opensees soilopensees soil----pile interaction pile interaction study under...
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August 16, 2006 - University of
California, Berkeley 1
OPENSEES SoilOPENSEES SoilOPENSEES SoilOPENSEES Soil----Pile Interaction Pile Interaction Pile Interaction Pile Interaction Study under Lateral Spread LoadingStudy under Lateral Spread LoadingStudy under Lateral Spread LoadingStudy under Lateral Spread Loading
Po-Lam - EarthMechanics
Pedro Arduino UW
Peter Mackenzie-Helnwein UW
9/11/2008 Kinematic Analysis of Piles using OpenSees 2
Overview
� Introduction
� Background & Common Practice
� 3D Analysis of Soil-Pile Interaction
� Beam-Solid Approach
� Contact Formulation & Implementation
� Practical Applications
� Summary and Conclusions
August 16, 2006 - University of
California, Berkeley 2
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Problem DescriptionProblem DescriptionProblem DescriptionProblem Description
Kinematic loading on the pile from the upper unliquefied soil mass
displacing relative to the underlying stable lower soil mass
Slippage displacement concentrated on a usually thin liquefied soil layer
between the two stiffer soil masses
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Common Solution strategiesCommon Solution strategiesCommon Solution strategiesCommon Solution strategies
� Fixed-fixed beam
� Uncoupled free-field displacement
� Uncoupled displacement considering pile
pinning
� 2-D FEM analysis
� 3-D FEM analysis
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9/11/2008 Kinematic Analysis of Piles using OpenSees 5
FixedFixedFixedFixed----fixed approachfixed approachfixed approachfixed approach
Shear, F = EI/L
Fixed-Fixed
Dis
tance, x
Effe
ctiv
e fix
ed
-fixed
Bea
m L
ength
, Leff
Max. Pile Moment
No
n L
iq. Z
one
Line of Symmetry
Max. Pile Moment
Distance, Lp
Thic
kn
ess o
f Liq
. Zon
e
Fixed-FixedBeam
Beam( = 6 ) Fixed-Fixed
( = 12 )Beam
Penetration
Soil Displacement,
Non
Liq
. Zo
ne
Moment, M = EI/L Deflection,
0+ +M
0
2
+F0
3
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Uncoupled freeUncoupled freeUncoupled freeUncoupled free----field displacementfield displacementfield displacementfield displacement(with and without pinning effect)
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2222----D FEM analysisD FEM analysisD FEM analysisD FEM analysis
9/11/2008 Kinematic Analysis of Piles using OpenSees 8
3D FEM Analysis3D FEM Analysis3D FEM Analysis3D FEM Analysis
Solid-Solid Model
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Soil: solid elementsPile: beam elements
Pile-Soil Interface:
Beam-Solid
Contact Element
New approach: BeamNew approach: BeamNew approach: BeamNew approach: Beam----Solid Contact ElementSolid Contact ElementSolid Contact ElementSolid Contact Element
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Laterally Loaded Piles (comparison with LPILE)
� Perform numerical load test � Compare results
3x Magnification
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9/11/2008 Kinematic Analysis of Piles using OpenSees 11
Laterally Loaded Piles
f(z,θ) piyi
p
y
z
θ
� Obtained by differentiation of pile bending moments
� Obtained directly from contact element force outputiiz yAMi∑ ⋅= σ
� Numerical p-y curves:
2
2
dz
Mdp =
dz
dV
dz
Mdp ==
2
2Solid pile:Beam pile:
Discretized beamDeformed beam with
interface forces, f (z,θ)
Deformed beam with interface
forces, pi = Σf (z,θ)r dθ and
displacement, yi
p-y curves
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Laterally Loaded Piles
� Normal interface stresses and radial soil stresses
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Laterally Loaded Piles
� Evaluation of beam response� Numerical p-y curves
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Laterally Loaded PilesLaterally Loaded PilesLaterally Loaded PilesLaterally Loaded Piles
� GiD Visualization of pile and soil deformation with interface forces
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9/11/2008 Kinematic Analysis of Piles using OpenSees 15
