NATO International Workshop on:
Advances in Earthquake Engineering for Urban Risk Reduction
Istanbul-Turkey, 30 May - 1 June, 2005
Shake-Table Experiment on OneStory RC Structure With and
Without Masonry Infill
Khalid M. Mosalam, PhD, PE
Associate Professor
Structural Engineering, Mechanics and Materials
Civil and Environmental Engineering
University of California, Berkeley
Visiting Professor
Department of Civil Engineering, METU, Turkey
Wednesday, 1 June, 2005
Outline
• The Big Picture
• Objectives
• Test Structure
• Test Stages
• Earthquake Loading
• Test Results
• Concluding Remarks
• Further Studies
The Big Picture …
Prototype
structure
Shaketable
tests
Pseudodynamic
tests
Damage sequence
& collapse
mechanism
Infill-RC
frame
interaction
Development of
element removal
algorithms
Improvement of
quasi-brittle
material models
Development
and validation
of FE model
Development
of new SAT
models
Development of new “progressively
collapsing” macro-elements for infilled frames
Validation of
pseudo-dynamic with
sub-structuring
Development of
hybrid control
algorithm with
mixed-variables
(mode switch
between force &
deformation)
Objectives
• Develop a “benchmark” shake-table experiment for
•
validation of “new” experimental techniques and
computational models
Develop a new experimental technique:
• Multiple physical sub-structures with different properties (bare versus URM
•
•
infilled RC frames) tested simultaneously (at different locations)
Mixed variable (force & displacement) pseudo-dynamic formulation based on
relative stiffness of sub-structures or change of stiffness of one sub-structure
Replacing physical modeling with a simulated model of one or more substructures, e.g. the connecting floor slab or upper stories
• Develop computational models for URM infill walls
• Model the collapse mechanisms of infilled frames
Test Structure (1/4)
C2
B
C1
E
C1
C
B1
A A1
F
A2
C
D
B2
C
B1
E
A1
F
C2
D
B2
B
A2
Prototype “hypothetical” building
Shake-table test structure
Test Structure (2/4)
• The prototype RC building is a 5-story structure
designed following ACI318-02 & NEHRP
recommendations in seismic regions.
• URM wall (clay bricks & type N mortar) in one of
the interior frames.
• Test structure is a ¾-scale of the first story with
column axial load (concentric post-tensioning)
simulating upper floors gravity load.
• Uniform mass is added to the slab such that the
base-shear on the test structure matches that of
the three middle frames of the prototype building
model subjected to the design ground motion.
Test Structure (3/4)
• 18 accelerometers measured the base and roof
accelerations at various locations and
directions.
• 95 displacement transducers measured global
and local displacements and rotations.
• 150 strain gages measured strains at different
locations of the reinforcing bars and column
post-tensioning rods.
• 17 high speed cameras monitored the
experiment.
Test Structure (4/4)
N
Test Stages (1/2)
Post-tensioning
Stage 1
Stage
Stages 2 and 3
Description
1
Infilled structure with column post-tensioning
2
Bare structure with column post-tensioning
3
Bare structure without column post-tensioning
Test Stages (2/2)
Test Movies
Camera
14 Movie
Description
1
Stage 1: Wall cracking
2
Stage 1: Wall crushing
3
Stage 1: Wall collapse
4
Stage 2: Post-tensioning acting as a self-centering system
5
Stage 3: On the verge of collapse (reaching the table limits)
Earthquake Loading (1/2)
Northridge, Tarzana
1.8
Spectral Acceleration [g]
1.6
Natural period range of the infilled structure
Natural period range of the bare structure
Design Spectra
1.4
1.2
Loma Prieta
1
Northridge
0.8
Duzce
1
0
-1
0
Acceleration [g]
2
5
1
0
-1
0
1
0
-1
0
0.6
0.4
0.2
0
0
0.5
1
Period [sec]
1.5
2
10
15
Duzce
20
25
5
10 15
20
Loma Prieta, Bran
25
5
25
10
15
time [sec]
20
Earthquake Loading (2/2)
From PEER Strong Motion Database
Ground Motion
Station
(Source)
Direction
PGA
[g]
PGV [in/sec
(mm/sec)]
PGD [in
(mm)]
Northridge, CA, ‘94
Tarzana
090
1.570
36.23 (920)
5.13 (130)
Duzce, Turkey, ‘99
Lamont
N
0.762
12.97 (329)
0.75 (19)
Loma Prieta, CA, ‘89
Bran
000
0.426
17.43 (443)
2.28 (58)
