numerical modeling and collapse safety assessment of an...

The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014

Numerical Modeling and Collapse Safety Assessment of an Unbonded Post-Tensioned Cast-In-Place Concrete Wall

Hao Wu, PhD Student, Tongji University

Visiting Research Associate, Lehigh University

Richard Sause, Professor, Lehigh University

Leary Pakiding, PhD Student, Lehigh University

Stephen Pessiki, Professor, Lehigh University

Xilin Lu, Professor, Tongji University

December 12, 2014


2

Outline

Background

Lehigh Wall #1

Numerical Modeling

Collapse Safety Assessment

Concluding Remarks

Acknowledgement


3

Background

Shear failure

Rebar

fracture

Concrete

crushed

2010 Chile Earthquake（From EERI）

From Fahnestock et al 2007

BRB框架

楼层

位移

(m

m,

MC

E)

Building codes use ductility from

inelastic actions to protect structures

against collapse during large

earthquakes. In conventional seismic

systems, however, this leads to:

• Distributed Structural Damage

• Residual Drifts


4

UPT Concrete Walls

Conventional RC wall

UPT PC-concrete wall Hybrid PC-concrete wall Hybrid CIP-concrete wall

F

D

F

D

F

D

F

D

Residual disp.

Perez (2004) Smith (2012) Pakiding et al (2014)


5

Elevation

Lehigh Wall (Ms/Mp=2.0)

3 #

7

#3 @2.25"

#4 @ 4.5"4" 4" 4" 5" 7" 7" 3.5" 6"1.5"

1.5

"10"

72"

CL

(2) bundles of

(5) 0.6" dia. strands

3 #

7

2 #

7

2 #

3

2 #

3

2 #

3

2 #

3

Wall 1

4" 4" 4" 5" 7" 7" 3.5" 6"1.5"

1.5

"10"

72"

CL

3 #

5

2 #

5

2 #

3

2 #

3

2 #

3

2 #

3

(2) bundles of


3 #

5

#3 @2.25"

#4 @ 4.5"

(1) bundle of


Reduced dia. of boundary rebar

(Ms/Mp=0.5) Increase PT

Wall 2

4" 4" 4" 5" 7" 7" 3.5" 6"1.5"

1.5

"10"

72"

CL

3 #

5

2 #

5

2 #

3

2 #

3

2 #

3

2 #

3

(2) bundles of


3 #

5

#3 @2.25"

#4 @ 4.5"

(1) bundle of


Unbonded boundary rebars

Wall 3


6

Lehigh Wall #1

Shear

failure Confined

concrete crushed

Bond slip of

long. rebars

Fracture/buckling

of long. rebars

Actu

ato

r h

eig

ht

15

0 in.

Unb

on

ded P

T h

eig

ht

30

0 in.

Test setup Loading protocol (ACI ITG5.1) Lateral force-disp. response

Yielding of

long. rebars

Concrete

spalling Yielding of PT

Concrete

cracking


7

Numerical modeling: Analytical model

Wall panel: Force-based fiber beam-column element PT: Corotational truss element Shear failure / Bond slip: zero-length element

(Front face) East

bar-slip fiber

section element

0

Shear spring

reaction wall

actuator support

fixture

actuator

load cell

load cell

foundation block

bearing

plate

PT anchorage

actu

ator

hei

ght

= 3

.81 m

wal

l hei

ght

= 6

.35 m

unbonded

hei

ght

= 7

.62 m

strong floor

1.5

2 m

test

specimen

(Front face) East

(c)

0

Compression-only

spring

critical

height, hcr

truss element

(PT)

node kinematic

constraint

fiber beam

column element

(wall panels)

critical height

element

zero-length

element

wall outline

Reference: Ghannoum, W.M., Moehle J.K., 2006, “Dynamic Collapse Analysis of a Concrete Frame Sustaining Column Axial Failures,” ACI Structural Journal, 109 (3), pp. 403–412 LeBorgne et al., 2014, "Analytical Element for Simulating Lateral-Strength Degradation in Reinforced Concrete Columns and Other Frame Members," Journal of Structural Engineering, V140(7), pp403-412.


