Fragility curves for rehabilitated bridges with seismic isolators...

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

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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)



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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

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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


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


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%

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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

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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)


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


August 20, 2013

Limit states: buckling Data analysis from CDM tests

Interpolated parabolic curves

Maximum of parabola corresponds to a point of instability


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


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.


August 20, 2013

Component capacity

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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

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Fragility Curves – slight damage

Fragility Results: effects of isolation

August 20, 2013

Fragility Curves – moderate damage


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Fragility Curves – extensive damage


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Fragility Curves – complete damage

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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

Fragility curves for rehabilitated bridges with seismic isolators...

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