Probabilistic Seismic Performance of Rocking-Foundation and Hinging-Column Bridges

Lijun DengAdvisors: Prof. Bruce Kutter, Prof. Sashi Kunnath

University of California, Davis

2011 UC Davis GGSS RoundtableApril 8, 2011

Outline• Research motivation• Development of computational model• Preliminary simulation results • Conclusions

Plastic hinge

Conventional fixed-base foundation

Hinging-column system

Research motivation

Soil plastic hinge

Rocking-foundation system

vs.

Rocking foundation: Centrifuge tests

Rocking foundation:Kocaeli 1999

Hinging column:Kobe 1995

Hinging column: Centrifuge tests

Case histories and experiment studies

Outline• Research motivation• Development of computational model• Preliminary simulation results • Conclusions

...... ......

Lf

Computational model configuration

-0.04 0 0.04

-1

-0.5

0

0.5

1

RotationM

omen

t / M

cap

Footing

-1

-0.5

0

0.5

1 Column hinge

Mom

ent /

Mca

p

RotationDisp.

Force

Hc (m) Period, T (s) Cy / Cr Remarks

Short: 3 0.3, 0.5

0.3 / 0.4 Hinging-column dominated

0.4 / 0.3 Rocking-foundation

Tall: 10 0.5, 1.0

0.3 / 0.4 Hinging-column

0.4 / 0.3 Rocking-foundation

Model parameters• Cy, Cr: base shear coefficients for column & rocking footing

• Two yielding mechanisms: Cr > Cy Hinging column system;

Cy > Cr Rocking foundation system

Realistic values for highway bridges

Model parameters• Input ground motions from PEER database

Baker et al. (2010)

• Concept of Incremental Dynamic Analysis (IDA)

Outline• Research motivation• Development of computational models• Preliminary simulation results• Conclusions

Selected animations

• Cy=0.3, Cr=0.4, T=0.5 s (Hinging column)

• Cy=0.4, Cr=0.3, T=0.5 s (Rocking foundation)

On-verge-of-collapse case

Collapse caseOn-verge-of-collapse case

Collapse case

0.01 0.1 1 10Period (sec)

0.01

0.1

1

10

Sa (g

)

Sa (T) vs. Max Deck Drift curves

T

0.01 0.1 1 10Period (sec)

0.01

0.1

1

10

Sa (g

)Sa (T)

0.01 0.1 1 10Max Drift (m)

0.1

1

10S a

(T) (

g)

Sa (T) vs. Max Deck Drift curves

Elastic

Nonlinear

Collapse

Instability limit~=3 m

0.3 g

Rocking-footing system(Cy=0.4, Cr=0.3, T=0.5 s, Hc=10 m)

Probabilistic AnalysisRocking Footing (Cy=0.4, Cr=0.3, T=0.5 s, Hc=10 m)

Note: Equivalent Static Analysis: a linear static pushover method

0.01 0.1 1 10Max Drift (m)

0.1

1

10

S a (T

) (g)

Equivalent Static Analysis

0.01 0.1 1 10Max Drift (m)

0.1

1

10

S a (T

) (g)

Equivalent Static Analysis

0.01 0.1 1 10Max Drift (m)

0.1

1

10

S a (T

) (g)

Median84%16%

98%2%ESA

0.001 0.01 0.1 1 10Median max drift (m)

0.01

0.1

1

10

S a (T

) (g)

Rocking-foundationHinging-columnESA predicted

Hc=10.0 m

T=0.5 s

Probabilistic Performance Comparison

• Probabilistic performance of two systems are similar under less-intense motions, but rocking foundation is superior under intense motions.

