bridge modeling in openseesopensees.berkeley.edu/workshop/openseesdays2008/b04...10 15 20 25 30...
TRANSCRIPT
9/11/2008
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OpenSees Days 2008
OpenSees Days 2008
Bridge Modeling in OpenSees
Matthew Dryden
Prof. Greg Fenves
University of California, Berkeley
Shaking Table Tests at Univ. of Nevada, Reno
OpenSees Days 2008
Motivation
• Soil-foundation-structure interaction (SFSI) is difficult to test at the system
level.
• Test various components of the bridge using available experimental facilities.
• Integrate the results from the tests into a simulation model used to study system effects.
Failure of the Hanshin Expressway
1995 Kobe Earthquake
(http://nisee.berkeley.edu)
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Focus of this Research
• Simulate the response of the 2-span and 4-span reinforced concrete bridges tested at UNR.
• Assess the validity of simulation models using the measured response at both the global and local levels.
10 15 20 25 30 35-6
-3
0
3
6
Time (Sec)
Dri
ft R
atio
(%
)
Test 18 - Bent 3
Table 3 PGA = 1.6 g
Exp BWH
OpenSees Days 2008
Design of 2-Span Bridge
• Built at 1/4-scale based on a prototype bridge with 4 ft diameter columns, and 120 ft spans.
• Columns designed in accordance with NCHRP 12-49/Caltrans SDC provisions.
• Column Heights• Bent 1 – 6 ft
• Bent 2 – 8 ft
• Bent 3 – 5 ft
ρlong = 1.6 %
ρlat = 0.9 %
Axial Load Ratio = 0.08
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Test Protocol
• 1994 Northridge Century City North ground motion.
• Series of 23 ground motions successively applied in the transverse
direction, 14 of which were low-level motions prior to yielding of the structure.
Peak Table Acceleration (g)Test Table 1 Table 2 Table 3
15 0.67 0.65 0.72
16 0.98 0.94 1.25
17 1.20 1.50 1.09
18 1.56 1.81 1.59*
*Drift ratio exceeded 5.5% at bent 3.
OpenSees Days 2008
Simulations of 2-Span Bridge
Multiple support excitation command
Recorded table displacements
Rayleigh damping (2%) with the last
committed stiffness
elasticBeamColumn element
deck depth = 14 in.
deck width = 90 in.
rigid joint offsetelasticBeamColumn
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Column Modeling
Lp
nonlinear
BeamWithHinges
elastic
-0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0-8
-6
-4
-2
0
Strain (in./in.)
Str
ess (
ksi)
Confined
Unconfined
0 0.02 0.04 0.06 0.080
20
40
60
80
100
Strain (in./in.)
Str
ess (
ksi)
Simulation
Coupon 1
Coupon 2
Coupon 3
HystereticConcrete02
Lp/Dcol
Bent 1 Bent 2 Bent 3Priestley 0.52 0.60 0.48Berry 0.37 0.42 0.34
EIeff/EIgBent 1 Bent 2 Bent 3
M-κ 0.37 0.37 0.37Berry 0.32 0.37 0.29
OpenSees Days 2008
Modifying the Script to Obtain Convergence
while {$tCurrent < $tFinal && $ok == 0} {
test $testtype $tol $maxNumIter 0;set ok [analyze 1 $DtAnalysis]
if {$ok != 0} {
set ok [analyze 1 [expr $DtAnalysis/20.0]];
}
if {$ok != 0} {
set ok [analyze 1 [expr $DtAnalysis/50.0]];
}
if {$ok != 0} {
set ok [analyze 1 [expr $DtAnalysis/100.0]];
}
Reducing the analysis time step
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Modifying the Script to Obtain Convergence
if {$ok != 0} {test $testtype $tol 1000 0;algorithm Newton -initial set ok [analyze 1 [expr $DtAnalysis/20.0]]test $testtype $tol $maxNumIter 2;
}
if {$ok != 0} {puts "Trying Broyden .."algorithm Broyden 8set ok [analyze 1 [expr $DtAnalysis/20.0]]
}
if {$ok != 0} {puts "Trying NewtonWithLineSearch .."algorithm NewtonLineSearch .8set ok [analyze 1 [expr $DtAnalysis/20.0]]algorithm Newton
}
Changing the solution algorithm
OpenSees Days 2008
Validation of Simulations
10 15 20 25 30 35-6
-3
0
3
6
Time (Sec)
Dri
ft R
atio
(%
)
Test 18 - Bent 3 Table 3 PGA = 1.6 g
Exp Lp Priestley
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-20
-10
0
10
20
Time (Sec)
φ/ φ
y
Bottom of West Column
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Validation of Simulations
12 13 14 15 16 17 180
3
6
Pe
ak D
rift R
atio
(%
)
Test
Bent 3Exp
Lp Priestley
Lp Berry
12 13 14 15 16 17 180
10
20
30
Test
φ/ φ
y
Bottom of West Column
OpenSees Days 2008
Design of 4-Span Bridge
• Table excitation applied in both horizontal directions.
• Actuators impose displacements in the longitudinal direction at the abutments.
• Column Heights• Bent 1 – 5 ft
• Bent 2 – 7 ft
• Bent 3 – 6 ft
• Same column reinforcement as in the 2-span bridge.
