tips
NEES
Tools for Isolation and Protective Systems
Collapse Evaluation of Seismically Isolated
Building Impacting Moat Wall
Armin Masroor
Graduate Research Assistant
Gilberto Mosqueda
Associate Professor
Department of Civil, Structural and Environmental Engineering
University at Buffalo
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
NEES TIPS: Tools for Isolation and Protective Systems
Four year research and education effort aimed at increasing applications of seismic isolation in the United
States (NSF Grant No. CMMI-0724208, PI Keri Ryan)
Conduct a series of “limit state” tests that examine the ultimate behavior of isolated
buildings under various failure modes. Such failure modes include:
 Isolated building pounding against an
 Elastomeric bearings subjected to large
outer moat wall
strain limits (beyond stability limits)
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Prototype Building-Basic Design Information





Code : IBC 2006, ASCE 7-05, and AISC Steel Manual
Building Location: Los Angeles, CA
Site Class: D (Vs=180 m/s to 360 m/s)
Mapped spectral accelerations: Ss = 2.2 g, S1 = 0.74 g
Lateral System
R
Isolated Intermediate Moment Frame (IMRF)
1.67
 Properties of isolation systems
Isolator Properties
DBE
MCE
Effective Period (TD, TM)
2.77 s
3.07 s
Effective Damping (BD,BM)
24.2%
15.8%
Isolator Displacement (DD, DM)
12.7 in.
24.3 in.
Total isolator displacement (DTD, DTM)
15.3 in.
29.4 in.
Quake Summit
July 2012
Drift Limit
1.5%
3D View (Isolated IMRF)
tips
NEES
Tools for Isolation and Protective Systems
Test Setup
•
The test specimen represents a
single bay of an internal moment
frame in the prototype structure.
•
The test setup consisted of :
–
Structural frame (¼ scale 3-story IMRF)
–
Gravity frame (one by one bay frame
with, pin-pin columns and braced out of
plane)
–
Isolators (single friction pendulum R=30
in. and displacement capacity of 7 in.).
–
The effective period of the isolated
model at MCE displacement is 1.5 sec.
–
Concrete blocks (designed to simulate
impact surfaces)
–
Retaining walls (consist of concrete wall
with soil back fill and rigid steel wall)
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Moat wall setup
• Different scaled concrete wall thicknesses of 2, 4, and 6 in were
tested to examine the effect of wall stiffness on the pounding
behavior.
• A rigid steel wall was also used to cover a wider range of wall
properties (With and without weld).
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Overview of the tests conducted
• System identification tests
– Snap back, Pull back, White noise, Sine sweep, Table impulse, Sinusoidal
• Fixed base model
– Investigate the post-yield behavior of the fixed-base structure.
• Isolated base model without impact
– Investigate properties of isolation device and isolated base structure under
MCE motions.
• Isolated base model with impact
–
–
–
–
Investigate the effect of pounding on superstructure
Different wall stiffness
Variable gap distance
Different contact surface
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Ground motion selection
•
•
Based on capacity limits of the shake table, five ground motions were selected from
the SAC and PEER database.
All the ground motions were scaled to MCE level based on target periods T=0-3 sec.
Newhall Fire Station-comp. 2
Takatori-comp. 2
Sylmar Converter Station-comp. 1
Erzincan-NS
Erzincan-EW
MCE scale
factor
1.46
0.89
1.11
1.76
1.76
Scaled
PGA (g)
0.86
0.55
0.68
0.91
0.87
Magnitude
(M)
6.69
6.90
6.69
6.69
6.69
Quake Summit
July 2012
Duration
(sec)
40.0
40.9
40
21.3
21.3
Peak base
plate disp. (in)
4.24
2.83
4.88
6.62
3.36
DM/4 = 6 in
tips
NEES
Tools for Isolation and Protective Systems
 Fixed base structure
• The maximum interstory drift ratio exceeding 5% drift occurs at the middle level.
• All levels start to show softening behavior due to yielding at 2% drift.
 Base isolated structure without impact
• Base shear versus maximum roof drift ratio:
-It can be conclude that the base isolation model
withstood the MCE level ground motion with only
slight yielding
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
7
4 in gap
6 in gap
No impact
5
Acceleration (g)
Velocity (in/s)
Base isolated structure with impact
50
40
30
20
10
0
-10
-20
-30
-40
-50
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Displacement (in)
• The second impact to the east wall occurred at a
higher velocity due to the rebound from first impact.
• The sudden drop in base velocity at the instances of
impact can be observed for both the 4 and 6 in. gaps.
• This increased acceleration could consist of the
effect of both rigid body motion and also local waves in
the steel plate where the accelerometers were installed.
