Using Field Observations to Calibrate Constitutive Models

Richard J. Finno

Outline

• Inverse analysis– Overview– Chicago-State example– Other projects

• Challenges

Parameter optimization algorithmParameter optimization algorithm(Flowchart)(Flowchart)

NO YES

Observations

Computedresults

Optimizedinput parameters

Is the modeloptimized?

FE run

Compute Objective Function

ComputeSensitivity X

Perform NonlinearRegression

Updatedinput parameters

Initialinput parameters

FE run Updatedresults

Perturb bk byuser-defined amount

FE run

Computed results

Calculate Xik=∂yi/∂bk(for i = 1 to ND)

Repeat fork=1 to NP

ND = Number of observationsNP = Number of parameters to optimize

“Synthetic” excavations

• Observations: lateral movements based on excavation simulation with a given set of parameters (base case)

• Varied input parameters by ¼, ½ 2 and 4 times values used for base case as input to same excavation history as base case

• Always converged to within 98% of initial parameters

Chicago – State Excavation

Finite element schematic

InclinometersWEST EAST

+14’

+2’-1’

-15’

-23’

-35’

-50’

-60’

-80’

Sand fill

Clay crust

Upper Blodgett

Lower Blodgett

Deerfield

Park Ridge

Tinley

Hard Pan InclinometersWEST EAST

+14’

+2’-1’

-15’

-23’

-35’

-50’

-60’

-80’

Sand fill

Clay crust

Upper Blodgett

Lower Blodgett

Deerfield

Park Ridge

Tinley

Hard Pan

Stage 1 Drill secant pile wallStage 2 Excavate [+9’] and install strutsStage 3 Excavate [-3’] and install 1st level tiebacksStage 4 Excavate [-16’] and install 2nd level tiebacksStage 5 Excavate [-25’]

Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

Observation sets

FE model (schematic)FE model (schematic)

-15

-10

-5

0

5

10-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350

Elev

atio

n (m

CC

D)

1 - Install SP Wall (Day 2 to Day 11)2 - Install Strut 4 (Day 60)3 - Install Strut 5 (Day 74)4 - Stress 1st Level Tieback (Day 87)5 - Stress 2nd Level Tieback (Day 105)

7 - Pour Base Slab (Day 172 to Day 177)8 - Pour E. Ext. Wall (Day 197 to Day 207)9 - Remove Struts 4, 5, and 6 (Day 258)6 - Chip Face to Flange EL +3.35 to EL -7.62 (Day 110 to Day 140)

1 1 2 3

4 5

6 6 7

7

8 8 9

0

10

20

30

40

50

60

-50 -25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350

Construction Day Number

Mov

emen

t (m

m)

EL -3.7 (m CCD)

EL -7.9 (m CCD)

EL -11 (m CCD)

School Settlement (W10)

Wall installationExcavation and support Station renovation and backfill

1

Modelingstages

2 3 4 5

Stage 4 Stage 5 Stage 1 Stage 2 Stage 3

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5

displacement (in)

Elev

atio

n (ft

CC

D)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5displacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5

displacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5

displacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5

diplacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5

Elev

atio

n (ft

CCD

)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5

Measured field data Computed displacements

Initial estimate of input parameters

WE

ST s

ide

EA

ST s

ide

Computed vs. measured responseComputed vs. measured response

8

E50ref (psf) Parameter

valuesBlodgett 6,000Deerfield 6,000

Park Ridge 8,600

Stage 1

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

displacement (in)

Elev

atio

n (ft

CC

D)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

Elev

atio

n (ft

CC

D)

Measured field data Computed displacements

Observations used for regression analysis

Stage 4 Stage 5 Stage 1 Stage 2 Stage 3

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

displacement (in)

Elev

atio

n (ft

CC

D)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

displacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

displacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

displacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2diplacement (in)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

Elev

atio

n (ft

CC

D)

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2

Measured field data Computed displacements

Observations used for regression analysis

Parameters optimized based on

observations from stage 1

WE

ST s

ide

EA

ST s

ide

Computed vs. measured responseComputed vs. measured response

9

E50ref (psf) Parameter

valuesBlodgett 6,370Deerfield 17,960

Park Ridge 42,310

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20-3.0 -2.0 -1.0 0.0

Movement (in)

Ele

vatio

n (ft

CC

D)

Stage 4Stage 5Stage 6

PLAXIS

Field Data

Computed and observed lateral movements: North Wall at Lurie excavation with Chicago-State optimized parameters

E l e v a t i o n ( m

C C D )

F i l l ( S M )

