Soft Computing Approaches to Constitutive Modeling in ... Web Page/nsf workshop...

Soft Computing Approaches to Constitutive Modeling in Geotechnical Engineering

Jamshid Ghaboussi and Youssef M. HashashDepartment of Civil and Environmental Engineering

University of Illinois at Urbana-Champaign

Contents

Introductory Remarks on Soft ComputingSelfSim: Constitutive Modeling from System ResponseSeveral Applications of SelfSimField Calibration of constitutive Models in Deep Excavations

Soft Computing

Soft computing methods are inspired by the computing and problem solving strategies in nature.

They Are fundamentally different than the mathematically based problem solving methods.

Soft computing tools are neural networks, genetic algorithm and fuzzy logic.

Problem Solving in NatureNature solves very difficult inverse problems.

Nature does not use mathematics.

Two main components of nature’s problem solving strategies are:

LearningReduction in disorder

Nature utilizes random search and gradual improvement.

Forward Problems

Inverse Problems

Type 1. Input is unknown

Type 2. System is unknown

Inverse Problem of Constitutive Modeling

Material Test

Inverse Problem of Constitutive Modeling from Field Measurements

In many geotechnical problems it is too difficult to sample or perform realistic material tests.Often field measurements are available.

Autoprogressive Algorithm

Autoprogressive Algorithm

Structure is modeled by FE and constitutive model is represented by a NN.

Pre-train NN material model to learn linearly elastic constitutive behavior

Apply boundary forces: apply ∆Pn, compute ∆Un

Enforce boundary displacements

11

1

( ,... : ...)

n n nj j

t n n nj j j

n n n

n n n

P P P

K U P I

U U U

δ

δσ σ ε

−

−

−

= + ∆

= −

∆ = ∆ += NN

( ) (( ),... : ...)nn n

n n n n

U U Uδσ δσ ε δε

= ++ = +ΝΝ

Train Neural Networks

(( ),... : ...)n n n nσ σ ε δε= +NN

Learning Material Behavior from Response of a Simple Structure

NN TrainingFE Analysis A,Force BC

xε yε xyγ

…

…

xσ yσ xyτ

FE Analysis B,Displacement BC

Simulated Experiment, Von-Mises Plasticity with hardening

Train a NN to learn the material behavior from the response of this structure

Evolution of Load-Displacement

pre-training

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load

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NN Learning of Material Behavior

s11-e11 (pre-train)

0.00E+00

5.00E+01

1.00E+02

1.50E+02

2.00E+02

2.50E+02

3.00E+02

-6.00E-03 -5.00E-03 -4.00E-03 -3.00E-03 -2.00E-03 -1.00E-03 0.00E+00

s22-e22 (pre-train)

0.00E+00

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s11-e11 (pre-train)

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s22-e22 (pre-train)

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s11-e11 (pass 04)

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s22-e22 (pass 04)

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s11-e11 (pass 05)

0.00E+00

5.00E+01

1.00E+02

1.50E+02

2.00E+02

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-6.00E-03 -5.00E-03 -4.00E-03 -3.00E-03 -2.00E-03 -1.00E-03 0.00E+00

s22-e22 (pass 05)

0.00E+00

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0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02

s11-e11 (pass 08)

0.00E+00

5.00E+01

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1.50E+02

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-6.00E-03 -5.00E-03 -4.00E-03 -3.00E-03 -2.00E-03 -1.00E-03 0.00E+00

s22-e22 (pass 08)

0.00E+00

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0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02

s11-e11 (pass 10)

0.00E+00

5.00E+01

1.00E+02

1.50E+02

2.00E+02

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3.00E+02

-6.00E-03 -5.00E-03 -4.00E-03 -3.00E-03 -2.00E-03 -1.00E-03 0.00E+00

s22-e22 (pass 10)

0.00E+00

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2.00E+02

3.00E+02

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0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02

s11-e11 (pass 11)

0.00E+00

5.00E+01

1.00E+02

1.50E+02

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-6.00E-03 -5.00E-03 -4.00E-03 -3.00E-03 -2.00E-03 -1.00E-03 0.00E+00

s22-e22 (pass 11)

