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ResearchResearch carriedcarried out out withinwithin the the contextcontext of PBEEof PBEE
Paolo FranchinPaolo Franchin
A relaxed workshop on PBEECapri, July 2nd-4th 2009
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AcknowledgementsAcknowledgements
• People I learnt from, I had fun with, I owe much (I’m not going to quote each and every one when neededlater on, hence I just thank them all now):
– Paolo E. Pinto– Armen Der Kiureghian– Ove Ditlevsen– Filip C. Filippou– Alessio Lupoi– Marko IJke Schotanus– Giorgio Lupoi– Rajeev Pathmanathan– Fatemeh Jalayer– Fabrizio Noto– Terje Haukaas
• Introduction• Topic 1• Topic 2
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ResearchResearch areasareas
• Probabilistic methods in earthquake engineering– Seismic risk for intact and damaged structures (collapse & progressive
collapse risk)• FORM• Response surface• IM-based methods• Simulations with fully probabilistic models
– Performance of hospital systems– Performance of infrastructural systems (road networks)
• Seismic assessment of existing structures– Epistemic uncertainty– Non-linear static methods– Masonry and reinforced concrete
• Seismic design and analysis of bridges– Non-uniform support excitation
• Modelling– Nonlinear frame elements, response sensitivities– Soil-structure interaction: retaining structures
• Introduction• Topic 1• Topic 2
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FocusFocus themesthemes
• Today, focus on:– Earth-retaining structures, simplified non-linear
dynamic modelling• Relevance
– Structural and geotechnical communities traditionally havedifferent language/approach
– Typically structures are “lollipops” for geotechnical engineers, while the soil is “some springs” for their structural counterparts
– Consistent seismic performance evaluation of foundations & retaining structures is thus challenging, given the “boundary”nature of the topic
– Probability of collapse for sequential shocks• Relevance
– key to emergency response management, both for buildingsand for infrastructure
• Some open questions
• Introduction• Topic 1• Topic 2
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TopicTopic 11
BD
AE
F
C(a)
BD
AE
F
C
BD
AE
F
C(a)
(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
α
(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
αα
hε(Tensile)(Compressive)
Bha ,σBh ,0σ
Ah ,0σ
Ahp ,σ
hσ
(b)BhE ,
AhE ,
hε(Tensile)(Compressive)
Bha ,σBh ,0σ
Ah ,0σ
Ahp ,σ
hσ
(b)BhE ,
AhE ,
A
B
A
B
τ
γ
( )b ( )c(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
α
(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
αα
hε(Tensile)(Compressive)
Bha ,σBh ,0σ
Ah ,0σ
Ahp ,σ
hσ
(b)BhE ,
AhE ,
hε(Tensile)(Compressive)
Bha ,σBh ,0σ
Ah ,0σ
Ahp ,σ
hσ
(b)BhE ,
AhE ,
A
B
A
B
τ
γ
( )b ( )c
0 5 10 15 20 25-1
0
1
ac
ce
lera
tion
(g
)
0 10 20-20
-15
-10
-5
0
top wall settlement (mm)
0 10 20
-60
-40
-20
0
horizontal displacement (mm)
SeismicSeismic performance performance evaluationevaluation ofofflexibleflexible retainingretaining structuresstructures::
1D 1D nonlinearnonlinear dynamicdynamic modellingmodelling
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RetainingRetaining structuresstructures: : motivationmotivation
• Several hundreds km of highways currentlyundergoing upgrading (including seismic)
• Large number of non-seismically designedearth-retaining structures in existing road networks
• Current analysis based (99%) on pseudo-staticmethods
– FEA/FDA still too demanding and unwarranted foruse in the profession
• Shift in focus from forces to displacement(maximum and residual)
• This situation stimulates the development of simple non linear dynamic models satisfying the requirements of:
– Being affordable and sufficiently accurate– Allowing evaluation of residual (cumulative)
