Incremental Dynamic Analyses on Bridges on

various Shallow Foundations

Lijun DengPI’s: Bruce Kutter, Sashi Kunnath

University of California, Davis

NEES & PEER annual meetingSan Francisco

October 9, 2010

Outline

• Introduction and centrifuge model tests• Incremental Dynamic Analysis (IDA) model• Preliminary results of IDA

Maximum drift Instability limits of rocking and hinging systems Residual drift

• Conclusions

Damaged columns in past earthquakes

Load Frame

N

x

A A

B B

0 12 24 36

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

inch

meter

NLF

SF ISF4CSF 60

9.6

304.9

N

393.0 381.0 592.0 387.0

254.

039

6.0

254.

0

198.

0

1006.5

1366.0

Centrifuge test matrix

Rocking Foundation Centrifuge Tests

5

max BaseMotion( ) 0.6192

20 25 30 351

0.5

0

0.5

1

Time (sec)

Accel

(g)

min BaseMotion( ) 0.8824

10 20 30 40 500.4

0.2

0

0.2

0.4

Time (sec)

Dis

p. (m

)

10.88

7.35

SF

10.88

7.35

ISF

Remediating concrete pads

Gazli earthquake, pga= 0.88 g

Hinging Column Centrifuge Test

6

9.64

12.20

Notches

LF

max BaseMotion( ) 0.6192

20 25 30 351

0.5

0

0.5

1

Time (sec)

Accel

(g) min BaseMotion( ) 0.8824

10 20 30 40 500.4

0.2

0

0.2

0.4

Time (sec)

Dis

p. (m

)

Gazli earthquake, pga= 0.88 g

Photos of hinging column after 0.88g Gazli shake

7

8

9.64

12.20

Notches

LF

max BaseMotion( ) 0.1611

20 40 600.3

0.2

0.1

0

0.1

0.2

Time (sec)

Accel

(g

) min BaseMotion( ) 0.2292

20 40 600.2

0.1

0

0.1

0.2

Time (sec)

Dis

p.

(m

)

CHY024, pga=0.23 g

Hinging Column Centrifuge Test

Collapse of hinging column

9

• SDOF bridges on rocking foundation survived after 20 scaled GM’s, but the one on fixed foundation and hinging column collapsed

OpenSees model for IDA and parametric study

Moment

Rotation

Column hinge spring

Foundation: zerolength elements

Column: Stiff elasticBeamColumn

xi

ki

Lf

Kθ

Mass = m

Footing mass = m*rm

Footing center

Fixed ground center

Hc

Validate model through centrifuge data

0.02 0.01 0 0.01 0.02 0.032 10

7

1 107

0

1 107

2 107

3 107

CentrifugeOpenSees

Footing rotation (rad)

Roc

king

mom

ent (

N*m

)

0 10 20 30 400.04

0.02

0

0.02

0.04

0.06

CenrifugeOpenSees

Time (s)

Dec

k dr

ift (

rad)

0.01 0 0.01

2 107

1 107

0

1 107

2 107

Column hinge rotation

Nor

m. c

ol. b

ase

mom

ent

0.02 0.01 0 0.01 0.02 0.032 10

7

1 107

0

1 107

2 107

3 107

CentrifugeOpenSees

Footing rotation (rad)

Roc

king

mom

ent (

N*m

)

0 10 20 30 400.04

0.02

0

0.02

0.04

0.06

CenrifugeOpenSees

Time (s)

Dec

k dr

ift (

rad)

0.01 0 0.01

3 107

2 107

1 107

0

1 107

2 107

3 107

CentrifugeOpenSees

Footing rotation (rad)

Roc

king

mom

ent (

N*m

)

10 20 30 40 50 600.03

0.02

0.01

0

0.01

0.02

0.03

CenrifugeOpenSees

Time (s)

Dec

k dr

ift (

rad)

10.88

7.35

SF

Centrifuge model (Cy/Cr=5, T_sys=1 s, FSv=11.0)

Input parameters in IDA model• Cy, Cr: base shear coefficients for column or rocking footing• Two yielding mechanisms:

Cr > Cy Hinging column system; Cy > Cr Rocking foundation system

yy

c

MC

m g H

1 12

f cr m

c

L AC r

H A

2 2 2

2

1

1 14

sprsys c N

i ii

T m HK

k x

yM

fL

K

k

Ac/A=0.2, rm=0.2(Footing length)

(Column hinge strength)

Equally spaced foundation elements

(Column hinge stiffness)