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0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02

s11-e11 (pass 12)

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s22-e22 (pass 12)

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s11-e11 (pass 13)

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s22-e22 (pass 13)

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NN Learning of Material Behavior

s22-e22 (pre-train)

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s12-e12 (pre-train)

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s22-e22 (pre-train)

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s12-e12 (pre-train)

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s22-e22 (pass 04)

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s12-e12 (pass 04)

-2.00E+01

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s22-e22 (pass 05)

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s12-e12 (pass 05)

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s22-e22 (pass 08)

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s12-e12 (pass 08)

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s22-e22 (pass 10)

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s12-e12 (pass 10)

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s22-e22 (pass 11)

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s12-e12 (pass 11)

-2.00E+01

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-1.00E-03 0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03 6.00E-03

s22-e22 (pass 12)

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s12-e12 (pass 12)

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s22-e22 (pass 13)

0.00E+00

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0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02

s12-e12 (pass 13)

-2.00E+01

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Time dependent behavior of reinforced concrete

Creep of Concrete Beam

pass00

0.000 0.001 0.002

strain

CL

3504 mm

150 mm

100 mm

20 mm

20 mm

pass00

0

5

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defle

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m) pass05

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m)

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strain

pass10

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pass20

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pass20

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defle

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n (m

m)

top surface

bottom surface

insta

nt12

day

s60

day

s13

0 da

ys51

3 da

ys

Experiment by Bakoss et al. (1982)

Field Calibration of Time-Dependent Behavior in Segmental Bridges Using Self-Learning Simulation

Case study: Pipiral Bridge (Colombia)

each span: 125m

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Jan 10, 2002: 73 days (12 segments)Feb 14, 2002: 108 days (all 18 segments)Jul 11, 2002: 255 days (all 18 segments)design camber at the completion

cam

ber (

mm

)

distance from the pier P4 (m)

The Challenge: Deflection Control

Field Calibration of the Pipiral Bridge

-30

-25

-20

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pre-trainmeasurement

disp

lace

men

t (m

m)

distance from the pier (m)

step 5

-30

-25

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-5

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pass 10measurement

disp

lace

men

t (m

m)


step 5

-30

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-5

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pass 20measurement

disp

lace

men

t (m

m)


step 5

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disp

lace

men

t (m

m)


step 6

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disp

lace

men

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step 6

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disp

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step 6

Improvement of Camber by Using SelfSim

0

5

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adju

stm

ent t

o ca

stin

g cu

rves

(mm

)


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0 10 20 30 40 50 60 70

Jan 10, 2002: 73 days (12 segments)Feb 14, 2002: 108 days (all 18 segments)Jul 11, 2002: 255 days (all 18 segments)design camber at the completion

cam

ber (

mm

)

distance from the pier P4 (m)

Learning the hysteretic behavior of soil from the seismic site response

Application of SelfSim to synthetically generated downhole array data- case1

-0.08

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Hyperbolic model + Masing rule(Target)

Initialized NN (Linear)

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Hyperbolic model + Masing rule(Target)Initialized NN (Linear)SelfSim (1st pass)

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t(ft)

Hyperbolic model + Masing rule(Target)Initialized NN (Linear)SelfSim (3rd pass)

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Dis

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t(ft)

Hyperbolic model + Masing rule(Target)Initialized NN (Linear)SelfSim (7th pass)

Layer1

•Sinusoidal motion •single layer

•Sinusoidal motion •single layer


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Strain

Stre

ss

Hyperbolic model + Masing rule (Target)

Initialized NN (Linear)

-0.8

-0.6

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Strain

Stre

ss

Hyperbolic model + Masing rule (Target)Initialized NN (Linear)SelfSim (1st pass)

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-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Strain

Stre

ss

Hyperbolic model + Masing rule (Target)Initialized NN (Linear)SelfSim (3rd pass)

-0.8

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Strain

Stre

ss

Hyperbolic model + Masing rule (Target)Initialized NN (Linear)SelfSim (7th pass)

