9/11/2008
Bridge Modeling in OpenSees
Shaking Table Tests at Univ. of Nevada, Reno
Matthew Dryden Prof. Greg Fenves University of California, Berkeley
OpenSees Days 2008 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.
Drift Ratio (%)
6 Exp
Test 18 - Bent 3 Table 3 PGA = 1.6 g
3
BWH
0 -3 -6
10
15
20 Time (Sec)
25
30
35
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 1249/Caltrans SDC provisions. ρlong = 1.6 %
• Column Heights
ρlat = 0.9 %
• Bent 1 – 6 ft • Bent 2 – 8 ft
Axial Load Ratio = 0.08
• Bent 3 – 5 ft
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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.
Test
Peak Table Acceleration (g) 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.
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Simulations of 2-Span Bridge elasticBeamColumn element deck depth = 14 in. deck width = 90 in.
elasticBeamColumn rigid joint offset Multiple support excitation command Recorded table displacements Rayleigh damping (2%) with the last committed stiffness
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Column Modeling Lp/Dcol Bent 1 Bent 2 Bent 3 Priestley 0.52 0.60 0.48 Berry 0.37 0.42 0.34
nonlinear elastic Lp
M-κ Berry
BeamWithHinges
EIeff/EIg Bent 1 Bent 2 Bent 3 0.37 0.37 0.37 0.32 0.37 0.29
0
100 80
Stress (ksi)
Stress (ksi)
Confined Unconfined -2
-4
-6
60 40 Simulation Coupon 1 Coupon 2 Coupon 3
20
-8 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005
0
0 0
Strain (in./in.)
Concrete02
0.02
0.04
0.06
0.08
Strain (in./in.)
Hysteretic
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 $DtAnalysis/20.0]]; }
Reducing the analysis time step
if {$ok != 0} { set ok [analyze 1 [expr $DtAnalysis/50.0]]; }
if {$ok != 0} { set ok [analyze 1 [expr $DtAnalysis/100.0]]; }
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Modifying the Script to Obtain Convergence if {$ok != 0} { test $testtype $tol 1000 0; algorithm Newton -initial set ok [analyze 1 [expr $DtAnalysis/20.0]] test $testtype $tol $maxNumIter 2;
Changing the solution algorithm
} if {$ok != 0} { puts "Trying Broyden .." algorithm Broyden 8 set ok [analyze 1 [expr $DtAnalysis/20.0]] } if {$ok != 0} { puts "Trying NewtonWithLineSearch .." algorithm NewtonLineSearch .8 set ok [analyze 1 [expr $DtAnalysis/20.0]] algorithm Newton }
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Validation of Simulations Drift Ratio (%)
6 Exp
Test 18 - Bent 3 Table 3 PGA = 1.6 g
3
Lp Priestley
0 -3 -6
10
15
20
20 Time (Sec)
25
30
35
25
30
35
Bottom of West Column
φ/φ y
10 0 -10 -20 10
15
20 Time (Sec)
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Validation of Simulations Peak Drift Ratio (%)
6 Exp Lp Priestley 3
0
Bent 3
Lp Berry
12
13
14
15 Test
16
17
18
16
17
18
30 Bottom of West Column φ/φ y
20
10
0
12
13
14
15 Test
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Design of 4-Span Bridge • Same column reinforcement as in the 2-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 OpenSees Days 2008
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Test Protocol Max Table Acceleration (g) Transverse Longitudinal Table 1 Table 2 Table 3 Table 1 Table 2 Table 3 0.00 0.00 0.00 0.11 0.14 0.13 0.00 0.00 0.01 0.10 0.13 0.12 0.14 0.12 0.11 0.12 0.14 0.15 0.18 0.20 0.18 0.26 0.38 0.36 0.29 0.29 0.28 0.41 0.70 0.48 0.01 0.03 0.02 0.88 1.22 1.25 0.01 0.01 0.01 0.81 0.91 0.91 0.01 0.01 0.01 0.78 0.92 0.78 0.66 0.66 0.65 0.69 0.89 0.85 0.98 1.01 1.01 0.90 1.08 1.09 1.34 1.32 1.43 1.28 1.54 1.43 1.20 1.18 1.26 1.23 1.26 1.27
Test 1B 1C 1D 2 3 4A 4B 4C 4D 5 6 7
*Bridge restrainers present during Tests 1B, 4A, and 4B.
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Simulations of 4-Span Bridge
N
Bent 2
Bent 3
Force (kips)
Bent 1
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Extending the Existing Code uniaxialMaterial ImpactMaterial $matTag $K1 $K2 $Delta_y $gap 4
x 10
Pounding Force (kips)
2
1
0
∆E = -1
K eff = k h δ m
-2 -2
(
k hδ mn+1 1 − e 2 n +1
-1
0 Displacement (in.)
1
2
)
K 1 = K eff +
K 2 = K eff −
∆E aδ m2 ∆E
(1 − a )δ m2
δ y = aδ m (Muthukumar and DesRoches, 2006)
OpenSees Days 2008
Simulations of 4-Span Bridge rigid offset M- model inverted-T cap beam rigidLink bar Hydrostone at interface
rigidLink beam
dowel rod rectangular cap beam rigid offset
column
*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 Drift Ratio (%)
10
Test 6 - Bent 1 Longitudinal
Exp
Sim
5 0 -5 -10
5
10
15
20
25
30
20
25
30
Time (Sec)
Drift Ratio (%)
10
Transverse
5 0 -5 -10
5
10
15 Time (Sec)
OpenSees Days 2008
Simulations of 4-Span Bridge Displacement (in.)
10
Test 6 - Measured Response
t = 11 sec 0 t = 10.85 sec
-10 South Abutment
Bent 1
Bent 2
Plan View of North Abutment During Pounding Event
Bent 3
North Abutment
NW
t = 10.85 sec
t = 11 sec
NE
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Simulations of 4-Span Bridge Drift Ratio (%)
8 Bent 1 - Exp
4 0 -4 -8
5
10
15
20
25
30
Displacement (in.)
Displacement (in.)
Time (sec) 10
Experiment t = 11.29 sec
0 t = 11 sec -10 South Abutment
Bent 1
10
Bent 2
Bent 3
North Abutment
Bent 3
North Abutment
Simulation t = 11.29 sec
0 t = 11 sec -10 South Abutment
Bent 1
Bent 2 Location Along Bridge Deck
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.
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Abutment Model
Resisting Force (kN) per meter of abutment width
uniaxialMaterial HyperbolicGapMaterial $matTag $Kmax $Kur $Rf $Fult $gap 400
Based on shaking table tests by Wilson and Elgamal at UCSD.
300 200 100
F ( x) =
0
x 1 K max
+ Rf
x Fult
-100 -200
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
K ur
-300 -400 -0.1
-0.05
0 Displacement (m)
0.05
0.1
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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 Elgamal Patrick Wilson
OpenSees Days 2008
Questions?
[email protected]
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