opensees user workshop geotechnical tools

OpenSees User Workshop

Geotechnical tools

Boris Jeremic

Department of Civil and Environmental Engineering

University of California, Davis

Jeremic, Sept. 2004 1

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

http://cee.engr.ucdavis.edu/

http://www.ucdavis.edu/


Enabling Technologies Overview

• Object Oriented Framework (OpenSees core, nDarray, )

• Template Elasto–Plasticity

• Full Coupling of Solid and Fluid

• Domain Reduction Method

• Distributed Memory Parallel Computing

• General Large Deformations

• Stochastic Elasto–Plasticity

• Visualization



Applications Overview

• Template Elasto–Plasticity and Damage (constitutive behavior,

isotropic, kinematic, distortional hardening/softening)

– Small deformations

– Large deformations

• Static behavior of pile–soil systems

– Single piles in layered soils

– Interaction of piles in pile groups

• Wave (synthetic and seismic) propagation in soils (1D – 3D)

– Single phase soils (dry)

– Multiphase phase soils (saturated, coupled fluid–solid)

• Seismic Soil–Foundation–Structure (SFS) Interactions

– Free field motions in 1D, 2D and 3D

– SFS Interaction in 1D, 2D and 3D



Template Elasto–Plasticity

Yield function (or lack of YF), potential function (and/or flow

directions), hardening/softening laws (scalar, rotational/translational

kinematic, distortional...)

• Independent definitions of:

1. Yield function (and it’s derivatives)

2. Plastic flow direction (first and second derivatives of potential

function)

3. Evolutions laws for the above two

• This is used to create Template Elastic–Plastic Models



Template Commands

## Yield surfaceset ys "-DP"## Potential surfaceset ps "-DP 0.2"

## Isotropic evolution law:set ES1 "-Leq 0.0"## Kinematic evolution law:set ET1 "-Linear 100.0"

## Elastic modelnDMaterial ElasticIsotropic3D 1 70000.0 0.2 1.8

## EPState_____________alpha___kset EPS "-NOD 1 -NOS 2 0.2 2.0"

## Creating nDMaterial-----MatTag--ElMatTag--nDMaterial Template3Dep 2 1 -YS $ys -PS $ps -EPS $EPS -ELS1 $ES1 -ELT1 $ET1

##_______________tag_____8 nodes________matID__bforce1_bforce2_bforce3_rhoelement Brick8N 1 5 6 7 8 1 2 3 4 2 0.0 0.0 0.0 1.8



Template Elastic–Plastic Models

• Yield surfaces: von Mises VM, Drucker–Prager DP, Rounded Mohr–

Coulomb RMC, Cam–Clay CC, Parabolic Leon PL, User added (really

easy),

• Plastic flow directions (potential surfaces): von Mises VM, Drucker–

Prager DP, Rounded Mohr–Coulomb RMC, Cam–Clay CC, Manzari–

Dafalias MD, Parabolic Leon PL, User added (really easy),



Template Elastic–Plastic Models(contd)

• Isotropic and/or kinematic and/or distortional hardening/softening

– linear and/or nonlinear isotropic hardening/softening

– linear or nonlinear kinematic hardening/softening

∗ Armstrong–Fredericks nonlinear kinematic hardening/softening

∗ Bounding surface nonlinear (Dafalias–Popov) kinematic hard-

ening/softening

– User defined distortional hardening

• Hierarchical database of models (by materials)



3D Solid Elements

Three types of brick elements:

• 8 node brick element Brick8N#_______________tag_____8 nodes_____matID__bforce1_bforce2_bforce3_rho

element Brick8N 1 1 2 3 4 5 6 7 8 1 0.0 0.0 $g $rho

• 20 node brick element Brick20N

• 27 node brick element Brick27N



Template E-P Examples

• SmallDeformationExamples.tcl

• Pure_Shear_Test.ops

• Triaxial_Test.ops

• Simple_Shear_Test.ops



Template Examples

0 2 4 6 8 100

5

10

15

20

25

30

35

40

εa (%)

q (k

Pa)

0 2 4 6 8 10−7

−6

−5

−4

−3

−2

−1

0

1

εa (%)

ε v (%

)0 2 4 6 8 10

0

5

10

15

20

25

30

εa (%)

q (k

Pa)

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

εa (%)

ε v (%

)

0 2 4 6 8 100

5

10

15

20

25

30

εa (%)

q (k

Pa)

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

3.5

εa (%)

ε v (%

)

0 2 4 6 8 100

5

10

15

20

25

30

35

40

εa (%)

q (k

Pa)

0 2 4 6 8 10−1

−0.5

0

0.5

εa (%)

ε v (%

)

0 2 4 6 8 100

50

100

150

200

εa (%)

q (k

Pa)

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

εa (%)

ε v (%

)