Back to our problem…Back to our problem…Back to our problem…Back to our problem…
Undeformed mesh
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Base Soil & Pile PropertiesBase Soil & Pile PropertiesBase Soil & Pile PropertiesBase Soil & Pile Properties
Soil profileE
[kPa]
Poisson’s
ratio
Unit weight
[kN/m3]
Top strong layer (brown) 25,000 0.35 17.0
Middle soft layer (white) 2,500 0.47 17.0
Bottom strong layer
(brown)25,000 0.35 17.0
Soil profile K
[kPa]
G
[kPa]
Friction
angle φφφφ[[[[degrees]]]]
Cohesion
c
[kPa]
Unit weight
[kN/m3]
Top strong layer
(brown)
27778.0 9259.3 32 5 17.0
Middle soft layer
(white)
13888.0 862.0 0 10 17.0
Bottom strong
layer (brown)
27778.0 9259.3 325 5 17.0
Elasto-plastic (Drucker Prager) soil properties
Elastic isotropic soil properties
August 16, 2006 - University of
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Base Soil & Pile propertiesBase Soil & Pile propertiesBase Soil & Pile propertiesBase Soil & Pile properties
Beam material Diam Area
[m2]
I
[m4]
E
[kPa]
G
[kPa]
RC Concrete beam 2.5m 2.4544 1.7854 25,000,000 12,5000,000
RC Concrete beam 54” 0.73878 0.04780 25,000,000 12,5000,000
RC Concrete beam 24” 0.146 004680 25,000,000 12,5000,000
Interface Friction
coefficient
(µ=µ=µ=µ=tan(φφφφ))
Stiffness (for sticking)
[kPa]
Beam-solid contact 0.1 1000
Pile elastic properties
Contact element material properties
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GiDGiDGiDGiD post processing post processing post processing post processing Self Weight Self Weight Self Weight Self Weight ---- Vertical and Horizontal stresses due to self Vertical and Horizontal stresses due to self Vertical and Horizontal stresses due to self Vertical and Horizontal stresses due to self weight (notice near isotropic condition in liquefied layer)weight (notice near isotropic condition in liquefied layer)weight (notice near isotropic condition in liquefied layer)weight (notice near isotropic condition in liquefied layer)
Vertical Stress Horizontal Stress
Notice horizontal and vertical stresses are similar (fluid) in the liquefiable layer
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GiDGiDGiDGiD post processingpost processingpost processingpost processingInitial Conditions OpenSees
Vertical stresses Contact Forces
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PushPushPushPush----over deformation patternover deformation patternover deformation patternover deformation pattern
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GiDGiDGiDGiD post processingpost processingpost processingpost processingσxx stresses after displacement
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GiDGiDGiDGiD post processingpost processingpost processingpost processingContact Forces at the end of displacement
Perspective View XZ Plane View
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GiDGiDGiDGiD post processingpost processingpost processingpost processingContours of Contact Forces at the end of Displacement
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GiDGiDGiDGiD post processingpost processingpost processingpost processingForces in the Beam at the End of Displacement
XZ Plane ViewPerspective View
August 16, 2006 - University of
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GiDGiDGiDGiD post processingpost processingpost processingpost processing
(a) Contact forces at soil-pile interface and (b) Horizontal pile forces at the end of loading
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GiD GiD GiD GiD Diagrams
Shear diagram Bending moment diagram
August 16, 2006 - University of
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Parametric StudyParametric StudyParametric StudyParametric Study
� Pile diameters � D1=2.50 m, D2=54in., and D3=24in.
� Soft Layer Thicknesses� T1=1D, T2 = 2D, and T4=4D.
� Piles stiffness, EI� (scale factors for base EI values
� “E-3”=0.125, “E-2”=0.25, “E-1”=0.50, “E0”=1.0, “E1”=2.0, “E2”=4.0, and “E3”=8.0.