(Foundation element stiffness)

(1 )mult

f

r m g FSv Lq

L

(Foundation

element strength)

Input parameters in IDA model• Input ground motions from PEER database

Forty pulse-like ground motions at soil sites(Baker et al. 2010)

T_sys (sec) Cy Cr # GM # Scale factors0.5 0.5 0.2 40 pulse-like 0.2, 0.40.8 0.3 0.2 40 broad-band 0.6, 0.80.2 0.2 0.2 1.0, 1.51.0 0.2 0.3 2.0, 2.51.2 0.2 0.5 3.0, 4.01.5  2

0.01 0.1 1 10Period (sec)

0.01

0.1

1

10

Ac

cel

. re

sp

on

se s

pe

ctr

a (

g)

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Sa(

T_s

ys

)(g

)

PL_28_SN

PL_29_SN

PL_3_SN

PL_30_SN

PL_31_SN

PL_32_SN

PL_33_SN

PL_34_SN

PL_35_SN

PL_36_SN

PL_37_SN

PL_38_SN

PL_39_SN

PL_4_SN

PL_40_SN

PL_5_SN

PL_6_SN

PL_7_SN

PL_8_SN

PL_9_SN

ESA prediction for T=0.85 s

Cy=0.2, Cr=0.5, T_sys=0.85 s

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Sa

(T_

sys

)(g

)

PL_28_SN

PL_29_SN

PL_3_SN

PL_30_SN

PL_31_SN

PL_32_SN

PL_33_SN

PL_34_SN

PL_35_SN

PL_36_SN

PL_37_SN

PL_38_SN

PL_39_SN

PL_4_SN

PL_40_SN

PL_5_SN

PL_6_SN

PL_7_SN

PL_8_SN

PL_9_SN

ESA prediction for T=0.85 s

Cy=0.5, Cr=0.2, T_sys=0.85 s

IDA results: Sa(T=T_sys) vs. max drift

Elastic zone

Nonlinear zone

Failure zone

Instability limit~=2.2 m

Elastic zone

Nonlinear zone

0.2 g

Instability limit~=2 m

Rocking Footing (Cy=0.5, Cr=0.2, T_sys=0.85 s)

0.2 g

Hinging column (Cy=0.2, Cr=0.5, T_sys=0.85 s)

Failure zone

• A hinge is a hinge• Hinges can be engineered at either position

– A hinge forms at the edge when rocking occurs

• P-delta is in your favor for rocking – recentering• Instability limits are related to Cy and Cr values

Collapse mechanisms

Elastic footing

Rocking footing

P

D

P

D

Selected animations

• Cy=0.2, Cr=0.5, T=0.85 s (Hinging column)

• Cy=0.5, Cr=0.2, T=0.85 s (Rocking foundation)

On-verge-of-collapse case

Collapse caseOn-verge-of-collapse case

Collapse case

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Sa(

T_

sy

s)(g

)

PL_28_SN

PL_29_SN

PL_3_SN

PL_30_SN

PL_31_SN

PL_32_SN

PL_33_SN

PL_34_SN

PL_35_SN

PL_36_SN

PL_37_SN

PL_38_SN

PL_39_SN

PL_4_SN

PL_40_SN

PL_5_SN

PL_6_SN

PL_7_SN

PL_8_SN

PL_9_SN

ESA prediction for T=0.85 s

Cy=0.2, Cr=0.5, T_sys=0.85 s

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Sa

(T_

sys

)(g

)

PL_28_SN

PL_29_SN

PL_3_SN

PL_30_SN

PL_31_SN

PL_32_SN

PL_33_SN

PL_34_SN

PL_35_SN

PL_36_SN

PL_37_SN

PL_38_SN

PL_39_SN

PL_4_SN

PL_40_SN

PL_5_SN

PL_6_SN

PL_7_SN

PL_8_SN

PL_9_SN

ESA prediction for T=0.85 s

Cy=0.5, Cr=0.2, T_sys=0.85 s

IDA results: Sa(T=T_sys) vs. max drift

• 50% median of Sa vs. max drift and +/-σ

50% Median

Compare medians of Sa vs. max drift for various T_sys

• Longer periods lead to higher drift• The max drift is not sensitive to Cy/Cr ratio• The max might rely on min{Cy, Cr}, to be confirmed with further

study

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Me

dia

n S

a(T

_s

ys)(

g)

T_sys=0.85 s for 5 Cr, Cr combinations

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Me

dia

n S

a(T

_s

ys)(

g)