0 5 10 150

10

20

30

40

50

60

εa (%)

q (k

Pa)

0 5 10 15−12

−10

−8

−6

−4

−2

0

2

εa (%)

ε v (%

)



Template Cyclic Examples

−0.4 −0.2 0 0.2 0.4−10

−5

0

5

10

15

εa (%)

q (k

Pa)

−0.4 −0.2 0 0.2 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

εa (%)

ε v (%

)

−0.4 −0.2 0 0.2 0.4−10

−5

0

5

10

εa (%)

q (k

Pa)

−0.4 −0.2 0 0.2 0.4−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

εa (%)

ε v (%

)

−0.15 −0.1 −0.05 0 0.05 0.1 0.15−20

−10

0

10

20

30

εa (%)

q (k

Pa)

−0.1 −0.05 0 0.05 0.1 0.15−0.5

0

0.5

1

1.5

2

2.5

3

εa (%)

ε v (%

)



Winkler Springs (aka PY springs)

uniaxialMaterial PySimple1 matTag? soilType? pult? y50? Cd? <c>

uniaxialMaterial TzSimple1 matTag? tzType? tult? z50? <c>

uniaxialMaterial QzSimple1 matTag? qzType? qult? z50? <suction? c?>

uniaxialMaterial PySimple1 1 1 100 0.01 0.0

element zeroLength 2 2 3 -mat 1 -dir 1

• Type is usually set to 1 for clay and 2 for sand.

• Note that p and pult p are distributed loads [force per length

of pile] in common design equations, but are both loads for this

uniaxialMaterial [i.e., distributed load times the tributary length of

the pile].



Full Coupling of Solid and Fluid

• General form, full coupling, (currently only small deformations)

• DOFs: uLj → solid displacement pL → fluid pressure ULj → fluid

displacement

• 8 node brick element Brick8N_u_p_U#(28 args)____________tag____8 nodes____matID_bforce1_bforce2_bforce3

porosity alpha solid_density fluid_density

perm_x perm_y perm_z s_bulk_modu f_bulk_modu pressure

element Brick8N_u_p_U 1 5 6 7 8 1 2 3 4 1 0.0 0.0 -9.81

0.8 1.0 1.8 1.0

10e-5 10e-5 10e-5 10e5 10e5 0

• 20 node brick element Brick20N_u_p_U



Plastic Bowl Loading(aka Domain Reduction Method)

• Based on work by Bielak et al. at CMU.

• Seismic motions and accelerations input at the layer of elements

that encompass an elastic–plastic zone (using SHAKE, Green’s

functions, Quake, SCEC...), non–reflective boundaries• pattern PBowlLoading 1 -pbele "$Dir/PBElements.dat"

-acce "$Dir/Inp_acce.dat" -disp "$Dir/Inp_disp.dat" -dt 0.02-factor 1 -xp 6.0 -xm -6.0 -yp 6.0 -ym -6.0 -zp 0.0 -zm -17.5

Fault

Plastic (Soil) "Bowls"



General Large DeformationsHyperelasto–Plasticity

• Based on the multiplicative decomposition of the deformation

gradient.

• More general approach (applicable to anisotropic material, cyclic

loading) than current state of the art (based on Simo’s work)

0 2 4 6 8 100

2

4

6

8

10

12

14x 10

6

shear strain γ

σ 13 [P

a]

Neo−HookeanLogarithmicMooney−RivlinOgden

−0.2 −0.1 0 0.1 0.2 0.3 0.4−40

−30

−20

−10

0

10

20

30

40

50

60

Shear Ratio

σ 13 (

kPa)

EP MonotonicEP Cyclic



Geotechnical Applications

• Constitutive behavior of test specimens

• Behavior of piles in layered soils

• Interactions of piles in pile groups

• Wave propagation in saturated soils

• Seismic behavior of soils and soil-structure interactions (1D and

3D)



Long Specimen

Progression of plastic zone for a long specimen with high friction

end platens



Non–Level End Platens



Constitutive Response?

0 0.5 1 1.5 2 2.5 30

50

100

150

200

250

300

350

Shear Strain ε (%)

q (k

Pa)

Without Friction − Cubic Sample With Friction − Cubic SampleWithout Friction − 2 to 1 Sample With Friction − 2 to 1 Sample

0 0.5 1 1.5 2 2.5 3 3.534

34.5

35

35.5

36

36.5

37

37.5

38

Max. inclination angle (deg)

Mob

ilize

d fr

ition

ang

le a

t 2.0

% a

xial

str

ain

Actual friction angle: 37.0o



Single Pile in Layered Soils

−1000 0 1000 2000−10

−8

−6

−4

−2

0

2

SAND

φ = 37.1o

−1.718

SOFT CLAY

Cu = 21.7 kPa

−3.436

SAND

φ = 37.1o

Bending Moment (kN.m)