displacements
• Introduction• Topic 1• Topic 2
m5
m8
3/20 mkN=γ°=°= 23 35 δφ
( )kPazE s ⋅= 13000GPaEc 31=mtw 80.0=
( )a( )b( )c
g2.0g1.0
200400600800Bending moment M (kNm/m)
Dep
thz
(m)
13−
11−
9−
5−
3−
m5
m8
3/20 mkN=γ°=°= 23 35 δφ
( )kPazE s ⋅= 13000GPaEc 31=mtw 80.0=
( )a( )b( )c
g2.0g1.0
200400600800Bending moment M (kNm/m)
Dep
thz
(m)
13−
11−
9−
5−
3−
FLACSRMM-O
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AvailableAvailable modelsmodels//methodsmethods
• Pseudo-static methods (Woods, Mononobe-Okabe)
• Newmark method
• Inelastic (usually some brand of plasticity) dynamicfinite element/difference methods (DYNAFLOW, GEFDYN, FLAC, PLAXIS, OPENSEES, etc)– Violate the requirement of affordability (computationally and
in terms of required background)
• Viscoelastic solutions (Wood, Veletsos and co-workers)– Cannot assess inelastic displacements
• Winkler-type analysis– Crude but practical, applied to a variety of linear/nonlinear,
static and dynamic problems– Apparently not yet employed for nonlinear dynamic analysis of
flexible retaining structures
• Introduction• Topic 1• Topic 2
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ProposedProposed 1D model 1D model (1/2)(1/2)
The problem is one of imposed displacements, characterised bythe lack of symmetry
BD
AE
F
C(a)
BD
AE
F
C
BD
AE
F
C(a)
bedrock
Model base (absorbent boundary)
Common base
Far-field(undisturbed)Far-field
(undisturbed)Interface soil(disturbed)
Interface soil(disturbed)
zΔ
zΔ
zΔ
zΔ
zΔ
(b)
zΔ
zΔ
zΔ
zΔ
zΔ
(b)
A B
C D E
F
Dampercb = ρbVsb
Input forcef(t)=cbv(t)
“Uphill”(layered)
soilcolumn
Mas
s-sp
ring
mod
elof
soi
lcol
umn
Non-symmetricWinkler springs“Downhill”
(layered)soil
column
• Introduction• Topic 1• Topic 2
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ProposedProposed 1D model 1D model (2/2)(2/2)
(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
α
(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
αα
hε(Tensile)(Compressive)
Bha,σBh ,0σ
Ah ,0σ
Ahp,σ
hσ
(b)BhE ,
AhE ,
hε(Tensile)(Compressive)
Bha,σBh ,0σ
Ah ,0σ
Ahp,σ
hσ
(b)BhE ,
AhE ,
A
B
A
B
τ
γ
( )b ( )c(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
α
(a)
αcosu
uhff =
α2coskkh = u
f
αcos0
0ff h =
αα
hε(Tensile)(Compressive)
Bha,σBh ,0σ
Ah ,0σ
Ahp,σ
hσ
(b)BhE ,
AhE ,
hε(Tensile)(Compressive)
Bha,σBh ,0σ
Ah ,0σ
Ahp,σ
hσ
(b)BhE ,
AhE ,
A
B
A
B
τ
γ
( )b ( )c
Non-symmetric:Elastic-plastic
shifted in tension
Non-symmetric:Elastic-plastic
shifted in compression
Symmetric:Bouc-Wen
Tie-backs Soil-wall interfaceSoil columns
Force-displacement laws for the model components
(England et al, 2001)
• Introduction• Topic 1• Topic 2
Soil springs for both columns and interface elements are functionsof the overburden pressure as well as the OCR, they are updatedduring excavation
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The The nextnext slidesslides
• Sample results– Unanchored diaphragm wall– Tie-back wall (retrofitted abutment)
• Limited/preliminary validation through:– Comparison with 2D-FE analysis (PLAXIS), good– Comparison with shake-table test performed in
Pavia, not bad– Both of the above can’t be used to validate all the
features of the model
• Further research
• Introduction• Topic 1• Topic 2
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11SampleSample resultsresults, , unanchoredunanchored wallwall
(1/3)(1/3)
mtGPaE
mkN
c
c
50.02.0 30
/25 3
=
==
=
ν
γ
φδ
φ
ν
γ
32
0' 353.0 /250
/6.19 3
=
=°=
==
=
kPacsmVmkN
s
s
m 0.6
m 0.5
m 0.9
mtGPaE
mkN
c
c
50.02.0 30
/25 3
=
==
=
ν
γ
φδ
φ
ν
γ
32
0' 353.0 /250
/6.19 3
=
=°=
==
=
kPacsmVmkN
s
s
m 0.6
m 0.5
m 0.9
Dry cohesion-less soil!
• Introduction• Topic 1• Topic 2
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12SampleSample resultsresults, , unanchoredunanchored wallwall
(2/3)(2/3)
0 5 10 15
-0.2
-0.1
0
0.1
0.2
0.3
time (s)
acc.
