1

Rocking Seismic Isolation of Bridges Supported by Spread Foundation

基礎ロッキング免震

Kazuhiko KawashimaTokyo Institute of Technology

Requirements of Foundations in Seismic Design基礎の耐震設計の要件

Bearing capacity耐力

Sliding渇動

Rocking転倒

Static Seismic Design

Dynamic Response

Sliding + Rocking

Rocking + Jump

Requirements for Rocking Responsein the Static Design静的な転倒照査

aB eVMe <=

⎩⎨⎧=

6/3/

ll

ea

Eccentricity偏心率

Allowable Eccentricity

Static

Static+Seismic

Bearing Capacity耐力

aB q

lbM

lbVq <+= 2max

6

eEccentricity

l

V

bmaxq

BM

Akashi Strait BridgeThe World Longest Bridge

In the static design, overturning was the major factor for sizing those foundations

Is it true that such a large foundation overturns under a seismic excitation??

MassNatural periodFrequency content of a ground motion

Overturning of Foundation-Tower System of Akashi Straight Bridge明石海峡大橋の耐震設計

Static Analysis on Overturning of Foundation-Tower System was eliminated from seismic design

This is because static overturning analysis is unrealistic

Decision of design was made based on nonlinear dynamic response analysis and a preliminary static design based on critical velocity which results in overturning

2

Rion Antirion Bridge, Greece

Courtesy of Dr. Alain Pecker

Seismic Rocking Isolation

Concept of Rocking Isolation of RionAnti-Rion Bridge

Fault dislocation as large as 2 m is anticipated although the location of fault is not known.

Rocking isolation reduces bridge response.

Rion Antirion Bridge

Requirements for Rocking Responsein the Static Design

Start to Uplift

Fθ

BMV

Static Equilibrium

Fsv Ground

Uplifted at the Left

Fθ

BMV

x

Separation

Nonlinear Interaction between a Column Plastic Hinge and a Foundation

Plastic deformation of a column

Rocking response of a foundation

3

Plastic Hinge

Vertical Displacement

Subgrade Reaction

Compression

Tension

Uplift of Foundation

Analytical Idealization

Fsv 4.5m

12m

7m

2m6.5m

N-Value500

Sand

Gravels

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

SA

(m/s

ec2

)

Ground Accelerations Subjected to Bridge

JMA Kobe (NS)

Takatori Station (NS)

50

0.5

1.5

1.0

0

Response Displacement

Response Acceleration

0

10

20

30

50Natural Period (s)

Time (s)0 10 20

-10

0

-10

SD

(m/s

ec2

)

Natural Period (s)

Acc

eler

ation

(m/s

ec2

)

0 10 20-10

0

-10

Acc

eler

ation

(m/s

ec2

)

Time (s)

1995 Kobe, Japan earthquake

-10-505

10

Acc

eler

atio

n (m

/s2 )

-10-505

10

Acc

eler

atio

n (m

/s2 )

-0.3

0

0.3

Dis

pl(m

)-0.01

00.01

Dis

pl (m

)

-0.010

0.01

0 10 20 30

Rot

atio

n

Time (sec)

(rad

)

Seismic Response of the Bridge When Supported by Soil Springs Which Resist Tension一般の解析

Deck Acceleration

Footing Acceleration

Deck Displacement

Footing Displacement

Footing Rotation

ch

Fθ

pcθ

fhpL

Contribution of Footing Displacement and Column Displacement to Deck Response桁の応答変位には何が寄与するか？

FD uu =

)( fcF hh ++θ

)2

( pcpcL

h −+θ

Cfu+

Contribution of Footing Rotation to the Deck Displacement

)2

()( pcpccffcFFDL

huhhuu −++++= θθ

-0.01

0

0.01

0 10 20 30

Rot

atio

n

Time (sec)

(rad

)

Footing Rotation

Deck Displacement

ch Fθ

Fθ

pcθ

Contribution by Footing Rotation

fhpL

Du

-0.3

0

0.3

Dis

pl(m

)

4

Footing Rotation

Effect of the Uplift of Foundation基礎浮き上がりの影響

-0.3

0

0.3

Dis

pl(m

)

-0.3

0

0.3

Dis

pl(m

)

-0.02

0

0.02

0 10 20 30

Rot

atio

n

Time (sec)

(rad

) Footing Rotation

Deck DisplacementDeck Displacement

Underlying ground resists tension

Separations are allowedbetween footing and underlying ground

-0.02

0

0.02

0 10 20 30

Rot

atio

n

Time (sec)

(rad

)

Uplift of the Foundation from the Underlying Ground基礎はどれだけ浮き上

がるか？

-0.1

0

0.1

0 10 20 30

Dis

pl (m

)

Uplift

Downward

Time (s)

UpliftVertical Reaction

-5

0

0 10 20 30Ver

tical

Rea

ctio

n(M

N)

Time (s)

0

10

20

Tim

e (s

)

Distance (m)-3.25 3.250

Separations between the Foundation andthe Underlying Ground基礎の浮き上がり量の時間履歴

Peak Subgrade Reaction under the Footing基礎底面の最大反力

-4

-2

0

Max

For

ce

Distanance from the Center of the Footing (m)

0-3.25 3.25

(MPa

)

mm

Effect of local softening

Effect of yield of the underlying ground

Moment vs. Rotation Relation of the Foundation

∫ ⋅= 2/ 2* )(lX svF dxxxkK θ

∫ ⋅= −2/2/

2)(ll svF dxxxkK θ

)(xksv

x

l )(xksv

x

l

*Xx =

Underlying ground resists tension

Separations are allowedbetween the footing and the underlying ground

Moment vs. Rotation of the Footing曲げモーメント～回転角の履歴

-60

0

60

-0.02 0 0.02

Mom

ent (

MN

m)

Rotation (rad)

)(xksv

x

)(xksv

x

-60

0

60

-0.02 -0.01 0 0.01 0.02

Mom

ent (

MN

m)

Rotation (rad)

5

Column and Foundation Interaction

-40

0

40

-0.02 0 0.02

Mom

ent (

MN

m)

Curvature (1/m)

-40

0

40

-0.02 0 0.02M

omen

t (M

Nm

)Curvature (1/m)

-60

0

60

-0.02 0 0.02Rotation (rad)

Mom

ent (

MN

m)

-60

0

60

-0.02 0 0.02Rotation (rad)

Mom

ent (

MN

m)

Underlying ground resists tension

Separations of the footing from the underlying ground

-10

0

10

20

0 10 20 30Acc

eler

atio

n (m

/s2 )

Time (s)

Collision between the Footing and the Underlying Ground基礎底面と地

盤表面には衝突が起こる

-10

0

10

20

30

40

0 10 20 30

Acc

eler

atio

n (m

/s2 )

Time (s)

-10

0

10

20

0 10 20 30Acc

eler

atio

n (m

/s2 )

Time (s)

Effect of Bilateral Excitation２方向

載荷の影響Moment vs. Rotation Hysteresis of the Foundation

Effect of Yield of Underlying Ground基礎底面地盤が降伏すると、どうなるか？

Vertical reaction

Vertical displacement vs. stress Vertical displacement