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2011 UC Davis GGSS Roundtable April 8, 2011. Probabilistic Seismic Performance of Rocking-Foundation and Hinging-Column Bridges. Lijun Deng Advisors: Prof. Bruce Kutter , Prof. Sashi Kunnath University of California, Davis. Outline. Research motivation - PowerPoint PPT Presentation
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Probabilistic Seismic Performance of Rocking-Foundation and Hinging-Column Bridges
Lijun DengAdvisors: Prof. Bruce Kutter, Prof. Sashi Kunnath
University of California, Davis
2011 UC Davis GGSS RoundtableApril 8, 2011
Outline• Research motivation• Development of computational model• Preliminary simulation results • Conclusions
Plastic hinge
Conventional fixed-base foundation
Hinging-column system
Research motivation
Soil plastic hinge
Rocking-foundation system
vs.
Rocking foundation: Centrifuge tests
Rocking foundation:Kocaeli 1999
Hinging column:Kobe 1995
Hinging column: Centrifuge tests
Case histories and experiment studies
Outline• Research motivation• Development of computational model• Preliminary simulation results • Conclusions
...... ......
Lf
Computational model configuration
-0.04 0 0.04
-1
-0.5
0
0.5
1
RotationM
omen
t / M
cap
Footing
-1
-0.5
0
0.5
1 Column hinge
Mom
ent /
Mca
p
RotationDisp.
Force
Hc (m) Period, T (s) Cy / Cr Remarks
Short: 3 0.3, 0.5
0.3 / 0.4 Hinging-column dominated
0.4 / 0.3 Rocking-foundation
Tall: 10 0.5, 1.0
0.3 / 0.4 Hinging-column
0.4 / 0.3 Rocking-foundation
Model parameters• Cy, Cr: base shear coefficients for column & rocking footing
• Two yielding mechanisms: Cr > Cy Hinging column system;
Cy > Cr Rocking foundation system
Realistic values for highway bridges
Model parameters• Input ground motions from PEER database
Baker et al. (2010)
• Concept of Incremental Dynamic Analysis (IDA)
Outline• Research motivation• Development of computational models• Preliminary simulation results• Conclusions
Selected animations
• Cy=0.3, Cr=0.4, T=0.5 s (Hinging column)
• Cy=0.4, Cr=0.3, T=0.5 s (Rocking foundation)
On-verge-of-collapse case
Collapse caseOn-verge-of-collapse case
Collapse case
0.01 0.1 1 10Period (sec)
0.01
0.1
1
10
Sa (g
)
Sa (T) vs. Max Deck Drift curves
T
0.01 0.1 1 10Period (sec)
0.01
0.1
1
10
Sa (g
)Sa (T)
0.01 0.1 1 10Max Drift (m)
0.1
1
10S a
(T) (
g)
Sa (T) vs. Max Deck Drift curves
Elastic
Nonlinear
Collapse
Instability limit~=3 m
0.3 g
Rocking-footing system(Cy=0.4, Cr=0.3, T=0.5 s, Hc=10 m)
Probabilistic AnalysisRocking Footing (Cy=0.4, Cr=0.3, T=0.5 s, Hc=10 m)
Note: Equivalent Static Analysis: a linear static pushover method
0.01 0.1 1 10Max Drift (m)
0.1
1
10
S a (T
) (g)
Equivalent Static Analysis
0.01 0.1 1 10Max Drift (m)
0.1
1
10
S a (T
) (g)
Equivalent Static Analysis
0.01 0.1 1 10Max Drift (m)
0.1
1
10
S a (T
) (g)
Median84%16%
98%2%ESA
0.001 0.01 0.1 1 10Median max drift (m)
0.01
0.1
1
10
S a (T
) (g)
Rocking-foundationHinging-columnESA predicted
Hc=10.0 m
T=0.5 s
Probabilistic Performance Comparison
• Probabilistic performance of two systems are similar under less-intense motions, but rocking foundation is superior under intense motions.
0.001 0.01 0.1 1 10Median max drift (m)
0.01
0.1
1
10
S a (T
) (g)
Rocking-foundationHinging-columnESA predicted
Hc=10.0 m
T=0.5 sT=1.0 s
0.001 0.01 0.1 1Median max drift (m)
Rocking-foundationHinging-columnESA predicted
Hc=3.0 m
T=0.3 s
T=0.5 s
0.001 0.01 0.1 1 10Median max drift (m)
0.01
0.1
1
10
S a (T
) (g)
Rocking-foundationHinging-columnESA predicted
Hc=10.0 m
T=0.5 sT=1.0 s
0.001 0.01 0.1 1Median max drift (m)
Rocking-foundationHinging-columnESA predicted
Hc=3.0 m
T=0.3 s
T=0.5 s
0.0001 0.001 0.01 0.1 1Median residual rotation (rad)
0.1
1
10
S a (T
) (g)
Rocking-foundationHinging-column
Hc=10.0 m
T=0.5 s
Sa (T) vs. Residual Deck Rotation
• Bridge with rocking foundation have smaller rotation than hinging column illustrates the recentering benefits
1E-005 0.001 0.1 10Deck residual rotation (rad)
0.1
1
10
S a (T
) (g)
Median84%
16%98%
0.0001 0.001 0.01 0.1 1Median residual rotation (rad)
0.1
1
10
S a (T
) (g)
Hc=10.0 m
T=1.0 s
Conclusions• Probabilistic performance of rocking-foundation and
hinging-column bridge systems was evaluated using IDA methodology.
