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STRUCTURAL ROBUSTNESSAGAINST ACCIDENTS
Franco Bontempi*, Marco Lucidi, Pier Luigi Olmati*PhD, PE, Professor of Structural Analysis and Design
School of Civil and Industrial EngineeringUniversity of Rome La Sapienza
Rome - ITALY
1
introduction
2
LINEAR interactions NONLINEAR
LOO
SE
co
up
lings
TIG
HT
3
4
5
6
7
8
Design Complexity(Optimization)
Loosely – Tightly Couplings (Interactions)
No
nlin
ear
–Lin
ear
Be
hav
ior
9
SYSTEM CONTINGENCY
NatureCharacteristics
Weakness…
NatureCharacteristics
Strengths…
COUPLINGS / INTERACTIONSNONLINEARITY
10
Joh
n B
oyd
du
rin
g th
e K
ore
an W
ar
11
12
Structural Robustness =
Structural Survivability
13
SYSTEMS
14
Structural Sistems Performance
15
RESILIENCE
16
Levels of Structural Crisis
Us
ua
l U
LS
& S
LS
Veri
fica
tio
n F
orm
at
Structural Robustness
Assessment
1st level:
Material
Point
2nd level:
Element
Section
3rd level:
Structural
Element
4th level:
Structural
System
17
Structural Robustness (1)
ATTRIBUTES
RELIABILITY
AVAILABILITY
SAFETY
MAINTAINABILITY
INTEGRITY
SECURITY
FAILURE
ERROR
FAULT
permanent interruption of a system ability
to perform a required function
under specified operating conditions
the system is in an incorrect state:
it may or may not cause failure
it is a defect and represents a
potential cause of error, active or dormant
THREATS
NEGATIVE CAUSEST
RU
CT
UR
AL
QU
AL
ITY
more robust
less robust
18
•Capacity of a construction to show regular decrease of its structural quality due to negative causes.
• It implies: a) some smoothness of the decrease of
structural performance due to negative events (intensive feature);
b) some limited spatial spread of the rupture (extensive feature).
Structural Robustness (2)
19
202020
Connect
21
Robustness comparison
5
8 6 97
12 10 1311
4 2 31
l
VIERENDEEL STRUCTURE ROBUSTNESS
00
,51
0 1 2 3 4 5 6 7 8 9 10Damage Level
PU [ad] MAX MIN
6
6
1
2
3
7 8 9 4 5 1010
TRUSS STRUCTURE ROBUSTNESS
00
,25
0,5
0,7
51
0 1 2 3 4 5 6 7 8 9Damage Level
PU [ad] MAX MIN
High element connectionHigh element number
14
5 3 1 2 4 6 8
l
7 5 3 1 2 4 6 8
14
11 9 1210
18 20 1921
13 15 1617
l
STATICINDETERMINANCY
i = 4 i = 12
9
3
12
1 2
11 5 6 13 14
17
22
2323
Subdivide
24
25
•Capacity of a construction to show regular decrease of its structural quality due to negative causes.
• It implies: a) some smoothness of the decrease of
structural performance due to negative events (intensive feature);
b) some limited spatial spread of the rupture (extensive feature).
Structural Robustness (2)
26
Bad vs Good CollapseSTRUCTURE
& LOADSCollapse
Mechanism
NO SWAY
“IMPLOSION”OF THE
STRUCTURE
“EXPLOSION”OF THE
STRUCTURE
is a process in which
objects are destroyed by
collapsing on themselves
is a process
NOT CONFINED
SWAY
27
Cascade Effect / Domino Effect
• A cascade effect is an inevitable and sometimes unforeseen chain of events due to an act affecting a system.
• In biology, the term cascade refers to a process that, once started, proceeds stepwise to its full, seemingly inevitable, conclusion.
• A domino effect or chain reaction is the cumulative effect produced when one event sets off a chain of similar events.
• It typically refers to a linked sequence of events where the time between successive events is relatively small.
