Real-Time Hybrid Testing of Laminated Rubber Dampers for Seismic Retrofit of Bridges

Akira Igarashi, Fernando Sanchez, Kenta Fujii Kyoto University

Hirokazu Iemura Kinki Polytechnic College

and

Akihiro Toyooka Railway Technical Research Institute

Background

  Seismic Retrofit & Upgrading of existing bridges   Mainly focused on bridges designed before 1995

(Elastic design, Level-2 Earthquakes were not considered)

  Long-span bridges /w center span longer than 300m: more than 30 bridges

　 One of the retrofit measures ⇒Application of Seismic Dampers 　　　　　　　 （Energy Dissipation

Devices）

Retrofit Project: Higashi Kobe Bridge

_______________________________________________________ Type 3 span continuous cable stayed bridge _______________________________________________________________ Type of Highway Group 2 Class 1 _______________________________________________________________ Length 200+485+200=885m _______________________________________________________________ Width 13.5 x 2 decks _______________________________________________________________ Main Tower High 146.5m _______________________________________________________________ Main Girder Warren Truss (High 9m) _______________________________________________________________ Cables Harp type (12 parallel) _______________________________________________________________

Girder 14,100 Main tower 7,900

Weight Cables 1,300 Total 27,400 Abutment 1,700 Others 2,400 _______________________________________________________________

Design spectrum (orig.) Updated Interplate Eq. spectrum

Updated Intraplate Eq. spectrum

Longitudinal period

Insufficient seismic performance against interplate earthquakes

Background

  Issues of seismic dampers for long-span bridges   Large desplecements of decks & girders ⇒ Need

of Large Displacement Stroke Capacity   Massive Structure ⇒ Need of High damping force

capacity   Cost requirements in manufacturing, installation

work, maintenance

Conventional Dampers ＜Mechanism> ＜Load-Displ.＞

Friction type

Viscous type

Elastoplastic type

＜Problems＞

・Reliability & stability of axial force and damping force ・Residual displ.

・Size

・Cost, Maintenance

・Relatively small deformation⇒Large size for large stroke

・Residual Displ. Steel bar

Oil Piston Orifice

Chamber Chamber

Laminated Ｒubber Damper

  Use of energy dissipation capacity of High Damping Rubber (HDR) in shear deformation

  HDR: advantage in known performance via many test results, practical application to seismic isolators as laminated r. aseemblies

  Mechanism & principle: advantage in economy of manufacturing and maintenance compared with other conventional types of dampers

  Axial force not required: larger strain range and rubber thickness than the case of seismic isolators ⇒Large stroke capacity

High Damping Rubber (laminated rubber assemblies)

Displ.

Shear

Shear Displ.

Laminated Rubber Dampers & Implementation for a Cable Stayed Bridge

Laminated Rubber Assembly

Damper cable

Girder

Main Tower

Verification Testing Program

  Trial Manufacturing of a scaled Laminated Rubber Damper model

  Verification of restoring force characteristics   Experimental validation of performance as a

seismic damper for bridges

1. Cyclic loading tests

2. Hybrid simulation tests

3. Real-time hybrid simulation tests

Test Setup

Actuator’s capacity   Stroke ・・・±２５０[mm]   Load ・・・４００[ｋN]

Specimen Strong wall Reaction

frame Dynamic Actuator

2359ｍｍ 2305ｍｍ

Load cell

<Plan>

Rigid floor

＜Elevation＞

1401ｍｍ

Test System

Laminated Rubber Damper Model

Laminated high damping rubber assemblies

Direction of Loading

Steel plate

No. of Laminated Rubber blocks

2

Rubber dimensions 150mm×150mm

Rubber layer thickness

7mm×5 layers

Shear Modulus 1.2 N/mm class

Cyclic Loading Test

  Objectives   Energy dissipation performance of laminated

rubber assemblies without axial loads   Strain & strain rate dependence of equivalent

stiffness and equivalent damping ratio

  Loading condition   Unidirectional   Sinusoidal displacement 11 cycles   Frequency：0.1Hz   Amplitude： strain of 25%,

50%，75%，100%，150%，200%

Test Result ＜Shear strain-load　hysteresis loop＞

Influence of repeated cycles of loading can be observed

-80 -60 -40 -20 0 20 40 60 80

200

150

100

50

0

-50

-100

-150

Displ. (mm)

Load

(kN)

100% 200%

Equivalent Stiffness & Damping

  Equivalent Damping：0.16～0.2   Although decrease of equivalent stiffness and equivalent

damping ratio for larger shear strain levels can be seen, the test result indicates LR damper’s stable behavior and efficient performance as a energy dissipation device.

