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, UWDan Kuchma, Chris Hart, Ken

Marley, UIUC

UNIVERSITY of ILLINOIS

Research Objective• Establish the

seismic performance of modern reinforced concrete walls and develop the response and damage-prediction models required to advance performance- based 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 TestingOf Planar Walls

Experimental Test Program• Prototype structure • Experimental test matrix

Core Wall under Construction (Courtesy of MKA, Seattle)

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’.

A B

A

B

LVL 3

LVL 2

LVL 1

LVL 0

1'-8" 1'-8"6'-8"

4'-0

"4'

-0"

4'-0

"1'

-9"

1'-9

"Structural Wall Elevation

Scale: Not to Scale

A

10'-0"6"

MARK REINFORCEMENTEMBED LENGTH

LAP LENGTH

A (3) #4 @ 3" 1' - 8" 2' - 0"

B (2) #2 @ 6" 7" 9"

REINFORCEMENT SCHEDULE

Section A

B

NOTES:

Scale: Not to Scale

#2 TIES @ 2" o.c. (TYP.)

Detail BScale: Not to Scale

HOOKS OVERLAP TIE3" (TYP.)

2” (

TY

P.)

Planar Wall Test Specimens• 1/3-scale with details reflecting modern

construction practice.Boundary Elements (3.5%)

Splice atBase of Wall

Full Scale:12’ high/18 in. thickLab:4’ high/ 6 in. thick

Planar Wall Test MatrixMoment-toShear Ratio

Distribution of Reinforcement Splices?

STUDYPARAMETE

RS

Wall 1

Wall 2

Wall 3

Wall 4

Mb = 0.71hVb

Vb = 2.8f’c = 0.7Vn

UNIFORM

NO

YESBE at EDGE

BE at EDGE

BE at EDGE

YES

YES

Mb = 0.50hVb

Vb = 4.0f’c = 0.9VnMb = 0.50hVb

Vb = 4.0f’c = 0.9VnMb = 0.50hVb

Vb = 4.0f’c = 0.9Vn

Global Response: Base Moment v. 3rd Floor Drift

-2.0 -1.0 0.0 1.0 2.0

-6000

-3000

0

3000

6000

-2.0 -1.0 0.0 1.0 2.0

-6000

-3000

0

3000

6000

-2.0 -1.0 0.0 1.0 2.0

-6000

-3000

0

3000

6000

-2.0 -1.0 0.0 1.0 2.0

-6000

-3000

0

3000

6000Mn

% Drift % Drift

% Drift% Drift

M, k-ft

M, k-ft M, k-ft

M, k-ftMn

Mn Mn

Response of PW 4: No Splice

Final Damage States for Planar Walls

Wall 1: Vb = 3.6f’c 1.5% drift (3rd story)2.1% drift (10th story)

Wall 2: : Vb = 5.0f’c 1.5% drift (3rd story)1.8% drift (10th story)

Wall 3: Vb = 4.5f’c 1.25% drift (3rd story)1.6% drift (10th story)

Wall 4: Vb = 4.6f’c 1.0% drift (3rd story)1.4% drift (10th story)

Experimental Testingof 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 finite-

element 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 capacity-designed for shear. Coupling beams:

• aspect ratio = 2.0

• rdiag = 1.25%• Vn =

gc Af6.4

Boundary Element• rlong = 3.5%• rtrans = 1.4%

Web• rlong = 0.27%• rhorz = 0.27%

Construction

Testing of the Coupled Wall Specimen

• ∆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

(edited image)

Dx,Fx,total

My,total

Fz,total

Testing of the Coupled Wall Specimen

• ∆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

(edited image)

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

bottom 3 stories of 10-story prototype 3-story test specimen

Principal concrete compressive strain field at 0.75 in. lateral displacement

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 (%) 1.90 0.40 3.00

rhorz (%) 0.60 0.00 1.70

P/Agf’c 0.04 0.00 0.20Vu/af’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. Neuenhofer and Filippou (1997, 1998), Taucer et al. (1991), Spacone and Filippou (1992)2. Oyen (2006)3. Massone et al. (2006), Massone (2006)4. http://www.civ.utoronto.ca/vector/, Wong and Vecchio (2003)

Ratio of Simulated-to-Observed Response

Wall Config.

Stiffness to Yield Maximum Strength Displacement CapacityForce-Based

Flex-Shear 2D Force-

BasedFlex-Shear 2D Force-

BasedFlex-Shear 2D

Rect. Slender(30/66)

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)

Barbell Slender

(9/66)

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)

Rect. Squat(15/66)

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)

Flanged Squat(12/66)

- - - 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

Spalling at base

Steel fracture

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 0.5f’c (psi) 5500 3000 11300 2000rbe (%) 3.5 0.8 11.4 2.0rweb (%) 0.6 0.1 2.3 0.6rhorz (%) 0.5 0.2 1.4 0.2P/Agf’c 0.1 0.0 0.2 0.05

Vu/(Acvf’c) (psi) 4.8 1.0 11.0 2.0Vu/Vn 0.7 0.2 1.4 0.3

Damage States / Method of RepairDamage

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”

Replace Concrete

DS 5

• Core crushing• Bar buckling and/or fracture• Web crushing• Bond slip failure• Shear failure

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 State

Median Drift (%) Dispersion

DS1 0.09 0.78DS2 0.63 0.85DS3 0.96 0.50DS4 1.10 0.64DS5 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 ImpactAxial load ratio Significant

Shear demand Significant

Aspect ratio / shear span (Mbase/Vbase/Lw) Significant

Displacement history (uni- versus bi-directional)

Apparently significant*

Shape (planar, flanged, c-shaped, etc.) Minimal

Scale Minimal

Shear demand-capacity ratio Minimal

DS versus drift with data grouped by axial load ratio

* Too few test specimens with bi-directional displacement histories

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

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Dia

go

na

l Re

info

rce

me

nt

Ra

tio

Aspect Ratio

Diagonal Reinf. Coupling Beams

Galano 2000

Kwan 2004

Paulay 1971

Shiu 1978

Tassios 1996

BTT

EH

FS

MFC

NEESR Wall

Evaluation of Response Using Local Instrumentation Data

2"11

"11

"22

"2"

16"2" 40" 40" 16" 2"

2"22

'22

"2"

2"22

"22

"

External Instrumentation – November 2007

Scale: ½” = 1'-0"

25 g

ages

13 g

ages

8+23

=31

gag

es

46+23= 69

B

F

D

B

D

E

C

A

C

A

G

C

A

E

D

B

C

B

D

A

000103 02040507 060809101112

EAST WESTNORTH FACE

Krypton and Disp. Transducer Data

Drift at top of specimen Drift at top of specimen

Wall 1 Wall 2

Wall 3 Wall 4

Cracking

Cracking

Cracking

Cracking

Yielding

Yielding

Yielding

Yielding

3rd floor shear 2nd floor shear 1st floor shear 3rd floor flexural 2nd floor flexural 1st floor flexural Base rotationBase slip

Con

trib

utio

n to

tot

al d

rift

(%)

Con

trib

utio

n to

tot

al d

rift

(%)

Wall 4 Shear Strain from Krypton Data