28
29
CONTINGENCIES
30
High Probability Low Consequences
HPLCevents
31
Low
Pro
bab
ility
Hig
h C
on
seq
uen
ces LPHC
events
32
3333
NTC2005
34
HPLCHigh Probability
Low Consequences
LPHCLow Probability
High Consequences
release of energy SMALL LARGE
numbers of breakdown SMALL LARGE
people involved FEW MANY
nonlinearity WEAK STRONG
interactions WEAK STRONG
uncertainty WEAK STRONG
decomposability HIGH LOW
course predictability HIGH LOW
HPLC – LPHC EVENTS
35
RUNAWAY (1)
effect
time
decomposability
course predictability
36
EFFECT
RU
NA
WA
Y (
2)
decomposability
course predictability
37
Framework of Analysis
HPLCEventi Frequenti con
Conseguenze Limitate
LPHCEventi Rari con
Conseguenze Elevate
Complessità:Non linearita’,
Interazioni,Incertezze
Impostazionedel problema:
Deterministica
Probabilistica
ANALISIQUALITATIVA
DETERMINISTICA
ANALISIQUANTITATIVA
PROBABILISTICA
ANALISIPRAGMATICACON SCENARI
38
A Black Swan is an event with the following three attributes.
1. First, it is an outlier, as it lies outside the realm of regular expectations,
because nothing in the past can convincingly point to its possibility.
Rarity -The event is a surprise (to the observer).
2. Second, it carries an extreme 'impact'.
Extreme impact - the event has a major effect.
3. Third, in spite of its outlier status, human nature makes us concoct
explanations for its occurrence after the fact, making it explainable and
predictable.
Retrospective (though not prospective) predictability -
After the first recorded instance of the event, it is rationalized by hindsight,
as if it could have been expected; that is, the relevant data were available
but unaccounted for in risk mitigation programs.
References: Taleb, Nassim Nicholas (April 2007). The Black Swan: The Impact of the Highly Improbable (1st ed.).
London: Penguin. p. 400. ISBN 1-84614045-5.
Black Swan Events
39
Word Cloud
40
41
42
43
HAZARD
IN-D
EPTH
DEFE
NCE
HOLES DUE TO
ACTIVE ERRORS
HOLES DUE TO
HIDDEN ERRORS
FAILURE PATH
44
Structural Robustness =
Structural Survivability
45
STUDIES
46
47
48
• The cladding system is a crucial component of the
building for protecting the inside against external
explosions.
• In this experimental program three specimens aretested.
• The first specimen (A) is conventionally designed witha minimum amount of required reinforcement (0.15%),
• the second specimen (B) is designed to achieve aspecific maximum deflection if subjected to a specificblast demand,
• and the third specimen (C) is equal to the specimen(B), subjected to a larger explosive charge.
Introduction
49
• All the specimens are horizontally simply supported andthe explosive charge is orthogonally suspended at 1500mm from the center of the exposed blast side of theconcrete panel.
• The experimental texts were conducted at the facility ofthe R.W.M. ITALIA s.p.a. (www.rwm-italia.com) atDomusnovas (Sardinia - Italy).
• Finite Element Analyses (FEAs) are carried out with theexplicit Finite Element (FE) code LS-Dyna® for predictingthe deflection of the precast panels. Solid elements areutilized for modeling the concrete instead beamelements are adopted for modeling the reinforcement.Contact algorithm for modeling the boundary conditionsis utilized.
Introduction
Specimen A-B-C
50
campione A
51
campioni B e C
52
Test bed arrangement
53
54
55 Test matrix
The specimens are simply horizontally supported, and the supports are made by concrete blocks.The explosive charge is suspended at 1500 mm from the panel surface and it is orthogonal with thecenter of panel surface. The supports are 400 mm high and the lateral open space between thepanels and the ground is closed by sandbags (see Fig.1). In this way the shock wave would be notable to diffract on the back face of the panels.
Fig. 2 - Longitudinal section of the testing site
The explosive, provided by the R.W.M. ITALIA s.p.a., is the PBXN-109 (composed by the 64.12 % of RDX, the 19.84 % of Aluminum, and the 16.04 % of Binder)
Panelt a b c
[mm] [mm] [mm] [mm]
A 150 1550
B 200 1160 1550
C 200 880 1550 2030
Thickness of the panels and position of the meter devices
Two kinds of displacement meter are used andprovided by the R.W.M. ITALIA s.p.a.: the combdevice and the coaxial tube device, as well asshown in figure.
56
57
58 Experimental results
Specimen A
The specimen A is designed with the minimum reinforcement for a concrete cladding wall panel.