8

1. Sample section at the element end where the bending moments are largest in the absence of member loads;

2. Integrate quadratic polynomials exactly to provide the exact solution for linear curvature distributions;

3. Integrate deformations over the specified lengths lpI and lpJ using a single section in each PH region.

Numerical modeling: PH int. method in FBE

Lp

M

My

F

Fy

M

My

F

Fy

Lp=0

Bi-linear model Hardening Softening

My

EI

Curvature

Mom

ent

Lp

Lp=0

Loss of objectivity

01

( ) ( ) ( ( ) ( ) )p

i

NL

x i

i

x x dx x x

T T

v b e b eCompatibility 0

1

( ) ( ) ( ) ( ( ) ( ) ( ) )p

i

NL

e

x i

i

x x x dx x x x

T T

s s

vf b f b b f b

q

Flexibility Matrix

Reference: M.H. Scott, G.L. Fenves. Plastic hinge integration methods for the force-based beam-column elements. J. Struct. Engrg., 132 (2006), pp. 244–252

Do NOT sample int. pt. at the end of the element to allow initial damage to be occurred at

a certain distance from the end of the element.


9

Numerical modeling: PH int. method in FBE

Modified G-R int.

(Scott et al., 2006)

1 = lpI 2 = 3lpI 3 = 3lpJ 4 = lpJ

L

1 = 0 2 = 8lpI/3 3 = 8lpJ/3 4 = L

Linear

elastic

1 = lpI 2 = lpI 3 = lpJ 4 = lpJ

L

1 = 0.4226lpI 2 = 1.5774lpI 3 = 1.5774lpJ 2 = 0.4226lpJ

Linear

elastic

Modified G-L int.

0 20 40 60 800

100

200

300

400

500

600

700Tanaka and park (1990)

Top disp. (mm)

Late

ral fo

rce (

kN

)

Experimental

DRAIN-2DX

OS, DRAIN's concept

OS, Modified G-L

OS, Modified G-R

L p 57

0m

m

DRAIN’s Concept in OS, to check M-Φ

2L p

Modified G-L

4L p

Modified G-R


10

Numerical modeling: Details of fiber model

-150

-100

-50

0

50

100

150

-0.10 -0.05 0.00 0.05 0.10

Stre

ss (

ksi)

Strain (in./in.)

US #7

esu=12%

Mild reinforcing steel

0

50

100

150

200

250

300

0.00 0.01 0.02 0.03 0.04

Stre

ss (

ksi)

Strain (in./in.)

PT

ePTu=2%

PT B

ase

shea

r

Shear spring deformation

Backbone

Loading PN

Loading NP

Initiation of lateral-strength degradation Unloading point

Kdeg

Vr

Kelastic

Unloading pinching point

Reloading pinching point

Stiffness damage

Strength damage

Kdeg

Vr

0

20

40

60

80

100

120

0.00 0.10 0.20 0.30 0.40

Stre

ss (

ksi)

Strain (in./in.) or Slip (in.)

Wall element fiber

Bar slip fiber

US #7 mild steel

0

2

4

6

8

10

12

0.00 0.05 0.10 0.15 0.20

Stre

ss (

ksi)

Strain (in./in.)

Wall element fiber

Bar slip fiber

Confined concrete

V

V

P

M

P

Mwall element

fiber section

bar slip element

fiber section

obs

kwe

c’ c


11

Numerical modeling: Results

-400

-200

0

200

400

-6 -4 -2 0 2 4 6

Late

ral f

orc

e (k

ips)

Loading pt. drift (%)

Test data

Model

Flexure only

-400

-200

0

200

400

-6 -4 -2 0 2 4 6

Late

ral f

orc

e (k

ip)


Test data

Model

Flexure + Bond-slip

-400

-200

0

200

400

-6 -4 -2 0 2 4 6

Late

ral f

orc

e (k

ips)


Test data

Model

Flexure + Bond-slip + Shear failure

0

100

200

300

-6 -4 -2 0 2 4 6

PT

forc

e (k

ip)


Test data

ModelEast side PT


12

Collapse Safety Assessment 7 bays @30’=210’

PT-CIP Wall (typ.)

Gravity load frame

N

Included in lean-on column model

7 b

ays

@3

0’=

21

0’

SFO, F4, R=6 LAX, F6, R=6

Rigid beam

Wall outline

Node

Truss ele. (PT)

Kinematic constraint

Fiber beam column ele.

(Wall panels)

Gravity load on prototype wall

Length of PH, hcr

Critical PH ele.