� Total cases = 84 cases
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Final OpenSees MeshesFinal OpenSees MeshesFinal OpenSees MeshesFinal OpenSees Meshes
Finite element meshes for different soft layer thickness. (a)T=1D, (b)T=2D, and (c)T=4D
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Characteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyEffect of soil displacementEffect of soil displacementEffect of soil displacementEffect of soil displacement
−16000 −14000 −12000 −10000 −8000 −6000 −4000 −2000 0 20000
5
10
15
20
25
Shear force in (kN)
He
igh
t a
bo
ve
ba
se
in
(m
)
Shear force distribution V for EI= 2390.00 MNm2
Shear diagrams
−2 −1 0 1 2 3
x 104
0
5
10
15
20
25
Moment in (kNm)
Heig
ht above b
ase in (
m)
Moment distribution M for EI= 2390.00 MNm2
Bending Moment diagrams
Location and value of maxV and maxM
changes with soil displacement
9/11/2008 Kinematic Analysis of Piles using OpenSees 30
Characteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyEffect of pile stiffness EIEffect of pile stiffness EIEffect of pile stiffness EIEffect of pile stiffness EI
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
x 104
0
5
10
15
20
25
Moment in (kNm)
He
igh
t a
bo
ve
ba
se
in
(m
)
Moment distribution M for EI= 1195.00 MNm2
−4 −3 −2 −1 0 1 2 3 4
x 104
0
5
10
15
20
25
Moment in (kNm)
He
igh
t a
bo
ve
ba
se
in
(m
)
Moment distribution M for EI= 4780.00 MNm2
−12000 −10000 −8000 −6000 −4000 −2000 0 20000
5
10
15
20
25
Shear force in (kN)
Heig
ht above b
ase in (
m)
Shear force distribution V for EI= 1195.00 MNm2
−20000 −15000 −10000 −5000 00
5
10
15
20
25
Shear force in (kN)
He
igh
t a
bo
ve
ba
se
in
(m
)
Shear force distribution V for EI= 4780.00 MNm2
Location and value of maxV and maxM
varies for different EI
EI1less stiff
EI2stiffer
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Characteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyBasic definitionsBasic definitionsBasic definitionsBasic definitions
T
10D
10D
Leff/D
D
(Leff-T)/2D
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Characteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studymaxM and locationmaxM and locationmaxM and locationmaxM and location
11 12 13 14 15 16 17 18 19 20
−2
−1
0
1
2
3
x 104
pseudo time
Mom
ent M
in (
kN
m)
extreme values for moment M for EI= 2390.00 MNm2
abs(max M) in top layerabs(max M) in bottom layer
10 11 12 13 14 15 16 17 18 19 206
8
10
12
14
16
18
20
pseudo time
He
igh
t a
bo
ve
ba
se
in
(m
)
Location of extreme moments M for EI= 2390.00 MNm2
position of maxM in top layerposition of maxM in bottom layerL
effective
Leff
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9/11/2008 Kinematic Analysis of Piles using OpenSees 33
Characteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyCharacteristic Results of Parametric studyPile deformationPile deformationPile deformationPile deformation
0 0.2 0.4 0.6 0.8 1 1.2 1.40
5
10
15
20
25
pile displacement (m)
de
pth
(m
)
9/11/2008 Kinematic Analysis of Piles using OpenSees 34
Non-dimensional characteristic parameter
� Es modulus o elasticity of stiff soil layer
� EI stiffness of pile
� T thickness of liquefiable layer
� D outer diameter of pile
2 2
sET D
EIβ =
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Embedment length in stiff soil layer (approximated as average of top and bottom layer)
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0.001 0.01 0.1 1 10 100
Es D^2 T^2 / EI