N 3 - 7

S a n d ( S P ) N

1 5 - 2 6

S o f t t o M e d i u m

C l a y S u

2 9 - 4 3 k P a

S t i f f C l a y S u

1 0 5 k P a

H a r d C l a y S u

3 8 3 k P a

F i n a l E x

-25

-20

-15

-10

-5

0

5

c a v a t i o n G r a d e

( T y p i c a l )

2 0 o

1 0 o

3 0 o

Movement (in)

-88

-78

-68

-58

-48

-38

-28

-18

-8

2

1200.20.40.60.81

Ele

vatio

n (ft

, EC

D)

Last stage

Field data

PLAXIS

Computed and observed lateral movements: Ford Center excavation with Chicago-State optimized parameters

Existing Building

She

ridan

Roa

d

~44.2m

~36.

6m

N

76

5 4

Vertical Supports

3

2 1

Existing Building

She

ridan

Roa

d

~44.2m

~36.

6m

N

76

5 4

Vertical Supports

3

2 1

Upper Supports, +1.5 m

Lower Supports, -1.0 m

+3.7 m+4.9 m

+2.0 m+1.5 m

-3.7 m

-9.5 m

W36x230 Waler

W24x141 Waler

Upper Supports, +1.5 m

Lower Supports, -1.0 m

+3.7 m+4.9 m

+2.0 m+1.5 m

-3.7 m

-9.5 m

W36x230 Waler

W24x141 Waler

Challenges

• Material models features • Plane strain versus 3-D conditions

– Effects of unbalanced loads– Excavation surface selection– Geometry effects

• Effects of initial conditions

Constitutive responses must include small strain nonlinearity

0.0001 0.001 0.01 0.1 1Local Triaxial Shear Strain, ε

sl (%)

0

10

20

30

40

50

60

Seca

nt S

hear

Mod

ulus

, Gse

c (M

Pa)

TC1TC2TCrRTE1RTE2RTEr

• δh dominated by larger strains near wall• δv distribution impacted by all strain levels

Variation in shear and bulk modulus with direction of loading

88.5 89 89.5 90 90.5 91 91.5 92Effective Mean Normal Stress p' (kPa)

64

64.5

65

65.5

66

66.5

67

67.5

Dev

iato

ric S

tres

s q

(kPa

) 8.213.214.816.3

24.3

50.9

65.6

43.1

Initial K0 Stress State(p'=89.9 kPa, q=66.3 kPa)

TE

CMSE

RTE

AU

RTC CMS TC

ALG0.001 (MPa)

89 89.5 90 90.5 91Effective Mean Normal Stress p' (kPa)

65

65.5

66

66.5

67

Dev

iato

ric S

tres

s q

(kPa

) 22.6

12.5

62.1

38.8

29.3

Initial K0 Stress State(p'=89.9 kPa, q=66.3 kPa)

32.848.4

TE

RTE

AU

CQUCQL

TC

AL

K0.001 (MPa)

All tests on specimens cut from block samples of low OCR Chicagoclay and Ko consolidated to the initial vertical effective stress

Ford Design Center

Tech BuildingAlley

Sand/FillClay Crust

Soft ClayMedium Stiff Clay

Stiff ClayHardpan

5.2m0m

-1m-5m

-13.1 m-16.8 m

-24.4m

3.7m 3.7m 2.0m-3.7m

Tech BuildingAlley

Sand/FillClay Crust

Soft ClayMedium Stiff Clay

Stiff ClayHardpan

5.2m0m

-1m-5m

-13.1 m-16.8 m

-24.4m

3.7m 3.7m 2.0m-3.7m

28 mm

40 mm

0 mm

Inc. Location

Lateral Soil DisplacementLateral Soil Displacement

0 2 4 6 8 10 12L/HE

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PSR,

δ3D

/δ2D

0 1 2 3 4L/B

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

PSR,

δ3D

/δ2D

L/2L/2B/2B/2

HHEE

L/2L/2B/2B/2

HHEE

3-D versus Plane strain

Erratic excavation sequence – predicting contractor behavior?

Lurie Center Excavation –1 ramp location

3-D Laser Scanning (UIUC)to measure excavated surface

Cyrax 2500– Range up to 100m– Accuracy

• Position: +/- 6mm (Range 1.5m to 50m)

• Distance: +/- 4mm• Angle: +/- 60 micro-radians• Surface precision: +/- 2mm

Laser scan of Ford Center excavation

Conclusions• Inverse analysis is a promising method to

calibrate constitutive parameters based on full scale field performance

• Constitutive models must include important responses for each problem

• Field conditions at the time when observations are made must be known with precision

• Know limitations of analysis - they are not all related to constitutive behavior