Lumped mass (typ.)

Gravity load on lean-on column

Lean-on column

0

Bar-slip fiber section

Shear spring

Nodes slaved to lean-on column

Compression only spring

SFO, F4 R=6/8


13

DBE/MCE

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

Tn (sec.)

Sa (

g)

Mean

ASCE 7-10

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

Tn (sec.)

Sa (

g)

Mean

ASCE 7-10

(a) (b)

SFO, DBE

Unscaled Scaled

0

1

2

3

4

5

6

0 10 20 30 40 50

Max

. sto

ry d

rift

rat

io (

%)

Ground motion No.

R=6R=8Mean, R=6Mean, R=8

2.06%

2.15%

0.0

0.1

0.2

0.3

0 10 20 30 40 50

Res

idu

al r

oo

f d

rift

rat

io (

%)

Ground motion No.

R=6

R=8

Mean, R=6

Mean, R=8

0.04%

0.03%

(a) (b)


14

Collapse Safety Assessment: IDA models


15

Collapse Safety Assessment: IDA, Fragility

Definition of collapse

Excessive lateral drift (qs,max > 10%)

Excessive shear deformation (disp. of zero-length ele.)

Excessive vertical disp. (disp. of the top node)

0 20 40 60 80 1000

2

4

6

8

10

12

Vertical disp. of roof node (cm)

Sa

(T1=

0.5

5s)

[g]

Collapse

0 0.05 0.1 0.15 0.20

2

4

6

8

10

12

Shear deformation (mm)

Sa

(T1=

0.5

5s)

[g]

Collapse

0 0.02 0.04 0.06 0.08 0.1 0.120

2

4

6

8

10

12

Maximum interstory drift ratio

Sa

(T1=

0.5

5s)

[g]

Collapse

LAXF6R6 0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Co

llap

se f

ragi

lity

Sa(T1=0.55s)/SaMCE(T1=0.55s)

Fitted

bRTR=0.4

RTR + Model

RTR + Model + SSF

bRTR = record-to-record variability

Model = dispersion from analytical model

SSF = spectral shape function


16

Collapse Safety Assessment: Fragility curves

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Co

llap

se F

ragi

lity

Sa(T1=0.56s)/SaMCE(T1=0.56s)

fitted

bRTR=0.4

RTR + Model

RTR + Model + SSF

SFOF4R6

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Co

llap

se F

ragi

lity

Sa(T1=0.65s)/SaMCE(T1=0.65s)

fitted

bRTR=0.4

RTR + Model

RTR + Model + SSF

SFOF4R8

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Co

llap

se F

ragi

lity

Sa(T1=0.55s)/SaMCE(T1=0.55s)

fitted

bRTR=0.4

RTR + Model

RTR + Model + SSF

LAXF6R6 LAXF6R8

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Co

llap

se F

ragi

lity

Sa(T1=0.63s)/SaMCE(T1=0.63s)

fitted

bRTR=0.4

RTR + Model

RTR + Model + SSF


17

Collapse Safety Assessment

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Fitt

ed C

olla

pse

Fra

gilit

y

Sa(T1=0.56s)/SaMCE(T1=0.56s)

SFOF4R6

SFOF4R6 (PT1%)

SFOF4R6 (RS10%)

SFOF4R6 (Vna)

SFOF4R6 (ALLna)


18

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Co

llap

se F

ragi

lity

Sa(T1)/SaMCE(T1)

SFOF4R6

SFOF4R8

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Co

llap

se F

ragi

lity

Sa(T1)/SaMCE(T1)

LAXF6R6

LAXF6R8


19

Concluding Remarks

• The amount of PT provided for Lehigh Wall #1 (Ms/Mp =

2.0) was not effective to produce enough restoring force

in reducing residual drift.

• Proposed numerical model is capable to capture the

complicated nonlinear behavior of the test wall as

observed.

• Modeling different potential failure mechanisms does

influences the fragility curves of the prototype structure

and further the probability of collapse. Seismic collapse

safety of the prototype wall in this study is satisfying.


20

Acknowledgement

Project: The Charles Pankow Foundation: Unbonded Post-Tensioned Cast-in-Place Concrete Walls for Seismic Resistance

Sponsor:

Chinese Scholarship Council (CSC)

Thank You!

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numerical modeling and collapse safety assessment of an...

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