UNIVERSITY of ILLINOIS
NEES Small-Group Research Project:
Seismic Behavior, Analysis and
Design of Complex Wall Systems
(NSF Grant CMMI-0421577)
Laura Lowes, Dawn Lehman, Anna Birely,
Joshua Pugh, UW
Dan Kuchma, Chris Hart, Ken Marley, UIUC
Research Objective
• Establish the seismic
performance of modern
reinforced concrete walls
and develop the response
and damage-prediction
models required to
advance performancebased design of these
systems
Photo courtesy of MKA Seattle
Research Activities to Date
• Experimental testing:
– Testing of four planar walls completed in 2008
– Testing of a planar coupled wall to be completed Nov. 2010
– Testing of three c-shaped walls to be completed in 2011
• Simulation: development, calibration and evaluation of
– Elastic, effective stiffness models
– Fiber-type beam-column models w/ and w/o flexure-shear
interaction
– Two-dimensional continuum models
• Performance-prediction models:
– Development of data relating damage and demand
– Development of fragility functions for walls
Experimental Testing
Of Planar Walls
Experimental Test Program
• Prototype structure
Core Wall under Construction
(Courtesy of MKA, Seattle)
• Experimental test matrix
NEES Experimental Testing
•
•
•
Bottom three stories of 10-story
of a planar prototype wall.
Shear and moment applied to
simulate lateral load distribution
in 10-story prototype
Target axial load of 0.1Agfc’.
Planar Wall Test Specimens
• 1/3-scale with details reflecting modern
construction practice.
10'-0"
B
6"
LVL 3
Section A
4'-0"
1'-9"
Boundary Elements (3.5%)
Scale: Not to Scale
3" (TYP.)
HOOKS OVERLAP TIE
LVL 2
2” (TYP.)
B
4'-0"
A
A
LVL 1
4'-0"
REINFORCEMENT SCHEDULE
1'-9"
6'-8"
1'-8"
Structural Wall Elevation
Scale: Not to Scale
(3) #4 @ 3"
EMBED
LENGTH
1' - 8"
LAP
LENGTH
2' - 0"
(2) #2 @ 6"
7"
9"
MARK REINFORCEMENT
LVL 0
1'-8"
Detail B
Scale: Not to Scale
A
B
Full Scale:
12’ high/18 in. thick
Lab:
4’ high/ 6 in. thick
#2 TIES @ 2" o.c. (TYP.)
A
B
Splice at
Base of Wall
NOTES:
Planar Wall Test Matrix
Moment-to
Shear Ratio
Distribution of
Reinforcement
Splices?
Wall 1
Mb = 0.71hVb
Vb = 2.8f ’c = 0.7Vn
BE at EDGE
YES
Wall 2
Mb = 0.50hVb
Vb = 4.0f ’c = 0.9Vn
BE at EDGE
YES
Wall 3
Mb = 0.50hVb
Vb = 4.0f ’c = 0.9Vn
UNIFORM
YES
Wall 4
Mb = 0.50hVb
Vb = 4.0f ’c = 0.9Vn
BE at EDGE
NO
STUDY
PARAMETERS
Global Response: Base Moment v. 3rd Floor Drift
6000
M, k-ft
Mn
3000
-1.0
0.0
-3000
1.0
2.0
-2.0
-1.0
0.0
-3000
6000
Mn
3000
1.0
2.0
1.0
2.0
M, k-ft
Mn
3000
% Drift
0
-6000
% Drift
-6000
6000 M, k-ft
-1.0
0.0
-3000
Mn
0
-6000
-2.0
M, k-ft
3000
% Drift
0
-2.0
6000
% Drift
0
-2.0
-1.0
0.0
-3000
-6000
1.0
2.0
Response of PW 4: No Splice
Final Damage States for Planar Walls
Wall 1: Vb = 3.6f’c
1.5% drift (3rd story)
2.1% drift (10th story)
Wall 2: : Vb = 5.0f’c
1.5% drift (3rd story)
1.8% drift (10th story)
Wall 3: Vb = 4.5f’c
1.25% drift (3rd story)
1.6% drift (10th story)
Wall 4: Vb = 4.6f’c
1.0% drift (3rd story)
1.4% drift (10th story)
Experimental Testing
of a Coupled Wall
Objective: To determine what is the seismic
behavior of a modern coupled wall
• Review inventory of modern coupled walls
– 17 buildings with coupled-core wall systems designed for construction in CA or WA in
last 10 years.