0.001 0.01 0.1 1 10Median max drift (m)

0.01

0.1

1

10

S a (T

) (g)

Rocking-foundationHinging-columnESA predicted

Hc=10.0 m

T=0.5 sT=1.0 s

0.001 0.01 0.1 1Median max drift (m)

Rocking-foundationHinging-columnESA predicted

Hc=3.0 m

T=0.3 s

T=0.5 s

0.001 0.01 0.1 1 10Median max drift (m)

0.01

0.1

1

10

S a (T

) (g)

Rocking-foundationHinging-columnESA predicted

Hc=10.0 m

T=0.5 sT=1.0 s

0.001 0.01 0.1 1Median max drift (m)

Rocking-foundationHinging-columnESA predicted

Hc=3.0 m

T=0.3 s

T=0.5 s

0.0001 0.001 0.01 0.1 1Median residual rotation (rad)

0.1

1

10

S a (T

) (g)

Rocking-foundationHinging-column

Hc=10.0 m

T=0.5 s

Sa (T) vs. Residual Deck Rotation

• Bridge with rocking foundation have smaller rotation than hinging column illustrates the recentering benefits

1E-005 0.001 0.1 10Deck residual rotation (rad)

0.1

1

10

S a (T

) (g)

Median84%

16%98%

0.0001 0.001 0.01 0.1 1Median residual rotation (rad)

0.1

1

10

S a (T

) (g)

Hc=10.0 m

T=1.0 s

Conclusions• Probabilistic performance of rocking-foundation and

hinging-column bridge systems was evaluated using IDA methodology.

• Rocking systems with Cr=0.3 produce less residual drift and similar max drift, and have lower probability of collapse in comparison with hinging column systems with Cy=0.3.

• 3-m-tall system is easier to topple than 10- m-tall system.• The use of rocking foundation should be encouraged in

seismic design of soil-foundation-structure systems.

Acknowledgments• Caltrans (M. DeSalvatore, S. McBride, T. Shantz, and M.

Khojasteh, contract 59A0575) • NSF-NEESR Project Soil and Structure Compatible Yielding

to Improve System Performance• PEER project Last Hurdles for Rocking Foundations for

Bridges• Student assistants: T. Algie (Auckland Univ., NZ), E. Erduran, J.

Allmond (UCD), M. Hakhamaneshi (UCD).

P E E R

The end

Validate model through centrifuge data

0.02 0.01 0 0.01 0.02 0.032 107

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

0.06CenrifugeOpenSees

Time (s)

Dec

k dr

ift (r

ad)

0.01 0 0.012 107

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 0.032 107

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

0.06CenrifugeOpenSees

Time (s)

Dec

k dr

ift (r

ad)

0.01 0 0.013 107

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

0.03CenrifugeOpenSees

Time (s)

Dec

k dr

ift (r

ad)

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 rH A

2 2 2

2

1

1 14sprsys 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 LqL

(Foundation

element strength)

0 2 4 6 8 10Sa(T) (g)

0

0.2

0.4

0.6

0.8

1

P (E

DP>

Drif

t | S

a)

Drift = 0.1 mDrift = 0.5 mDrift = 2 m

Hc=10.0 m, T= 1.0 sCy=0.4, Cr=0.3

0 2 4 6 8 10Sa (T) (g)

Drift = 0.1 mDrift = 0.5 mDrift = 2 m

Hc=10.0 m, T= 1.0 sCy=0.3, Cr=0.4

Fragility curves for two case studies

0.01 0.1 1 10Max Drift (m)

0.1

1

10

S a (T

) (g)

0.01 0.1 1 10Max Drift (m)

0.1

1

10

S a (T

) (g)

Sa (T) vs. Max Deck Drift curves

Elastic

Nonlinear

Collapse

Instability limit~=3 m

Elastic

Nonlinear

0.3 g

Instability limit~=3 m

Rocking Footing (Cy=0.4, Cr=0.3, T=0.5 s, Hc=10 m)

0.3 g

Hinging column (Cy=0.3, Cr=0.4, T=0.5 s, Hc=10 m)

Collapse

• 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 favor for rocking – recentering• Instability limits are related to min{Cy, Cr}

Collapse mechanisms

Elastic footing

Rocking footing

P

P