Seismic Performance Assessment
and Retrofit of Non-Ductile RC
Frames with Infill Walls
P. Benson Shing
Ioannis Koutromanos
Andreas Stavridis
Marios Kyriakides
Sarah Billington
Kaspar Willam
NEES & PEER Quake Summit
San Francisco, October 8-9, 2010
Masonry-Infilled RC Frames
• Complicated structural systems.
• Additional complexity introduced for older
construction, where shear failures are expected
in concrete columns.
• Mixed performance in past earthquakes.
Collaborative research project to develop
understanding of behavior, modeling techniques
and retrofit schemes for masonry-infilled frames.
Cyclic Behavior of Infilled Frames
Single-Story, single-bay, non-ductile reinforced
concrete frames, infilled with solid brick masonry
panel, tested at CU Boulder by Willam et al.
W
= 156kN
2
W
= 156kN
2
370mm
Lateral
displacement
W
= 156kN
2
W
= 156kN
2
370mm
Lateral
displacement
8 #5 bars
#2 @ 265mm stirrups
8 #5 bars
#2 @ 265mm stirrups
794mm 1870mm
1870mm
280mm
280mm
610mm
280mm
280mm
836mm
280mm
3380mm
280mm
280mm
912mm
3380mm
280mm
Cyclic Behavior of Infilled Frames
Modeling Scheme
• Plane stress smeared cracking continuum
elements to describe distributed cracking &
crushing.
• Interface elements to describe strongly
localized cracks as well as mortar joint crackingsliding.
Modeling Approach – RC Columns
Cracks are modeled in discrete and smeared
fashion.
Triangular smeared
crack element
Interface element to
model discrete cracks
Stavridis and Shing, 2010
Modeling Approach – Infill Panels
Anticipated cracking pattern mainly runs through
the mortar joints, with some brick splitting cracks
Quadrilateral smeared
crack elements (each
elem. = half brick)
Interface (for bed joints)
Interface (for head joints)
Interface (for possible splitting cracks)
Stavridis and Shing, 2010
Smeared Crack Element
Originally formulated by Lotfi and Shing (1992)
Uncracked material: Failure surface combines Von Mises
criterion with a tension cutoff criterion.
σe
σ2
σ2
ft
ft
f΄c m
Tension cutoff
ft
ft σ 1
σ1
σee
σ
f΄f ' m
m
2e
σσ2e
ffo
o
σσe e
2
2
 2ε 2ε2ε
p 
2 f  2ε p p 
p
σ
=f
+
f'






2ε
2ε
e
o
c
o
2
σ e =f o +  f ' m σ fe o=f
 o + pf'm 2 pf o   ε1pε1p ε1p2ε1p 

 ε1p ε1p  
f'cf'm

  m

m
σ e = σ 2e +  rp σf e'm-σσ2e2e +1-exp
ε p -ε
rpf'm - σ 2e 1- exp
  
ε p ε2p

 2p

r  f ' -σ 2e
rm
f'  σ
σ e = σ 2e + rpf'c - σp2e m1- exp
 - p  m ε2ep - ε 2p  


σσ
2e2e
f of
o
-m
σe
Failure surface of uncracked material
εe1p
p1
εe2p
ε1p
p2

 r f' - σ
 p c 2e

m
-m
1
f΄c m

11rp∙f΄m
ε2p
εp
ep
rpf'c
εp
Nonlinear isotropic hardeningsoftening law for effective strength



