Geo Tech Models

8/10/2019 Geo Tech Models

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Geotechnical Elements and

Models in OpenSees

Pedro ArduinoUniversity of Washington, Seattle

OpenSees Days 2014,Beyond the Basics, Friday September 26, 2014U.C. Berkeley, CA


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What do we need??! Solid elementsto characterize the soil domain

(continuum).

! Appropriate boundary conditionsto accurately

represent the soil domain boundaries.! Robust constitutive modelsto characterize the

soil stress-strain response under monotonic andcyclic loading conditions

! Interface elementsto capture the interactionbetween the soil and adjacent structures.

! Everything elseyou are learning in thisworkshop (i.e., how to create beam elements,apply loads and boundary conditions, recordresults, perform the analysis, etc.


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Outline! Finite Elements (for solids)

" Single-phase

" Multi-phase (coupled) finite elements

" Zero length element" Contact element

! Material Models" Elastic

" Elasto-plastic Continuum Models

" Elasto-plastic Uniaxial models

! Boundary Conditions" Equal DOF

" Absorbent boundaries


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Finite Elements (solids)! Single-phase formulations

" To capture the response of dry soils (or totalstress analysis) #need one single phase

" Phase 1 soil skeleton

! Multi-phase formulations" To capture the response of saturated soils

(effective stress analysis) #need two phases" Phase 1 #soil skeleton

" Phase 2 #pore water

! Zero-Length & contact elements" To capture interface response between solid and

beam elements, and to apply absorbentboundary conditions


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Single Phase Formulations

! Small deformation solid elements

" 2-D quadrilateral elements (4, 9 nodes)

" 3-D solid elements, brick (8, 20 nodes)

n1 n2

n3n4

n2

n1

n3

n4

n6n5 n7

n8

quad (4 node) stdBrick (8 node)


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quadelement definition

n1 n2

n3n4

quad (4 node)

element quad$eleTag $n1 $n2 $n3 $n4 $thick $type $matTag

Must define first all the required arguments. In particular:Nodes$n1, $n2, $n3, $n4 andMaterialtype$matTag

The arguments in are optional


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Multi-Phase Formulations! Fully coupled u-p elements (2D & 3D)

! Fully coupled u-p-U elements (3D) forsmall deformations

Degrees of Freedom (DOFs) are:" u #solid displacement, on

" P #pore fluid pressures, on

" U #pore fluid displacements, on

n1 n2

n3n4

quadUP

n1 n2 n3

n4

n5n6n7

n8

n9

9_4_quadUP


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zerolengthelement

! Connects two points at the samecoordinate

n1 n2

n3n4

element zeroLength$eleTag $n1 $n2 mat$matTag1 $matTag2 -dir$dir1 $dir2

zero-length element

solid element

n5

n6

beam element


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Recent Developments at UW

n1 n2

n3n4

n2

n1n3

n4

n6

n5n7

n8

quad (4 node) stdBrick (8 node)

Standard 2D and 3D solid Elements

n1 n2

n3n4

n2

n1

n3

n4

n6

n5n7

n8

SSPquad (4 node) SSPBrick (8 node)

Stabilized Single Point 2D and 3D Solid Elements


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Recent Developments at UW

n1 n2

n3n4

n2

n1n3

n4

n6

n5n7

n8

SSPquad (4 node) SSPBrick (8 node)

Stabilized Single Point 2D and 3D Solid Elements

n1 n2

n3n4

n2

n1

n3

n4

n6

n5n7

n8

SSPquad-up (4 node) SSPBrick-up (8 node)

UP - Stabilized Single Point 2D and 3D Solid Elements


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Material Models

! Linear Elastic Material model (nDMaterial)

" To characterize the response of the soil (or othercontinuum) in its elastic regime

! Elasto-Plastic Material models (nDMaterial)

" To characterize the nonlinear stress-strainresponse of soils

! Elasto-plastic Uniaxial models" To characterize the interface response between soil

and structural elements (uniaxialMaterial).


