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Earthquake Engineering and Structural Dynamics Research Center
Centre de recherche en génie parasismique et en dynamique des structures
Département de génie civil, Faculté de génie
CRGP
2013 UBC – Tongji – CSRN Symposium
Fragility curves for rehabilitated
bridges with seismic isolators
using experimental results
Patrick PAULTRE
Danusa Haick Tavares, Gustavo Henrique Siqueira,
Adamou Saidou Sanda,
Jamie E. Padgett
Vancouver - August 20, 2013
August 20, 2013
August 20, 2013
Bridge portfolios in Quebec
August 20, 2013
Bridges in Quebec: year of construction
August 20, 2013
Bridges in Quebec
75 % of bridges are 30 years old or more
21.0% of structures are MultiSpan Continuous Concrete bridges (MSCC)
Seismic design standards were at an early stage of development
Changes in NBCC 2010 (2015):Increase in earthquake hazard accross Canada
Some structures may be seismically deficient: need for vulnerabilityassessment
Challenges for Quebec: upgrading and rehabilitation of bridges
August 20, 2013
Statistical Tool
Define the probability of meeting or
exceeding a level of damage
according to an intensity measure
(IM): PGA, PGV, Sa(0.1), Sa(tm), …
Physical meaning: functionality
Seismic vulnerability assessment
Uncertainties in demand/capacity
Pre-earthquake planning
Effectiveness of retrofitting strategies
Fragility curves
August 20, 2013
MSC Concrete-girder bridges OpenSees models
Superstructure: Concrete deck
Supported on four concrete girders
Piers and foundations Moment resisting frame
Three circular columns
Transverse beam – top
Nonlinear behavior
Shallow footing foundations
Seat-type abutments
Bridge Model and Uncertainties
August 20, 2013
MSC concrete-girder bridges Geometric parameters
Macro-variables
Statistical Distributions
Using LHS (latin hypercube sampling)
to generate a sample of plausible collections
of parameter values (computer experiments)
Bridge Model and Uncertainties
MSC_Concrete Spans Total Deck Column *Lmr
Length (m) Width (m) Height (m)
Block 1 3 100.98 13.04 6.72 0.30
Block 2 3 64.79 8.35 8.35 0.52
Block 3 3 54.61 23.43 9.78 0.36
Block 4 3 75.27 17.65 4.73 0.47
Block 5 3 45.93 10.72 3.77 0.46
Block 6 3 114.49 15.23 7.8 0.32
Block 7 3 67.96 11.8 6.15 0.43
Block 8 3 89.27 16.16 4.24 0.39
* Ratio between middle span length and total length of the bridge
August 20, 2013
MSCC concrete-girder bridges
Plastic-hinges
Generic Bridge Model and Uncertainties
August 20, 2013
Natural rubber devices
Seismic Isolation Retrofit
Usual elastomeric bridge bearings
Elastomeric seismic isolation bearings
August 20, 2013
Elastomeric seismic isolation bearings
Modeled with a bilinear element
Target periods: 1.85s to 2.5s
Mean displacement – 100mm
UHS ± σ
Seismic Isolation Retrofit
August 20, 2013
Seismic isolators: experimental study
Specimens 2 series of full-scale specimens and 1 serie of reduced-scale specimens
Varying parameters
shape factor 𝑆 =𝑟𝑢𝑏𝑏𝑒𝑟 𝑙𝑜𝑎𝑑𝑒𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒
𝑓𝑟𝑒𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑟𝑢𝑏𝑏𝑒𝑟 𝑙𝑎𝑦𝑒𝑟(rubber confinement)
Slenderness
Objectives pertaining to fragility curves determination Characterize mechanical properties considering uncertainties
Define limit states: capacity at buckling
4 specimens(450mm x 450mm)
4 specimens(300mm x 300mm)
5 specimens(100mm x 100mm)
August 20, 2013
Seismic isolators: experimental study
Experimental set-up: Full-scale tests:
Capacities:Max specimen dimensions: 500 mm x 500 mmCompression: 11 400 kNShear: 500 kNLateral stroke: +/- 500 mmFrequencies up to 0.5Hz
August 20, 2013
Seismic isolators: experimental study Experimental set-up:
Reduced-scale tests:
Capacities:
Max specimen dimensions: 150 mm x 150 mm
Compression and shear: 100kN
Lateral stroke: +/- 65 mm
Frequencies up to 2Hz
August 20, 2013
Seismic isolators: experimental study