The deflection of the specimen A reached the fullscale value of the coaxial tubes device. The panelduring the deflection impacted the external tubeof the coaxial tubes device and the panel stoppedits deformation.
The maximum and residual deflection of the panel is so 108 mm.
59 Experimental results
Specimen B
This panel is designed to achieve a specific performance under a blast load, so the specimen B isdesigned for blast (the amount of explosive is the same of the specimen A, 3.5 Kg TNTeq).
The maximum and the residual deflection achieved by the specimen B is of 70 mm and 35 mm respectively.
The specimen B shows a ductile failure with a diffuse crack patterns on the central one third ofthe panel span (the major cracks are 3 mm width). However, some radial crack patterns are present,this is due to the short stand-off distance, and develops a flexural mechanism as designed.
60 Experimental results
Specimen C
The specimen C is equal to the specimen B but the blast demand is greater for leading significantdamages to the panel without reach a failure. The specimen C would test the blast resisting rangeof the panel over the limit of his specific design (the amount of explosive is increased at 5.5 Kg TNTeq).
The maximum and the residual deflection are of 123 mm and 82 mm respectively.
Heavy crack patterns are assessed. Along the mid-span of the panel diffuse cracks are presentwith significant width until 10 mm. Moreover some cracks at the mid-span pass through thepanel cross section thickness (maximum width of the crack passing is the 5 mm)
61 Numerical investigation
In order to reproduce the experimental tests numerically the explicit Finite Elements (FE) code LS-Dyna® is adopted.To simulate physic phenomena, in this study a “Lagrangian” method is adopted and the uncoupledapproach is preferred, thus the blast load is computed and applied independently from thestructural response of the concrete wall panels.The FE models have constant solid stress elements for the concrete, and beams elements for thereinforcement. To bond the beams and solid elements, the LS-Dyna® keyword ConstrainedLagrange in Solid is used.For reducing the computational effort the model of the specimens are only a square part of thepanel, so opportune boundary conditions are provided.
Support
Blast load BC
Panel
Detail view of the finite element model
The concrete supports of the panels are explicitlymodeled and the contact between the panel and thesupport is provided by the LS-Dyna® keywordContact Automatic Surface to Surface. Furthermore,in order to take into account correctly the clearingeffect the boundary conditions for the blast load areprovided; a rigid surface modeling the other threequarter of the panel is added.
Numerical investigation
The material constitutive law of the reinforcement is the kinematic hardening plasticity modeland the strain rate effects is accounted for by the Cowper and Symonds strain-rate model.
The parameters selected for this model are:• D=500 s-1;• q=6;• steel Young’s modulus=200 Gpa;• Poisson coefficient=0.3;• yielding stress=543 MPa 0
2
4
6
8
0.001 0.1 10 1000
DIF
[-]
Strain-rate [1/sec]
CompressiveTensile
AB
C
Reflecting surface
Reflecting surface
Dynamic Increase Factor relation
1
Density 2.248 lbf/in
4 s2
2.4*103 kg/m3
fcm 4060 psi
28 N/mm2
Cap
retraction active
Rate
effect active
Erosion none
Input data for the concrete model
Concrete model input data
Due to the walls delimiting the testing site, multiple reflections of the original shock waveoccurred. Consequently the blast load on the specimens is greater than the blast load on aspecimen tested in an open space.
Using the uncoupled approach theimage charge method (instead of the
ALE method) provides acceptableresults without increasing thecomputational effort.
Elementary scenario of reverberatingShock waves
Image charge
side
Stand-off α
[m] [degrees]
West 6009 27
North 4705 35
South 4705 35
East 13505 13
Table 1: Image charge positions 1
62
63 Numerical investigation
0
40
80
120
160
200
240
280
0 0.05 0.1 0.15 0.2 0.25
δ[m
m]
time [sec]
Experimental
Numerical
Specimen A
δmaxδres
0
10
20
30
40
50
60
70
80
0 0.05 0.1 0.15
δ[m
m]
time [sec]
NumericalExperimental
Specimen B
δmax
δres
(a) (b)
0
20
40
60
80
100
120
140
0 0.05 0.1 0.15
δ[m
m]
time [sec]
Numerical
Experimental
Specimen C
δmax
δres
0
40
80
120
160
200
240
280
0 0.05 0.1 0.15 0.2 0.25
δ[m
m]
time [sec]
Specimen A
Specimen B
Specimen C
(c) (d)
Figure 1: Experimental and numerical mid-span displacement
1
64 Numerical investigation
The following table shows the summary of the results for each specimen reporting both themaximum and the residual deflections of the experimental and numerical investigations. Moreoverthe support rotation θ is shown for both the experimental and numerical investigations.