T_sys=0.85 s for 5 Cr, Cr combinationsT_sys=0.43 s for 5 Cy, Cr combinations

IDA results: Sa (T_sys) vs. Residual Rotation

1E-006 1E-005 0.0001 0.001 0.01 0.1 1 10Residual rotation (rad)

0.01

0.1

1

10

Sa

(T_

sy

s) (

g)

PL_28_SN

PL_29_SN

PL_3_SN

PL_30_SN

PL_31_SN

PL_32_SN

PL_33_SN

PL_34_SN

PL_35_SN

PL_36_SN

PL_37_SN

PL_38_SN

PL_39_SN

PL_4_SN

PL_40_SN

PL_5_SN

PL_6_SN

PL_7_SN

PL_8_SN

PL_9_SNCy=0.5, Cr=0.2, T_sys=0.85 s

50% Median

IDA results: Sa (T_sys) vs. Residual rotation

• Bridge with rocking foundation have smaller rotation than hinging column re-confirm the recentering benefits

1E-005 0.0001 0.001 0.01 0.1 1Residual drift (rad)

0.1

1

Me

dia

n S

a(T

_sy

s)(

g)

Cy=0.5, Cr=0.2, T_sys=0.85 s

Cy=0.2, Cr=0.5, T_sys=0.85 s

1E-005 0.0001 0.001 0.01 0.1 1Residual drift (rad)

0.1

1

Me

dia

n S

a(T

_s

ys

)(g

)

Cy=0.5, Cr=0.2, T_sys=0.43 s

Cy=0.2, Cr=0.5, T_sys=0.43 s

Hinging column

Rocking foundation

Hinging column

Rocking foundation

Conclusions• Rocking foundations provide recentering effect that

limits the accumulation of P-D demand (i.e., much smaller residual rotation)

• Experiments and IDA simulations show column with rocking footing is more stable than hinging column (i.e., fewer collapse cases)

• ESA approach is not conservative for highly nonlinear cases

• Analysis is ongoing, and fragility functions are being developed from the results. We are also evaluating the adequacy of Sa(T_sys) as an Intensity Measure of ground motions

Panagiotou

CODE

DEVELOPERS

Collaborators

Kutter

Browning

Moore

Martin

Jeremic

Mar

Comartin

McBride

Mahan

Desalvatore

KhojastehShantz

BRIDGES

BUILDINGS

Mejia

BOTH

GEOTECHNICAL

STRUCTURAL

Mahin

Kunnath

Ashheim

Stewart

Hutchinson

THEORYDESIGNCONSTRUCTION

Acknowledgments• Current financial support of California Department of

Transportation (Caltrans).• Network for Earthquake Engineering Simulation (NEES) for

using the Centrifuge of UC Davis. • Other student assistants: T. Algie (Auckland Univ., NZ), E.

Erduran (USU), J. Allmond (UCD), M. Hakhamaneshi (UCD).

The end

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Sa(

T_s

ys

)(g

)

PL_28_SN

PL_29_SN

PL_3_SN

PL_30_SN

PL_31_SN

PL_32_SN

PL_33_SN

PL_34_SN

PL_35_SN

PL_36_SN

PL_37_SN

PL_38_SN

PL_39_SN

PL_4_SN

PL_40_SN

PL_5_SN

PL_6_SN

PL_7_SN

PL_8_SN

PL_9_SN

ESA prediction for T=0.85 s

Cy=0.2, Cr=0.5, T_sys=0.85 s

0.01 0.1 1 10Max drift (m)

0.01

0.1

1

10

Sa

(T_

sys

)(g

)

PL_28_SN

PL_29_SN

PL_3_SN

PL_30_SN

PL_31_SN

PL_32_SN

PL_33_SN

PL_34_SN

PL_35_SN

PL_36_SN

PL_37_SN

PL_38_SN

PL_39_SN

PL_4_SN

PL_40_SN

PL_5_SN

PL_6_SN

PL_7_SN

PL_8_SN

PL_9_SN

ESA prediction for T=0.85 s

Cy=0.5, Cr=0.2, T_sys=0.85 s

IDA results: Sa(T=T_sys) vs. max driftRocking Footing (Cy=0.5, Cr=0.2, T_sys=0.85 s)

Hinging column (Cy=0.2, Cr=0.5, T_sys=0.85 s)

• Equivalent Static Analysis (ESA) commonly used in codes may underestimate the displacement.