Scale Factors for Different Levels of Input Table Motion
Level
1
probability of being exceeded in 50 years -
2
3
4
50% 30% 10%
6
7
8
9
-
2%
Northridge, CA, ‘94 (TAR)
0.05 0.17
0.23
0.39
0.59 -
-
Duzce, Turkey, ‘99 (DUZ)
-
-
-
-
-
1.50
2.00 2.53
Loma Prieta, CA, ‘89 (LomaPr)
-
0.31
0.44
0.67
1.00 1.50
1.95 2.19
Design
MCE
Higher demands
Test Results (1/7)
Damaged infill wall
200
Maximum Base Shear (kips)
180
160
140
120
100
80
60
Test Results
Elastic with wall
Elastic without wall
40
20
Damaged RC frame
0
0
0.5
1
1.5
2
Maximum Drift(%)
2.5
3
Test Results (2/7)
In-plane (North-South direction)
Conditions of the test
structure at time of the
snap-back (pull) test
Out-of-plane (East-West
direction)
Natural
Period
[sec]
Damping
Ratio [%]
Stiffness
[kips/in
(kN/mm)]
Natural
Period
[sec]
Damping Stiffness
Ratio
[kips/in
[%]
(kN/mm)]
Before building the wall
No additional mass
0.135
4.30
113.3
(19.84)
0.134
4.40
134.0
(23.47)
After building the wall
Columns prestressed
No additional mass
0.055
5.70
425.5
(74.52)
0.122
4.30
167.1
(29.26)
After building the wall
Columns prestressed
With additional mass
0.134
6.85
431.0
(75.48)
0.232
4.25
168.0
(29.42)
Test Results (3/7)
350
300
250
Test results
200
Initial stiffness with wall
150
Initial stifness without wall
180
160
100
Masonry Infill
RC Frame
140
50
0
TAR 1
TAR 2
TAR 3
TAR 4
TAR 6
DUZ 7
DUZ 8 DUZ 7-2
Test Levels
Variation of the effective stiffness
From column shears using B.M.
obtained from strain measurements
and section properties
Base Shear [kips]
Effective Stiffness [kips/in]
400
120
100
80
60
40
20
0
TAR 3 TAR 4 TAR 6 DUZ 7 DUZ 8 DUZ 7-2
Test Levels
Distribution of base shear between
the URM infill wall and the RC frames
200
200
150
150
100
100
Base Shear [kips]
Base Shear [kips]
Test Results (4/7)
K = 386 kips/in
50
0
-50
-50
-150
-150
-3
-2
-1
0
1
Displacement [in.]
2
3
Tarzana level 3
K = 284 kips/in
200
K = 190 kips/in
150
100
50
K = 57 kips/in
0
-50
-100
-3
-2
-1
0
1
Displacement [in.]
2
3
Tarzana level 6
200
150
K = 273 kips/in
100
50
K = 53 kips/in
0
-50
-100
-150
-150
K = 150 kips/in
-200
-200 K = 168 kips/in
-3
-200
Base Shear [kips]
Base Shear [kips]
0
-100
Stage 1
of
testing
K = 270 kips/in
50
-100
-200
K = 359 kips/in
-2
-1
0
1
Displacement [in.]
Ducze level 7
2
3
-3
-2
-1
0
1
Displacement [in.]
Ducze level 8
2
3
Test Results (5/7)
2.5
← Begining of the test
← TAR 6
Spectral Acceleration [g]
2
← Removal
of the wall
LomaPrieta
Duzce
Northridge
Design Spectra
← Before removal of
prestressing
← After removal of
prestressing
1.5
← End of
1
the test
0.5
0
0
0.2
0.4
0.6
Period [sec]
0.8
1
Change in spectral demand due to the change in natural period of the test structure
Test Results (6/7)
2500
2000
Maximum Base Moment [kip-in]
Stage 1
Stage 2
Stage 3
DUZ 8
1500
LomaPr 7
1000
LomaPr 9
DUZ 7
LomaPr 9-2
500
0
0
LomaPr 7-2
AWR-DUZ 7
0.01
0.02
0.03
0.04
0.05
C2
B
C1
Maximum Top Moment [kip-in]
2500
2000
AWR-DUZ 8
Stage 1
Stage 2
Stage 3
LomaPr 9
1500
1000
500
LomaPr 9-6
LomaPr 8-2
DUZ 8
LomaPr 9-2-4
LomaPr 6-2
DUZ 7
LomaPr 4-2
0
0
0.01
0.02
0.03
0.04
0.05
Maximum Top Rotation [rad]
Column A2, beam-column joint
0.06
C
B1
E
LomaPr 9 LomaPr 9-4
LomaPr 7-2
DUZ 7
500
0.01
0.02
0.03
0.04
0.05
0.06
Maximum Base Rotation [rad]
F
A2
C
D
B2
LomaPr 7
1000
0
0
Column A2, column-foundation joint
DUZ 8
1500
0.06
Maximum Base Rotation [rad]
Stage 1
Stage 2
Stage 3
2000
Column B1, column-foundation joint
A1
2500
Maximum Top Moment [kip-in]
Maximum Base Moment [kip-in]
2500
LomaPr 9
LomaPr 9-6
LomaPr 9-2-4
2000 LomaPr 7
Stage 1
Stage 2
Stage 3
LomaPr 4-2
1500
DUZ 8
1000
AWR-TAR 4
500
DUZ 7
0
0
TAR 4
0.01
0.02
0.03
0.04
0.05
Maximum Top Rotation [rad]
Column B1, beam-column joint
0.06
Test Results (7/7)
200
180
DUZ 7
DUZ 8
Stage 1
Stage 2
Stage 3
LomaPr 9
Maximum Base Shear [kips]
160
LomaPr 7
140
TAR 6
LomaPr 9-6
DUZ 7-2
120
AWR-DUZ 8
LomaPr 7-2
100
LomaPr 9-2-1
TAR 4
AWR-DUZ 7
80
LomaPr 6-2
60
LomaPr 9-2-4
TAR 3
LomaPr 4-2
40
LomaPr 3-2
LomaPr 2-2
20
0
0
LomaPr 8-2
1
2
3
4
5
Maximum Drift [%]
Global Results
6
7
8
Concluding Remarks (1/2)
• Test structure at design level showed 17% reduction
of stiffness, but the overall behavior is almost linear.