0 0.5 1 1.5 2

4

3

2

1

Shear strain

Keq

(kN/m

m)

0 0.5 1 1.5 2

0.22

0.2

0.18

0.16

0.14

Shear strain

heq

Influence of Loading Rate

  Decrease of equivalent damping ratio for higher loading rate

Hybrid Simulation Test

  Objective：Validation of LR damper’s response reduction performance as a energy dissipation device applied to a real bridge structure

  Loading rate：Real time vs. conventional loading rate

  Similitude: considered to evaluate the performance of prototype structure based on the bahavior of the scaled model specimen

Concept of Hybrid Simulation Test System

Input seismic ground acceleration

AD DA

DSP system

Displ. Command signal

Servo Controller

Filter

measurement

Damper load

Recording Test Control

Test

Displ.

Control signal

Host PC

PCI bus 64 bit floating point DSP system

Chip: TMS320C6701 (167MHz)

Type ADM16-4 DAM16-4N In 4ch ‐

Out ‐ 4ch Resolution 16bit 16bit

Conversion Time 10 µ sec 1 µ sec Input/Output range ±1v and ±2.5v

±5v and ±10v ±5v and ±10v

Input/Output Interface AD/DA

DSP board system

Issues on Real-time Hybrid Simlation Test

  In the actual test due to the inherent delay in the response of the actuator and the delay in the data transfer between the computational hardware, the control signal is not properly achieved in real-time (Need of delay compensation).

  Most of the displacement-controlled approaches for delay compensation conventionally used are based on the extrapolation and interpolation of the actuator displacements

Real-time Implementation in this study

  The velocity-based loading developed by the authors was adopted for simple coding framework

  Time-slicing in a single step into substeps for computation (time integration) and continuous actuator movements.

d

t i i+1

Δt

v(i-1) v(i)

Δt

v(i+1)

i-1

d(i)

Actuator motion

Calculation and sending of target displacement to the actuator

Corrections and calculation of the final displacement, velocity and acceleration vectors

time 10@0.001=0.01

sec. Δt =0.01

Calculated command signal

time Sent command signal

Evaluation of Actuator Response Delay

  Actuator delay can be estimated as δ=0.030 sec

Assumed Structure：　Cable Stayed Bridge

442.5ｍ

Vane damper

Application of HDR dampers

Natural period: approx. 4 sec.

187.2ｍ

Natural Modes

  T1=4.3329 sec   Transverse

motion

  T2=2.4148sec   Lateral motion

1st mode

2nd mode

Assumed Damper Installation

  Dampers are effective in longitudinal modes, not hindered by the lateral & transverse modes

Reduced 3-DOF Model for Hybrid Simulation Tests

m2

k2

k1

k3

m1 m3 Vane

damper

HDR damper

Experimental substructure

x3 x1

m2 (tower 2) m3 (girder) m1 (tower 1)

x2

Scaling of LR damper specimen and prototype structure

Prototype

Specimen

Sdispl=5.7

Sload=28.1

Requirements： 　Max shear strain：250% 　max damper loads ：2000kN

Similitude： Sdispl＝Sspec height Sload=Sarea×No. of LR assemblies

25mm X 8 layers

6mm X 5 layers

Test result

Relative displ. (Girder-Tower)

LR Damper Hysteresis Loop

JMA Kobe （Hyogoken Nanbu Earthquake）

0 5 10 15 20 25

0.6 0.4 0.2

0 -0.2 -0.4 -0.6

Time (sec)

Dis

plac

emen

t (m

) w/o damper /w damper

-3 -2 -1 0 1 2

60 40 20 0

-20 -40 -60 -80

Displacement (cm)

Load

(kN

)

Test result　Maximum Response

Without damper With Damper

Relative Displ. Girder-Tower (m) 0.3579 0.1149

Relative Vel. (m/s) 1.0899 0.8123 Girder acceleration (m/

s2) 0.9842 1.6810

Factor of response reduction： Approx. 30.6% （relative disp.）

Real-time vs. Conventional loading

  Difference is considered to be due to the effect of the loading rates.   For conventional hybrid simulation tests, the restoring force characteristics

can be measured to be lower than the actual performance, which is the issue that can be avoided by the use of real-time tests.

Quasi-Static Hybrid Sim. Real-Time Hybrid Sim.

(a) Displacement response (b) Specimen hysteresis loop

Bending Moment Requirement Check

1,080,000(kN・m） ≦ Allowable

• 66-DOF numerical model • Push-over of the bridge girder to simulate maximum loading to the main towers

Conclusions (1)

  LR damper has been proposed as a new seismic energy dissipation device

  Laminated rubber assemblies without axial loads show considerably good energy dissipation performance

  In order to evaluate the behavior of LR dampers that can show strain rate dependence, a real-time hybrid loading test system was developed.

  The real-time hybrid experimental system was implemented using the concept of velocity-based loading control.

Conclusions (2)

  Real-time and conventional hybrid loading tests of LR dampers, simulating dynamic response of a long-span steel cable stayed bridge with the LR damper were conducted. Comparison shows the difference that reflects the loading rate effect on the LR damper specimen, suggesting the necessity of real-time testing in the evaluation of the performance of LR dampers.

  For the case of cable stayed bridge, the factor of response reduction by the application of LR damper is shown to be as much as 30.6%