computational geomechanics: simulations of static...

Computational Geomechanics:Simulations of Static and Dynamic

Behavior of Foundation System

Boris JeremicDepartment of Civil and Environmental Engineering

University of California, Davis

OpenSees User Workshop

August 21-22, 2003 , Richmond Field Station

Supported in part by the NSF, PEER, Caltrans, and Cal–EPA.

Collaborators: Professors Zhaohui Yang (UAA), Sashi Kunnath (UCD), Gregory Fenves (UCB),

Jacobo Bielak (CMU), Zhaojun Bai (UCD), George Karypis (UMN), Drs. Francis McKenna

(UCB), and graduate students Xiaoyan Wu (UCD) Ritu Jain (UCD), Qing Liu (UCD), Jinxiu

Liao (UCD). Guanzhou Jie (UCD).

Jeremic, OpenSees Workshop, Aug. 2003 1

Motivation

• Create high fidelity models of constructed facilities (bridges, build-

ings, port structures, dams...).

• Models will live concurrently with the physical system they repre-

sent.

• Models to provide owners and operators with the capabilities to

assess operations and future performance.

• Use observed performance to update and validate models through

simulations.


Goal

• Develop and use Computational tools based on

• Geomechanics to

• Investigate behavior of solids and structures made of geomaterials


Overview

• Enabling Technologies (ET)

– Template Elasto–Plasticity– Full Coupling of Solid and Fluid– Domain Reduction Method– Distributed Memory Parallel Computing

• Geomechanics Applications (GA)

– 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

• Currently in Works (CW)

– General Large Deformations– Distributed Parallel Computing


ET: 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


ET: Template Elastic–PlasticModels

• von Mises

• Drucker–Prager

• Rounded Mohr–Coulomb

• Cam–Clay

• Mazari–Dafalias (bounding surface plasticity)

• Parabolic Leon

• User added

• Any combination of the above using isotropic or kinematic hard-

ening

• Hierarchical database of models (by materials)


ET: 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 8 100

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 (%

)


ET: 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 (%

)


ET: Full Coupling of Solid and Fluid

General form (Zienkiewicz et al.), full coupling, (currently only small

deformations)

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

displacement

(Ms)KijL 0 0

0 0 0

0 0 (Mf)KijL

¨uLj

¨pL¨ULj

+

(C1)KijL 0 −(C2)KijL0 0 0

−(C2)LjiK 0 (C3)KijL

˙uLj

˙pL˙ULj

+

(KEP )KijL −(G1)KiL 0

−(G1)LjK −(P )KL −(G2)LjK0 −(G2)KiL 0

uLjpLULj

=

(fs)Ki0

(ff)Ki

(C1)KijL = (C2)KijL = (C3)KijL =

∫Ω

Nu,UK n

2k−1ij N

u,UL dΩ


ET: Domain Reduction Method

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

• Superposition of the large scale domain + local geologic feature

• Seismic motions and accelerations input at the layer of elements

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

functions, Quake, SCEC...)

• Non–reflecting boundaries

Fault

Plastic (Soil) "Bowls"


Geomechanics 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


GA: Long Specimen

Progression of plastic zone for a long specimen with high friction

end platens


GA: Non–Level End Platens


GA: 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


GA: Constitutive Response?

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


GA: 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)


GA: p− y Response for Single Pilein Layered 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


GA: Pile Group Simulations

• 4x3 pile group model and plastic zones


GA: Out of Plane Effects

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

• Out-of-loading-plane deformation.


GA: 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


GA: Piles Interaction at -2.0m

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

response for multiple piles)


GA: Comparison with CentrifugeTests

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


GA: Layering Effects (S–C–S)

0.5 0.6 0.7 0.8 0.9 1 1.10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Dis

tanc

e fr

om L

ayer

Inte

rfac

e (x

D)

Lateral Pressure Ratio Psand clay

/ Psand

Sand:φ = 37o, Clay:Su = 15kPaSand:φ = 37o, Clay:Su = 25kPaSand:φ = 37o, Clay:Su = 35kPa

Strength reduction (layering effects) extending to 4xD (in thiscase)


GA: Seismic Wave PropagationModel

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

)


GA: 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


GA: 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


GA: SSI Model

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−38.0

−30.0−28.0

−20.0

−16.0

−12.0

−8.0

−4.0

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 5−38.0−30.0

−28.0

−20.0

−16.0

−12.0

−8.0

−4.0

0.0

Time (s)

Dis

plac

emen

t (m

)


GA: SSI Model Free FieldStiff Elastic–Plastic Soil

0 1 2 3 4 5 6 7 8 9 10

0.0000−38.0

0.0052−30.00.1055−28.0

0.1142−20.0

0.1183−16.0

0.1219−12.0

0.1576 −8.0

0.1947 −4.0

0.2002 0.0

Time (s)

Dis

plac

emen

t (m

)

Z(m) Max

0 1 2 3 4 5 6 7 8 9 10

0.2002 0.0

0.1937 4.0

0.1749 8.0

0.1261 12.0

0.1231 16.0

0.1139 24.0

0.0124 26.0

0.0000 34.0

Time (s)

Dis

plac

emen

t (m

)

Z(m) Max


GA: SSI Model Pile–ColumnStiff Elastic–Plastic Soil

0 1 2 3 4 5 6 7 8 9 10

0.0000−38.0

0.0052−30.00.1055−28.0

0.1142−20.0

0.1183−16.0

0.1222−12.0

0.1496 −8.0

0.1899 −4.0

0.2091 0.0

Time (s)

Dis

plac

emen

t (m

)

Z(m) Max

0 1 2 3 4 5 6 7 8 9 10

0.2091 0.0

0.1935 4.0

0.1751 8.0

0.1262 12.0

0.1232 16.0

0.1139 24.0

0.0124 26.0

0.0000 34.0

Time (s)