– Information collected included geometry, aspect ratios, reinforcement ratios, degree of
coupling, shear demand-capacity ratio, pier wall axial demand-capacity ratio, etc.
• Review previous experimental tests
– Numerous tests of coupling beams with different reinforcement layouts, ratios and
confinement details.
– Only seven (7) coupled-wall tests found in the literature.
– Coupled wall test specimens are not representative of current design practices.
• Design and evaluate multiple 10-story planar coupled walls
– Design walls following the recommendations of the SEAOC Seismic Design Manual, Vol.
III, using ASCE 7-05, and meeting requirements of ACI 318-08.
– Progression of yielding and failure mechanism was evaluated via continuum finiteelement analysis using VecTor2.
– Design was updated to ensure yielding of coupling beams and wall piers.
Coupled Wall Test Specimen
• Specimen is bottom three
stories of a 10-story planar
coupled wall.
• Coupling beams have
aspect ratio of 2.0 and
diagonal reinforcement.
• Seismic loading results in
yielding in coupling beams
and wall piers.
• Pier walls are capacitydesigned for shear.
Boundary Element
• rlong = 3.5%
• rtrans = 1.4%
Web
• rlong = 0.27%
• rhorz = 0.27%
Coupling beams:
• aspect ratio = 2.0
• rdiag = 1.25%
• Vn = 4.6 fc Ag
Construction
Testing of the Coupled Wall Specimen
Fz,total
My,total
Dx,Fx,total
(edited image)
• ∆x
- prescribed (i.e. disp. control)
• Fz,total = constant
- chosen as 0.1fcAg
• My,total = k*Fx,total
- k is defined by chosen lateral load dist.
- Fx measured in lab for given Dx
Testing of the Coupled Wall Specimen
(edited image)
• ∆x = (∆x1 + ∆x2)/2
- prescribed (i.e. disp. control)
• Fz1 + Fz2 = constant
- chosen as 0.1fcAg
• My,total = k*(Fx1 + Fx2)
- k is defined by chosen lateral load dist.
• Fx2 – Fx1 = f(Fx,tot)
- f(Fx,tot) is determined by analysis before
testing
• θy1 = n*∆x1; θy2 = n*∆x2
- n is determined by analysis before testing
Validation of the Loading Protocol
• Compare simulated response of 10-story prototype
and 3-story laboratory test specimen
3rd story load versus displacement response
prototype
specimen
Validation of the Loading Protocol
• Compare simulated response of 10-story prototype
and 3-story laboratory test specimen
Principal concrete compressive strain field at 0.75 in. lateral displacement
bottom 3 stories of 10-story prototype
3-story test specimen
Simulation: Model Development and
Evaluation
Experimental Database
•
•
•
•
66 wall tests from 13 different test programs
60% are slender (AR > 2); 40% are squat (AR < 2)
78% tested cyclically; 22% tested monotonically
Failure modes
– Slender walls: 85% in flexure; 10% in shear; 5% in flex-shear
– Squat walls: 40% in flexure; 60% in shear
• Design parameters:
Parameter
Average
Min.