(g)
Outcropping
0 5 10 15
-0.2
-0.1
0
0.1
0.2
0.3
time (s)
acc.
(g)
Deconvolved
0 1 2 30
0.1
0.2
0.3
0.4
0.5
0.6
period (s)
Sa (g
)
( )ta
( )ta
sbb Vρ , space-half
( )tvde
conv
olut
ion
integration
ss Vρ ,deposit
sbbsb VAc ρ⋅= 2
( ) ( )tvctf b=
Model response
0 05
-0.045
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
( )tu( )ta
( )ta
sbb Vρ , space-half
( )tvde
conv
olut
ion
integration
ss Vρ ,deposit
sbbsb VAc ρ⋅= 2
( ) ( )tvctf b=
Model response
0 05
-0.045
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
( )tu
Outcropping Deconvolved Spectra
• Introduction• Topic 1• Topic 2
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13SampleSample resultsresults, , unanchoredunanchored wallwall
(3/3)(3/3)
Bending moment distr. Top displacement TH
• Introduction• Topic 1• Topic 2
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SampleSample resultsresults, , tietie--backback wallwall
-200 0 200 400 600 800 1000-12
-10
-8
-6
-4
-2
0
Bending moment (kNm/m)
Dep
th (m
)
Fixed bearingSliding bearingSlidingbearing,anchored
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
Time (s)
Top
disp
lacem
ent (
m)
Sliding bearing, anchored
Sliding bearing
Fixed bearing
-0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01-12
-10
-8
-6
-4
-2
0
Displacement (m)
Dep
th (m
)
Fixedbearing
Slidingbearing
Slidingbearing,anchored
H=
6.0m
D=
6.0m
2.0m
8.0m
L=10.0m
α=15°
L=30.0m
3.0m/s 250
kPa 0'
32 35kN/m 6.19
30,
3
=
==
=
°=°=
=
ν
φφ
γ
ss
cvpeak
s
VVc
t=0.7m
H=
6.0m
D=
6.0m
2.0m
8.0m
L=10.0m
α=15°
L=30.0m
3.0m/s 250
kPa 0'
32 35kN/m 6.19
30,
3
=
==
=
°=°=
=
ν
φφ
γ
ss
cvpeak
s
VVc
t=0.7m
• Introduction• Topic 1• Topic 2
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Model Model validationvalidation ((partialpartial!) !) (1/3)(1/3)
• 2D plane strain model in the commercial code PLAXIS– Elastic-plastic with Mohr-Coulomb failure criterion (small “stability”
cohesion 1kPa)– Non-rigid interface with R = tanδ/tanφ = 0.62 (δ/φ = 0.67)– Newmark damping α = 0.6 and β = 0.3025– (Use of large model width and fixed base due to lack of
transparent boundaries)
• Introduction• Topic 1• Topic 2
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Model Model validationvalidation ((partialpartial!) !) (2/3)(2/3)
Artificial signalRicker wavelet
Recorded motionColfiorito (Italy)
Response spectraA
ccel
erat
ion
Dis
plac
emen
t
• Introduction• Topic 1• Topic 2
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Model Model validationvalidation ((partialpartial!) !) (3/3)(3/3)
1D modelPlaxis
• Introduction• Topic 1• Topic 2
Ricker wavelet
Colfiorito recorded GM
• Note:– High-frequency
content, model isfixed-base
– Largedisplacements and moments, no radiation damping
– (Too) good match with “higher-order”method
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ComparisonComparison withwith experimentalexperimental testtest
• Large scale shake-table test of an unanchored diaphragm wall in dry cohesionless soil
• Data kindly made available from the EUCENTRE researchfoundation in Pavia, Italy (Carlo Lai and co-workers)– Details can be found in “Large scale 1-g shaking table test of an
unanchored earth-retaining RC diaphragm” Borg et al 2009• Our simulation
– Constant unit weight, fixed soil columns, no degradation and average value of friction angle between φ’ and φCV
Laminar box Pluviation device Instrument scheme
But… But…
• Introduction• Topic 1• Topic 2
But…
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Model Model vsvs ExperimentExperiment
0 5 10 15 20 25-1
0
1
ac
ce
lera
tion
(g
)
0 10 20-20
-15
-10
-5
0
top wall settlement (mm)
0 10 20
-60
-40
-20
0
horizontal displacement (mm)
• Introduction• Topic 1• Topic 2
+NAT4 NAT5=-NAT4 +NAT6 NAT7=-NAT6 +NAT8 NAT9=-NAT8
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FurtherFurther developmentsdevelopments
• Include interface-soil cyclic degradation (φ’→φCV)
• Cantilever retaining wall with direct and indirect foundation(abutments)
• Introduction• Topic 1• Topic 2
Active φ’
Active φCV
Passive φ’
Passive φCVDecreasein restraint
at base
Increasein uphillpressure
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SummarySummary & & conclusionsconclusions of of TopicTopic 11
• A simple 1D nonlinear dynamic model is developed to be:– Capable of capturing the main features of the problem (lack of
symmetry, imposed motion, cumulative inelasticdisplacements)
– Computationally affordable– Sufficiently accurate, as compared to other computational
tools
• What is still needed:– A more “robust” validation, for tie-back walls, with compliant
base, more records and parameters sets
• Uses:– Preliminary design– Reliability analysis (as for instance the base model in a Model
Correction Factor Method)
• Open questions– In the pursue for more reliable performance estimates is it still
feasible to separate the design tasks between structural and geotechnical engineers? Or shouldn’t SSI analysis become a more widespread tool?