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Test Protocol
Test
Max Table Acceleration (g)
Transverse Longitudinal
Table 1 Table 2 Table 3 Table 1 Table 2 Table 3
1B 0.00 0.00 0.00 0.11 0.14 0.13
1C 0.00 0.00 0.01 0.10 0.13 0.12
1D 0.14 0.12 0.11 0.12 0.14 0.15
2 0.18 0.20 0.18 0.26 0.38 0.36
3 0.29 0.29 0.28 0.41 0.70 0.48
4A 0.01 0.03 0.02 0.88 1.22 1.25
4B 0.01 0.01 0.01 0.81 0.91 0.91
4C 0.01 0.01 0.01 0.78 0.92 0.78
4D 0.66 0.66 0.65 0.69 0.89 0.85
5 0.98 1.01 1.01 0.90 1.08 1.09
6 1.34 1.32 1.43 1.28 1.54 1.43
7 1.20 1.18 1.26 1.23 1.26 1.27 *Bridge restrainers present during Tests 1B, 4A, and 4B.
OpenSees Days 2008
Simulations of 4-Span Bridge
Bent 1
Bent 2
Bent 3
N
Force (kips)
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Extending the Existing Code
-2 -1 0 1 2
-2
-1
0
1
2
x 104
Displacement (in.)
Pou
ndin
g F
orc
e (
kip
s)
uniaxialMaterial ImpactMaterial $matTag $K1 $K2 $Delta_y $gap
( )1
121
+
−=∆
+
n
ekE
n
mhδ
mheff kK δ=
21
m
effa
EKK
δ
∆+=
( ) 221 m
effa
EKK
δ−
∆−=
my aδδ =
(Muthukumar and DesRoches, 2006)
OpenSees Days 2008
Simulations of 4-Span Bridge
rigid offset
rigid offset
rigidLink beam
inverted-T cap beam
rectangular cap beam
column
M- model
rigidLink bar
Hydrostone at interface
dowel rod
*Elastic stiffness for M-θ model calibrated to match
the results from system identification studies. 0.49 sec
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Simulations of 4-Span Bridge
5 10 15 20 25 30-10
-5
0
5
10
Time (Sec)
Dri
ft R
atio
(%
)
Test 6 - Bent 1
Longitudinal Exp Sim
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-5
0
5
10
Time (Sec)
Dri
ft R
atio
(%
)
Transverse
OpenSees Days 2008
Simulations of 4-Span Bridge
South Abutment Bent 1 Bent 2 Bent 3 North Abutment-10
0
10Test 6 - Measured Response
t = 10.85 sec
Dis
pla
cem
ent
(in.)
t = 11 sec
NE
NW
t = 10.85 sec t = 11 sec
Plan View of North Abutment
During Pounding Event
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Simulations of 4-Span Bridge
5 10 15 20 25 30-8
-4
0
4
8
Bent 1 - Exp
Time (sec)
Dri
ft R
atio (
%)
South Abutment Bent 1 Bent 2 Bent 3 North Abutment-10
0
10Experiment
t = 11 sec
Dis
pla
cem
ent
(in
.)
t = 11.29 sec
South Abutment Bent 1 Bent 2 Bent 3 North Abutment-10
0
10Simulation
t = 11 sec
Location Along Bridge Deck
Dis
pla
cem
ent
(in.)
t = 11.29 sec
OpenSees Days 2008
Challenges in Modeling the Response of the 4-Span Bridge
• Accumulation of damage prior to Test 4D, the first test considered in the simulations.
• Use of bridge restrainers for several tests prior to Test 4D as part of a NEES payload project.
• Interaction between the bridge and the compliant hydraulic system of the actuator.
• Rotation of the abutment during pounding events.
• Contact between the bridge deck and abutment for a finite period of time during pounding.
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Ongoing Work
• Bins of ground motions with different magnitude and distance are considered.
• Soil parameters based on centrifuge tests.
• Abutment response using data from UCSD test.
OpenSees Days 2008
Abutment Model
uniaxialMaterial HyperbolicGapMaterial $matTag $Kmax $Kur $Rf $Fult $gap
-0.1 -0.05 0 0.05 0.1-400
-300
-200
-100
0
100
200
300
400
Displacement (m)
Resis
ting
Fo
rce (
kN
) p
er
me
ter
of a
bu
tme
nt w
idth
Kur
Recommended values:
Kmax = 20300 kN/m of abutment width
Kur = Kmax for unloading/reloading stiffness
Rf = 0.7
Fult = -326 kN per meter of abutment width
ult
fF
xR
K
xxF
+
=
max
1)(
Based on shaking table tests by
Wilson and Elgamal at UCSD.
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Acknowledgments
University of Nevada, Reno
Prof. Saiid Saiidi
Dr. Nathan Johnson
Robby Nelson
Dr. Patrick Laplace
University of Washington
Prof. Marc Eberhard
Dr. Tyler Ranf
Prof. Pedro Arduino
Dr. Hyungsuk Shin
University of California, Berkeley
Prof. Greg Fenves
Dr. Frank McKenna
Dr. Silvia Mazzoni
University of California, San Diego
Prof. Ahmed ElgamalPatrick Wilson
OpenSees Days 2008
Questions?