
50
P offset  0 .055 p c (
0.5Pc
E ss  
Esi = k s x
Y is a function of
0
y50 (50)
y  A s y 50 1 . 25
)
A s y 50
Asy50
y50
6Asy50
Deflection, y (in.)
18Asy50
0 .0625 p c
y 50
Pu is a function of
c, and b
RATIO OF SOIL RESISTANCE, P/ PU
O’Neill’s Integrated Clay
P  PU
F O R X  X Cr
1.0
P
PU
 0 .5 ( YY ) 0 . 387
C
0.5
P
PU
0.0
Fs is a function of 100
Yc is a function of b and 50
1
6
 FS  (1  FS )
20
RATIO OF DEFLECTION,
Y
YC
X
X Cr
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 Information
Help 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
P-y Curves
Auburn, Alabama
PMTPressuremeter
P-y Curves
- Auburn
2000
1800
1600
1m
2m
3m
4m
6m
8m
10 m
P (kN/mm)
1400
1200
1000
800
600
400
200
0
0
5
10
15
20
y (mm)
25
30
35
40
DMT Dilatometer
P-y Curves
Auburn
P-y Curves-Auburn,
Alabama
2500
P(kN/m)
2000
0.6 m
2.1 m
3m
4.2 m
6.3 m
7.2 m
1500
1000
500
0
0
50
100
150
200
y (mm)
250
300
350
Actual and Predicted Lateral Top of Shaft Deflections
Auburn
Predictions
Auburn, Alabama
1000
900
PMT
DMT
CPT
Shaft 1
Shaft 2
Shaft 3
Shaft 6
Lateral Load (kN)
800
700
600
500
400
300
200
100
0
0.0
10.0
20.0
30.0
40.0
Lateral Deflection (mm)
50.0
60.0
P-y Curves for PMT1
Pascagoula, Mississippi
PMT P-y Curves Pascagoula
6
5
9.7
10.7
11.7
12.7
13.8
14.8
15.8
16.8
17.8
18.8
P (kN/mm)
4
3
2
1
0
0
20
40
60
80
100
y (mm)
120
140
160
180
200
P-Y Curves from DMT 1
DMT P-y Curves
Pascagoula
Pascagoula, Mississippi
1.8
1.6
y (kN/mm)
1.4
9.6
10.8
11.7
12.6
16.0
16.9
17.8
1.2
1
0.8
0.6
0.4
0.2
0
0
10
20
30
p (mm)
40
50
60
Pascagoula Predictions
4500
4000
Load (kN)
3500
DMT
3000
2500
2000
PMT
1500
1000
Actual
500
0
0
10
20
30
Deflection (mm)
40
50
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
M
P
Y(z)
Pile Deflection
Y’(z)
M(z)
Slope Moment
M’(z)
Shear
P(z)
Soil Reaction
Strain Gages  Bending Moment
Bending Moment versus Depth
Bending Moment (kN*m)
0
200
400
600
800
1000
1200
0
1
Lateral
Load in
Kilonewtons
Depth (m)
2
3
4
5
6
36
62
93
121
153
182
211
258
Bending Moment vs. Depth
M
P
Y(z)
Pile Deflection
Y’(z)
M(z)
Slope Moment
M’(z)
Shear
P(z)
Soil Reaction
Two Integrals to Deflection
M
P
 
Y(z)
Pile Deflection
Y’(z)
M(z)
Slope Moment
M’(z)
Shear
P(z)
Soil Reaction
Two Derivatives to Load
M
P
Y(z)
Pile Deflection
Y’(z)
M(z)
Slope Moment

z
M’(z)
Shear

z
P(z)
Soil Reaction
Non-linear Concrete Model
Test Pile T1
1.0E+06
2
EI (kN-m )
8.0E+05
6.0E+05
4.0E+05
2.0E+05
0.0E+00
0.0E+00
2.0E-03
4.0E-03 6.0E-03 8.0E-03
Curvature,  (1/m)
1.0E-02
P-y Curves from Strain Gages
140
D. to G.S.
(m)
120
p (kN/m)
100
1.0
2.0
3.0
4.1
80
60
40
20
0
0
5
10
15
20
Displacement, y (mm)
25
30
35
Slope Inclinometer  Slope
Deflection versus Depth
Horizontal Displacement (m)
-0.01
-2
0
Depth (m)
2
4
6
8
10
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Lateral
Load in
Kilonewtons
36
62
90
122
153
183
208
243
Slope Inclinometer → Slope vs. Depth
M
P
Y(z)
Pile Deflection
Y’(z)
M(z)
Slope Moment
M’(z)
Shear
P(z)
Soil Reaction
One Integral to Deflection
M
P

Y(z)
Pile Deflection
Y’(z)
M(z)
Slope Moment
M’(z)
Shear
P(z)
Soil Reaction
Three Derivatives to Load
M
P
Y(z)
Pile Deflection
Y’(z)

z
M(z)
Slope Moment

z
M’(z)
Shear

z
P(z)
Soil Reaction
P-y Curves from Slope Inclinometer
140
D. to GS
(m)
120
p (kN/m)
100
1.0
2.0
3.0
4.0
80
60
40
20
0
0
5
10
15
20
Displacement, y (mm)
25
30
35
Comparison of P-y Curves
80
SG
inc
PMT/DMT
SPT
p (kN/m)
60
40
20
0
0
5
10
15
20
Displacement, y (mm)
25
30
35
Prediction of Pile Top Deflection
300
W. line
FLPIER-sg
FLPIER-inc
250
Load (kN)
200
150
100
50
0
0
20
40
60
Top Displacement (mm)
80
100
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 T- Models
– Lateral P-Y Models
– Nonlinear Pile Structural Models
• FB-MultiPier Input and Output
– Example #1 Single Pile
Pile Discrete Element Model
h
2
M1
h
M3
h
2
X
Universal Joint
Spring
(Top View)
Z
Rigid center-blocks
Y
M4
M2
X
(Side View)
Rigid end Block
Curvature-Strain-Stress-Moment
N2
N1
a) Strain due to
z-axis bending
b) Strain due to
y-axis bending
c) Strain due to
axial thrust
F
y
x
Fi
z
dAi
,
,
i
dFi
e) Stress-strain relationship
d) Combined strains
Stress-Strain Curves for Concrete & Steel
Strains -> Stress -> Moments
dFi=si*dAi
Mx 
 dF* y
y
x
Integration_Points
z
dAi
dFi
d) Combined strains
Stiffness of Cross-Section: Flexure, Axial
M
y
x
z
dAi
dFi
d) Combined strains
Mx 
 dF* y
Integration_Points

Failure Ratio Calculation
Actual Length
Failure Ratio =
Surface Length
P
Mx
Pactual
Mxo
Myo
My
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 T- Models
– Lateral P-Y Models
– Nonlinear Pile Structural Models
• FB-MultiPier Input and Output
– Example #1 Single Pile