Semi-Active Rocking Wall Systems
for Enhanced Seismic Energy
Dissipation
K.J. Mulligan, M. Fougere, J.B. Mander, J.G. Chase,
G. Danton, R.B Elliott
Departments of Mechanical and Civil Engineering, University of
Canterbury, Christchurch
B.L Deam
Leicester Steven EQC Lecturer in Earthquake Engineering,
University of Canterbury, Christchurch
Sponsor: EQC Research Grant # 03/497
Why Semi-active?
• Broad range of control
–
–
–
–
respond to changes in structural behaviour/response
Resistive forces when most beneficial due to added information from sensor(s)
significant added damping can be added to systems
guaranteed stability
• Supplemental damping for all rocking cycles, not only subsequently
larger cycles as with tendon or some other passive designs
• Relatively very simple to implement from design equations suitable
for use in standard design methods (see talk #2 Thursday 10:30-12:00,
Session Th10 Rm 226)
• Customised control of hysteresis loops (see same talk)

It’s all about providing effective, practicable, repeatable structural
response energy management
Simple Rocking Wall
Roof
Wr
Fd
Wr
Device
Better device
locations are
possible (?)
R
h
b
O’
O
O
Fd

I θ  MgHθ  MgB  Fd B  F(t)2H
Device
Valve
Cylinder
Valve and valve controller
Test
Jig
Resetable
Device
Piston
Two chambered design:
•
•
•
•
Utilises each side independently
Resetting can occur at any piston
displacement
Portions of motion may have both
valves open
Existing experimentally validated
models (linear and nonlinear)
Test
Machine
20-100kN devices using air
as the working fluid!
Semi-Active Rocking Wall
•
•
•
Resist motion away
Allow gravity and free
fall to dissipate max
energy (a 1-3 device)
A = area of extra
dissipated energy
Non-linear device
Wall starts to rock
Cc
Cc 
B
2H
Slope depends on
stiffness of semi-active
device
A
 max
Slope = -1
B
 tip 
2H
Pre-tensioned
Tendon “Flag”
Schematic (see
Mander et al)

Only 1 “flag” per tendon unless
the rocking angle increases
Method & Analysis
• Design with free vibration = initial tradeoff analysis:
– Peak reduction factors, R.F and equivalent viscous damping, ξ
– Several initial angles
• Normalise results to uncontrolled case for design over several
device stiffness values
– Approximately 6, 11, 16% effective added stiffness compared to uncontrolled
period of motion (1, 5, 10 kN/m devices)
• Analyse results with forced vibration:
– Same performance metrics (R.F. and ξ)
• Suite of ground motions used to analyse efficacy of semi-active
system to a realistic variety possible events
– Medium suite from SAC project as it has mix of near and far field events of “good
size”
– ‘Maximum events’ with 475 yr return period
Free Vibration
0.1
•
Device only restricts
motion away
0.08
Uncontrolled
0.06
•
Hence, initial slopes
to 0deg are the same
Non-linear impact on
wall period
Kact = 1000kN/m
0.04
theta (rad)
•
0.02
0
-0.02
•
Stiffer devices lead
to faster attenuation
-0.04
Kact = 5000kN/m
-0.06
•
However, less cycles
is less attenuation!
Kact = 10000kN/m
-0.08
0
Device begins to act only on first
cycle away from equilibrium
1
2
3
4
time (sec)
Less stiff devices lead to longer period due to
lesser effect on reducing amplitude
5
Free Vibration Summary
Initial angle
(degrees)
•
•
•
•
1000kN/m
5000kN/m
10000kN/m
R.F
ξ
R.F
ξ
R.F
ξ
1
1.00
5
1.02
5.22
1.03
5.45
3
1.11
6.64
1.39
11.53
1.64
16.72
5
1.15
7.19
1.55
14.83
1.89
23.14
Mean
(Geom.)
1.09
6.28
1.33
10.18
1.53
14.07
5kN/m or more (>10% of effective stiffness) shows significant effect
RFs are non-linear over stiffness
Added effective damping is significant (6-14%), minimum of 5%
All values rise as initial angle rises showing that longer stroke provides
increasing effect – as expected for a stiffness based damping device
theta (rad)
theta (rad)
theta (rad)
theta (rad)
2
ground motion m/s
Typical Seismic Response
2
•
0
-2
0
0.02
5
10
15
20
5
10
15
time (sec), Kact = 0
20
10
15
time (sec), Kact = 1000E3
20
K=0
0
-0.02
0
0.02
K = 1kN/m
0
-0.02
0
0.02
5
0
0.02
5
10
15
time (sec), Kact = 5000E3
20
10
15
time (sec), Kact = 10000E3
20
25
K = 10kN/m
0
5
30
Very stiff device has
almost no rocking
almost no
25 and thus 30
energy dissipation
from the rocking
system (good?)
0
-0.02
25
•
K = 5kN/m
0
-0.02
Initial rocking
unchanged in this
25
30
case
• Number of cycles
is reduced
• 25 Less enhancement
30
of rocking as at
10sec of K=0 case
30
Seismic Response
K=1000 kN/m
K = 5000 kN/m
K= 10000 kN/m
R.F geometric mean
1.01
1.14
1.21
R.F mult. variance
1.10
1.27
1.43
ξ geometric mean
5.11
5.47
7.12
ξ mult. variance
1.15
2.13
2.30
A geometric mean
2.54
5.55
3.94
A mult. variance
1.83
2.60
2.80
•
•
Similar results, however differences between devices are smaller
Area inside hysteresis curve (A) adds another dissipation metric based on
number of cycles and device stiffness
•
Variation is very high across the suite due to significant changes in period and
thus amplitude as device stiffness rises, as well as variation in records
Note that a less stiff devices oscillate more and thus may dissipate more
energy  A significant design tradeoff
•
Summary
•
Semi-Active rocking systems offer the opportunity for significant added
energy dissipation in a repeatable fashion using these devices
– Particularly applicable to joints with low inherent structural damping
– Thus, suitable for damage avoidance designs
•
Semi-Active rocking systems designed and analyzed, and the tradeoffs
presented in terms of standard structural design metrics of R.F. and
added viscous damping x
– Effects of devices are non-linear with device size (and likely placement)
– Performance metrics are characterised statistically over suites of ground motions to
account for realistic variation and a broad range of possible inputs
•
Outcomes are suitable for performance based design methods or
developing design equations similar to a spectral analysis approach.
•
Approach can be generalised to any similar design or system or device,
such as joints with low inherent structural damping
The Future?
• Full-scale experimental validation
• Other designs
– Tendons and multiple devices at sides of wall to provide greater forces
in resistance
– Sacrificial tendons?
• Better models and analysis of larger building systems
incorporating semi-active rocking dissipation to more fully
understand the benefit that might be gained and for what
structures.
Acknowledgements
Special thanks to Ms Kerry Mulligan, Mr. Maxime
Fougere and all our co-authors
This research was funded by the NZ Earthquake
Commission (EQC) Research Foundation
and an
ENISE, St. Etienne Research Travel Grant