Dep

th (

m)

SAND

φ = 37.1o

−1.718

SOFT CLAY

Cu = 21.7 kPa

−3.436

SAND

φ = 37.1o

SAND

φ = 37.1o

−1.718

SOFT CLAY

Cu = 21.7 kPa

−3.436

SAND

φ = 37.1o

−400 −200 0 200 400 600−10

−8

−6

−4

−2

0

2

Shear Force (kN)−100 0 100 200 300

−10

−8

−6

−4

−2

0

2

Lateral Resistance (kN/m)−1000 0 1000 2000

−10

−8

−6

−4

−2

0

2

SAND

φ = 37.1o

−1.718

SOFT CLAY

Cu = 21.7 kPa

−3.436

SAND

φ = 37.1o

Bending Moment (kN.m)

Dep

th (

m)

−400 −200 0 200 400 600−10

−8

−6

−4

−2

0

2

Shear Force (kN)−100 0 100 200 300

−10

−8

−6

−4

−2

0

2

Lateral Resistance (kN/m)



p− y Response for Single Pile inLayered Soils

0 2 4 6 8 10 120

50

100

150

200

250

300

Lateral Displacement y (cm)

Late

ral P

ress

ure

p (k

N/m

)

Depth −0.322Depth −0.537Depth −0.752Depth −0.966Depth −1.181Depth −1.396Depth −1.611Depth −1.825Depth −2.040Depth −2.255Depth −2.470Depth −2.684

0 2 4 6 8 10 120

50

100

150

200

250

300

Lateral Displacement y (cm)La

tera

l Pre

ssur

e p

(kN

/m)

Depth −0.322Depth −0.537Depth −0.752Depth −0.966Depth −1.181Depth −1.396Depth −1.611Depth −1.825Depth −2.040Depth −2.255Depth −2.470Depth −2.684

• Influence of soft layers propagates to stiff layers and vice versa

• Can have significant effects in soils with many layers



Examples

• Number of example models available at

http://cml00.engr.ucdavis.edu/~guanzhou/NEES_Project/

• Single pile (elastic solid beam or inelastic beam-column) in inelastic

soil (solids)

• Stages of loading (self weight for soil only, static pushover, dynamic

motions (seismic, surface shaker)






Pile Group Simulations

• 4x3 pile group model and plastic zones



Out of Plane Effects

• Out-of-loading-plane bending moment diagram,

• Out-of-loading-plane deformation.



Load Distribution per Pile

0 1 2 3 4 5 6 7 8 9 10 115

6

7

8

9

10

11

12

13

14

15La

tera

l Loa

d D

istr

ibut

ion

in E

ach

Pile

(%

)

Displacement at Pile Group Cap (cm)

Trail Row, Side PileThird Row, Side PileSecond Row, Side PileLead Row, Side PileTrail Row, Middle PileThird Row, Middle PileSecond Row, Middle PileLead Row, Middle Pile



Piles Interaction at -2.0m

• Note the difference in response curves (cannot scale single pile

response for multiple piles)



Validation with Centrifuge Tests

0 1 2 3 4 5 6 7 8 9 1015

20

25

30

35

40

45

Late

ral L

oad

dist

ribut

ion

in e

ach

row

(%

)

Lateral Displacement at Pile Group Cap (cm)

FEM − Trail RowFEM − Third RowFEM − Second RowFEM − Lead RowCentrifuge − Trail RowCentrifuge − Third RowCentrifuge − Second RowCentrifuge − Lead Row



Seismic Wave Propagation Model

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−27.3

−23.3

−21.8

−18.3

−14.8

−11.8

−8.8

−6.3

−3.3

−1.8

0.0

Time (s)

Acc

eler

atio

n (m

/s2 )

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−27.3

−23.3

−21.8

−18.3

−14.8

−11.8

−8.8

−6.3

−3.3

−1.8

0.0

Time (s)

Dis

plac

emen

t (m

)



Seismic Wave PropagationSoft Soil

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.0625−27.3

0.0633−23.3

0.0678−21.8

0.0749−18.3

0.0846−14.8

0.0960−11.8

0.1076 −8.8

0.1160 −6.3

0.1208 −3.3

0.1207 −1.8

0.1181 0.0

Max

Time (s)

Dis

plac

emen

t (m

)

Z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.0622−25.0

0.0779−21.0

0.0837−19.5

0.0982−15.0

0.1069−11.0

0.1123 −7.0

0.1169 −4.3

0.1174 −3.6

0.1179 −1.8

0.1181 0.0

0.1183 1.8

0.1178 3.6

0.1173 4.3

0.1129 7.0

0.1075 11.0

0.0984 15.0

0.0837 19.5

0.0779 21.0

0.0622 25.0

Max

Time (s)

Dis

pala

cem

ent (

m)