 
Smeared Crack Element
Cracked material: Orthotropic stress-strain law:
σ
Initial stiffness
unloading/reloading
ε2 ε1
Exponential
softening
ft
ε
Secant stiffness
unloading/reloading
Exponential
softening
fc
Parabola
Interface Element
n
4
3
1
2
t
Local coordinate system
τ2 – μ2(σ – s)2 – 2r(σ – s) = 0
τ
μ, r, s: strength parameters
1
Displacement vector:
elastic
d = del + dpl + dg
1
μr
initial
final
μο
co = μο2s2o + 2roso
so
σ
geometric
plastic
Yield surface (Lotfi and Shing 1994)
Interface Element
σ
Koutromanos and Shing (2010)
σ
3.5
Tensile Stress (MPa)
3.0
2.5
Experiment
Analysis
2.0
1.5
σ
dn1
dn2
dn1
dn2
dn1
dn2
dn1
dn2
Loading-unloading
dn
dn
1.0
σ
0.5
0.0
-0.5
-1.0
0
20
40
60
80
100
120
Normal Displacement (μm)
Tensile Stress vs. Normal Crack Opening
Reloading
dn
dn
Interface Element
Shear Stress (MPa)
1.5
Test on mortar joint by Mehrabi and Shing (1994)
1.0
0.5
100-psi Normal Compression
0.0
-0.5
Axial Compression
experiment
analysis
-1.0
-1.5
-10
-5
0
5
10
Shear
Normal Displacement (mm)
Shear Displacement (mm)
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
Joint Dilatation & Compaction
experiment
analysis
-10
-5
0
5
Shear Displacement (mm)
10
V/W
Verification – Quasi-static Tests
-1.0
V/W
-1.5
-1.5
-1.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5-0.5 0.0
0.5
1.0
1.5
-1.0
Experiment
-1.5
Analysis
-2.0
-2.5
drift ratio (%)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5-0.5 0.0
0.5
1.0
1.5
-1.0
Experiment
-1.5
Analysis
-2.0
-2.5
drift ratio (%)
Verification – Quasi-static Tests
Shake Table Test 1
WEST
EAST
Prototype 3-story Building
R/C frame with solid brick infill panels, representing
design practice in California in the 1920s.
1
18’
2
A
22’
B
22’
C
22’
D
Slab with joists
18’
3
Base Acceleration Time Histories
El Centro NS Record, 1940
Imperial Valley Earthquake
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0
10
20
-0.2
30
40
Acceleration (g)
Acceleration (g)
Gilroy 3 000 Record, 1989
Loma Prieta Earthquake
0.0
0
20
-0.2
-0.4
-0.4
-0.6
-0.6
time (sec)
10
time (sec)
30
40
Motion Sequence
Trial
Motion
1
2
3
4
5
6
7
8
Gilroy 40%
Gilroy 67%
Gilroy 67b%
Gilroy 83%
Gilroy 91%
Gilroy 100%
Gilroy 120%
El Centro 250%
Stavridis et al, 2010
Specimen Damage
Bottom Story Response
Motion
Drift
Damage
G40
0.01%
None
G67
0.10%
Slight
G67b
0.12%
Slight
G83
0.28%
Moderate
G91
0.40%
Moderate
G100
0.55%
Important
G120
1.06%
Severe
E250
-
Collapse
After G67 ( = DE level)
Specimen Damage
Bottom Story Response
Motion
Drift
Damage
G40
0.01%
None
G67
0.10%
Slight
G67b
0.12%
Slight
G83
0.28%
Moderate
G91
0.40%
Moderate
G100
0.55%
Important
G120
1.06%
Severe
E250
-
Collapse
After G91 ( = MCE level)
Specimen Damage
Bottom Story Response
Motion
Drift
Damage
G40
0.01%
None
G67
0.10%
Slight
G67b
0.12%
Slight
G83
0.28%
Moderate
G91
0.40%
Moderate
G100
0.55%
Important
G120
1.06%
Severe
E250
-
Collapse
After G120
Final Test - Collapse
El Centro 250% Motion
Verification – Shake Table Test 1
• Response is examined for a sequence of 5
motions: Gilroy 67% (twice), 83%, 91%, 100%,
120%.
• Initial stiffness-proportional Rayleigh damping:
0.050
0.045
0.040
0.035
0.030
ζ 0.025
0.020
0.015
0.010
0.005
0.000
0.0
0.5
1.0
T(s)
1.5
2.0
Bottom Story Drift Time Histories
G67b Motion
0.30
0.10
0.10
0.20
0.05
0.00
3
4
5
6
Experiment
Analysis
0.00
-0.05
27
-0.15
0.00
-0.10
0.00
77
78
Experiment
Analysis
-0.40
79
drift ratio (%)
0.10
Experiment
Analysis
G120 Motion
G120
Motion
1.20
0.20
0.00
-0.20
99
100
101
102
Experiment
Analysis
-0.40
Experiment
Analysis
0.80
0.40
0.00
123
124
125
-0.40
-0.80
-0.60
time (sec)
54
time (sec)
0.40
0.20
53
-0.30
0.60
0.30
52
-0.20
G100 Motion
0.40
76
51
time (sec)
G91 Motion
-0.30
30
Experiment
Analysis
time (sec)
-0.20
29
-0.10
-0.15
-0.10 75
28
0.10
drift ratio (%)
-0.05
0.05
drift ratio (%)
0.15
-0.10
drift ratio (%)
G83 Motion
0.15
drift ratio (%)
drift ratio (%)
G67 Motion
time (sec)
time (sec)
126
Bottom Story Hysteretic Plots
1.00
1.00
0.75
0.75