• Rocking systems with Cr=0.3 produce less residual drift and similar max drift, and have lower probability of collapse in comparison with hinging column systems with Cy=0.3.
• 3-m-tall system is easier to topple than 10- m-tall system.• The use of rocking foundation should be encouraged in
seismic design of soil-foundation-structure systems.
Acknowledgments• Caltrans (M. DeSalvatore, S. McBride, T. Shantz, and M.
Khojasteh, contract 59A0575) • NSF-NEESR Project Soil and Structure Compatible Yielding
to Improve System Performance• PEER project Last Hurdles for Rocking Foundations for
Bridges• Student assistants: T. Algie (Auckland Univ., NZ), E. Erduran, J.
Allmond (UCD), M. Hakhamaneshi (UCD).
P E E R
The end
Validate model through centrifuge data
0.02 0.01 0 0.01 0.02 0.032 107
1 107
0
1 107
2 107
3 107
CentrifugeOpenSees
Footing rotation (rad)
Roc
king
mom
ent (
N*m
)
0 10 20 30 400.04
0.02
0
0.02
0.04
0.06CenrifugeOpenSees
Time (s)
Dec
k dr
ift (r
ad)
0.01 0 0.012 107
1 107
0
1 107
2 107
Column hinge rotation
Nor
m. c
ol. b
ase
mom
ent
0.02 0.01 0 0.01 0.02 0.032 107
1 107
0
1 107
2 107
3 107
CentrifugeOpenSees
Footing rotation (rad)
Roc
king
mom
ent (
N*m
)
0 10 20 30 400.04
0.02
0
0.02
0.04
0.06CenrifugeOpenSees
Time (s)
Dec
k dr
ift (r
ad)
0.01 0 0.013 107
2 107
1 107
0
1 107
2 107
3 107
CentrifugeOpenSees
Footing rotation (rad)
Roc
king
mom
ent (
N*m
)
10 20 30 40 50 600.03
0.02
0.01
0
0.01
0.02
0.03CenrifugeOpenSees
Time (s)
Dec
k dr
ift (r
ad)
10.88
7.35
SF
Centrifuge model (Cy/Cr=5, T_sys=1 s, FSv=11.0)
Input parameters in IDA model• Cy, Cr: base shear coefficients for column or rocking footing• Two yielding mechanisms:
Cr > Cy Hinging column system; Cy > Cr Rocking foundation system
yy
c
MC
m g H
1 12
f cr m
c
L AC rH A
2 2 2
2
1
1 14sprsys c N
i ii
T m HK
k x
yM
fL
K
k
Ac/A=0.2, rm=0.2(Footing length)
(Column hinge strength)
Equally spaced foundation elements
(Column hinge stiffness)
(Foundation element stiffness)
(1 )mult
f
r m g FSv LqL
(Foundation
element strength)
0 2 4 6 8 10Sa(T) (g)
0
0.2
0.4
0.6
0.8
1
P (E
DP>
Drif
t | S
a)
Drift = 0.1 mDrift = 0.5 mDrift = 2 m
Hc=10.0 m, T= 1.0 sCy=0.4, Cr=0.3
0 2 4 6 8 10Sa (T) (g)
Drift = 0.1 mDrift = 0.5 mDrift = 2 m
Hc=10.0 m, T= 1.0 sCy=0.3, Cr=0.4
Fragility curves for two case studies
0.01 0.1 1 10Max Drift (m)
0.1
1
10
S a (T
) (g)
0.01 0.1 1 10Max Drift (m)
0.1
1
10
S a (T
) (g)
Sa (T) vs. Max Deck Drift curves
Elastic
Nonlinear
Collapse
Instability limit~=3 m
Elastic
Nonlinear
0.3 g
Instability limit~=3 m
Rocking Footing (Cy=0.4, Cr=0.3, T=0.5 s, Hc=10 m)
0.3 g
Hinging column (Cy=0.3, Cr=0.4, T=0.5 s, Hc=10 m)
Collapse
• A hinge is a hinge• Hinges can be engineered at either position
– A hinge forms at the edge when rocking occurs
• P-delta is in favor for rocking – recentering• Instability limits are related to min{Cy, Cr}
Collapse mechanisms
Elastic footing
Rocking footing
P
P