• Introduction• Topic 1• Topic 2
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0 5 10 15 20 25 30 35 40-4
time (s)
0 5 10 15 20 25 30 35 40-0.15
-0.1
-0.05
0
0.05
0.1
time (s)
disp
lacem
ent (
m)
-4
-2
0
2
4
acce
lerat
ion
(m/s
2 )
0 1
0 1 20
5
10
15
Y
Sa (m
/s2 )
0 5 10 150
2
4
6
8
SaY=1 (m/s2)
0 5 10 150
0.2
0.4
0.6
0.8
Sa (m/s2)
P(D
S3|D
S2,S
a)
0 1 20
5
10
15
Y
Sa (m
/s2 )
0 5 10 150
5
10
15
SaY=1 (m/s2)
η β
0 5 10 150
0.2
0.4
0.6
0.8
Sa (m/s2)
P(D
S3|S
a)
100 101 102 10310-3
10-2
10-1
t (days)
λ3m
λ1,3a T = 365 days
λ2,3a T = 365 days
λ1,3a T = 180 days
λ2,3a T = 180 days
Mm = 5.5
TopicTopic 22
RiskRisk of of aftershockaftershock--inducedinduced collapsecollapseasas a a criterioncriterion forfor
closureclosure//rere--openingopening of of bridgesbridges
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Statement of the Statement of the problemproblem
• Decision on transitability of bridges in the aftermath of a damaging mainshock currently based on expert judgementon damage state
• Expert judgement not replaceable but could be usefully complemented by pre-analysis of bridges in the network
• Proposed criterion: transitability decision based on collapse risk due to aftershocks
• Implemented method requires– Aftershock hazard– Capability of assessing state of damage of each bridge: linking
visual observation with mechanical damage
• The idea was inspired by Gee Like Yeo PhD work (Stanford, 2005), and more generally by work carried out in California for PGE on the topic of building tagging
• Introduction• Topic 1• Topic 2
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DifficultiesDifficulties withwith DamageDamage
Actual
Visual Numerical
Damageas assessed
during field visit
Damage assimulated by FE analysis
Real damageexperienced
by the structure
• Introduction• Topic 1• Topic 2
Both visual inspection and FEA have limitations. Evaluation of true damage and of residual capacity is a challenging task.