Layer1

•cyclic motion •single layer

•cyclic motion •single layer


0

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9

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0.01 0.1 1 10

Period (sec)

Sa

(g)

DEESPSOIL (NN)DEEPSOIL (hyperbolic)DEEPSOIL+LinearNN

Pass1

0

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Period (sec)

Sa

(g)


Pass2

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(g)


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2

3

4

5

6

7

8

9

10

0.01 0.1 1 10

Period (sec)

Sa

(g)


Pass4

Layer1

Layer2

Layer3

Layer4

•seismic motion •multiple layers•same soil properties



-4 .0 0 E-0 2

-3 .0 0 E-0 2

-2 .0 0 E-0 2

-1 .0 0 E-0 2

0 .0 0 E+0 0

1 .0 0 E-0 2

2 .0 0 E-0 2

3 .0 0 E-0 2

4 .0 0 E-0 2

0 2 4 6 8 1 0

T im e (s e c )

Dis

plac

emen

t(ft

)

S e lfS imD E E P S O IL + hy p e rb o lic (Ta rg e t )D E E P S O IL + line a rN N

-5.0E+03

-4.0E+03

-3.0E+03

-2.0E+03

-1.0E+03

0.0E+00

1.0E+03

2.0E+03

3.0E+03

-3.0E-01 -2.0E-01 -1.0E-01 0.0E+00 1.0E-01 2.0E-01 3.0E-01

Strain(%)

Stre

ssTargetLayer4Layer3Layer2Layer1

Layer1

Layer2

Layer3

Layer4



SelfSim in Bio-Engineering

J. Ghaboussi, D. A. Pecknold, Y. M. Hashash

Applications in Ophthalmology Characterizing the material properties of human cornea for simulating Individualized laser surgeryMeasurement of intra-ocular pressure (IOP)Developing a new instrument

Applications in bio-medical imagingCharacterizing the material properties of soft tissueImaging of the material properties of soft tissue for diagnostics and disease progression

Simulation of Goldman Applanation Tonometer

0.02mm

15mmHg

First step

Applanation

Second stepBefore loading steps

Real-time soil model for tool-medium interaction in virtual reality environment

DEM Machine-Medium Interaction

Integration of numerical modeling Integration of numerical modeling and field observations for deep and field observations for deep excavationsexcavations

1. Field Measurements

2. SelfSim Training FEM, iterated

Neural Network Constitutive Soil Model

Stress-Strain PairsTraining of NANN

σ,ε

Initializing or Pre-training stress strain data from:1. Linear elastic2. Laboratory tests3. Case histories4. Approximate constitutive models

a) Simulate Construction Sequence=> extract stresses

b) Apply Measurements=> extract strains

Similar excavationsNext excavation stage

3.Forward FEM analysis with trained NN material model

and/or

εσ

Synthetic Synthetic ““FieldField”” MeasurementsMeasurements

02468100

5

10

15

20

25

30

35

40

Dep

th (m

)

2.5

5.0

10

15

MIT-E3 "Field" Measurements

Lateral Wall Deflection (cm)

7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)MIT-E3 "Field" Measurements

Distance behind the wall (m)

B/2=20m

H=15m

Support Spacing =2.5m

Diaphragm WallThickness =0.9mE=2.3*104 MPaυ=0.2

No SelfSim training

02468100

5

10

15

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30

35

40

Dep

th (m

)

2.5

5.0

10

15

Elastic Pre-trained


7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Elastic Pre-trained


SelfSim training SelfSim training

02468100

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25

30

35

40

Dep

th (m

)

2.5

5.0

10

15

Training: Pass #1using Exc. depth =2.5m data


7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #1

using all Exc. depth =2.5m data



02468100

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30

35

40

Dep

th (m

)

2.5

5.0

10

15

Training: Pass #1using Exc. depth=5m data


7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #1

using Exc. depth=5m data



02468100

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30

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40

Dep

th (m

)

2.5

5.0

10

15

Training: Pass #1using Exc. depth=7.5m data


7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #1

using Exc. depth=7.5m data



02468100

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20

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35

40

Dep

th (m

)