Uncertainties in mechanical properties Useful properties
Effective lateral stiffness (or shear modulus) and effective damping ratio
Influencing parameters :
Shear strain
Compression level
Shape factor and slenderness of specimen
Others: temperature, aging of material, scragging and Mullin’s effect, …
August 20, 2013
Seismic isolators: experimental study
Uncertainties in mechanical properties Experimental data considered
All tested specimens
Shear strains: 50% to 125%
Compression: 5.0 to 7.5MPa
Lognormal distributions to be used for fragility curves
Results:
Shear modulus: 0.65MPa to 1.03MPa
Damping: 5.3% to 9.5%
August 20, 2013
Seismic isolators: experimental study
Limit states Failure modes of elastomeric isolators
Instability under compression in a laterally deformed state (Buckling)
Failure of the material in shear (Tearing)
Buckling
Tearing
August 20, 2013
Limit states: buckling Buckling capacity
Combination of compressive force and displacement when tangent stiffness of the
bearing is zero (loss of recentering capcity).
Capacity curve of a bearing plotted from several combinations.
(Numerical results)
Seismic isolators: experimental study
August 20, 2013
Limit states: buckling Test using Direct Method (DM)
Constant compression P0 and increasing displacement u(t) until tangent stiffness is null.
1 point on instability curve = 1 destroyed specimen
Test using constant displacement method (CDM)
Constant displacement u0 and increasing compression P(t) until elastic shear force is null.
Several tests on one specimen at increasing displacement levels = complete instability
curve
Seismic isolators: experimental study
August 20, 2013
Limit states: buckling Data analysis from CDM tests
Interpolated parabolic curves
Maximum of parabola corresponds to a point of instability
Seismic isolators: experimental study
Direct curves from tests(constant displacements)
Extracted curves from tests(constant shear force)
August 20, 2013
Limit states: buckling Validation of CDM
Experimental curves plotted for constant compression
Curve from a Direct Method test
Seismic isolators: experimental study
August 20, 2013
Limit states: buckling Results: complete instability curves obtained for 3 full-scale specimens
To be used for calibration and verification of a numerical model
Use of a FE model for a wide range of geometries of isolators (ADINA)
Statistical values of critial loads and displacements to be used in fragility curves.
Seismic isolators: experimental study
August 20, 2013
Component capacity
August 20, 2013
Methodology (Nielson et DesRoches, 2007)
Fragility curves for isolated bridges
2 2
|
ln( / )[ | ] D C
D IM C
S SP LS IM
C (capacity) – related to LSD (demand) – related to the response GMTH
Modeled by a lognormalcumulative distribution function
|
[ ]
,
,
D C
D IM C
S S
– standard normal cumulative distribution
– median structural demand and capacity
– logarithmic standard deviation
System fragilitySeries approximation
Monte Carlo simulationJoint PSDM
Union probability – bridge components exceeding the same LS
26/42
August 20, 2013
Fragility Curves – slight damage
Fragility Results: effects of isolation
August 20, 2013
Fragility Curves – moderate damage
Fragility Results: effects of isolation
August 20, 2013
Fragility Curves – extensive damage
Fragility Results: effects of isolation
August 20, 2013
Fragility Results: effects of isolation
Fragility Curves – complete damage
August 20, 2013
Retrofitted MSC concrete-girder bridges Significant reduction of fragility of key components: columns
System fragility:
As-built bridges
Different components controlling the fragility
Depending on the LS
Isolated bridges
Wing wall is the component controlling fragility of the system
All LS
Protection of key components: columns and foundations
Less time and lower cost to restore bridge functionality
Conclusions