NEESR-CR: Design of soil and structure compatible yielding
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Transcript NEESR-CR: Design of soil and structure compatible yielding
Incremental Dynamic
Analyses on Bridges on
various Shallow Foundations
Lijun Deng
PI’s: Bruce Kutter, Sashi Kunnath
University of California, Davis
NEES & PEER annual meeting
San Francisco
October 9, 2010
Outline
• Introduction and centrifuge model tests
• Incremental Dynamic Analysis (IDA) model
• Preliminary results of IDA
Maximum drift
Instability limits of rocking and hinging systems
Residual drift
• Conclusions
Damaged columns in past earthquakes
Centrifuge test matrix
N
381.0
B
254.0
393.0
592.0
387.0
LF
B
198.0
254.0
A
SF
609.6
396.0
1366.0
4CSF
ISF
A
1006.5
304.9
0
12
x
36
24
inch
Load Frame
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1 meter
Rocking Foundation Centrifuge Tests
10.88
ISF
Remediating
concrete pads
7.35
10.88
SF
7.35
max( Bas eMo ti on) 0 .61 92
mi n( Bas eMo ti on) 0 .88 24
Gazli earthquake,
pga= 0.88 g
Accel (g)
1
0.5
0
0.5
1
20
5
25
30
35
Hinging Column Centrifuge Test
9.64
LF
Notches
12.20
max( Bas eMo ti on) 0 .61 92
mi n( Bas eMo ti on) 0 .88 24
Gazli earthquake,
pga= 0.88 g
Accel (g)
1
0.5
0
0.5
1
20
6
25
30
35
Photos of hinging column
after 0.88g Gazli shake
7
Hinging Column Centrifuge Test
9.64
LF
Notches
12.20
max( BaseMo ti on) 0 .16 11
mi n( BaseMo ti on) 0 .22 92
CHY024,
pga=0.23 g
Accel (g)
0.2
0.1
0
0.1
0.2
0.3
8
20
40
60
Collapse of hinging column
• SDOF bridges on rocking foundation survived
after 20 scaled GM’s, but the one on fixed
foundation and hinging column collapsed
9
Mass = m
Column hinge spring
Column: Stiff
elasticBeamColumn
Moment
OpenSees
model for IDA
and
parametric
study
Kθ
Hc
Rotation
Foundation: zerolength
elements
Fixed ground
center
Footing center
Footing mass = m*rm
ki
xi
Lf
Norm. col
Validate model through centrifuge data
7
110
7
210
0.01
Column
7
0.06
0.06
Cenrifuge
Cenrifuge
OpenSees
OpenSees
7
2107
210
Deck
Deckdrift
drift(rad)
(rad)
Rocking
Rockingmoment
moment(N*m)
(N*m)
3107
310
7
1107
110
0
0
Centrifuge
Centrifuge
OpenSees
OpenSees
7
1107
110
7
2107
210
0.02 0.01
0.02 0.01
0
0
0.01
0.01
0.02
0.02
0.04
0.04
0.02
0.02
0
0
0.02
0.02
0.04
0.04 0
0
0.03
0.03
10
10
Footing rotatio
rotationn (rad)
(rad)
Footing
20
20
30
30
40
40
T ime
ime (s)
(s)
T
7
0.03
7
110
0
7
110
Centrifuge
OpenSees
7
210
7
7.35
Cenrifuge
OpenSees
7
210
310
0.01
Centrifuge model
(Cy/Cr=5, T_sys=1 s, FSv=11.0)
0
0.01
Footing rotation (rad)
Deck drift (rad)
10.88
SF
Rocking moment (N*m)
310
0.02
0.01
0
0.01
0.02
0.03
10
20
30
40
T ime (s)
50
60
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
Cy
Tsys 2
My
m g Hc
M y (Column hinge
strength)
k (Foundation
Equally spaced
1
1
element stiffness)
foundation elements
4 2 m H c 2
Nspr
K
2
(Column hinge
K
k
x
i
i
stiffness)
i 1
L f Ac
Ac/A=0.2, rm=0.2
L f (Footing length)
Cr
1 1 rm
2 Hc
A
(1 rm ) m g FSv L