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nDMaterial

Elasto-Plastic (Small Deformations)

! J2-Plasticity Material (von Mises)

! Drucker-Prager Material (UW)

! Cam-Clay Material (Berkeley, UW)

! MutiYield Materials (San Diego)

! Manzari-Dafalias (new)(UW)


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nDMaterial

J2Plasticity

! von-Mises type

nDMaterial J2Plasticity $matTag $K $G $sig0 $sigInf $delta $H

dd-inf

d-0

dVon-Mises Yield SurfaceStress-strain curve


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nDMaterial

Template Elasto-Plastic Material

! Versatile tool to generate multiple typesof elasto-plastic materials by combining

yield surfaces, plastic potentials andevolution laws

! Developed byBoris Jeremic at UC Davis

http://sokocalo.engr.ucdavis.edu/~jeremic


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nDMaterial

Template Elasto-Plastic MaterialnDMaterial Template3Dep $matTag $ElmatTagYS$ys PS$ps EPS$eps

-YS #Yield surfaces(von Mises, Drucker Prager, Mohr-Coulomb, Camclay)-PS #Plastic potentials(von Mises, Drucker-Prager Mohr-Coulomb, Camclay, Leon)-EPS Initial state of stress-ELS1 Scalar evolution lawsfor isotropic hardening (linear,nonlinear Camclay)-ELT1 Tensorial evolution lawsfor Kinematic hardening (linear,

nonlinear Armstrong-Frederick)Von-Mises Drucker Prager Mohr-Coulomb Camclay


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nDMaterial

MultiYieldMaterials

! Material models based on MultiyieldPlasticity (Mroz et al., Prevost et al.)

! Two types

" Pressure Independent Multi-yield (for total stressanalysis)

" Pressure Dependent Multi-yield (captures well theresponse of liquefiable soils)

! Developed by Elgamal et al. at UCSD

http://cyclic.ucsd.edu/opensees/


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nDMaterial

PressureDependentMultiYield

15 parameters!!??

nDMaterial PressureDependMultiYield $matTag $nd $rho$refShearModul $refBulkModul $frictionAng $peakShearStra$refPress $pressDependCoe $PTAng$contrac $dilat1 $dilat2, $liquefac1 $liquefac2 $liquefac3


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nDMaterial

PressureDependentMultiYieldnDMaterial PressureDependMultiYield $matTag $nd $rho$refShearModul $refBulkModul $frictionAng $peakShearStra$refPress $pressDependCoe $PTAng$contrac $dilat1 $dilat2, $liquefac1 $liquefac2 $liquefac3


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nDMaterial

PressureDependentMultiYield02nDMaterial PressureDependMultiYield02 $matTag $nd $rho$refBulkModul $frictionAng $peakShearStra $refPress$pressDepenCoe $PTAng$contrac1 $contrac3 $dilat1 $dilat3


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nDMaterial

PressureIndependentMultiYieldnDMaterial PressureIndependMultiYield $matTag $nd $rho$refShearModul $refBulkModul $cohesi $peakShearStra$frictionAng $refPress=101 $pressDependCoe=0.


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nDMaterial

FluidSolidPorousMaterial

! Couples the response of twophases:fluid and solid developed tosimulate the response of saturated porous media

nDMaterial FluidSolidPorousMaterial $matTag $nd$soilMatTag $combinedBulkModul

$soilMatTag#

the tag of previously defined material$combinedBulkModul#combined undrained bulk modulus,Bc=Bf/n


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nDMaterial

FluidSolidPorousMaterial

! Couples the response of twophases:fluid and solid developed tosimulate the response of saturated porous media

nDMaterial FluidSolidPorousMaterial $matTag $nd$soilMatTag $combinedBulkModul

$soilMatTag#

the tag of previously defined material$combinedBulkModul#combined undrained bulk modulus,Bc=Bf/n


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Additional commands for multiyield

materials

! Help perform stage analysis

updateMaterialStage material $matTag stage$sNum

$MatTag #the tag of previously defined material$sNum #(0 - elastic, 1-plastic, 2 linear elastic constant f( 3))

updateParameter material $matTag refG$newVal

$MatTag #the tag of previously defined material$sNewVal #new parameter value


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nDMaterial

Other Models under developmentnDMaterial BoundingCamClay (Clays)

nDMaterial Manzari-Dafalias (Sands)

bbb=!=

"

ddd=!=

"

ps /1

ps /2

ps /3

O

n#

$

b

d

n

#

$#+%

yield surface

bounding surface

critical surface

dilatancy surface

b

!

