Numerical Modeling and Collapse Safety Assessment of an...
Transcript of 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
The 6th Kwang-Hua Forum, Tongji University, Shanghai, P. R. China, December 12-14, 2014
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Outline
Background
Lehigh Wall #1
Numerical Modeling
Collapse Safety Assessment
Concluding Remarks
Acknowledgement
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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
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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)
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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
(7) 0.6" dia. strands
3 #
5
#3 @2.25"
#4 @ 4.5"
(1) bundle of
(5) 0.6" dia. strands
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
(7) 0.6" dia. strands
3 #
5
#3 @2.25"
#4 @ 4.5"
(1) bundle of
(5) 0.6" dia. strands
Unbonded boundary rebars
Wall 3
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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
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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.
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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.
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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
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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
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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)
Loading pt. drift (%)
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)
Loading pt. drift (%)
Test data
Model
Flexure + Bond-slip + Shear failure
0
100
200
300
-6 -4 -2 0 2 4 6
PT
forc
e (k
ip)
Loading pt. drift (%)
Test data
ModelEast side PT
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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
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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)
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Collapse Safety Assessment: IDA models
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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
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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
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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)
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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
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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.
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Acknowledgement
Project: The Charles Pankow Foundation: Unbonded Post-Tensioned Cast-in-Place Concrete Walls for Seismic Resistance
Sponsor:
Chinese Scholarship Council (CSC)