Incremental Dynamic Analyses on Bridges on
various Shallow Foundations
Lijun DengPI’s: Bruce Kutter, Sashi Kunnath
University of California, Davis
NEES & PEER annual meetingSan 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
Load Frame
N
x
A A
B B
0 12 24 36
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
inch
meter
NLF
SF ISF4CSF 60
9.6
304.9
N
393.0 381.0 592.0 387.0
254.
039
6.0
254.
0
198.
0
1006.5
1366.0
Centrifuge test matrix
Rocking Foundation Centrifuge Tests
5
max BaseMotion( ) 0.6192
20 25 30 351
0.5
0
0.5
1
Time (sec)
Acc
el (g
)
min BaseMotion( ) 0.8824
10 20 30 40 500.4
0.2
0
0.2
0.4
Time (sec)
Dis
p. (m
)
10.88
7.35
SF
10.88
7.35
ISF
Remediating concrete pads
Gazli earthquake, pga= 0.88 g
Hinging Column Centrifuge Test
6
9.64
12.20
Notches
LF
max BaseMotion( ) 0.6192
20 25 30 351
0.5
0
0.5
1
Time (sec)
Acc
el (g
) min BaseMotion( ) 0.8824
10 20 30 40 500.4
0.2
0
0.2
0.4
Time (sec)
Dis
p. (m
)
Gazli earthquake, pga= 0.88 g
Photos of hinging column after 0.88g Gazli shake
7
8
9.64
12.20
Notches
LF
max BaseMotion( ) 0.1611
20 40 600.3
0.2
0.1
0
0.1
0.2
Time (sec)
Acc
el (g
) min BaseMotion( ) 0.2292
20 40 600.2
0.1
0
0.1
0.2
Time (sec)
Dis
p. (m
)
CHY024, pga=0.23 g
Hinging Column Centrifuge Test
Collapse of hinging column
9
• SDOF bridges on rocking foundation survived after 20 scaled GM’s, but the one on fixed foundation and hinging column collapsed
OpenSees model for IDA and parametric study
Moment
Rotation
Column hinge spring
Foundation: zerolength elements
Column: Stiff elasticBeamColumn
xi
ki
Lf
Kθ
Mass = m
Footing mass = m*rm
Footing center
Fixed ground center
Hc
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)
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 factors0.5 0.5 0.2 40 pulse-like 0.2, 0.40.8 0.3 0.2 40 broad-band 0.6, 0.80.2 0.2 0.2 1.0, 1.51.0 0.2 0.3 2.0, 2.51.2 0.2 0.5 3.0, 4.01.5 2
0.01 0.1 1 10Period (sec)
0.01
0.1
1
10
Acc
el. r
espo
nse
spec
tra
(g)
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Sa(T
_sys
)(g)
PL_28_SNPL_29_SNPL_3_SNPL_30_SNPL_31_SNPL_32_SNPL_33_SN
PL_34_SNPL_35_SNPL_36_SNPL_37_SNPL_38_SNPL_39_SNPL_4_SN
PL_40_SNPL_5_SNPL_6_SNPL_7_SNPL_8_SNPL_9_SNESA prediction for T=0.85 s
Cy=0.2, Cr=0.5, T_sys=0.85 s
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Sa(T
_sys
)(g)
PL_28_SNPL_29_SNPL_3_SNPL_30_SNPL_31_SNPL_32_SNPL_33_SN
PL_34_SNPL_35_SNPL_36_SNPL_37_SNPL_38_SNPL_39_SNPL_4_SN
PL_40_SNPL_5_SNPL_6_SNPL_7_SNPL_8_SNPL_9_SNESA prediction for T=0.85 s
Cy=0.5, Cr=0.2, T_sys=0.85 s
IDA results: Sa(T=T_sys) vs. max drift
Elastic zone
Nonlinear zone
Failure zone
Instability limit~=2.2 m
Elastic zone
Nonlinear zone
0.2 g
Instability limit~=2 m
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)
Failure zone
• 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 your favor for rocking – recentering• Instability limits are related to Cy and Cr values