2.5

5.0

10

15

Training: Pass #1using Exc. depth=10m data


7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #1

using Exc. depth=10m data



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40

Dep

th (m

)

2.5

5.0

10

15

Training: Pass #1using Exc.depth=12.5m data


7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #1

using Exc.depth=12.5m data



02468100

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25

30

35

40

Dep

th (m

)

2.5

5.0

10

15

Training: Pass #1using all Exc. data


7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #1

using all Exc. data



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25

30

35

40

Dep

th (m

)

2.5

5.0

10

15



7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #2

using all Exc. data



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40

Dep

th (m

)

2.5

5.0

10

15



7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #4

using all Exc. data



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Dep

th (m

)

2.5

5.0

10

15



7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #6

using all Exc. data



02468100

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40

Dep

th (m

)

2.5

5.0

10

15



7.5

12.5

-5

-4

-3

-2

-1

00 50 100 150 200

Surf

ace

Settl

emen

t (cm

)Training: Pass #8

using all Exc. data


Evaluate a Trained NN modelEvaluate a Trained NN model

-20 0 20 40

SupportSpacingh=2.5m

H

CL

Distance from Diaphragm Wall, x (m)

Diaphragm WallLength, L=40m

Thickness, t =0.9m

E = 2.3x104MPa

ν =0.2

L

Dth

()

Trained NN model

-20 0 20 40

SupportSpacingh=2.5m

H

CL

Distance from Diaphragm Wall, x (m)

Diaphragm WallLength, L=40m

Thickness, t =0.9m

E = 2.3x104MPa

ν =0.2

L

Dth

()

SelfSim

AnalysisStress and

Strain

jσ

jε 1jε − 1jσ −

-120 10-3 -80 10-3 -40 10-3 0 1

05

10152025303540

Dep

th (m

)

12.5

22.5

5.0

0 20 40 60 80 100

Surfa

ce D

ispl

acem

ent (

mm

) Distance behind wall (m)

0

-20

-40

-60

12.522.5

5.0

NN

MIT E-3

mm

Simulate Laboratory Tests

σ

ε

Plane Strain TestsPlane Strain Tests (PST)(PST)

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-0.5 -0.25 0 0.25 0.5

(σ' v-σ

' h)/2*σ

' v0

εaxial

(%)

SelfSim MITE3 OCR1.0

SelfSim Elastic Pre-train

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-0.5 -0.25 0 0.25 0.5(σ

' v-σ' h)/2

*σ' v0

εaxial

(%)



-0.4

-0.2

0

0.2

0.4

0.6

0.8

-0.5 -0.25 0 0.25 0.5

(σ' v-σ

' h)/2*σ

' v0

εaxial

(%)



1

10

100

1000

0.01 0.1 1

MITE3SelfSim

Seca

nt M

odul

us,

(δσ 1-δ

σ 3)/2γσ

' 0

Maximum Shear Strain, γ (%)

PST compression

PST Extension

Learning from PrecedenceLearning from Precedence

Soft Clay Layer MIT-E3

OCR=1.3Crust Clay Layer MIT-E3 OCR=4

Stiff Layer MIT-E3 OCR=5

Rock Linear Elastic

5 m

30 m

45 m

40 m

he=2.5mhs=5.0m

B/2=40m

Case3

40 m Flexible Wall

5 m

35 m

40 m

40 m

30 m Stiff Wall

he=2.5m

hs=2.5&5.0 m

B/2=30m

Case25 m

45 m

30 m

40 m

he=2.5mhs=2.5m

40 m Flexible Wall

B/2=20m

Case1

New Excavation Site

35 m

25 m

60 m

40 m Stiff Wall

he=2.5mhs=2.5m

B/2=20m

Case1Case1 Case2Case2 Case3Case3SelfSim TrainingSelfSim Training

02460

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40

Dep

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)

2.5

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40m

Fle

xibl

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all


12.5

7.5

Soil

beha

vior

to b

e le

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d

hs=2.5m

B/2=20m

-3

-2

-1

00 50 100 150 200 Surface Settlement (cm

)

