Rocking Seismic Isolation of Bridges Supported by Direct Foundations

Kazuhiko KawashimaTokyo Institute of Technology

Caltrans-PEER Seismic Research SeminarSacramento, CA, USA

June 8, 2009

Requirements in the OverturningBased on Static Analysis

aB e

VMe <=

Eccentricity

⎩⎨⎧=

6/3/

ll

ea

Allowable Eccentricity

Static

Static+Seismic

Bearing Capacity

aB q

lbM

lbVq <+= 2max

6

el

V

bmaxq

BM

Eccentricity

Size effect is not included in the conventional static analysis

As long as the shape and mass density are the same, a foundation can overturn in the conventional static analysis no matter how the foundation is extremely large

Akashi Strait BridgeThe World Longest Bridge

In the static design, overturning was the major factor for sizing of those foundations based on the conventional analysis

Does such a 100m tall foundation overturn under seismic excitation??

MassNatural periodFrequency content of a ground motion

0.6m

0.2m

0.4m

1.0

Geometrical scale

Kawashima & Unjoh (1992)

0.33m

1m

0.66m

1.65

m=579kg

1.5m

0.5m

0.75m

2.5

m=1452kgm=139kgMass

Shake Table Experiment on the Effect of Size & Mass for Overturning of Rigid Foundations

Shake Table Experiment on the Effect of Size & Mass for Overturning of Rigid FoundationsPublic Works Research Institute

Kawashima & Unjoh (1992)

0 0.2 0.40.3

0.02

0.06

0.04

0.08

0

0.1

Rota

tion (

rad)

0.1 0.5Table Acceleration (g)

0.6m

1m

1.5m

How does the rocking of rigid foundations depend on the size?

Analytical Idealization for Rocking and Sliding Response of a Rigid Foundation

Analytical Correlation on the Rocking Response of a 1.5m Tall Rigid Foundation

Experimental

Analytical

Kawashima et al (1994)

Seismic Response Analysis of Kurushima Straight Bridge

62.973m

35m

45m

Seismic Response Analysis of Anchorages, Towers and Superstructure System of Kurushima Straight Bridge

Separation

Lateral forceTension

CompressionYield

Side Soils

Relative Disp.Lateral Force

Lateral Disp.

Lateral Sliding at Base

Kawashima & Unjoh (1994)

Uplift

Compression

Tension

Settlement

Base Vertical Springs

Yield

Peak Responses

Dis

pla

cem

ent

(cm

)

Time (s)

Response displacement at the top of a tower

Soft rock does not yield

Acc

eler

atio

n

(cm

/s)

Time (s)

Response rotation of an anchorage

Soft rock yields

Dis

pla

cem

ent

(cm

)

Time (s)

Response displacement at the top of a tower

Time (s)Acc

eler

atio

n

(cm

/s)

Response rotation of an anchorage

Anchorage

How frequently does the anchorage uplift?

Tim

e (s

)

Left edge Right edge

Tim

e (s

)

AnchorageSoft rock yields

Left edge Right edge

Soft rock does not yield

Peak uplift 0.114m 0.118m

0.138m 0.144m

Uplift & separation and contact of a foundation with the underlying ground

Static Equilibrium

Fsv Ground

Start to Uplift

Fθ

BMV

Uplifted at the Left Edge

Fθ

BMV

x

Separation

N increases

N decreases

Rotation

Moment

Nonlinear Interaction between 2 plastic hinges; (1) Column Plastic Hinge and (2) Foundation Nonlinear Behavior

Rocking response of a foundation

Plastic deformation of a column

Plastic HingeAnalytical Idealization

Vertical Displacement

Subgrade Reaction

Compression

Tension

Uplift of Foundation

Fsv

4.5m

12m

7m

2m6.5m

N-Value500

Sand

Gravels

Bridge Analyzed Designed based on the static analysis assuming 0.2g response acceleration

Deck Response under Longitudinal and Vertical Excitation

Rocking Isolation

-0.3

0

0.3

0 10 20 30Dis

plac

emen

t (m

)