qult
Lf
(Foundation
element strength)
Input parameters in IDA model
• Input ground motions from PEER database
Forty pulse-like ground motions
at soil sites(Baker et al. 2010)
T_sys (sec)
Cy
Cr
# GM
# Scale factors
0.5
0.8
0.2
1.0
1.2
1.5
2
0.5
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.5
40 pulse-like
40 broad-band
0.2, 0.4
0.6, 0.8
1.0, 1.5
2.0, 2.5
3.0, 4.0
IDA results: Sa(T=T_sys) vs. max drift
Rocking Footing (Cy=0.5,
Cr=0.2, T_sys=0.85 s)
0.2 g
Hinging column (Cy=0.2,
Cr=0.5, T_sys=0.85 s)
0.2 g
Failure zone
Nonlinear zone
Elastic zone
Failure zone
Nonlinear zone
Elastic zone
Instability limit
~=2.2 m
Instability limit
~=2 m
Collapse mechanisms
• A hinge is a hinge
• Hinges can be engineered at either position
– A hinge forms at the edge when rocking occurs
P
Elastic
footing
P
Rocking
footing
• P-delta is in your favor for rocking – recentering
• Instability limits are related to Cy and Cr values
Selected animations
• Cy=0.5, Cr=0.2, T=0.85 s (Rocking foundation)
On-verge-of-collapse case
Collapse case
• Cy=0.2, Cr=0.5, T=0.85 s (Hinging column)
On-verge-of-collapse case
Collapse case
IDA results: Sa(T=T_sys) vs. max drift
• 50% median of Sa vs. max drift and +/-σ
50% Median
Compare medians of Sa vs. max drift for various T_sys
• Longer periods lead to higher drift
• The max drift is not sensitive to Cy/Cr ratio
• The max might rely on min{Cy, Cr}, to be confirmed with further study
IDA results: Sa (T_sys) vs. Residual Rotation
50% Median
IDA results: Sa (T_sys) vs. Residual rotation
• Bridge with rocking foundation have smaller rotation than hinging
column re-confirm the recentering benefits
Conclusions
• Rocking foundations provide recentering effect that
limits the accumulation of P- demand (i.e., much
smaller residual rotation)
• Experiments and IDA simulations show column with
rocking footing is more stable than hinging column
(i.e., fewer collapse cases)
• ESA approach is not conservative for highly nonlinear
cases
• Analysis is ongoing, and fragility functions are being
developed from the results. We are also evaluating the
adequacy of Sa(T_sys) as an Intensity Measure of
ground motions
Collaborators
CONSTRUCTION
GEOTECHNICAL
Desalvatore
DESIGN
Khojasteh
THEORY
Shantz
Kutter
Martin
Mejia
Stewart
Jeremic
Hutchinson
Panagiotou
Browning
Kunnath
Comartin
McBride
Moore
Ashheim
Mar
STRUCTURAL
Mahan
Mahin
BRIDGES
BOTH
BUILDINGS
Acknowledgments
• Current financial support of California Department of
Transportation (Caltrans).
• Network for Earthquake Engineering Simulation (NEES) for
using the Centrifuge of UC Davis.
• Other student assistants: T. Algie (Auckland Univ., NZ), E.
Erduran (USU), J. Allmond (UCD), M. Hakhamaneshi (UCD).
IDA results: Sa(T=T_sys) vs. max drift
Rocking Footing (Cy=0.5,
Cr=0.2, T_sys=0.85 s)
Hinging column (Cy=0.2,
Cr=0.5, T_sys=0.85 s)
• Equivalent Static Analysis (ESA) commonly used in
codes may underestimate the displacement.