Case 1 after trainingwith all three cases


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Dep

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)

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5.0

10

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30m

Stif

f Wal

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12.5

7.5

Soil

beha

vior

to b

e le

arne

d

hs=5.0 & 2.5m

B/2=30m

-4

-3

-2

-1

00 50 100 150 200 Surface Settlem

ent (cm)

Case2 after trainingwith all three cases


0246810120

5

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30

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40

Dep

th (m

)

2.55.0

10

15

Exc. Depth (m)


12.5

7.5

Soil

beha

vior

to b

e le

arne

d

40m

Fle

xibl

e W

all

ht=2.5 & 5.0m

B/2=40m

-6-5-4-3-2-10

0 50 100 150 200 Surface Settlement (cm

)

Case 3 after trainingwith all three cases


0

5

10

15

20

25

30

35

40

012345678

Dep

th (m

)


2.5

5.0

10

1512.5

7.5

hs=2.5m

B/2=20m

Soil

beha

vior

to b

e le

arne

d20

-3

-2

-1

00 50 100 150 200 Surface Settlem

ent (cm)


Prediction of New CasePrediction of New Case

0

5

10

15

20

25

30

35

40

012345678

012345678

Dep

th (m

)


2.5

5.0

10

1512.5

7.5

hs=2.5m

B/2=20m

Prediction of "New" Case

Soil

beha

vior

to b

e le

arne

d20

-3

-2

-1

00 50 100 150 200

-3

-2

-1

0

Surface Settlement (cm

)


Prediction of "New" Case after training with Case 1

Prediction of New Case after Case1Prediction of New Case after Case1

0

5

10

15

20

25

30

35

40

012345678

012345678

Dep

th (m

)


2.5

5.0

10

1512.5

7.5

hs=2.5m

B/2=20m


Soil

beha

vior

to b

e le

arne

d20

-3

-2

-1

00 50 100 150 200

-3

-2

-1

0


)


Prediction of "New" Case after training with Case 1 and 2

Prediction of New Case after Case1&2Prediction of New Case after Case1&2

Prediction of New Case after Prediction of New Case after Case1,2&3Case1,2&3

0

5

10

15

20

25

30

35

40

012345678

012345678

Dep

th (m

)


2.5

5.0

10

1512.5

7.5

hs=2.5m

B/2=20m


Soil

beha

vior

to b

e le

arne

d20

-3

-2

-1

00 50 100 150 200

-3

-2

-1

0


)


Prediction of "New" Case after training with all three cases

LURIE RESEARCH CENTERLURIE RESEARCH CENTER

LurieLurie Research Center Research Center –– Plan and Plan and Cross Section ViewCross Section View

LR5

LR7

LR6

LR8

Embedded Soil Settlement Point

PK Nail

Utility Monitoring Point Inclinometer

LR3 LR2

LR4

Lurie Research Center

LR1

200 feet

60 meters

20 100

20 40

Soil Boring

E. Superior Street

E. Huron Street

Pedestrian tunnel

Pren

tice

Pavi

llion

(1

leve

l bas

emen

t)

N. F

airb

anks

Cou

rt

N

El. +2.1 mFill

Stiff/V. Stiff Silty Clay

Hard Silty Clay

208

308

PZ27 Sheeting

El. -1.2 m

El. -5.2 m

El. -14.9 m

Soft/Med Silty Clay

El. +3.4 m

Lake Sand

El. -20.7 m

El. -4.6 m

El. +0.6 m

El. -11.6 m

El. +4.3 m

108

-20

-15

-10

-5

0

5 0246810Lat. Wall Deflection (mm)

Elev

atio

n (m

)

(a) Stage 1:Exc. +1.5 m

-20

-15

-10

-5

0


Elev

atio

n (m

)


-20

-15

-10

-5

0

50204060

Elevation (m)(g) Stage 7:

