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Title Masonry Arch Bridges: Analysis Tools for Assessment - Finite Element Methods
Authors(s) Fanning, Paul
Publication date 2018-06-08
Conference details 1st UIC Workshop on Masonry Arch Bridges, Madrid, Spain, 7 - 8 June 2018
Publisher University College Dublin
Item record/more information http://hdl.handle.net/10197/10463
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Scoil na hInnealtoireachta
Sibhialta UCD
UCD School of Civil
Engineering
IRS 70778-3 : Section 3.4 & Appendix A
Finite Element Modelling
Professor Paul Fanning
Paul Fanning
• Finite element modelling of engineering structures works
well when:
• Geometry is well defined
• Material properties (linear and nonlinear regimes) are well defined and understood
• Loading and boundary conditions are clearly defined
• All of the above are challenging in respect of stone or
masonry arch bridges
Finite Element Modelling
Paul Fanning
• 2D/3D, linear or nonlinear (see Appendix A)
– 2D loses 3D effects, load dispersion across the arch
– Linear can be useful for identify load paths, and areas of concentrated load – beware tensile strength
• 3D Nonlinear (see Appendix A)
– Final sieve analysis
– More complex structures
– Heritage structures, irregular geometries
– Challenging
– Requires corroboration by other means, eg. Test data – this is often difficult to achieve
Finite Element Modelling
Paul Fanning
..tested 8 bridges….one to very high load
levels…
Paul Fanning
Greenfields Bridge
Paul Fanning
Finite Element ModellingStone Arch Bridge Research at UCD
• Testing, Modelling, Assessment
• 1999 – 2014
• National Roads Authority (Ireland)
• ICE (UK)
• EU FP5 Marie Curie Host Fellowship Scheme
• Dublin County Council
• UIC
Paul Fanning
• Same modelling approach used for all bridges!
• 3D 8-noded brick elements for masonry/mortar
continuum and fill elements
• Frictional/sliding contact between fill and masonry
Finite Element Modelling
Paul Fanning
Multi-stage analysis
1) Apply selfweight
2) Truck position 1
3) Truck position 2
4)…..etc.
Paul Fanning
Masonry/mortar modelled as abrittle material using a smearedcrack numerical model
Fill also modelled as a continuumbut with a Drucker-Prager yieldcriterion
Young’sModulus
(GPa)
Poisson’sRatio
Density
(kg/m3)
TensileStrength
(MPa)
CompressiveStrength
(MPa)
Masonry 10-15 0.3 2200 0.5-0.7 10
Young’sModulus(MPa)
Poisson’sRatio
Density
(kg/m3)
Cohesion
(MPa)
Angle ofFriction
(degrees)
Angle ofDilatancy(degrees)
Fill 15 0.23 1700 0.001 44 44
Paul Fanning
Importance of extent of fill modeled in capturing abutment behaviour!
Paul Fanning
Griffith Bridge
Crown on centreline
0
0.2
0.4
0.6
-5 0 5 10 15
Distance of Front Axle From Crown (m)
Deflect
ion (
mm
)
test 1 r test 2 f test 3 r test 4 f test 6 f FE(full)
-0.2
0
0.2
0.4
0.6
-5 0 5 10 15
Distance of Front Axle From Crown (m)
Deflect
ion (
mm
)test 1 r test 2 f test 3 r test 4 f test 6 f FE(full)
Griffith Bridge
Crown at edge
Paul Fanning
Loading is factored double axle bogey at close to quarter span
Crack propagation as load is incrementally increased
53t = 1.9*10 + 3.4*10, i.e. 10t axle
104t = 19.6t axle
From earlier:
tests 10.3t axles
Level 1 assessment ~ 7.4t
Paul Fanning
-0.05
0
0.05
0.1
0.15
0.2
-5 -3 -1 1 3 5 7 9
exp point 4
exp point 5
exp point 6
num point 4
num point 5
num point 6
num point 5
num point 4
num point 6
exp. point 5
exp. point 6
0 X
4, 5, 6
Front axle position , (m)x
Dis
pla
ce
men
t , (m
m)
u
exp. point 4
Greenfields Bridge, Crown
Paul Fanning
Adjusting published FE model results for different wheel base and axle loads
Fanning P.J., Salomoni, V. and Boothby, T.E., “Ultimate and Service Load Simulations for a Masonry Arch Bridge Scheduled for Controlled Demolition”, Systems-
Based Vision for Strategic and Creative Design, Proceedings 2nd International Structural and Construction Conference ISEC02, Rome, 23 – 26 September 2003,
Vol. 2, pp 1051 – 1056, Edited by F. Bontempi, Published by A.A. Balkema, ISBN 90-5809-599-1.
Modelling completed in advance of tests – good correlation predictability of response !!
Paul Fanning
-0.05
0
0.05
0.1
-1 1 3-3 5-5 7 9
Front axle position , (m)x
Dis
pla
cem
en
t ,
(mm
)v
7, 8 9,10
-0.15
-0.1
0 X
exp point 7
exp point 8
exp point 9
exp point 10
num point 7
num point 8
num point 9
num point 10
num point 10
num point 9
exp. point 9
exp. point 10
num point 7
num point 8exp. point 7
exp. point 8
Greenfields Bridge, Abutments
Paul Fanning
Paul Fanning
Two patch loads, max load of 60T
Cracked model stiffness consistent
with measured bridge stiffness
Indication of presence of cracks
before testing?
Spandrel wall separation?
Paul Fanning
• Standard modelling procedure
– Effective for “family” of bridges tested
• Good correlation with test data (both service
level and high level loading)
• Extremely informative – diagnostic tool
• Benefit of test data obvious
Finite Element Modelling