Collapse mechanisms
Elastic footing
Rocking footing
P
P
Selected animations
• Cy=0.2, Cr=0.5, T=0.85 s (Hinging column)
• Cy=0.5, Cr=0.2, T=0.85 s (Rocking foundation)
On-verge-of-collapse case
Collapse caseOn-verge-of-collapse case
Collapse case
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Sa(T
_sys
)(g)
PL_28_SNPL_29_SNPL_3_SNPL_30_SNPL_31_SNPL_32_SNPL_33_SN
PL_34_SNPL_35_SNPL_36_SNPL_37_SNPL_38_SNPL_39_SNPL_4_SN
PL_40_SNPL_5_SNPL_6_SNPL_7_SNPL_8_SNPL_9_SNESA prediction for T=0.85 s
Cy=0.2, Cr=0.5, T_sys=0.85 s
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Sa(T
_sys
)(g)
PL_28_SNPL_29_SNPL_3_SNPL_30_SNPL_31_SNPL_32_SNPL_33_SN
PL_34_SNPL_35_SNPL_36_SNPL_37_SNPL_38_SNPL_39_SNPL_4_SN
PL_40_SNPL_5_SNPL_6_SNPL_7_SNPL_8_SNPL_9_SNESA prediction for T=0.85 s
Cy=0.5, Cr=0.2, T_sys=0.85 s
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
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Med
ian
Sa(T
_sys
)(g)
T_sys=0.85 s for 5 Cr, Cr combinations
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Med
ian
Sa(T
_sys
)(g)
T_sys=0.85 s for 5 Cr, Cr combinationsT_sys=0.43 s for 5 Cy, Cr combinations
IDA results: Sa (T_sys) vs. Residual Rotation
1E-006 1E-005 0.0001 0.001 0.01 0.1 1 10Residual rotation (rad)
0.01
0.1
1
10
Sa (T
_sys
) (g)
PL_28_SNPL_29_SNPL_3_SNPL_30_SNPL_31_SNPL_32_SNPL_33_SNPL_34_SNPL_35_SNPL_36_SN
PL_37_SNPL_38_SNPL_39_SNPL_4_SNPL_40_SNPL_5_SNPL_6_SNPL_7_SNPL_8_SNPL_9_SNCy=0.5, Cr=0.2, T_sys=0.85 s
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
1E-005 0.0001 0.001 0.01 0.1 1Residual drift (rad)
0.1
1
Med
ian
Sa(T
_sys
)(g)
Cy=0.5, Cr=0.2, T_sys=0.85 sCy=0.2, Cr=0.5, T_sys=0.85 s
1E-005 0.0001 0.001 0.01 0.1 1Residual drift (rad)
0.1
1
Med
ian
Sa(T
_sys
)(g)
Cy=0.5, Cr=0.2, T_sys=0.43 sCy=0.2, Cr=0.5, T_sys=0.43 s
Hinging column
Rocking foundation
Hinging column
Rocking foundation
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
PanagiotouCODE
DEVELOPERS
Collaborators
Kutter
Browning
Moore
Martin
Jeremic
Mar
Comartin
McBride
Mahan
Desalvatore
KhojastehShantz
BRIDGES
BUILDINGS
Mejia
BOTH
GEOTECHNICAL
STRUCTURAL
Mahin
Kunnath
Ashheim
Stewart
Hutchinson
THEORYDESIGNCONSTRUCTION
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).
The end
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Sa(T
_sys
)(g)
PL_28_SNPL_29_SNPL_3_SNPL_30_SNPL_31_SNPL_32_SNPL_33_SN
PL_34_SNPL_35_SNPL_36_SNPL_37_SNPL_38_SNPL_39_SNPL_4_SN
PL_40_SNPL_5_SNPL_6_SNPL_7_SNPL_8_SNPL_9_SNESA prediction for T=0.85 s
Cy=0.2, Cr=0.5, T_sys=0.85 s
0.01 0.1 1 10Max drift (m)
0.01
0.1
1
10
Sa(T
_sys
)(g)
PL_28_SNPL_29_SNPL_3_SNPL_30_SNPL_31_SNPL_32_SNPL_33_SN
PL_34_SNPL_35_SNPL_36_SNPL_37_SNPL_38_SNPL_39_SNPL_4_SN
PL_40_SNPL_5_SNPL_6_SNPL_7_SNPL_8_SNPL_9_SNESA prediction for T=0.85 s
Cy=0.5, Cr=0.2, T_sys=0.85 s
IDA results: Sa(T=T_sys) vs. max driftRocking 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.