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Seismic Performance Assessment and Retrofit of Non-Ductile RC
Frames with Infill WallsP. Benson Shing
Ioannis Koutromanos
Andreas Stavridis
Marios Kyriakides
Sarah Billington
Kaspar Willam
NEES & PEER Quake SummitSan 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.
280mm 3380mm 280mm
1870mm
370mm
#2 @ 265mm stirrups8 #5 bars
280mm
280mm
= 156kN
Lateral displacement
W2
= 156kNW2
#2 @ 265mm stirrups8 #5 bars
280mm
280mm
Lateral displacement
280mm3380mm280mm
1870mm
370mm
912mm836mm
610mm
794mm
= 156kNW2
= 156kNW2
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 cracking-
sliding.
Modeling Approach – RC Columns
Triangular smeared crack element
Interface element to model discrete cracks
Cracks are modeled in discrete and smeared fashion.
Stavridis and Shing, 2010
Modeling Approach – Infill Panels
Anticipated cracking pattern mainly runs through the mortar joints, with some brick splitting cracks
Interface (for possible splitting cracks)
Quadrilateral smeared crack elements (each elem. = half brick)
Interface (for bed joints) Interface (for head joints)
Stavridis and Shing, 2010
Smeared Crack Element
Uncracked material: Failure surface combines Von Mises criterion with a tension cutoff criterion.
c
c
2
p pe o c o 2
1p 1p
2ε 2εσ =f + f' f
ε ε
σe
cf'
of
σ2e
ε1p ε2p εp
σe
mf'
of
σ2e
2
p pe o m o 2
1p 1p
2ε 2εσ =f + f' f
ε ε
e 2e p m 2e p 2p
p m 2e
mσ σ + r f' σ 1- exp ε ε
r f' σ
-m
1
m1
e 2e p c 2e p 2pp c 2e
mσ = σ + r f' σ 1 exp ε - ε
r f' - σ
- - -
p cr f'c
c
2
p pe o c o 2
1p 1p
2ε 2εσ =f + f' f
ε ε
σe
cf'
of
σ2e
ε1p ε2p εp
σe
mf'
of
σ2e
2
p pe o m o 2
1p 1p
2ε 2εσ =f + f' f
ε ε
e 2e p m 2e p 2p
p m 2e
mσ σ + r f' σ 1- exp ε ε
r f' σ
-m
1
m1
e 2e p c 2e p 2pp c 2e
mσ = σ + r f' σ 1 exp ε - ε
r f' - σ
- - -
p cr f'
Failure surface of uncracked materialNonlinear isotropic hardening-softening law for effective strength
σ1
σ2
σe
ft
ftσe
Originally formulated by Lotfi and Shing (1992)
Smeared Crack Element
Cracked material: Orthotropic stress-strain law:
ε1ε2
fc
ft
ε
σ
Secant stiffness unloading/reloading
Initial stiffness unloading/reloading
Exponential softening
Parabola
Exponential softening
Interface Element
Local coordinate system
initialfinal
Yield surface (Lotfi and Shing 1994)
σ
ττ2 – μ2(σ – s)2 – 2r(σ – s) = 0
d = del + dpl + dg
Displacement vector:
so
co = μ2so + 2roso2
μο
1
μr
1
μ, r, s: strength parameters
ο
1
4
2
3
n
t
elastic
plastic
geometric
Tensile Stress vs. Normal Crack Opening
Koutromanos and Shing (2010)
Interface Element
σ
dndn1 dn2
σ
dndn1 dn2
σ
dndn1 dn2
σ
dndn1 dn2
σ
dndn1 dn2
σ
dndn1 dn2
σ
dndn1 dn2
σ
dndn1 dn2
Loading-unloading
Reloading
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 20 40 60 80 100 120
Normal Displacement (μm)
Te
ns
ile S
tre
ss
(M
Pa
) ExperimentAnalysis
Joint Dilatation & Compaction
100-psi Normal Compression
Shear
Axial Compression
Interface Element
Test on mortar joint by Mehrabi and Shing (1994)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-10 -5 0 5 10
Shear Displacement (mm)
Sh
ea
r S
tre
ss
(M
Pa
)
experimentanalysis
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
-10 -5 0 5 10
Shear Displacement (mm)
No
rma
l Dis
pla
ce
me
nt
(mm
)
experimentanalysis
Verification – Quasi-static Tests
-2.5-2.0-1.5
-1.0-0.50.00.51.0
1.52.02.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
drift ratio (%)
V/W
ExperimentAnalysis
-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
drift ratio (%)
V/W
Experiment
Analysis
Verification – Quasi-static Tests
Shake Table Test 1
EASTWEST
Prototype 3-story Building
R/C frame with solid brick infill panels, representing design practice in California in the 1920s.