0.75
0.25
0.00
0.00
-0.25
0.05
0.10
-0.50
Experiment
Analysis
0.25
0.00
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
-0.25
-0.75
-0.75
-1.00
-1.00
drift ratio (%)
drift ratio (%)
0.50
0.25
0.00
-0.30
-0.20
-0.10
0.00
-0.25
drift ratio (%)
G120 motion
0.75
0.75
0.75
0.00
0.10
-0.50
-0.75
-1.00
drift ratio (%)
0.20
0.30
0.40
Experiment
Analysis
normalized shear, V1/W
1.00
-0.40 -0.30 -0.20 -0.10 0.00
-0.25
0.50
0.25
0.00
-0.60
-0.40
-0.20
0.00
-0.25
0.30
-1.00
1.00
0.25
0.20
Experiment
Analysis
-0.75
1.00
0.50
0.10
-0.50
G100 motion
G91 motion
normalized shear, V1/W
Experiment
Analysis
-0.50
0.20
-0.50
-0.75
0.40
0.60
Experiment
Analysis
normalized shear V1/W
-0.05
0.50
normalized shear, V1/W
1.00
0.50
-0.10
G83 motion
G67b motion
normalized shear, V1/W
normalized shear, V1/W
G67 motion
0.50
0.25
0.00
-1.20
-0.80
-0.40
0.00
-0.25
0.40
0.80
1.20
-0.50
-0.75
-1.00
-1.00
drift ratio (%)
drift ratio (%)
Experiment
Analysis
Cracking Pattern
Experiment
Analysis
After G91
Cracking Pattern
Experiment
Analysis
After G100
Cracking Pattern
Analysis
Experiment
After G120
Shake Table Test 2
Panel with ECC retrofit
Application of ECC Retrofit
Dowels
Anchors (1’ x 1’ grid)
Unbonded dowels (with grease)
Application of ECC Retrofit
ECC Retrofit Behavior
1/5 scale specimens tested quasi-statically at Stanford
University by Kyriakides and Billington.
Unretrofitted Wall
Lateral Load (kN)
Retrofitted Wall
No retrofit
With ECC Retrofit
Drift (%)
Damage at Specimen
crush
Frame/panel
separation
Second Story Strengthening
Epoxy injections at major cracks
GFRP overlay (by Fyfe Co.)
1 layer of Tyfo SEH51A System, Oriented
Horizontally
12”
12”
1 layer of Tyfo BC
1 layer of Tyfo
SEH-51A System
Oriented
Vertically
Motion Sequence
T1 before testing
T1 after testing
1
2
3
4
5
6
7
8
9
Gilroy 40%
Gilroy 67%
Gilroy 83%
Gilroy 91%
Gilroy 100%
Gilroy 120%
Gilroy 150%
El Centro 150%
El Centro 200%
G40
3.5
Motion
G67
3.0
G83
2.5
SA (g)
Trial
MCE
2.0
G91
G100
DE
G120
1.5
G150
1.0
0.5
0.0
0.0
0.2
0.4
0.6
period (sec)
0.8
1.0
Effectiveness of 2nd Story Repair
0.8
G67
G83
G91
V2/W
G100
0.6
0.4
0.2
0.0
-0.5 -0.4 -0.3 -0.2 -0.1 0
-0.2
0.1
0.2
0.3
0.4
0.5
V2/W
G50
G40
G67
G83
G91
G100
G120
G150
E150
E200
0.8
0.6
0.4
0.2
0.0
-0.5 -0.4 -0.3 -0.2 -0.1 0.0
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
Drift Ratio (%)
Before FRP Retrofit
0.1
Drift Ratio (%)
After FRP Retrofit
0.2
0.3
0.4
0.5
Bottom Story Response
V1/W
1.2
specimen 1 peak
1.0
0.8
0.6
0.4
0.2
0.0
-0.2 0.0 0.2 0.4 0.6 0.8
-0.8 -0.6 -0.4 -0.2
-0.4
-0.6
specimen 1 peak
-0.8
-1.0
-1.2
Drift Ratio (%)
G40
G67
G83
G91
G100
G120
G150
E150
E200
Motion
Drift
Damage
G40
0.09%
Slight1
G67
0.15%
Slight
G83
0.17%
Slight
G91
0.19%
Slight
G100
0.24%
Slight
G120
0.34%
Moderate
G150
0.65%
Severe
E150
0.52%
Severe
E200
0.67%
Severe
1Damage
due to previous motions
Final Damage
Signs of delamination
joint failure
Failure of top
ECC/frame shear
dowel connection
Shear/sliding Crack at Bottom Story
Failure of shear dowels
Conclusions
• Infills can significantly increase the lateral
strength of a non-ductile frame, thus improving
seismic performance.
• Retrofit using ECC overlay increased the
resistance of the infilled frame, however it may
not always be possible to increase ductility.
• Repair based on epoxy injection/GFRP is fast
and efficiently restores the strength of an infill
panel.
Conclusions
• The proposed analysis methodology offers
satisfactory agreement with recorded data in
terms of global response quantities and failure
mechanism.
• Further numerical investigation of system
performance for different configurations is
feasible.
Acknowledgements
- Research sponsored by NSF (under the Network
for
Earthquake
Engineering
Simulation
Research Program).
- Professional Advisory Panel:
Joe Maffei, John Kariotis, David Breinholtz,
Michael Valley, Gregory Kingsley, Ronald
Mayes.
- Johnson Western Gunite Company.
- Fyfe Co. (Scott Arnold).
Thank you
• Questions?