c

!

d

!

r_

Bounding Surface Model


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nDMaterial

Manzari-Dafalias (2004)Conventional Triaxial TestCTC Undrained Dense Sand

Loose Sand

Confinement

Displacement


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nDMaterial

Manzari-Dafalias (2004)Cyclic Constant Mean StressTC Undrained

Confinement

Cyclic Shear Stress

K$=0

K$=Ko


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Initial State for Geotechnical

Problems

Soilprofile

Initial deformation

Gravity

# turn on initial state analysis feature

InitialStateAnalysis on

# create incremental gravity loadpattern Plain 3 {Series -time {0 10 10000} -values {0 1 1} -factor 1} {

eleLoad -ele 1 -type selfWeighteleLoad -ele 2 -type selfWeight...

}

analysis steps

# turn on initial state analysis feature

InitialStateAnalysis off


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Elasto-plastic Uniaxial models! To capture interface response between solid

(soil) and beam elements (pile)

Py Tz Qz Uniaxial Materials

PySimple1TzSimple1

QzSimple1

PyLiq1TzLiq1


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uniaxialMaterial

PySimple1uniaxialMaterial PySimple1 matTag $soilType $pult $Y50 $Cd

y

p

pult (Reese 1974)

y50 (API 1993)

$soilType #=1 Matlock (clay), =2 API (sand)

$pult#

ultimate capacity of p-y material$Y50 #displ. @ 50% of pultCd #drag resistance (=1 no gap,


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uniaxialMaterial

TzSimple1& QzSimple1uniaxialMaterial TzSimple1 matTag $tzType $tult $z50

$tzType#=1 Reese & ONeill (clay), =2 Mosher (sand)

$tult#

ultimate capacity of t-z material$z50 #displ. @ 50% of tult$c #viscous damping

uniaxialMaterial QzSimple1 matTag $qzType $qult $z50

$qzType#=1 Reese & ONeill (clay), =2 Vijayvergiya (sand)$qult = ultimate capacity of q-z material$z50 = displ. @ 50% of qult$suction #uplift resistance = suction*qult$c viscous damping


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uniaxialMaterial

PyLiq1uniaxialMaterial PyLiq1 $matTag $soilType $pult $Y50 $Cd $c$pRes $solidElem1 $solidElem2

$soilType #=1 Matlock (clay), =2 API (sand)

$pult#

ultimate capacity of p-y material$Y50 #displ. @ 50% of pultCd #drag resistance (=1 no gap,


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uniaxialMaterial

PyLiq1


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Boundary Conditions! EqualDof

Same lateraldeformation

equalDOF $rNodeTag $cNodeTag $dof1 $dof2

$rNodeTag#

master node$cNodeTag #slave node$dof1 $dof2 #constrained dofs


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Absorbent/transmitting Boundaries

Lysmer (1969)

1. set DampP 7552. set DampN 1216

3. uniaxialMaterial Elastic 1 0 $DampP4. uniaxialMaterial Elastic 2 0 $DampN5. node 1 16.0 0.0

6. node 2 16.0 0.07. element zeroLength1 1 2 -mat 1 2

-dir 1 2 orient 1 2 0 2 1 0

Quad Element

PP

SN

VbC

VaC

!

!

=

=

zeroLength Element &

uniaxial material


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Contact Elements available in

OpenSees

Beam-Solid ModelSolid-Solid Model Fiber element

Moment curvature response for single shaft


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OpenSees

3D Node-to-SurfaceElement

2D Node-to-LineElement

3D Beam-to-SolidElement

3D End-Beam-to-Solid Element

Master node

Slave node

tn

g


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OpenSees

element SimpleContact2D $eleTag $iNode $jNode $sNode$lNode $matTag $gTol $fTol

$eleTag #unique integer tag identifying element object$iNode $jNode #master nodes$sNode #slave node$lNode #Lagrange multiplier node$matTag #unique integer tag associated with previously-defined nDMaterial object

$gTol #gap tolerance$fTol #force tolerance

Master node

Slave node


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Many more capabilities currentlyunder development!!

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