• At MCE, first significant damage occurred with 25%
shift of stiffness from beginning to end of motion
with cracking along column-wall interface and small
vertical cracks in mortar joints at the corners.
• Most significant change in behavior occurred at DUZ
7 (1.5 original) with significant wall cracks (large
cracks at 60o with hrz. connected with a hrz. crack &
45o crack into opposite bottom corners.)
• For small drifts (< 0.2%), cracks opened and closed
without engaging the wall. Once the cracks closed,
the wall picked up load causing stiffness increase
and further wall damage.
Concluding Remarks (2/2)
• At small forces, static friction between cracked
surfaces existed and the wall acted as a whole
increasing the stiffness. Afterwards, the stiffness
reduced approaching to that of the bare RC frames.
• Damage in the URM infill increased the natural period
from 0.13 sec to 0.36 sec (167% increase).
• Removal of post-tension rods increased the natural
period from 0.44 sec to 0.61 sec (39% increase).
• URM infill wall significantly changed the demands and
the key global and local response parameters, e.g.
drift ratio, base shear and joint rotations.
• The experimental findings represent benchmark
dynamic test data to validate newly developed on-line
testing with hybrid control and sub-structuring.
Further Studies
Pseudo-Dynamic Experimentation
Computational
substructure
3-frame
5-story
building
Physical substructures
Bare frame
Infilled frame
Setup in nees@berkeley facility for pseudo-dynamic testing
Comparisons
Shake-table
test
Shake-table results
Pseudo-dynamic test
Pseudo-dynamic results
200
200
100
TAR 6
140
DUZ 8
DUZ 7-2
120
100
60
40
0
0
0
-50
-100
-150
-150
-2
-1
0
1
2
-200
-3
3
160
Shake-table test
TAR 2
TAR 1
0.5
Masonry Infill
1
1.5
2
Maximum Drift [%]
2.5
3
1
2
3
Masonry Infill
RC Frame
160
140
120
100
80
60
120
100
80
60
40
40
20
20
0
0
RC Frame
140
TAR 3
-1
180
180
TAR 4
-2
Displacement [inch]
Displacement [inch]
Pseudo-dynamic test
20
-50
50
-100
Base Shear [kips]
80
0
-200
-3
Duzce Level 7
Duzce Level 8
100
50
Base Shear [kips]
Maximum Base Shear [kips]
160
DUZ 8
150
Duzce Level 8
Base Shear [kips]
180
Duzce Level 7
150
DUZ 9
Base Shear [kips]
DUZ 7
200
TAR 3 TAR 4 TAR 6 DUZ 7 DUZ 8 DUZ 7-2
Test Levels
0
TAR 3 TAR 4 TAR 6 DUZ 7 DUZ 8 DUZ 9-2
Test Levels
Errors (1/3)
Fw: Infill resisting force
FI: Inertia force
FD: Damping force
FF: Concrete frame resisting force
FI + FF + FW + FD = ε
Model for ε as error in a similar run after removal of the wall
FW = 0 ⇒ ε1 = FI + FF = − FD + ε = −C.uɺ + ε ⇒ ε
Inputs (U): FF , ground displacement
ε : error term
na
nb
nc
i =1
j =1
k =1
ε (t ) = −∑ ai .ε (t − i ) + ∑ b j .U (t − j − 1) + ∑ ck .ε o (t − k )
FˆW = − FI − FD − FF − ε = − m.uɺɺt − C .uɺ − FF − ε
Estimate of FW considering the error terms
with model
without model
150
100
100
50
FW [kip]
with model
without model
0
-50
-100
-150
14.7
14.8
14.9
15
15.1
15.2
15.3
15.4
Time [sec]
0
with model
without model
100
-50
50
FW [kip]
FW [kip]
Better estimation of infill
resisting force (FW) using
ARMA model
50
-100
0
-50
-100
-150
5
10
15
Time [sec]
20
25
30
8
8.2
8.4
Time [sec]
8.6
8.8
Displacement [inch]
Errors (2/3)
5
comand
