Hybrid Experimental Analysis of Semi-active Rocking Wall Systems K.J. Mulligan, M. Fougere, J.B. Mander, J.G. Chase, G. Danton,

R.B ElliottDepartments of Mechanical and Civil Engineering, University of

Canterbury, Christchurch

B.L DeamLeicester Steven EQC Lecturer in Civil Engineering, University

of Canterbury, Christchurch

Sponsor: EQC Research Grant # 03/497

Why use Semi-active system?

• Provide a broad range of control

- respond to changes in structural behaviour

• Provide supplemental damping for all rocking cycles, not only subsequently larger cycles

• Provide resistive forces when most benificial to system

Device DynamicsValve

PistonCylinder

Two chambered design:

-Utilises each side independently

-Resetting can occur at any prescribed point of piston displacement

-Portions of motion may dictate both valves to be open

Valve and valve controller

ResetableDevice

Test Machine

TestJig

Rocking Wall Dynamics

Fd

Wr Fd

O

b

h

Wr

Roof

R

OO’

F(t)2HBFMgBMgHθθI d

Hybrid TestingPhysical system

Measured Force and Displacement

Displacement command

Valve Control

Virtual System

Hybrid Testing Procedure

• Wall model calculations determine rotation of wall depending on applied forces

• Rotation of the wall converted into linear displacement for actuator, signal sent to the dynamic test rig

• Valve control determined for current time step • Dynamic test rig supplies displacement to

physical semi-active device• Force developed in device returned to virtual

system and used in subsequent time-step calculation.

Analysis Procedure

• Normalised to uncontrolled case

• Presented as:

-peak reduction factors, R.F

-equivalent viscous damping, ξ

• Suite of ground motions used to analyse efficacy of semi-active system to a variety possible events.

Results0 5 10 15 20 25 30

-1.5

-1

-0.5

0

0.5

1

1.5

2

time (sec)

m/s

2

Imperial Valley (1979)

0 5 10 15 20 25 30-0.03

-0.02

-0.01

0

0.01

0.02

0.03

time (sec)

theta

(rad)

uncontrolled

controlled

Rotation about point 0’

Rotation about point 0 Uncontrolled

Controlled

Device Reponse

-0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-1500

-1000

-500

0

500

1000

1500

Act

ua

tor

Fo

rce

(N)

linear displacement (m)Displacement (m)

Dev

ice

F

orc

e (

N)

Change in Structural Period

15 20 25 30 35-3

-2

-1

0

1

2

3

time (sec)

m/s

2

Loma Prieta, Gilroy

15 20 25 30 35-0.015

-0.01

-0.005

0

0.005

0.01

0.015

time (sec)

thet

a (

rad

)

rocking towardscentre position

rocking away fromcentre position

uncontrolled

controlled

subsequent cycles are larger for controlled casecompared to uncontrolled case

large pulse

Comparison with Analytical Model

0 5 10 15 20-5

0

5

time (sec)

m/s2

Loma Prieta, Gilroy

0 5 10 15 20-0.02

0

0.02

time (sec)

theta

(ra

d)

0 5 10 15 20-0.02

0

0.02

time (sec)

theta

(ra

d)

a) hybrid result

b) analytical result

Full Scale Rocking Wall

Metric K=1000 kN/m K = 5000 kN/m

K= 10000kN/m

R.Fgeometric mean

1.01 1.14 1.21

R.Fmultiplicative variance

1.10 1.27 1.43

ξgeometric mean

5.11 5.47 7.12

ξmultiplicative variance

1.15 2.13 2.30

Summary

• Significantly reduce peak rotations of seismically excited rocking wall systems

• Provide additional restoring forces to the system when it is most benifical

• Model accurately predicts test results allowing scaling to a variety of applications

• Results are dependent on ground motion, hence important to examine using a suite of ground motions