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MainshockMainshock vsvs AftershocksAftershocks
Seismichazard
Structuralfragility
Risk orMAF of DS
(e.g. collapse)
( ) ( )xx SaSa λλ =year 1
PSHA
( ) ( )xSDSPxF aii ==
Fragility analysis
( ) ( )∫∞
=0
xdxF Saii λλ
Mainshock Aftershock
APSHA
( )txSa ,λ
Fragility analysis (damaged)
( ) ( )xSDSDSPxF ajiij =→=
( ) ( ) ( ) ( )∫∞
=0, dxxfxFtt Saijji αλ
• Introduction• Topic 1• Topic 2
IM-based approach: Risk from hazard and fragility
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APSHA and APSHA and AftershockAftershock riskrisk
( ) ( ) ( ) nilma
T
t
ai
ylm
ai PMMtd
tTT
MMt ,
3,1
3, ,,~,,~⋅=
−= ∫ αττλλ
( ) ( ) ( ) ( ) ( ) nilmaaSailma
ai PMMtdxxfxFMMtt ,0 3,3, ,,,, ⋅== ∫
∞ααλ
( )( )
( )pMMba
ma ctMMt
m
+=
−+10,,λ
Instantaneous rate of aftershocks(Modified Omori-law, Reasenberg and Jones 1989)
Instantaneous Collapse Frequency due to aftershocks
Equivalent Mean Annual Collapse Frequency due to aftershocks
• Introduction• Topic 1• Topic 2
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StructuralStructural fragilityfragility curvecurve
( )( )tCtDY DS
k
kIkNjt
DS
jm ∈== minmaxmax
,,1K
Global scalar index of structural performance, Jalayer et al 2007
minmin
max
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛ −Φ=≤=
21 lnln
i
iYa
xxSPβ
ηY
1
aSIDA
Y1
aSIDA ( ) ( ) ( )xSPxSaYPxF Y
aDSi
i ≤==>= =11
Median ηi, dispersion βi
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ModellingModelling forfor cycliccyclic degradationdegradation
crackV
peakV
.resV
.resγpeakγcrackγ
sres
scrackpeak
Nccrack
VV
VVVVVV
=
+=
+=
( )*arctan GA
( )a
-0.01 -0.005 0 0.005 0.01-2000
-1000
0
1000
2000
shear deformation γ
shea
r for
ce V
(kN
)
( )b
peakV≈crackV
.resV≈
crackV
peakV
.resV
.resγpeakγcrackγ
sres
scrackpeak
Nccrack
VV
VVVVVV
=
+=
+=
( )*arctan GA
( )a
-0.01 -0.005 0 0.005 0.01-2000
-1000
0
1000
2000
shear deformation γ
shea
r for
ce V
(kN
)
( )b
peakV≈crackV
.resV≈
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
∂∂
∂∂∂∂
∂∂∂∂
=
γ
φε
φε
VMMNN
s
0000
0
0
k
Opensees, flexibility-based element, section aggregator
Fiber section
Uniaxial material
Cyclic degradationBackbone curve
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The The HansuiHansui viaductviaduct, , KobeKobe 19951995
(from Marini and Spacone, ACI Struct. Jnl 2006)
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0 5 10 15 20 25 30 35 40-4
time (s)
0 5 10 15 20 25 30 35 40-0.15
-0.1
-0.05
0
0.05
0.1
time (s)
disp
lacem
ent (
m)
Sample model Sample model responseresponse 1/21/2
-4
-2
0
2
4ac
celer
atio
n (m
/s2 )
0 1
Mainshock Aftershock
Input ground acceleration
Output top displacement
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Sample model Sample model responseresponse 2/22/2
5 0 5
-5 0 5
x 10-3
-5 0 5
x 10-4
-2 0 2
x 10-4
-2 0 2
x 10-4
-2 0 2
x 10-4
-5 0 5
x 10-4
-1000
0
1000
2000
-5 0 5
x 10-4
-1000
0
1000
2000
-2 0 2
x 10-4
-1000
0
1000
-2 0 2
x 10-4
-1000
0
1000-2 0 2
x 10-4
-1000
0
1000-2 0 2
x 10-4
-1000
0
1000
2 0 2-1000
0
1000-2 0 2
x 10-4
-1000
0
1000-2 0 2
x 10-4
-1000
0
1000
-1 0 1
x 10-3
-1000
0
1000
2000
-5 0 5
x 10-4
-1000
0
1000
2000
-5 0 5
x 10-4
-2000
0
2000
05 0 0 05
2 0 2
x 10-3
2 0 2
x 10-3
5 0 5
x 10-3
1 0 1
x 10-3
5 0 5
x 10-3
-0.05 0 0.05-5000
0
5000
0 1 2
x 10-4
0
100
200
-0.05 0 0.05-5000
0
5000
-5 0 5
x 10-3
-2000
0
2000-1 0 1
x 10-3
-1000
0
1000-0.01 0 0.0-5000
0
5000
0 05 0 0 0-5000
0
5000-2 0 2
x 10-3
-2000
-1000
0
1000-5 0 5
x 10-3
-2000
0
2000
4000
-0.05 0 0.05-5000
0
5000
-5 0 5
x 10-4
-200
0
200
400
-0.05 0 0.05-5000
0
5000