feedback
0
-5
0
500
1000
1500
2000
2500
3000
3500
500
1000
1500
2000
2500
3000
3500
Displacement
[inch] (zoomed in)
Error [inch]
0.04
0.02
0
-0.02
-0.04
0
-0.5
comand
feedback
-0.6
-0.7
-0.8
-0.9
1209.5
1210
1210.5
1211
1211.5
1212
1212.5
1213
1213.5
Time Step
Error in implementing target displacement command is unavoidable in PID control
Errors (3/3)
FFT
0.3
Disp
100*Error
0.2
Er(t) = 0.03e
0.1
0
0
1
2
3
4
5
6
7
8
9
(0.78 v -1)
10
1000
0.035
500
0.03
0
0
1
2
3
4
5
6
7
8
9
10
1000
FFT
f*Disp/Error
500
0
0
1
2
3
4
5
Frequency, Hz
6
7
8
9
10
Absolute Value of Error [inch]
FFT
Disp/Error
0.025
0.02
0.015
Recorded
Modeled
0.01
0.005
0
0
0.2
0.4
0.6
0.8
1
Absolute Value of Velocity [inch/sec]
1.2
1.4
Developing Computational Models (1/2)
•
Assessment of existing algorithms
for manual and semi-automatic
element removal and potential for
use in progressive collapse
analysis
•
Case study: Masonry-infilled onestory structure:
– Masonry modeled by three
diagonal struts in compression
– Dynamic analysis: center strut
brittle failure during
Northridge Tarzana record
Case study specimen and OpenSees model rendition
Developing Computational Models (2/2)
Displacement envelope doubled
Center Strut Removed
0.2
0.1
0
-0.1
No Element Removal
(Ductile Center Strut)
Brittle Center Strut
-0.2
0
2
4
6
8
10
12
14
16
18
20
→
• Residual displ. reversed
• Demand on other elements
rose
more likely to fail
• Needs reliable automation
– Internal force release
– Element loads
– ”Dangling” nodes
Time (sec.)
Force in Opposite Center Strut (kip)
•
Roof Displacement (in.)
0.3
0
-10
-20
Ductile Center Strut
Brittle Center Strut
-30
Original Strut force history shown
in dotted light black for reference
(for the ductile softening case).
-50
Strut force capacity is 50 kips
and should be removed afterwards
-60
-40
0
2
4
6
Strut Force Capacity
Opposite Center Strut should fail. Procedure is
doable but tiresome and not guaranteed
8
10
12
14
16
18
20
Time (sec.)
Roof displacement and strut force time history for
ductile and brittle failure of one center strut
Developing Computational Models
Steel Shoe
Steel Shoe
t1
pi =
t2
z
x
y
ti
t1 + t 2
∑p
1
∑ ∫Vi (σ x )i dV
V
1
ε x = ∑ ∫ (ε x )i dV
Vi
V
i = 1 for brick & 2 for mortar
σx =
i
=1
Development of new SAT Models for infilled frames
• In-plane SAT models
12 9
8
• Combination of In-plane and
Out-of-plane SAT models
3 7
5
13
11
20
22
14
1013
21
19
8
14
12
2
7
1
1
1.2
5
Link element
6
• Material properties for various
elements of the SAT model
1
5
4
Axial Force(kips)
Stress(ksi)
0.8
0.6
3
2
0.4
1
0.2
0
-1
-15
0
0
0.2
0.4
0.6
0.8
Strain
1
1.2
1.4
1.6
-10
80
70
60
15
40
Horizontal Force(kips)
60
Horizontal Force(kips)
10
PushOver Analysis
80
50
40
PN/P D = 0
30
PN/P D = 0.01
PN/P D = 0.05
20
20
0
-20
-40
PN/P D = 0.10
PN/P D = 0.15
-60
PN/P D = 0.20
10
PN/P D = ∞
0
0
5
Axial Displacement(in)
-3
x 10
PushOver Analysis
• Considering the effects of outof-plane and cyclic loading in
in-plane degradation of the
infill.
-5
0
0.2
0.4
0.6
0.8
1
Horizontal Displacement(in.)
1.2
1.4
-80
-1
1.6
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Horizontal Displacement(in.)
4
2
6
18
16
Compression struts
6
10
17
15
11
3
9
4
0.6
0.8
1