Response Modification of Urban Infrastructure. 7 Chapter 7 Rocking Isolation of Foundations. Kazuhiko Kawashima Tokyo Institute of Technology

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1 Response Modification of Urban Infrastructure 7 Chapter 7 Rocking Isolation of Foundations Kazuhiko Kawashima Tokyo Institute of Technology

2 Requirements of Foundations in Seismic Design Static Seismic Design Bearing capacity Sliding Rocking Dynamic Response Sliding + Rocking Rocking + Jump

3 Requirements for Rocking Response in the Static Design M B V Eccentricity e l b q max Eccentricity M B e = < e a V Allowable Eccentricity e a = l l /3 / 6 Static Static +Seismic Bearing Capacity V 6M q max = + < lb lb B q 2 a

4 Akashi Strait Bridge The World Longest Bridge In the static design, overturning was the major factor for sizing those foundations

5 Is it true that such a large foundation overturns under a seismic excitation?? Mass Natural period Frequency content of a ground motion

6 Overturning of Foundation-Tower System of Akashi Straight Bridge 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

7 Shake Table verification on Overturning of 3 Blocks in 1989 Geometrical scale m.75m 2.5.4m.6m.2m 1m.33m 1.5m.5m Kawashima & Unjoh (1991)

8 Shake Table Verification on Overturning of 3 Blocks Public Works Research Institute Kawashima & Unjoh (1991)

9 How did a rigid block rotation depending on the size? Rotation (rad) m 1m Acceleration Amplitude (g).6m

10 Analytical Idealization of 2 Anchorage of a Suspension Bridge Base Vertical Springs Tension m Settlement Uplift 35m 45m Yield Compression Lateral Sliding at Base Lateral Force Kawashima & Unjoh (1991) Lateral Disp. Side Soils Lateral force Tension Separation Relative Disp. Yield Compression

11 Analytical Idealization of a tower, cables, and a rigid footing Kawashima et al (1994)

12 Seismic Rocking Isolation Rion Antirion Bridge, Greece Courtesy of Dr. Alain Pecker

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14 Concept of Rocking Isolation of Rion Anti-Rion Bridge Fault dislocation as large as 2 m is anticipated although the location of fault is not known. Rocking isolation reduces bridge response.

15 Rion Antirion Bridge

16 Requirements for Rocking Response in the Static Design Static Equilibrium Start to Uplift V vfs M B Ground Uplifted at the Left V M B θ F Separation x θ F

17 Nonlinear Interaction between a Column Plastic Hinge and a Foundation Plastic deformation of a column Rocking response of a foundation

18 Analytical Idealization Plastic Hinge Uplift of Foundation Subgrade Reaction v Fs Tension Compression Vertical Displacement

19 12m Bridge Analyzed Designed based on the static design method assuming.2g response acceleration N-Value 5 4.5m 7m 2m 6.5m Sand Gravels

20 Ground Accelerations Subjected to Bridge 1995 Kobe, Japan earthquake Acceleration (m/sec 2 ) Acceleration (m/sec 2 ) -1-1 JMA Kobe (NS) 1 2 Time (s) Takatori Station (NS) Time (s) Response Acceleration 3 JMA Kobe 2 Takatori Station 1 S A (m/sec 2 ) S D (m/sec 2 ) 5 Natural Period (s) Response Displacement 1.5 JMA Kobe 1. Takatori Station.5 5 Natural Period (s)

21 Acceleration (m/s 2 ) Acceleration (m/s 2 ) Seismic Response of the Bridge When Supported by Soil Springs Which Resist Tension Deck Acceleration Footing Acceleration Displ(m) Displ (m).3deck Displacement -.3 Footing Displacement Footing Rotation.1 Rotation (rad) Time (sec)

22 Contribution of Footing Displacement and Column Displacement to Deck Response h c h f θ F u F θ pc L p u Cf θ pc u D = u F +θf ( h c + h f ) + u Cf Lp +θ pc( hc ) 2 : displacement due to column (elastic) flexural deformation : rotation due to plastic deformation at the plastic hinge

23 Contribution of Footing Rotation to the Deck Displacement Displ(m).3 Deck Displacement u D Contribution by Footing Rotation h c h f u θ pc L p θ F D = u + θ ( h + h ) + u + θ F Rotation (rad) F c f Footing Rotation Time (sec) cf pc ( h c θ F L 2 p )

24 Effect of the Uplift of Foundation Underlying ground resists tension.3 Deck Displacement Separations are allowed between footing and underlying ground Deck Displacement.3 Displ(m) Displ(m) Rotation (rad) Footing Rotation Time (sec) Rotation (rad) Footing Rotation Time (sec)

25 Uplift of the Foundation from the Underlying Ground Uplift Vertical Reaction Displ (m).1 Uplift Downward Time (s) Vertical Reaction (MN) Time (s)

26 Separations between the Foundation and the Underlying Ground Time (s) Distance (m)

27 Peak Subgrade Reaction under the Footing Max Force (MPa) -2-4 Distanance from the Center of the Footing (m) -3.25m 3.25 m Effect of local softening Effect of yield of the underlying ground

28 Moment vs. Rotation Relation of the Foundation Underlying ground resists tension Separations are allowed between the footing and the underlying ground l / 2 KF θ = l / 2ksv ( l x k sv (x) x) x 2 dx KF θ x = X * l x l / 2 2 x X = k ( ) * sv x k sv (x) dx

29 Verification of Seismic Rocking Isolation by Shake Table Test Deck Column Ball Bearings Footing Rubber Block Shake Table

30 Experimental Model Deck Column Shake Table Footing Ground (Rubber Block)

31 Excitation of Model Foundation under a Ground Acceleration Recorded during the 27 M6.8 Niigata Chuetsu Earthquake

32 Correlation of the Experimental Response by Analysis Displacement (mm) Displacement (mm) Deck Displacement Uplift of Footing Experiment Analysis tim e (s) tim e ( s ) Uplift Deck Column

33 Moment vs. Rotation of the Footing x k sv (x) x k sv (x) Moment (MNm) Rotation (rad) Moment (MNm) Rotation (rad)

34 Moment (MNm) Moment (MNm) Column and Foundation Interaction Underlying ground resists tension Curvature (1/m) Rotation (rad) Separations of the footing from the underlying ground Moment (MNm) Moment (MNm) Curvature (1/m) Rotation (rad)

35 Acceleration (m/s 2 ) Collision between the Footing and the Underlying Ground Time (s) Acceleration (m/s 2 ) Acceleration (m/s 2 ) Time (s) Time (s)

36 Uplift of the Footing from the Underlying Ground t=. 1 t=4. t=4.5 t=5. t=5.5 t=6. Acceleration (m/sec 2 ) Acceleration (m/sec 2 ) Time (s) Longitudinal Acceleration (m/sec 2 ) Transverse

37 Increase of Reaction Force of the Underlying Ground at Corners D B Transverse Longitudinal A C Transverse Longitudinal

38 Effect of Bilateral Excitation Moment vs. Rotation Hysteresis of the Foundation Mergos, P.E. and Kawashima, K.: Rocking Isolation of a typical Bridge pier on Spread Foundation, Journal of Earthquake Engineering, 9(2), , 25

39 Effect of Yield of Underlying Ground Vertical displacement vs. stress Vertical displacement Vertical reaction