opensees soilopensees soil----pile interaction pile interaction study under...

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




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


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




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


Uncoupled freeUncoupled freeUncoupled freeUncoupled free----field displacementfield displacementfield displacementfield displacement(with and without pinning effect)




2222----D FEM analysisD FEM analysisD FEM analysisD FEM analysis


3D FEM Analysis3D FEM Analysis3D FEM Analysis3D FEM Analysis

Solid-Solid Model




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


Laterally Loaded Piles (comparison with LPILE)

� Perform numerical load test � Compare results

3x Magnification




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



� Normal interface stresses and radial soil stresses





� Evaluation of beam response� Numerical p-y curves


Laterally Loaded PilesLaterally Loaded PilesLaterally Loaded PilesLaterally Loaded Piles

� GiD Visualization of pile and soil deformation with interface forces




Back to our problem…Back to our problem…Back to our problem…Back to our problem…

Undeformed mesh


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




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


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




GiDGiDGiDGiD post processingpost processingpost processingpost processingInitial Conditions OpenSees

Vertical stresses Contact Forces


PushPushPushPush----over deformation patternover deformation patternover deformation patternover deformation pattern




GiDGiDGiDGiD post processingpost processingpost processingpost processingσxx stresses after displacement


GiDGiDGiDGiD post processingpost processingpost processingpost processingContact Forces at the end of displacement

Perspective View XZ Plane View




GiDGiDGiDGiD post processingpost processingpost processingpost processingContours of Contact Forces at the end of Displacement


GiDGiDGiDGiD post processingpost processingpost processingpost processingForces in the Beam at the End of Displacement

XZ Plane ViewPerspective View




GiDGiDGiDGiD post processingpost processingpost processingpost processing

(a) Contact forces at soil-pile interface and (b) Horizontal pile forces at the end of loading


GiD GiD GiD GiD Diagrams

Shear diagram Bending moment diagram




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


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




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


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

)


−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

)


−12000 −10000 −8000 −6000 −4000 −2000 0 20000

5

10

15

20

25

Shear force in (kN)

Heig

ht above b

ase in (

m)


−20000 −15000 −10000 −5000 00

5

10

15

20

25

Shear force in (kN)

He

igh

t a

bo

ve

ba

se

in

(m

)


Location and value of maxV and maxM

varies for different EI

EI1less stiff

EI2stiffer




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


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




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

)


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 =




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


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")




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")


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




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")


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")




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


Questions?

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