Ti me( s)

Deck Displacement

-10

0

10

Acc

eler

atio

n (m

/s2 )

Deck Acceleration

Conventional Analysis

-0.3

0

0.3

Dis

plac

emen

t (m

)

DeckDisplacement

-20

-10

0

10

20

Acc

eler

atio

n (m

/s2 )

Deck Acceleration

-0.01 0 0.01

Mom

ent

(MN

m)

Curvature(1/m)

10

-10

0

-0.01 0 0.01M

om

ent

(MN

m)

Curvature(1/m)

10

-10

0

Column Curvature at the Plastic Hinge under Longitudinal and Vertical ExcitationConventional Analysis Rocking Isolation

How Large Uplift occur at the Footing?

Uplift

Reaction of Underlying Ground

B A

Rea

ctio

n （Ｍ

Ｎ)

10

-1

Footing

LGTR

Uplif

t (m

)

0.15

0

0.15

Ａ-side

Ｂ-side

Conventional Analysis

Rocking Isolation

t=5.0t=6.0

Time (s)0 10 20

Acc

eler

atio

n

(m/s

ec2

)

ＮＳ

ＥＷ

ＵＤ

Acc

eler

atio

n

(m/s

ec2

)Acc

eler

atio

n

(m/s

ec2

)

-10

0

10-10

0

10-10

0

10t=0.0

Time (s)0 10 20

Acc

eler

atio

n

(m/s

ec2

)

ＥＷ

ＵＤ

Acc

eler

atio

n

(m/s

ec2

)Acc

eler

atio

n

(m/s

ec2

)

-10

0

10-10

0

10-10

0

10t=4.0t=4.5t=5.5

Longitudinal

Tra

nsv

erse

Uplift of the Footing from the Underlying Ground

Reaction Force of the Underlying Ground at Corners increases under Bilateral Excitation

LongitudinalTransverse

Bi-Lateral Tri-Directional

-0.3

0

0.3

0 10 20 30Dis

plac

emen

t (m

)

Ti me( s)

Deck Displacement

-10

0

10

Acc

eler

atio

n (m

/s2 )

Deck Acceleration

-0.3

0

0.3

0 10 20 30Dis

plac

emen

t (m

)

Ti me( s)

Deck Displacement

Seismic Response under 3 Directional Excitation

-10

0

10

Acc

eler

atio

n (m

/s2 )

Deck Acceleration

-120000

-80000

-40000

0

40000

80000

-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015

Rotation (rad)

Mom

ent (

kNm

)

Moment

Rotation Vertical Displacement

Subgrade reaction

Compression

TensionFsv

Why do we have an isolation effect by the foundation rocking no matter how we assume the elastic soil spring?

There is no energy dissipation in the soil spring if we assume the elastic behavior

Amplitude dependent period shift

-120000

-80000

-40000

0

40000

80000

-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015

Rotation (rad)

Mom

ent (

kNm

)

Moment

Rotation

Why do we have “hysteretic-like” moment vs. curvature relation no matter how we assume the elastic soil spring?

Moment vs. rotation relation depends on the vertical force, and this results in “hysteretic-like” relation under variation of the vertical force.

N increases

N decreases

Rotation

Moment

Factors which contribute to the energy dissipation of a foundation during rocking response

Nonlinear soil behavior around a foundation (nonlinearity of soils, yield of bearing capacity, sliding & slip, etc)

Energy dissipation due to pounding of the footing to the underlying ground

Radiational damping

…

Deck

Column

FootingBall Bearings

Rubber Block Shake Table

Verification of Seismic Rocking Isolation by a Shake Table Experiment

Experimental Model

Deck

Column

Footing

Ground (Rubber Block)

Shake Table

Excitation of Model Foundation under Niigata-Chuetsu Ground Motion

Correlation of the Experimental Response by Analysis

Deck

Column

Uplift

- 202468

1 0

5 1 0 1 5 2 0 2 5Dis

plac

emen

t (m

m)

t im e ( s )

