seismic assessment of bridges accounting for non-linear ... · pdf fileseismic code eak2000...

Aristotle University Thessaloniki, Department of Civil Engineering, Structural Division

Seismic assessment of bridges accounting for Seismic assessment of bridges accounting for nonnon--linear material and soil response linear material and soil response

and varying boundary conditions and varying boundary conditions

A.J. Kappos, Professor, Aristotle University ThessalonikiA. Sextos, Lecturer, Aristotle University Thessaloniki

Coupled site and soil-structure interaction effects with application to

seismic risk mitigationNATO ESP.EAP.ARW 983188


Problem statementProblem statement

Nonlinear static (pushover) analysisNonlinear static (pushover) analysis has become a popular tool for the seismic has become a popular tool for the seismic assessment of assessment of buildings, later also of bridgesbuildings, later also of bridges

Nonlinearity is associated associated (in most studies) with(in most studies) with material behaviourmaterial behaviour→→ yieldingyielding of reinforced concreteof reinforced concrete (R/C) sections

? additionaladditional material nonmaterial non--linearity mechanismslinearity mechanisms (in foundation and/or backfill soil) ? nonnon--linearitylinearity in in boundary conditionsboundary conditions (activation of control components such as

bearings, ‘stoppers’, or seismic joints)

The goalgoal of this paper, is to focus on a real bridge structure in order to assess the assess the importance of considering over neglecting importance of considering over neglecting various nonvarious non--linearity sources, thelinearity sources, the actual actual

stiffnessstiffness of the abutments and embankments, and the foundation subsystems.


Overcrossings (overpasses) Overcrossings (overpasses) in Egnatia Motorwayin Egnatia Motorway

OverpassesOverpasses UnderpassesUnderpasses


Overview of the bridge studiedOverview of the bridge studied

monolithic pier-to-deck connectiondeck is connected through two pot bearings that permit

sliding along the two principal bridge axes longitudinal 12cm joint separates deck from backwalltransverse displacement blocked at the abutments

19.0m 32.0m 19.0m

60.0m

A1 P1 P2 A2



PiersPiers P1P1, , P2P2

Pile capPile cap

2x2 Pile 2x2 Pile GroupGroup

DeckDeck

Pier top flexural reinforcementPier top flexural reinforcement::136.4136.4cmcm22

UncrackedUncracked section propertiessection propertiesconsidered in designconsidered in design



0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00

Rd

(m/s

ec2 )

Κατακόρυφη Συνιστώσα Rd,z

Οριζόντια Συνιστώσα Rd,y

Οριζόντια Συνιστώσα Rd,x

Design spectrumDesign spectrum

Time (sec)

Sa

(m/s

ec2 )

Horizontal component x-x (qx = 2.5)

Horizontal component y-y (qy = 3.5)

Vertical component z-z (qz = 1.0)

Soil category CPGA = 0.16g (Zone I)

‘Non-seismic’ design according to German Norms DIN 1055, 1045, 1072, 1075, 1054, 4227, 4085, 4014

Seismic Design according to Greek Seismic Code EAK2000 and Greek standards E39/99 for seismic design of bridges


Numerical Analysis: static soil stiffness Numerical Analysis: static soil stiffness

MultiMulti--linear plinear p--y,y,ppuu(z) from API (z) from API

(1991)(1991)

yy5050 = 0.05= 0.05yyuu = 15 = 15 ×× yy5050CCuu = = 3030 -- 200 200 ΚΚPaPaγγ = 1= 177 –– 22 kN/m22 kN/m33

(Model 4)


Numerical Analysis: Numerical Analysis: stiffness assumptionsstiffness assumptions

P-y29% EI4

P-y29% EI3

Fixed37% EI2

Fixed100% EI1

Foundation modellingPier EIeff

FE Model

ID#

4 alternative models developed 4 alternative models developed

for the bridge for the bridge

additional, separate models for the abutment and for additional, separate models for the abutment and for the abutmentthe abutment--embankmentembankment--foundation soil systemfoundation soil system


Numerical Analysis: static soil stiffness Numerical Analysis: static soil stiffness

80.0% y-yTranslational (transverse)1.090.5054




modal participation

factor2nd Mode shapePeriod of 2nd

mode (sec)

FE Model

ID#

98.8% x-xTranslational (longitudinal)1.971.0124


99.7% x-xTranslational (longitudinal)1.380.708 2


modal participation

factorFundamental Mode shapeRatio

Ti/T1

Fundamental Period T (sec)

FE Model

ID#

Dynamic characteristics of the 4 Dynamic characteristics of the 4 alternative FE modelsalternative FE models

??

Mode 1

Longitudinal

Mode 2

Transverse→ transverse stiffness controlled by blocked displacement at the abutments!


Finite Element Analysis Finite Element Analysis Separate pushover Separate pushover analysis for the abutment analysis for the abutment in both directionsin both directions

Soil yieldingSoil yieldingPile flexural failurePile flexural failure

PilePile head shear failurehead shear failure

Backfill soil yielding (in Backfill soil yielding (in transverse direction)transverse direction)

Sliding joint (in the Sliding joint (in the

longitudinal direction)longitudinal direction)

pile shear capacity/demand


Detailed modelling of the backfill-embankment-foundation soil system

ABAQUS Tetrahedral solid elements (C3D4),

different E and φ for each soil type


Detailed modelling of the backfill-embankment-foundation soil system

Longitudinal direction

Longitudinal direction

0

2000

4000

6000

8000

10000

12000

14000

0 0.02 0.04 0.06 0.08 0.1Displacement (m)

Forc

e (k

N)

Transverse direction

0

2000

4000

6000

8000

10000

12000

14000

0 0.05 0.1 0.15 0.2

Displacement (m)

Transverse direction

ABAQUS Tetrahedral solid elements (C3D4), different E and φ for

each soil type

→→ reasonable match only in the reasonable match only in the ttransverse directionransverse direction


Pushover curve and seismic assessment of the overall system Pushover curve and seismic assessment of the overall system (longitudinal direction)(longitudinal direction)

Pier yieldingPier yieldingJoint closure at δ=12cm

Backfill yielding Ultimate state due to unrecoverable abutment damage (δ=22cm)4 plastic hinges exhausting 35-49% of the available plastic rotation

Soil yielding

stiffsofter soil

2E2EEEEE 2E2E


Abutment pile head shear failure

Stiffness mainly provided by middle piers Collapse

Pushover curve and seismic assessment of the overall system Pushover curve and seismic assessment of the overall system (transverse direction)(transverse direction)

Soil y

ieldin

gPier yi

elding

Stiffness provided mainly by middle piers

2E2EEE EE 2E2E

??

The abutment piles fail in shear at their head, the The abutment piles fail in shear at their head, the abutment abutment becomes unstable at its base,becomes unstable at its base, and the and the high ductility of the piers is never high ductility of the piers is never mobilisedmobilised

No joints existNo joints exist


Conclusions

additional material non-linearity mechanisms(of the foundation and/or backfill soil)

BC non-linearity mechanisms (activation of control components such as ‘stoppers’ or seismic joints)

→ must be considered in analysis and design

The problem is even more complex…

Definition of system ductility

Ratcheting effect

Dynamic bridge abutment-embankment interaction (see presentation by Sextos…)

seismic assessment of bridges accounting for non-linear ... · pdf fileseismic code eak2000...

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