Quake Summit
July 2012
3
1
-1
-3
-5
-7
0
1
2
3
Time (s)
4
5
6
tips
NEES
Tools for Isolation and Protective Systems
Impact Force
75
65
55
15 cm thick concrete wall
Steel wall w/o weld
Steel wall with weld
45
35
25
15
5
-5
0
0.1
0.2
Time (s)
0.3
Contact Force (kips)
Contact Force (kips)
 In a structural collision, contact between two objects consists first a local phase
followed by a second global (vibration) response phase.
• Local behavior: The first phase of impact is indentation of two objects
at the point of the contact. The contact force generated in this phase is
generally a function of the shape and material properties of colliding
objects as well as impact velocity.
• Vibration aspect of impact: The contact force in this second phase can
be affected by external seismic forces, and dynamic properties of the
two objects including mass and stiffness.
0.4
Quake Summit
July 2012
75
65
55
45
35
25
15
5
-5
-1
0
1
2
Displacement (in)
3
tips
NEES
Tools for Isolation and Protective Systems
Effects of wall stiffness and gap
distance
•
Minimum and maximum acceleration and
interstory drift ratio are plotted in separate
figures to investigate effect of each impact.
•
By increasing the moat wall stiffness, both
acceleration and drift increased at all stories
of the model, although effect of the moat wall
stiffness is more apparent on lower floor
accelerations and upper floor drifts.
•
The effect of impact on interstory drift is
apparent after the first impact to west wall,
which yields the superstructure in the
negative direction, while maximum positive
drifts are influenced by both west and east
wall impacts.
•
Exceeding the response in the negative
direction as observed for the 4 and 6 in
concrete walls, the stiffer moat wall yielded
the superstructure after the first impact and
affects the drifts after second impact.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Numerical Simulation
•
A numerical model of the
experimental setup was developed
in OpenSees.
•
Elastic beam-column elements
and zero length nonlinear rotation
spring elements(Modified Ibarra
Krawinkler model, 2009)
•
Panel zones modeled using Gupta
and Krawinkler model (1999).
•
P-Delta effects were simulated by
a leaning column.
Figure from OpenSees wiki
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Classical theory of impact
•
The classical theory of impact, called stereomechanics, is based preliminary on
the impulse-momentum law for rigid bodies.
Coefficient of restitution
v 1t  v 1i  (1  e )
v
2t
v
2i
 (1  e )
m 2 (v 1 i  v
2i
)
2i
)
m1  m 2
m 1 (v 1i  v
m1  m 2
•
It is evident that this theory does not account for
• impact duration
• transient forces
• local deformations at the contact point
•
Assumes that a negligible fraction of the initial kinetic energy of the system is
transferred into local vibrations of colliding bodies.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Local Deformation Phase Produced by Impact
•
In this case, the two bodies will undergo a relative indentation in the
vicinity of the impact point. The energy required to produce this local
deformation may be an appreciable fraction of the initial kinetic energy.
•
Most research related to structural impact has proposed forcedisplacement models to capture this phenomenon such as a linear
spring, Kelvin, Hertz, and Hertz model with nonlinear dampers.
Contact Force
Hertz Damped
Model
Hertz
Model
0
0
Penetration
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Vibration Aspect of Impact
•
The disturbance generated at the contact point propagates into the
interior of the bodies with a finite velocity and its reflection from the
boundaries produces oscillations or vibrations in the solids.
•
Considerable amount of energy is transformed into vibrations in the
collision of bodies with low natural frequencies.
Using several beam
elements having plastic
hinges at both ends for
wall, and in-plane
elements for soil backfill
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Simplified Moat wall Model
•
•


 EI  x

2
x
A continuous cantilever beam supported by an elastic foundation and
external distributed damping was assumed.
A rotational spring was assumed at the base of the beam to capture the
post-elastic behavior due to the formation of a plastic hinge.
2
2
 v 
v
 Kv  m x
 2  C
x 
t

v
2
t
2
 F (x ,t )
Boundary conditions:
 v
2
v  x  0   0;
 v
2
x
2
EI
x
2
x
v
0
 K 
v
x
x
0
3
 0;
x L

x
3
0
x L

Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Simplified Moat wall Model
•
Solving homogeneous equation ( F ( x , t )  0 ) using separation of
variable:
v  x , t   X  x  .Y  t 
•
Yields to two ODEs:
 X
4
x
4
 X  0
4
A  Y
2
EI  t
•
2

