Rocking Seismic Isolation of Bridges Supported by Direct Foundations
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1 Caltrans-PEER Seismic Research Seminar Sacramento, CA, USA Rocking Seismic Isolation of Bridges Supported by Direct Foundations June 8, 29 Kazuhiko Kawashima Tokyo Institute of Technology
2 Requirements in the Overturning Based on Static Analysis Eccentricity M B e = < e a V Size effect V is not included in the conventional M static analysis B Allowable Eccentricity As long as the shape and mass density are the same, a foundation can overturn l /3 in Static the conventional static analysis e a = no matter how the foundation l / 6 Static Eccentricity eis extremely large +Seismic Bearing Capacity l b q max V 6M q max = + < lb lb B q 2 a
3 Akashi Strait Bridge The World Longest Bridge In the static design, overturning was the major factor for sizing of those foundations based on the conventional analysis
4 Does such a 1m tall foundation overturn under seismic excitation?? Mass Natural period Frequency content of a ground motion
5 Shake Table Experiment on the Effect of Size & Mass for Overturning of Rigid Foundations Geometrical scale 1..66m m 2.5.4m.6m 1m 1.5m Mass.2m m=139kg.33m m=579kg.5m m=1452kg Kawashima & Unjoh (1992)
6 Shake Table Experiment on the Effect of Size & Mass for Overturning of Rigid Foundations Public Works Research Institute Kawashima & Unjoh (1992)
7 How does the rocking of rigid foundations depend on the size? Rotation (rad) m 1m Table Acceleration (g).6m
8 Analytical Idealization for Rocking and Sliding Response of a Rigid Foundation
9 Analytical Correlation on the Rocking Response of a 1.5m Tall Rigid Foundation Experimental Analytical
10 Seismic Response Analysis of Kurushima Straight Bridge Kawashima et al (1994)
11 Seismic Response Analysis of Anchorages, Towers and Superstructure System of Kurushima Straight Bridge Base Vertical Springs Tension m Settlement Uplift 35m 45m Yield Compression Lateral Sliding at Base Lateral Force Lateral Disp. Kawashima & Unjoh (1994) Side Soils Lateral force Tension Separation Relative Disp. Yield Compression
12 Peak Responses Response displacement at the top of a tower Displacement (cm) Soft rock does not yield Time (s) Displacement (cm) Response rotation of an anchorage Soft rock yields Time (s) Acceleration (cm/s) Time (s) Response displacement at the top of a tower cceleration cm/s) Time (s) Response rotation of an anchorage
13 How frequently does the anchorage uplift? Soft rock does not yield Left edge Anchorage Right edge Soft rock yields Anchorage Left edge Right edge Peak uplift.114m.118m Time (s).138m.144m Time (s)
14 Uplift & separation and contact of a foundation with the underlying ground Static Equilibrium Start to Uplift V M B vfs Ground θ F Uplifted at the Left Edge V M B x θ F Moment N increases N decreases Rotation Separation
15 Nonlinear Interaction between 2 plastic hinges; (1) Column Plastic Hinge and (2) Foundation Nonlinear Behavior Plastic deformation of a column Rocking response of a foundation
16 Analytical Idealization Plastic Hinge Uplift of Foundation Subgrade Reaction v Fs Tension Compression Vertical Displacement
17 12m Bridge Analyzed Designed based on the static analysis assuming.2g response acceleration N-Value 5 4.5m 7m 2m 6.5m Sand Gravels
18 Deck Response under Longitudinal and Vertical Excitation Acceleration (m/s 2 ) Displacement (m) Conventional Analysis Deck Acceleration Deck Displacement Acceleration (m/s 2 ) Displacement (m) Rocking Isolation Deck Acceleration Deck Displacement
19 Column Curvature at the Plastic Hinge under Longitudinal and Vertical Excitation Conventional Analysis Rocking Isolation Moment (MNm) Curvature(1/m) Moment (MNm) Curvature(1/m)
20 How Large Uplift occur at the Footing? Conventional Analysis Rocking Isolation Uplift (m).15 Reaction ) side -side Uplift Reaction of Underlying Ground TR Footing B LG A
21 Uplift of the Footing from the Underlying Ground t=. t=4. t=4.5 t=5. t=5.5 t=6. 1 Acceleration (m/sec 2 ) Acceleration (m/sec 2 ) Longitudinal Acceleration (m/sec 2 ) Transverse
22 Reaction Force of the Underlying Ground at Corners increases under Bilateral Excitation Transverse Longitudinal
23 Acceleration (m/s 2 ) Seismic Response under 3 Directional Excitation 1-1 Bi-Lateral Deck Acceleration Tri-Directional Acceleration (m/s 2 ) 1-1 Deck Acceleration Displacement (m).3 Deck Displacement Displacement (m).3 Deck Displacement
24 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 Moment (knm) Rotation (rad) Moment Rotation Subgrade reaction v Fs Tension Vertical Displacement Compression
25 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 hystereticlike relation under variation of the vertical force. 8 Moment Moment N increases Moment (knm) Rotation N decreases Rotation -12 Rotation (rad)
26 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
27 Verification of Seismic Rocking Isolation by a Shake Table Experiment Deck Column Ball Bearings Footing Rubber Block Shake Table
28 Experimental Model Deck Column Shake Table Footing Ground (Rubber Block)
29 Excitation of Model Foundation under Niigata-Chuetsu Ground Motion
30 Correlation of the Experimental Response by Analysis Displacement (mm) Displacement (mm) Deck Displacement Uplift of Footing Experiment Analysis time (s) tim e ( s ) Uplift Deck Column
31 Implementation of Rocking Isolation to Analysis of a Whole Bridge 2m
32 Idealization of Interaction between Abutment and Backsoils Backsoils Overburd en Soil + Longitudinal P Transverse and Vertical P
33 Idealization of Target Bridge A1 P1 P2 P3 P4 A2
34 Response of Target Bridge under JMA Kobe Ground Motion
35 Response of P2 under JMA Kobe Ground Motion
36 Acceleration (m/s 2 ) Acceleration (m/s 2 ) Deck Acceleration at P2 The acceleration at the deck Conventional Longitudinal Vertical Time (s) Rocking Isolation Transverse Time (s) P2
37 Deck Displacement at P2 Displacement (m) Displacement (m) Conventional Longitudinal Vertical Time (s) Rocking Isolation Transverse Time (s) P2
38 Abutment and Backsoils Interaction in the Longitudinal Direction Reaction Force (kn) Conventional Displacement (m) Rocking Isolation Reaction Force (kn) Displacement (m)
39 Curvature at the Plastic Hinge of P2 Moment (MNm) Moment (MNm) 5 Conventional Longitudinal Curvature (1/m) 2 Transverse Curvature (1/m) Moment (MNm) Moment (MNm) 5 Rocking Isolation Curvature (1/m) 2 Longitudinal Transverse Curvature (1/m)
40 Effect of Yield of the Underlying Ground (.5MPa) Vertical stress Vertical displacement Stress vs. vertical displacement
41 Conclusions When 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.
42 Related publications 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 , 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, 23 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 , 25 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. 1-1, Geneva, Switzerland, 26
43 Thank you for your kind attention.
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