Dis

plac

emen

t (m

)

Y(m) Max


GA: SSI Model Free FieldSoft Elastic–Plastic Soil

0 1 2 3 4 5 6 7 8 9 10

0.0000−38.0

0.0140−30.00.0971−28.0

0.1096−20.0

0.1190−16.0

0.1261−12.0

0.1622 −8.0

0.2823 −4.0

0.3158 0.0

Time (s)

Dis

plac

emen

t (m

)

Z(m)

0 1 2 3 4 5 6 7 8 9 10

0.3158 0.0

0.2890 4.0

0.2545 8.0

0.1567 12.0

0.1512 16.0

0.1338 24.0

0.0362 26.0

0.0000 34.0

Time (s)

Dis

plac

emen

t (m

)

Y(m) Max


GA: SSI Model Pile–ColumnSoft Elastic–Plastic Soil

0 1 2 3 4 5 6 7 8 9 10

0.0000−38.0

0.0140−30.00.0976−28.0

0.1094−20.0

0.1207−16.0

0.1227−12.0

0.1328 −8.0

0.2448 −4.0

0.3680 0.0

Time (s)

Dis

plac

emen

t (m

)

Z(m) Max

0 1 2 3 4 5 6 7 8 9 10

0.3680 0.0

0.2896 4.0

0.2536

8.0

0.1549

12.0

0.1497

16.0

0.1331

24.0 0.0356

26.0

0.0000 34.0

Time (s)


SSI Model: Pile–Column Behavior

0 1 2 3 4 5 6 7 8 9 10−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

Dis

plac

emnt

(m

)

Time (s)0 1 2 3 4 5 6 7 8 9 10

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Dis

plac

emen

t (m

)

Time (s)

Stiff soil Soft soil


SSI Model: Preliminary SeismicResults

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


GA: Wave Propagation inSaturated Soils

0 0.05 0.1 0.15 0.2 0.25 0.3−4

−3

−2

−1

0

1

2x 10

−3

Sol

id D

ispl

acem

ent (

m)

Top node2m from top4m from top6m from top

0 0.05 0.1 0.15 0.2 0.25 0.3−0.5

0

0.5

1

Por

e pr

essu

re (

kPa)

0 0.05 0.1 0.15 0.2 0.25 0.3−4

−3

−2

−1

0

1

2x 10

−3

Time (sec)

Flu

id D

ispl

acem

ent (

m)

0 0.05 0.1 0.15 0.2 0.25 0.3−4

−3

−2

−1

0

1

2x 10

−3

Sol

id D

ispl

acem

ent (

m)

Top node2m from top4m from top6m from top

0 0.05 0.1 0.15 0.2 0.25 0.3−0.5

0

0.5

1

Por

e pr

essu

re (

kPa)

0 0.05 0.1 0.15 0.2 0.25 0.3−4

−3

−2

−1

0

1

2x 10

−3

Time (sec)

Flu

id D

ispl

acem

ent (

m)

Half space, ramp load k = 10−3,5m/s


GA: Soil–Structure Interaction


GA: SSI AdvantageousH

oriz

anta

l Dis

plac

emen

t (m

)

0.1

0.05

0

−0.05

−0.1

−0.150 5 10 15 20 25 30 35 40 45 50

Time (Sec)

Fixed Model SFSI Model

She

ar F

orce

(N

)

4

6

2

0

−2

−4

−6

−8

x 10

Fixed ModelSFSI model

−0.15 −0.1 −0.05 0Displacement (m)

0.05 0.1

6

Kobe–JMA


GA: SSI DisadvantageousH

oriz

anta

l Dis

plac

emen

t (m

)

Time (Sec)0 5 10 15 20 25 30 35 40

Fixed Model SFSI Model

0.5

0.4

0.3

0.2

0.1

0

−0.1

−0.2

−0.3

−0.4

−0.5

6

She

ar F

orce

(N

)

−2

0

2

4

6

−4

−6

−8−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

Displacement (m)

Fixed ModelSFSI model

x 10

LP–Corralitos


Currently in Works

General Large Deformations

Distributed Parallel Computing


CW: General Large Deformations

• LD (Eij = 12 (ui,j + uj,i + ui,juj,i)) vs. SD (εij = 1

2(ui,j + uj,i)• Multiplicative decomposition of (Fij = xi,j = F eki F

pkj)

• MacLaurin series expansion of the exponent of flow direction, for

general anisotropic material and cyclic loading• Stress measures (first and second Piola–Kirchhoff, Mandel, Kirch-

hoff, Cauchy)

ijε

Eij

500%

1000%

1500%

2000%

2500%

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Errorshea

r st

rain

deformation (arctan )Φ

Φ

Fp

Fe Fe

-1

Reference

Configuration

X

d X

Ω0Intermediate

Configurationdx

Ω

dx

Current

Configuration

x

Ω

σ x

F

X ux


CW: Distributed MemoryParallel Computing

• Distributed memory parallel (DMP) computational model.

• Portable from Beowulf clusters (local networks, bootable CDs) to

commercial parallel machines.


Pre– and Post–Processing

• Many small packages around, available for UNIX–like and/or MS

Windows systems (Mac?).

• Work on pre and post processing packages that are problem specific


Joey3D


Phantom


Conclusions

• Examples, lecture notes, executables available at:

http://sokocalo.engr.ucdavis.edu/ jeremicand at

http://opensees.berkeley.edu/

• Manual is constantly being improved

• Executables available for both UNIX-like (up–to–date, preferable)

and MS Windows.

• MS Windows, soon to have up to date executables


computational geomechanics: simulations of static...

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