 K
4 

  Y  0
EI  t
 EI

C Y
Solving the 2nd equation with boundary condition leads to characteristic
equation of:
 L  sin h   L  . co s   L   sin   L  . co sh   L
•
In which
K  
KL
EI
Quake Summit
July 2012
   K  1  co s   L  . co sh   L    0
tips
NEES
Tools for Isolation and Protective Systems
Simplified Moat wall Model
•
Substituting  i obtained from the frequency equation in equation of
motion leads to modal frequencies and shape functions:
K
i 
X
x

 

i 1
A

EI
A
Modal frequency
i
4
2 i L

sin( i L )  sinh( i L ) 
cos( i L )

K 
A i  cosh( i x ) 
sinh( i x )
cos( i L )  cosh( i L )



sinh( i L )  sin( i L ) 
 cos( i x ) 
•

A

2
n
X dx
0

Y
2
n
t
t 
2

 C

L
2
n
X dx
0
K 
cosh( i L )
cos( i L )  cosh( i L )
Using Modal orthogonality:
L
2 i L
Shape function


sin( i x ) 



generalized forced vibration equation

Y
n
t
t 

  EI

Quake Summit
July 2012

L
0
 X
4
x
n
4
.X n dx  K

L
0

2
X n dx Y

n
 t   F (t )
tips
NEES
Tools for Isolation and Protective Systems
Simplified Moat wall Model
•
Simulation of impact
forces in structural analysis should consider the two phases
i
of impact to capture both the effects of local deformation at the impact point and
the vibration aspect of the colliding objects.
•
Hertz damped model captures forces during the first phase of impact.
•
The force obtained in the first
phase can be implemented in
Single degree of freedom
(generalized forced vibration
equation) to find lateral
displacement of the wall and also
resisting force imposed on the
striker body.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Experimental Verification
•
The concentrate hinge stiffness,
was assumed equal to the post
concrete crack stiffness.
•
Winkler spring was assumed to
model soil backfill.
Wall thickness (in)
Local parameters
Vibration parameters
Wall type
Concrete
Steel
 k ips 
 k ip s
  % 
e
K 
4400
0.7
0.23
0.08
0.9
180
2
4400
0.7
0.10
0.15
1.2
160
6
4
4400
0.7
0.02
0.28
2.0
200
5
NA
8200
0.7
-
0.40
100.0
40
Front wall
Back wall
2
4
4
K
h
( k ips in
3 2
)
Quake Summit
July 2012
M
K
in
tips
NEES
Tools for Isolation and Protective Systems
Numerical
Experimental
0
0.05
0.1
Time (sec)
0.15
Contact Force (kips)
Contact Force (kips)
0.60
1
-1
0
0.05
9.5
0.1 0.15
Time (sec)
0.2
Contact Force (kips)
0.15 0.30 0.45
Displacement (in)
Contact Force (kips)
0
3
Numerical
Experimental
7.5
5.5
3.5
1.5
-0.5
0
34
29
24
19
14
9
4
-1
0.05
0.1
0.15
Time (sec)
0.2
Numerical
Experimental
0
0.1
0.2
0.3
Time (sec)
Quake Summit
July 2012
0.4
7
Numerical
Experimental
5
3
1
-1
-0.1
0.4
0.9
Displacement (in)
1.4
9.5
Numerical
Experimental
7.5
5.5
3.5
1.5
-0.5
-0.1
Contact Force (kips)
70
60
50
40
30
20
10
0
Numerical
Experimental
Numerical
Experimental
5
Contact Force (kips)
Contact Force (kips)
Contact Force (kips)
Impact Force
70
60
50
40
30
20
10
0
7
34
29
24
19
14
9
4
-1
-0.1
0.1
0.3 0.5 0.7
Displacement (in)
0.9 1
Numerical
Experimental
0.4
0.9 1.4 1.9 2.4
Displacement (in)
2.9
tips
NEES
Tools for Isolation and Protective Systems
Superstructure Response
(a) First Story
(b) Second Story
(c) Third Story
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
3-Dimensional Prototype Model
•
Detailed three-dimensional (3D) numerical model
of base isolated IMRF building was developed in
OpenSees (Sayani et al. 2011).
•
Elastic beam-column elements and zero length
nonlinear rotation spring elements(Modified Ibarra
Krawinkler model, 2009) assigned to beam
elements while fiber section used to define column
elements.
•
An elastic column element and an elastic-perfectly
plastic spring were assembled in parallel to obtain
the composite bilinear lateral force-deformation
behavior shown here (Sayani et al. 2011).
Sayani P. J., Erduran E., Ryan K. L. (2011). “Comparative Response Assessment of Minimally Compliant Low-Rise Base-Isolated and