(Le
ff -
T)/2
D
Data FitT=1D (2.50m)T=2D (2.50m)T=4D (2.50m)T=1D (54")T=2D (54")t=4D (54")T=1D (24")T=2D (24")T=4D (24")Es=5000 (54")Es=12500 (54")
Results encourage the use of a linear
regression for most of the parameter
space
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Dimensionless shear force demandshear force demandshear force demandshear force demand. Maximum shear occurs within the liquefied layer
0.0001
0.001
0.01
0.1
1
0.001 0.01 0.1 1 10 100
Es D^2 T^2 / EI
ma
xV
T^
2 D
/ E
I D
elt
a
Data Fit Es=5000 (54")
T=1D (2.50m) T=2D (2.50m)
T=4D (2.50m) T=1D (54")
T=2D (54") t=4D (54")
T=1D (24") T=2D (24")
T=4D (24") Es=5000 (54")
Es=12500 (54") Es=75000 (54")
Es=250000 (54")
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9/11/2008 Kinematic Analysis of Piles using OpenSees 37
Dimensionless bending momentbending momentbending momentbending moment (or curvature demand). Max M occurs at from the layer interface within the stiff layer
0.0001
0.001
0.01
0.1
1
0.001 0.01 0.1 1 10 100
Es D^2 T^2 / EI
ma
xM
T D
/ E
I D
elt
a
Data Fit Es=5000 (54")
T=1D (2.50m) T=2D (2.50m)
T=4D (2.50m) T=1D (54")
T=2D (54") t=4D (54")
T=1D (24") T=2D (24")
T=4D (24") Es=5000 (54")
Es=12500 (54") Es=75000 (54")
Es=250000 (54")
9/11/2008 Kinematic Analysis of Piles using OpenSees 38
Design ProcedureDesign ProcedureDesign ProcedureDesign Procedure
2max
V
EIV
T Dγ
∆= Maximum shear force in the pile
max M
EIM
T Dγ
∆= Maximum moment in the pile
embed LL Dγ= Location of maximum moment
100.5 logLγ β= −0.680.17Vγ β=
0.450.09Mγ β=
Non-dimensional coefficients
2 2
sE T D
EIβ =
Dimensionless characteristic
parameter
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Dimensionless shear force demand. Maximum shear Dimensionless shear force demand. Maximum shear Dimensionless shear force demand. Maximum shear Dimensionless shear force demand. Maximum shear occurs within the liquefied layer.occurs within the liquefied layer.occurs within the liquefied layer.occurs within the liquefied layer.
0
0.05
0.1
0.15
0.2
0.25
0.001 0.01 0.1 1 10
Es D^2 T^2 / EI
ma
xV
T^
2 D
/ E
I D
elt
a
Data Fit T=1D (2.50m)
T=2D (2.50m) T=4D (2.50m)
T=1D (54") T=2D (54")
t=4D (54") T=1D (24")
T=2D (24") T=4D (24")
Es=5000 (54") Es=12500 (54")
Es=75000 (54") Es=250000 (54")
9/11/2008 Kinematic Analysis of Piles using OpenSees 40
Dimensionless bending moment (or curvature demand). Dimensionless bending moment (or curvature demand). Dimensionless bending moment (or curvature demand). Dimensionless bending moment (or curvature demand). Max M occurs at LMax M occurs at LMax M occurs at LMax M occurs at Lembedembedembedembed from the layer interface within the from the layer interface within the from the layer interface within the from the layer interface within the stiff layer.stiff layer.stiff layer.stiff layer.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.001 0.01 0.1 1 10
Es D^2 T^2 / EI
ma
xM
T D
/ E
I D
elt
a
Data Fit T=1D (2.50m)
T=2D (2.50m) T=4D (2.50m)
T=1D (54") T=2D (54")
t=4D (54") T=1D (24")
T=2D (24") T=4D (24")
Es=5000 (54") Es=12500 (54")
Es=75000 (54") Es=250000 (54")
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Comparison of fixed-fixed vs. OpenSees
Moment relative to Fixed-Fixed Beam
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.01 0.1 1 10
Es D^2 T^2/EI
Ca
l. M
om
en
t to
Fix
ed
-Fix
ed
Mo
men
t
9/11/2008 Kinematic Analysis of Piles using OpenSees 42
Questions?