Slab with joists
1 2
A
B
C
D
22’
18’3
18’
22’
22’
El Centro NS Record, 1940 Imperial Valley Earthquake
Gilroy 3 000 Record, 1989 Loma Prieta Earthquake
Base Acceleration Time Histories
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 10 20 30 40
Ac
ce
lera
tio
n (g
)
time (sec)-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0 10 20 30 40A
cc
ele
rati
on
(g)
time (sec)
Motion Sequence
Trial Motion
1 Gilroy 40%
2 Gilroy 67%
3 Gilroy 67b%
4 Gilroy 83%
5 Gilroy 91%
6 Gilroy 100%
7 Gilroy 120%
8 El Centro 250%
Stavridis et al, 2010
Specimen Damage
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)
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)
Bottom Story Response
Specimen Damage
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
Bottom Story Response
Specimen Damage
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:
0.005
0.000
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.0 0.5 1.0 1.5 2.0
T(s)
ζ
Bottom Story Drift Time Histories
G67 Motion
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
3 4 5 6
time (sec)
dri
ft r
atio
(%
)
Experiment
Analysis
G67b Motion
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
27 28 29 30
time (sec)
dri
ft r
atio
(%
)
Experiment
Analysis
G83 Motion
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
51 52 53 54
time (sec)
dri
ft r
atio
(%
)
Experiment
Analysis
G91 Motion
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
75 76 77 78 79
time (sec)
dri
ft r
atio
(%
)
Experiment
Analysis
G100 Motion
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
99 100 101 102
time (sec)
dri
ft r
atio
(%
)
Experiment
Analysis
G120 Motion
-0.80
-0.40
0.00
0.40
0.80
1.20
123 124 125 126
time (sec)
dri
ft r
atio
(%
)
Experiment
Analysis
G120 Motion
Bottom Story Hysteretic PlotsG67 motion G67b motion G83 motion
G91 motion G100 motion G120 motion
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
-0.10 -0.05 0.00 0.05 0.10
drift ratio (%)
no
rma
lize
d s
he
ar,
V1/
W
Experiment
Analysis
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
drift ratio (%)
no
rma
lize
d s
he
ar,
V1/
WExperiment
Analysis
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30
drift ratio (%)
no
rma
lize
d s
he
ar,
V1/
W
Experiment
Analysis
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40
drift ratio (%)
no
rma
lize
d s
he
ar,
V1/
W
Experiment
Analysis
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
drift ratio (%)
no
rma
lize
d s
he
ar,
V1/
W
Experiment
Analysis
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
-1.20 -0.80 -0.40 0.00 0.40 0.80 1.20
drift ratio (%)
no
rma
lize
d s
he
ar
V1/
W
Experiment
Analysis
After G91
Cracking Pattern
Experiment Analysis
After G100Experiment Analysis
Cracking Pattern
After G120Experiment Analysis
Cracking Pattern
Panel with ECC retrofit
Shake Table Test 2
Anchors (1’ x 1’ grid)
Unbonded dowels (with grease)
Dowels
Application of ECC Retrofit
Application of ECC Retrofit
ECC Retrofit Behavior
1/5 scale specimens tested quasi-statically at Stanford University by Kyriakides and Billington.
No retrofit
Drift (%)
Lat
eral
Lo
ad
(kN
)
Unretrofitted Wall
Retrofitted Wall
With ECC Retrofit
crush
Damage at Specimen
Frame/panel separation
Epoxy injections at major cracks
Second Story Strengthening
1 layer of Tyfo BC
1 layer of Tyfo SEH-51A System Oriented Vertically
1 layer of Tyfo SEH-51A System, Oriented Horizontally
12”
12”
GFRP overlay (by Fyfe Co.)
Trial Motion
1 Gilroy 40%
2 Gilroy 67%
3 Gilroy 83%
4 Gilroy 91%
5 Gilroy 100%
6 Gilroy 120%
7 Gilroy 150%
8 El Centro 150%
9 El Centro 200%
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0 0.2 0.4 0.6 0.8 1.0
SA
(g)
period (sec)
G40
G67
G83
G91
G100
G120
G150
Motion Sequence
DE
MCE
T1 before testing
T1 after testing
Effectiveness of 2nd Story Repair
Before FRP Retrofit After FRP Retrofit
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Drift Ratio (%)
V2/
W
G50
G67
G83
G91
G100
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
Drift Ratio (%)
V2/
W
G40G67G83G91G100G120G150E150E200
-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
Drift Ratio (%)
V1/
W
G40G67G83G91G100G120G150E150E200
Bottom Story Response
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
specimen 1 peak
specimen 1 peak
Final Damage
Failure of top ECC/frame shear dowel connection
joint failure
Signs of delamination
Shear/sliding Crack at Bottom Story
Failure of shear dowels
• 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.
Conclusions
- 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).
Acknowledgements
• Questions?
Thank you