Y



Seismic Wave PropagationStiff Soil

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.0625−27.3

0.0658−23.3

0.0724−21.8

0.0735−18.3

0.0745−14.8

0.0753−11.8

0.0758 −8.8

0.0761 −6.3

0.0762 −3.3

0.0762 −1.8

0.0760 0.0

Max

Time (s)

Dis

plac

emen

t (m

)

Z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.0622−25.0

0.0715−21.0

0.0727−19.5

0.0737−15.0

0.0746−11.0

0.0754 −7.0

0.0759 −4.3

0.0759 −3.6

0.0760 −1.8

0.0760 0.0

0.0760 1.8

0.0759 3.6

0.0758 4.3

0.0754 7.0

0.0746 11.0

0.0737 15.0

0.0726 19.5

0.0715 21.0

0.0622 25.0

Max

Time (s)

Dis

plac

emen

t (m

)

Y



SSI Model: Seismic Results

0 5 10 15 20 25 30 35 40

0.0000−38.0

0.0077−30.0

0.0783−28.0

0.0791−20.0

0.0844−16.0

0.0878−12.0

0.1248 −8.0

0.1800 −4.0

0.1946 0.0

Time (s)

Dis

plac

emen

t (m

)

Z(m) Max

0 5 10 15 20 25 30 35 40

0.0000−38.0

0.0224−30.0

0.0879−28.0

0.1102−20.0

0.1161−16.0

0.1227−12.0

0.3961 −8.0

0.6258 −4.0

0.6928 0.0

Time (s)

Dis

plac

emen

t (m

)

Z(m) Max

Stiff soil Soft soil



DRM Model Analysis

• Self–equilibrating forces (almost) acting on a layer of element

• Dynamically equivalent to the far field dynamic excitation

• Externally radiating motions come from the structure

• examples available at

http://sokocalo.engr.ucdavis.edu/~jeremic/CG/Examples/SoilFoundationStructureInteraction/3D/






Seismic Motions Examples



1D Model (Verification Study)

• 1D model used for validation

• Vertically propagating shear wave

• Used both closed form and numerical

solutions for generating DRM forces

• Calibration springs used to model

support of soils on the side

• Outgoing waves represent the dynamic

characteristic of structure

• tested using harmonic and

fling (pulse) motions

• examples available at







Comparing Free Field and SFSI

0 2 4 6−0.014

−0.012

−0.01

−0.008

−0.006

−0.004

−0.002

0

Time [s]

x−D

isp.

[m]

Base, z = −13 m

0 2 4 6−0.03

−0.02

−0.01

0

0.01

0.02

0.03

Time [s]

x−D

isp.

[m]

Exterior domain, z = −9 m

0 2 4 6−0.03

−0.02

−0.01

0

0.01

0.02

0.03

Time [s]

x−D

isp.

[m]

Exterior node of boundary layer

0 2 4 6−0.5

0

0.5

1

Time [s]

x−D

isp.

[m]

Interior node of boundary layer

0 2 4 6−0.5

0

0.5

1

1.5

Time [s]

x−D

isp.

[m]

Interior domain, z = −3 m

0 2 4 6−0.5

0

0.5

1

1.5

2

Time [s]

x−D

isp.

[m]

Surface

DRM with Fixed BaseDRM with Absorbing Boundary

1D soil column subject to pulseFree−Field, effective forces obtained from large free−field model

0 2 4 6−0.5

0

0.5

Time [s]

x−D

isp.

[m]

Base, z = −13 m

0 2 4 6−0.5

0

0.5

Time [s]

x−D

isp.

[m]

Exterior domain, z = −9 m

0 2 4 6−1

−0.5

0

0.5

1

Time [s]

x−D

isp.

[m]

Exterior node of boundary layer

0 2 4 6−1

−0.5

0

0.5

1

Time [s]

x−D

isp.

[m]

Interior node of boundary layer

0 2 4 6−1

−0.5

0

0.5

1

1.5

Time [s]

x−D

isp.

[m]

Interior domain, z = −3 m

0 2 4 6−1

−0.5

0

0.5

1

1.5

2

Time [s]

x−D

isp.

[m]

Surface

DRM with Fixed BaseDRM with Absorbing Boundary

1D soil column subject to pulseAdded structure, effective forces obtained from large free−field model



Parametric Study: FF and SFSI

• Site amplification for harmonic motions

• Significant change of FF motions in presence of structure

• Can (should) be used in estimating optimal design for given type

of earthquake



Conclusions

• Lecture notes (work in progress)

http://sokocalo.engr.ucdavis.edu/~jeremic/CG/CompGeomechanicsLectureNotes.pdf

• Examples

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

• Applications/Examples Web Portal

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

• Fresh executables (Linux, MS Windows)

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

• Questions, comments (once you digest all of this):

[email protected]















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