Conventional Steel Moment-Resisting Frame Buildings”, Journal of Structural Engineering, Vol. 137, No. 10.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
3-Dimensional Moat Wall Model
•
Moat wall are modeled using a cantilever
column with concentrated plastic hinge.
•
Soil backfill was modeled using log-spiral
hyperbolic (LSH ) procedure (Shamsabadi et
al. 2007)
•
Local Impact was simulated using Hertz
Damped model.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
3-Dimensional Moat Wall Model
• Moat wall columns are connected to each other using shear
spring representing continues wall behavior.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
3-Dimensional Moat Wall Model
• Moat wall columns are connected to each other using shear
spring representing continues wall behavior.
• Shear springs are calibrated using Finite Element study of
concrete moat walls in Abaqus.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
3-Dimensional Moat Wall Model
• Moat wall columns are connected to each other using shear
spring representing continues wall behavior.
• Shear springs are calibrated using Finite Element study of
concrete moat walls in Abaqus.
140
120
Force (kips)
100
80
60
40
Single Wall
20
Continues Middle Wall
Continues Corner Wall
0
0
1
2
3
4
Displacement (in)
5
6
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Collapse Evaluation using the Methodology of
FEMA P695
• Far filed ground motion set (22 ground
motion) in FEMA P695 was selected
for collapse evaluation of isolated
model pounding moat wall.
9
Median
MCE Spectrum
8
• Ground motions were scaled using
PGV normalization method.
• IDA conducted for different moat wall
gap sizes and fragility curves plotted
based on 5% interstory drift ratio limit.
Quake Summit
July 2012
Acceleration Sa (g)
7
6
5
4
3
2
1
0
0
1
2
Period (sec)
3
4
tips
NEES
Tools for Isolation and Protective Systems
IDA Curves
• IDA conducted for different moat wall gap sizes and fragility
curves plotted based on 5% interstory drift ratio limit.
2.5
Intensity Scale Factor
Intensity Scale Factor
2.5
2
1.5
1
0.5
0
0
2
1.5
1
0.5
2
4
6
8
10
Maximum Interstory Drift Ratio (%)
Base Isolated Model without Moat wall
Quake Summit
July 2012
0
0
2
4
6
8
10
Maximum Interstory Drift Ratio (%)
Base Isolated Model with Moat Wall at
20” gap
tips
NEES
Tools for Isolation and Protective Systems
Fragility Curve
• Although the probability of
collapse at MCE intensity is
more than 10% for gap
distance of 20”, it’s still less
than 20% which is the limit for
outliers.
1
0.9
Probability of Collapse
• Fragility curves were plotted
using Adjusted Collapse
Margin Ratio (ACMR) and
total uncertainty of 0.4.
Quake Summit
July 2012
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
No moat wall
30" gap distance
20" gap distance'
1
2
3
Intensity Scale Factor
4
tips
NEES
Tools for Isolation and Protective Systems
Conclusions
• Shake table tests impacting a base isolated structure to the
moat wall were conducted as part o the NEES TIPS project.
• Unique data set was generated including structural impact at
base level and propagation to superstructure.
• A new impact element was proposed to simulate the effects of
two phases of impact. The required equations to calculate its
parameters were derived for a generic moat wall considering
nonlinearity in the moat wall and soil backfill.
• The response of full scale 3-story base isolated moment frame
was investigated for various gap distances using the
Methodology proposed in FEMA P695.
• The collapse margin ratio for the investigated moment frame is
relatively insensitive to gap distance.
Quake Summit
July 2012
tips
NEES
Tools for Isolation and Protective Systems
Thank you!
Quake Summit
July 2012