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Soil-Pile Interaction in
FB-MultiPier
Developed by: Florida Bridge Software Institute
Dr. J. Brian Anderson, P.E.
Session Outline
• Introduce FB-MultiPier Software
• 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
FB-MultiPier
• Nonlinear finite element analysis program
capable of analyzing multiple bridge pier
structures interconnected by bridge spans.
• The full structure can be subject to a full
array AASHTO load types in a static
analysis or time varying load functions in a
dynamic analysis.
FB-MultiPier
• Each pier structure is composed of pier
columns and cap supported on a pile cap
and piles/shafts with nonlinear soil.
• FB-Multipier couples nonlinear structural
finite element analysis with nonlinear static
soil models for axial, lateral and torsional
soil behavior to provide a robust system of
analysis for coupled bridge pier structures
and foundation systems.
FB-MultiPier
• FB-MultiPier performs the generation of the
finite element model internally given the
geometric definition of the structure and
foundation system as input graphically by
the designer.
Coupled Soil-Structure Interaction
Battered Piles
or Shafts
Ship Impact Ship Impact Scour
Scour
Plumb Piles/Shafts
(Shallow Water) (Deep Water)
Live and Dead Loading
Earthquake
Coupled Soil-Structure Interaction
SoilSoil
Florida Pier
FB-MultiPier
Florida Bride Software Institute
• FB-MultiPier and other software for bridge
analysis and design developed and
supported by BSI
• http://bsi-web.ce.ufl.edu
• Good educational discounts (free)
Session Outline
• Introduce FB-MultiPier Software
• 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
• Introduce FB-MultiPier Software
• 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
Lateral Nonlinear Spring
Torsional Nonlinear Spring
Nonlinear Tip Spring
Driven Piles - Axial Side Model
z r
d z
s
s
s r
s r + D s
r / D r d r
d
z
t
dr
r
t + D t / D r d r
to
r
roott
t (Randolph &
Wroth)
Driven Piles - Axial Side Model
z DZ
Dr
D
D
rd
zd
r
zGt
Also:
Substitute: Grd
zdt
Rearrange: drG
dzt
Previous r
roott
Substitute: drGr
rdz o 0t
rm r0
Also:
2
f
i 1
t
tGG
Substitute:
m
0
r
r
2
f
i
0
1
dr
Gr
rz o
t
t
t
Driven Piles - Axial Side Model
f
0 0
0m
0m
0
m
i
00 ,lnzt
t
t 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) tf = 1000psf
Gi = 3 ksi
Driven Piles - Axial Tip Model
2
f
i0P
P1Gr4
-1Pz
Where: 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)
0
50
100
150
200
250
300
0 1 2 3 4 5
z - Displacement (inches)
Tip
Load (
kip
s) Pf = 250 kips
Gi = 10 ksi
= 0.3
r0 = 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,
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
API Side Friction Model - Sand
• tf = K p’0 tan d
where
• k = dimensionless coefficient of lateral earth pressure (ratio of horizontal to vertical normal effective stress(for unplugged K=0.8 and for plugged K=1.0)
• p’0 = effective overburden pressure in stress units
• δ = friction angle between the soil and pile wall, which is defined as d = f – 5o
API Side Friction Model - Sand
API Side Friction Model - Clay
• tf = a cu
where
• cu = undrained shear strength
• a = a dimensionless factor, which is defined as
– a = 0.5-0.5 ≤ 1.0 for ≤ 1.0
– a = 0.5-0.25 ≤ 1.0 for > 1.0
= cu/p’0
API Side Friction Model - Clay
API Tip Model - Sand
• q = p’0 Nq
where
– p’0 = effective overburden pressure in stress units
– Nq = eπtan(f’)tan2(45 + f’/2)
• Qp = qA
• Where
– Qp is the total end bearing capacity
– A is the cross sectional area
API Tip Model Sand
API Tip Model - Clay
• q = 9cu
where
• cu = undrained shear strength
• Qp = qA
where
– Qp is the total end bearing capacity