Max.
f’c (psi)
5400
2370
10250
rvert (%)
rhorz (%)
1.90
0.40
3.00
0.60
0.00
1.70
P/Agf’c
0.04
0.00
0.20
Vu/af’c (psi)
5.70
1.13
12.80
Simulation Models and Software
• OpenSees fiber-type beam-column models
– Force-based, distributed plasticity element without
flexure-shear interaction1 and with linear, calibrated
shear flexibility2
– Displacement-based, lumped-plasticity with
flexure-shear interaction3
• Two-dimensional continuum model
– Modified compression field theory as implemented
in VecTor24
1.
2.
3.
4.
Neuenhofer and Filippou (1997, 1998), Taucer et al. (1991), Spacone and Filippou (1992)
Oyen (2006)
Massone et al. (2006), Massone (2006)
http://www.civ.utoronto.ca/vector/, Wong and Vecchio (2003)
Ratio of Simulated-to-Observed Response
Wall
Config.
Rect.
Slender
(30/66)
Barbell
Slender
(9/66)
Rect.
Squat
(15/66)
Flanged
Squat
(12/66)
Stiffness to Yield
Maximum Strength
Displacement Capacity
ForceBased
FlexShear
2D
ForceBased
FlexShear
2D
ForceBased
FlexShear
2D
0.91
(0.21)
1.23
(0.21)
1.02
(0.23)
0.99
(0.17)
1.07
(0.13)
1.09
(0.08)
0.66
(0.36)
1.00
(0.38)
1.14
(0.32)
1.55
(0.12)
1.72
(0.16)
1.36
(0.10)
1.00
(0.08)
1.18
(0.11)
1.01
(0.08)
0.41
(0.29)
2.23
(0.33)
1.12
(0.30)
0.89
(0.20)
1.63
(0.12)
1.28
(0.20)
1.00
(0.17)
1.01
(0.12)
1.02
(0.07)
1.11
(0.42)
0.65
(0.28)
0.69
(0.33)
-
-
-
3.99
(0.52)
1.57
(0.37)
1.25
(0.13)
2.49
(0.53)
0.49
(0.65)
0.66
(0.53)
Damage Prediction Models
Initial spalling
Steel fracture
Spalling at base
Experimental Database
•
•
•
•
•
66 wall tests from 18 different test programs
100% are slender with AR > 2
83% tested cyclically; 17% tested monotonically
92% tested uni-directionally, 8% tested bi-directionally
Design parameters: Parameter
Average
Min.
Max. Std. Dev.
Scale
0.4
0.2
5.0
0.5
f’c (psi)
5500
3000
11300
2000
rbe (%)
rweb (%)
rhorz (%)
3.5
0.8
11.4
2.0
0.6
0.1
2.3
0.6
0.5
0.2
1.4
0.2
P/Agf’c
0.1
0.0
0.2
0.05
Vu/(Acvf’c) (psi)
4.8
1.0
11.0
2.0
Vu/Vn
0.7
0.2
1.4
0.3
Damage States / Method of Repair
Damage
State
Description
Method of Repair
DS 1
• Initial cracking
• Initial yielding of reinforcement
Cosmetic Repair
DS 2
• Concrete crack widths > 1/16 in.
Epoxy Injection of Cracks
DS 3
• Spalling that does expose long.
reinforcement
Epoxy Injection of Cracks and
Patching of Concrete
DS 4
• Exposed longitudinal reinforcement
• Vertical cracks/splitting
• Cracks ≥ 1/8”
DS 5
•
•
•
•
•
Core crushing
Bar buckling and/or fracture
Web crushing
Bond slip failure
Shear failure
Replace Concrete
Replace Wall
Engineering Demand Parameters
• Maximum Drift
– displacement at top of specimen / specimen height
• Maximum 1st Story Drift
– Assume full-scale is a story height of 10 ft. and wall thickness of 12 in.
– Assume stiffness above the 1st of the wall is defined by 0.10GcAcv (shear) and
average EcIg for the entire wall.
– 1st story drift is then calculated using displacement measured at the top of the
wall specimen and above assumptions.