Uplift of Footing

-6 0

-3 0

0

3 0

6 0

10 1 5 2 0 25Dis

plac

emen

t (m

m)

t im e (s)

Deck Displacement

AnalysisExperiment

Implementation of Rocking Isolation to Analysis of a Whole Bridge

200m

Overburd en Soil

Backsoils

+

Idealization of Interaction between Abutment and Backsoils

δ

PLongitudinal P

δ

Transverse and Vertical

A1 A2P1 P2 P3 P4

Idealization of Target Bridge

Response of Target Bridge under JMA Kobe Ground Motion

Response of P2 under JMA Kobe Ground Motion

The acceleration at the deck Deck Acceleration at P2

-20

-10

0

10

20

Acc

eler

atio

n (m

/s2 )

Longitudinal

-10

0

10

20

0 10 20

Acc

eler

atio

n (m

/s2 )

Time (s)

Vertical

-20

-10

0

10

20

0 10 20Time (s)

Transverse

Conventional Rocking Isolation

P2

Deck Displacement at P2

-0.2

-0.1

0

0.1

0.2

Dis

plac

emen

t(m

)

Longitudinal

Conventional Rocking Isolation

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 10 20Time (s)

Transverse

-0.05

0

0.05

0 10 20Dis

plac

emen

t(m

)

Time (s)

Vertical

P2

-0.2 0 0.2-300

-150

0

150

300

Rea

ctio

n Fo

rce

(kN

)

Displacement (m)

Abutment and Backsoils Interaction in the Longitudinal Direction

Conventional

-0.2 0 0.2-300

-150

0

150

300

Rea

ctio

n Fo

rce

(kN

)Displacement (m)

Rocking Isolation

-0.002 0 0.002

Mom

ent (

MN

m)

Curvature (1/m)

50

-50

0

Longitudinal

Curvature at the Plastic Hinge of P2Conventional

-0.002 0 0.002

Mom

ent (

MN

m)

Curvature (1/m)

200

-200

0

Transverse

-0.002 0 0.002

Mom

ent (

MN

m)

Curvature (1/m)

200

-200

0

Transverse

-0.002 0 0.002

Mom

ent (

MN

m)

Curvature (1/m)

50

-50

0

Longitudinal

Rocking Isolation

Effect of Yield of the Underlying Ground (0.5MPa)

Stress vs. vertical displacement

Vertical displacementVertical stress

ConclusionsWhen separation of a footing from the

underlying ground due to rocking response is included in analysis, the plastic deformation of a column significantly decreases as a result of softening of the moment vs. rotation hysteresis of the footing.

If the underlying ground yields, it enhances the effect of rocking isolation, however it increases the deck response displacement and it can result in residual drift.

Bridge response acceleration decreases under the seismic rocking isolation, however bridge response displacement increases.

Kawashima, K., Unjoh, S. and Shimizu, H.: Analysis of rocking vibration of rigid foundations, Proc. 8th US-Japan Bridge Workshopn, Panel on Wind & Seismic Effects, UJNR, Chicago, USA, pp. 3-17, 1992

Kawashima, K., Unjoh, S., Shimizu, H. and Mukai, H.: Analytical method of seismic rocking response of a rigid foundation considering the response of superstructure, Journal of Civil Engineering, Vol. 36, No. 2, pp. 42-36, 1994

Kawashima, K. and Hosoiri, K.: Rocking response of bridge columns on direct foundation, Proc. Fib-Symposium, Concrete structures in seismic region, Paper No. 118 (CD-ROM), Athens, 2003

Mergos, P. E., and Kawashima, K.: Rocking isolation of a typical bridge pier on spread foundation, Journal of Earthquake Engineering, Vol. 9, Special Issue 2, pp. 395-414, 2005

Sakellaraki, D. and Kawashima, K.: Effectiveness of seismic rocking isolation of bridges based on shake table test, First European Conference on Earthquake engineering and Seismology, Paper No. 364, pp. 1-10, Geneva, Switzerland, 2006

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