– A is the cross sectional area
API Tip Model Clay
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 = p D L sv’
D L
L/2
sv’ = L/2
1.5 .135 L/2) 0.5 1.2> >0.25
Qt = 0.6 NSPT p D 2 / 4 NSPT < 75
Cast Insitu - Clay (FHWA):
D L
Qs = 0.55 Cu p D (L-5’-D)
Qt = 6 [1+0.2(L/D) ] Cu (p 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
bil
ize
d S
tre
ss
/ U
ltim
ate
Str
es
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
biliz
ed
Str
es
s /
Ult
imate
Str
es
s
End Bearing
Side Friction
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)
(rad)
T (F-L)
Tult =1/b
(dT/d)=1/a Gi
Tult = 2p r2 D L tult T = / a + b
Tult = tf Asurf r
tult = Ultimate Axial
Skin Friction
(stress)
Session Outline
• Introduce FB-MultiPier Software
• 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
Passive State
Active State
Y
Near Field: Lateral (Piles/Shafts)
r
y
X
P r dF
Lr
s
p
0
2
P r dF
Lr
s
p
0
2
r
Y=5”
sr
sr
Y=0
P = 0 P
Y
Pu
P rStiff
Clay
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
p k
y k
y m
yu p m
p u
m
y
P
ks x
Pu is a function of
f, , and b
Y is a function
of b (pile diameter)
0.0
0.5
1.0
PPU
y
y50
1.0 8.0
p
p0.5
y
yu 50
1 / 3
Matlock’s Soft Clay
Pu is a function of
Cu, , and b
Y is a function of
y50 (50)
Reese’s Stiff Clay Below Water
Deflection, y (in.)
Soil
Res
ista
nce
, p
(lb
/in
.)
18Asy506Asy50y50Asy50
Esi = ksx
0.5Pc
0
P Pcy
y 0 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 of
C, , ks and b
Y is a function of
y50 (50)
O’Neill’s Integrated Clay
Pu is a function of
c, 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, f
– 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
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
/mm
)
1 m
2 m
3 m
4 m
6 m
8 m
10 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 m
2.1 m
3 m
4.2 m
6.3 m
7.2 m
DMT P-y Curves - Auburn
Actual and Predicted Lateral Top of Shaft Deflections
Auburn, 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
oa
d (
kN
)
PMT
DMT
CPT
Shaft 1
Shaft 2
Shaft 3
Shaft 6
Auburn Predictions
P-y Curves for PMT1
Pascagoula, Mississippi
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160 180 200
y (mm)
P (
kN
/mm
)
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 1
Pascagoula, 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 (
kN
/mm
)
9.6
10.8
11.7
12.6
16.0
16.9
17.8
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
Lateral
Load 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 Model
Test 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-02
Curvature, f (1/m)
EI (k
N-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 (
kN
/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 (
kN
/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 (
kN
/m)
SG
inc
PMT/DMT
SPT
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
(k
N)
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
• Introduce FB-MultiPier Software
• 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 Element Model
hh2
h2
X
Z
X
Y
(Top View)
(Side View)
M M
M M
1 3
2 4
Universal Joint
Rigid center-blocks
Rigid end Block
Spring
Curvature-Strain-Stress-Moment
a) Strain due to
z-axis bending
b) Strain due to
y-axis bending
c) Strain due to
axial thrust
N
N
F
,
F
,i
i
1
2
x
y
z
dF
dA
i
i
e) Stress-strain relationship
d) Combined strains
Stress-Strain Curves for Concrete & Steel
Strains -> Stress -> Moments
x
y
z
dF
dA
i
i
d) Combined strains
dFi=si*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
Mxo
Myo
Pactual
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 T- Models
– Lateral P-Y Models
– Nonlinear Pile Structural Models
• FB-MultiPier Input and Output
– Example #1 Single Pile