Exc. -7.3 m-20

-15

-10

-5

0

50204060


Exc. -7.3 m

Simplified Construction SequenceSimplified Construction Sequence

CL CL

CL CL

CL CL

CL CL

+4.2+4.2+1.5

+1.5+4.2

-2.4

+4.2

-2.4

+4.2

-5.8

+4.2

-5.8

+4.2

-7.3

+4.2

Stage 0

ReferenceConfiguration

Stage 1Undrained Excavation16 days dewatering

Stage 2 Stage 3InstallationTieback 1

Undrained Excavation86 days dewatering

Stage 4InstallationTieback 2 Stage 5


Stage 6InstallationTieback 3 Stage 7


-20

-15

-10

-5

0

5010203040506070

Lateral Wall Deflection (mm)El

evat

ion

(m)

Pre-trainedMeasuredExc StageExc. 1.5 mTieback 1

Exc. -2.4 mTieback 2


Exc. -7.3 m

(a) No Training

0

10

20

30

40

50

0 10 20 30 40 50 60 70 80Distance behind the wall (m)

Surface Settlement (m

m)

(b) No Training

No TrainingNo Training

-20

-15

-10

-5

0

5010203040506070

Lateral Wall Deflection (mm)El

evat

ion

(m)

SelfSimMeasuredExc StageExc. 1.5 mTieback 1



Exc. -7.3 m

(a) 10 Passes of Training

0

10

20

30

40

50


Surface Settlement (m

m)

(b) 10 Passes of Training

SelfSim TrainingSelfSim Training


-20

-15

-10

-5

0

5-505101520Lat. Wall Deflection (mm)

Elevation (m)

(c) Stage 3:Exc. -2.4 m

-20

-15

-10

-5

0

5 -505101520

Elev

atio

n (m

)

(d) Stage 4:Tieback 2 -20

-15

-10

-5

0

50204060

Elevation (m)(e) Stage 5:

Exc. -5.8 m

0246810Lat. Wall Deflection (mm)

-20

-15

-10

-5

0

5

(b) Stage 2:Tieback 1

-20

-15

-10

-5

0

50204060


Exc. -7.3 m-20

-15

-10

-5

0

5 0204060LR3LR5

LR6LR7LR8

RepresentativeSelfSim(f) Stage 6:

Tieback 3

Elev

atio

n (m

)

-20

-15

-10

-5

0


Elev

atio

n (m

)


Lurie Center


0

10

20


Surf

ace

Settl

. (m

m)


0

10

20


Surface Settl. (mm

)

(b) Stage 2:Tieback 1

0

10

20

0 10 20 30 40 50 60 70 80

Surf

ace

Settl

. (m

m)

(c) Stage 3:Exc. -2.4 m

0

10

20

0 10 20 30 40 50 60 70 80 Surface Settl. (mm

)

(d) Stage 4:Tieback 2

01020304050

0 10 20 30 40 50 60 70 80

Surf

ace

Settl

. (m

m)

(e) Stage 5:Exc. -5.8 m

01020304050

0 10 20 30 40 50 60 70 80 Surface Settl. (mm

)

(f) Stage 6:Tieback 3

01020304050

0 10 20 30 40 50 60 70 80

Surf

ace

Settl

. (m

m)

(g) Stage 7:Exc. -7.3 m

Assessment of extracted soil modelAssessment of extracted soil model

-0.4

-0.2

0

0.2

0.4

0.6

-0.4 -0.2 0 0.2 0.4

(σ' v-σ

' h)/2σ'

v0

εaxial

(%)

Extracted Clay Model (SelfSim)Triaxial tests (Holman, 2005)

Elastic Pre-training

Concluding RemarksMost of the difficult engineering problems are inverse problems.

Very effective methods can be developed for solving these inverse problems by learning from nature’s problem solving strategies.

Neural networks, genetic algorithm and fuzzy logic enable development of these methods.

Soft computing methods use nature’s strategies of reduction in disorder and learning.

Concluding Remarks

Soft computing methods are fundamentally different from the conventional mathematically based methods.

Soft computing methods operate withImprecision toleranceNon-universalityFunctional non-uniqueness.

Soft Computing Approaches to Constitutive Modeling in ... Web Page/nsf workshop...

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Transcript of Soft Computing Approaches to Constitutive Modeling in ... Web Page/nsf workshop...