Specime
n
Experimental Numerical Experimental Numerical
δmax
[mm]
δres
[mm]
δmax
[mm]
δres
[mm]
θmax
[deg]
θres
[deg]
θmax
[deg]
θres
[deg]
A 108* 108* 244 240 4.0* 4.0* 8.9 8.8
B 70 35 58 50 2.6 1.3 2.1 1.8
C 123 82 114 106 4.5 3.0 4.2 3.9
* Full scale value
Looking at the maximum support rotations experimentally assessed:• specimen B goes over the Moderate
Damage CDL but does not exceed the Heavy Damage CDL;
• specimen C does not exceed the Heavy Damage CDL
Component damage levels θ [degree] μ [-]
Blowout >10° none
Hazardous Failure ≤10° none
Heavy Damage ≤5° none
Moderate Damage ≤2° none
Superficial Damage none 1
1
<<<<<<<<<<<<<
Component damage levels (CDLS) forU.S. antiterrorism performance-based
blast design approach
65 Numerical investigation
The below figure shows the simulated crack patterns of the three specimens; in view is the brittledamage parameter in the range from 0.95 to 1
Specimen C Specimen BSpecimen A
(a)
Specimen C
Specimen B
Specimen A
(b)
Figure 1: Crack patterns of the specimens: (a) back view, (b) longitudinal view
1
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conclusion
70
Structural Robustness =
Structural Survivability
71
Keywords
•Complexity
•Predictability
•Dependability
• Structural Robustness
•Accident Scenarios
•Back-analysis
• Learning
72
Next Dating
SPRING 2017
KICK-OFF MEETING ON
EXPLOSION GROUP IN ITALYUNIVERSITY OF ROME LA SAPIENZA
SCHOOL OF CIVIL AND INDUSTRIAL ENGINEERING
Scientific Coordination by Franco Bontempi
Technical Coordination by Dario Porfidia73
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bonus track
77
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79
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85
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risk
87
ATTRIBUTES
THREATS
MEANS
RELIABILITY
FAILURE
ERROR
FAULT
FAULT TOLERANT
DESIGN
FAULT DETECTION
FAULT DIAGNOSIS
FAULT MANAGING
DEPENDABILITY
of
STRUCTURAL
SYSTEMS
AVAILABILITY
SAFETY
MAINTAINABILITY
permanent interruption of a system ability
to perform a required function
under specified operating conditions
the system is in an incorrect state:
it may or may not cause failure
it is a defect and represents a
potential cause of error, active or dormant
INTEGRITY
ways to increase
the dependability of a system
An understanding of the things
that can affect the dependability
of a system
A way to assess
the dependability of a system
the trustworthiness
of a system which allows
reliance to be justifiably placed
on the service it delivers
SECURITY
High level / activeperformance
Low level / passiveperformance
88
Prevention
Pro
rect
ion
Risk = Probability · Magnitudo
89
Ris
k=
Pro
bab
ility
·Mag
nit
ud
od
od
iscr
etiz
atio
nin
log-
log
pla
ne
90
Ris
k tr
eat
me
nt
91
Option 1 – Risk avoidance, which usually means not proceeding to continue with the system; this is not always a feasible option, but may be the only course of action if the hazard or their probability of occurrence or both are particularly serious;
Ris
k tr
eat
me
nt
92
Option 2 – Risk reduction, either through (a) reducing the probability of occurrence of some events, or (b) through reduction in the severity of the consequences, such as downsizing the system, or (c) putting in place control measures;
Ris
k tr
eat
me
nt
93
Option 3 – Risk transfer, where insurance or other financial mechanisms can be put in place to share or completely transfer the financial risk to other parties; this is not a feasible option where the primary consequences are not financial;
Ris
k tr
eat
me
nt
94
Ris
k tr
eat
me
nt
Option 4 – Risk acceptance, even when it exceeds the criteria, but perhaps only for a limited time until other measures can be taken.
95
boyd
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101
102
103
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