Flexural (M-φ) Shear (V-γ)
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DefinitionDefinition of of limitlimit statesstates• Introduction• Topic 1• Topic 2
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Site, Site, seismogeneticseismogenetic areasareas, , hazardhazard
-200 -150 -100 -50 0 50 100-150
-100
-50
0
50
100
Zone 904
Zone 905
Zone 906
km
km
44.75
45
45.25
45.5
45.75
46
46.25
46.5
46.75
47
10.2510.510.7511 11.2511.511.7512 12.2512.512.7513 13.2513.513.7514 14.25
Site
100 10210110110-6
10-5
10-4
10-3
10-2
10-1
Sa (m/s2)
λSa
α = 0.14β = 1.12Ml = 4.76Mu = 6.14
α = 0.37β = 1.06Ml = 4.76Mu = 6.60
α = 0.11β = 1.14Ml = 4.76Mu = 6.14
NE Italy - Friuli region1976 M = 6.4 event
Three seismogeneticareas
MAF of Sa at T=0.45s
Lolli and Gasperini, 2003:
a = -2, b = 1, log10c = -1.65 and p = 0.9,
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IntactIntact structurestructure fragilitiesfragilities
0 1 20
5
10
15S
a (m/s
2 )
0 5 10 150
5
10
15η β
0 5 10 150
0.2
0.4
0.6
0.8
P(D
S1|S
a)
LDη=1.89 β=0.30
0 1 20
5
10
15
Sa (m
/s2 )
0 5 10 150
5
10
15
0 5 10 150
0.2
0.4
0.6
0.8
P(D
S2|S
a)
SDη=3.05 β=0.42
0 1 20
5
10
15
Y
Sa (m
/s2 )
0 5 10 150
5
10
15
SaY=1 (m/s2)
η β
0 5 10 150
0.2
0.4
0.6
0.8
Sa (m/s2)
P(D
S3|S
a)COη=4.01 β=0.41
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DamagedDamaged structurestructure fragilitiesfragilities
0 1 20
5
10
15S
a (m/s
2 )
0 5 10 150
5
10
0 5 10 150
0.2
0.4
0.6
0.8
P(D
S3|D
S1,S
a)
0 1 20
5
10
15
Y
Sa (m
/s2 )
0 5 10 150
2
4
6
8
SaY=1 (m/s2)
0 5 10 150
0.2
0.4
0.6
0.8
Sa (m/s2)
P(D
S3|D
S2,S
a)
LD to COη=3.98 β=0.38
SD to COη=2.86 β=0.48
0 1 20
5
10
15
Y
Sa (m
/s2 )
0 5 10 150
5
10
15
SaY=1 (m/s2)
η β
0 5 10 150
0.2
0.4
0.6
0.8
Sa (m/s2)
P(D
S3|S
a)CO η=4.01 β=0.41
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EquivalentEquivalent MAFMAF
100 101 102 10310-3
10-2
10-1
t (days)
λ3m
λ1,3a M
m = 5.5
λ2,3a M
m = 5.5
λ1,3a M
m = 6.0
λ2,3a M
m = 6.0
100 101 102 10310-3
10-2
10-1
t (days)
λ3m
λ1,3a T = 365 days
λ2,3a T = 365 days
λ1,3a T = 180 days
λ2,3a T = 180 days
T = 365 days Mm = 5.5
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SummarySummary & & ConclusionsConclusions of of TopicTopic 22
• An aftershock-risk-based bridge opening/closurecriterion is proposed. It requires:– Pre-analysis of bridges for intact and damaged conditions– APSHA immediately after the mainshock
• Pre-analysis, possibly with data acquired frominstruments (SMA) at the brigdes sites and network emergency traffic analysis, can better direct inspections and rationally support closure decision
• Still need considerable improvements:– In analysis tools (correct simulation of damage) and in
particular shear-flexure cyclic interaction– In correlation between visual observation and actual damage
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ContributionContribution toto generalgeneral discussiondiscussion
• As far as I know the role/weight of computer modelsand analysis is increasing and is likely to do even more as we press towards realistic performance estimation
– Is this an illusory step towards better/safer structures?
• Engineering has always relied on sound engineeringjudgement
– Is there a way to develop it in students?– Shouldn’t we invest more on finding more effective ways of
teaching?– I personally teach Structures to architects (yes, I know…):
succeding in teaching them an intimate understanding of structural behaviour isn’t going to make a larger differencethan all my research?
– What about dynamics? How to develop intuition aboutdynamic behaviour?