• Maximum Rotation Demand for a Lumped-Plasticity Model
– Hinge at base of the wall has a hinge length of ½ Lw
– Assume stiffness of the remaining height of the wall is defined by 0.50EcIg
(flexure) and 0.10GcAcv (shear)
– Hinge rotation is then calculated using displacement measured at the top of
the wall specimen and above assumptions.
Fragility Functions for Slender Walls
• Damage state –
demand data are
used to calibrate
lognormal CDF
Lognormal Distribution
Parameters
Damage Median
Dispersion
State Drift (%)
DS1
0.09
0.78
DS2
0.63
0.85
DS3
0.96
0.50
DS4
1.10
0.64
DS5
1.60
0.59
Investigation of the Impact of Design
Parameters on Damage Progression
• Objective: Develop suites of fragilities for walls with
different design parameter values
Parameter
Impact
Axial load ratio
Significant
Shear demand
Significant
Aspect ratio / shear span (Mbase/Vbase/Lw)
Significant
Displacement history (uni- versus bidirectional)
Apparently
significant*
Shape (planar, flanged, c-shaped, etc.)
Minimal
Scale
Minimal
Shear demand-capacity ratio
Minimal
* Too few test specimens with bi-directional displacement histories
DS versus drift with data
grouped by axial load ratio
Conclusions
• Laboratory testing of rectangular planar walls
– Drift capacity of rectangular concrete walls with modern detailing and
representative load distributions ranges from 1.0% to 1.5% (1.4% to
2.0% at roof of 10-story structure).
– Damage was concentrated in the first story; other stories cracked but
otherwise pristine.
– Drift was due to base rotation (15-25%), flexure (55-60%), and shear
(~25%). Flexural deformation of 3rd floor was much smaller than 1st
and 2nd.
Conclusions
• Simulation
– Strength
• Planar walls: All models provide accurate and precise simulation of strength
• The continuum model also provides acceptable accuracy and precision for flanged,
squat walls
– Stiffness to yield
• For rectangular, slender walls the models provide reasonably accurate and precise
simulation of stiffness: error in simulated stiffness ranges from 23% to 2% with a
cov of approximately 20%
• The continuum model provides the best accuracy and precision for all of the wall
configurations considered
– Displacement capacity
• None of the models does a particularly good job of simulating displacement
capacity for all of the wall configurations considered
• The continuum models provides acceptable accuracy and precision for slender
walls; errors are less than 15% with a cov of approx. 30%
Conclusions
• Performance-based design
– For slender walls, the median drift at which wall replacement is
required is 1.6%
THANK YOU!
Questions?
Coupling Beam Reinforcement Ratio
Diagonal Reinforcement Ratio
Diagonal Reinf. Coupling Beams
2.50%
Galano 2000
2.00%
Kwan 2004
Paulay 1971
1.50%
Shiu 1978
NEESR Wall
Tassios 1996
BTT
1.00%
EH
FS
0.50%
MFC
0.00%
0.00
1.00
2.00
3.00
Aspect Ratio
4.00
5.00
6.00
Evaluation of Response Using Local
Instrumentation Data
NORTH FACE
22"
D
22"
C
B
8+23=31 gages
WEST
EAST
2" 2"
A
E
22'
C
B
13 gages
22"
D
2" 2"
A
G
11"
E
D
11"
C
25 gages
22"
F
B
2"
A
D
C
B
A
2"
12
16"
11
10
40"
09 08
40"
07
06
05
2"
16"
04
03
02
01
00
External Instrumentation – November 2007
Scale: ½” = 1'-0"
46+23
= 69
Krypton and Disp. Transducer Data
Contribution to total drift (%)
3rd floor shear
2nd floor shear
1st floor shear
3rd floor flexural
2nd floor flexural
1st floor flexural
Base rotation
Base slip
Wall 2
Contribution to total drift (%)
Wall 1
Wall 3
Drift at top of specimen
Wall 4
Drift at top of specimen
Wall 4 Shear Strain from Krypton Data