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DCEE4
Proceedings of the
4th International Workshop on Design in Civil and Environmental Engineering
Shang-Hsien (Patrick) Hsieh Shih-Chung (Jessy) Kang Editors
4th International Workshop on Design in Civil and Environmental Engineering
October 30TH -31ST, Taipei City, Taiwan
Organized by
National Taiwan University
Supported by
Ministry of Science and Technology, R.O.C.
Committees
Workshop Chairs
Shang-Hsien “Patrick” Hsieh
Shih-Chung “Jessy” Kang
Organizing Committee
Shang-Hsien “Patrick” Hsieh
Shih-Chung “Jessy” Kang
Hervé Capart
Shih-Yao Lai
Mei-Mei Song
Advisory Committee
Ren-Jye Dzeng
Bing-Jean Lee
Liang-Jenq Leu
Feng-Tyan Lin
Ching-Wen Wang
Pao-Shan Yu
International Advisory Committee
Franco Bontempi
Chris Brown
Tahar El-Korchi
Renate Fruchter
Timo Hartmann
Lotte Bjerregaard Jensen
Adib Kanafani
Giuseppe Longhi
Ashwin Mahlingram
Dominik Matt
Chansik Park
Ser Tong Quek
Mary Kathryn Thompson
Nicola Tollin
Nobuyoshi Yabuki
National Taiwan University
National Taiwan University
University of Rome “LA SAPIENZA”
Worcester Polytechnic Institute
Worcester Polytechnic Institute
Stanford University
Twente University
Technical University of Denmark
University of California, Berkeley
Master Processi Construttivi Sostenibili IUAV
Indian Institute of Technology Madras
Fraunhofer Italia Research
Chung-Ang University
National University of Singapore
Technical University of Denmark
Bradford Centre for Sustainable Environments
Osaka University
National Taiwan University
National Taiwan University
National Taiwan University
National Taiwan University
Tamkang University
National Chiao Tung University
Feng Chia University
National Taiwan University
National Cheng Kung University
National Chung Hsing University
National Cheng Kung University
Foreword
Design has always been an essential subject in Civil and Environmental Engineering (CEE) education and practice but needs more attention as it deserves. Buildings and civil facilities are meant for a long period of time of use and are greatly related to the safety and welfare of human society. In recent years, the increasing frequency and impact of natural disasters resulted from global climate change have demanded the CEE design to address more on the disaster prevention/reduction and sustainability of built environments. Obviously, CEE designers and engineers have to think beyond now and into the future more than ever before. I am very glad to have the opportunity to organize DCEE 2015 in NTU, Taipei, Taiwan, following previous successful DCEE workshops hosted by KAIST, South Korea in 2011, WPI, USA in 2013, and DTU, Denmark in 2014. We planned a pre-conference workshop: “Sustainable City – A Hundred Years from Now”, facilitated by Prof. Pirjo Haikola (Finland) and Prof. Mei-Mei Song (Taiwan), in hope to bring on some discussions one step further into the future and it turned out to be an inspiring event that enriches all participants’ thinking about our future cities. This year’s workshop features 3 keynote speeches and 13 technical presentations by researchers from Japan, U.S.A., Denmark, Italy and Taiwan. The presentations spanned a wide range of studies related to Design in CEE, from environmental design, structural design, to engineering design education. A mini-workshop was also organized for discussing the futures of DCEE. The discussions were facilitated using Futures Thinking tools and fruitful outcomes from the discussions were reported at the end of this proceedings. I would like to thank all of the presenters, particularly the three excellent keynote speakers, Prof. Hideyuki Horii from Japan (Designing Innovation Workshop: i.School UTokyo), Prof. Eduardo Miranda from USA (Performance Based Design), Mr. Ying-Chih Chang from Taiwan (Structural design for best integration with Architecture), and the two professors, Profs. Haikola and Song, for facilitating the pre-workshop and mini-workshop. My sincere thanks also go to my co-chair, the organizing committee, international advisory committee, sponsors and all the participants and staff of the workshop. Finally, we are very much looking forward to the next DCEE Workshop to be held in Sapienza University of Rome, Italy in October 6-8, 2016 and hopping that you will join us for the continuation of important and interesting discussions on all aspects of design in CEE.
Shang-Hsien (Patrick) Hsieh Chairman, DCEE 2015 Organizing Committee Professor, Department of Civil Engineering, National Taiwan University June 20, 2016
Design for Robustness, Resilience and Anti-Fragility in the Built
and Urban Environment: Considerations from a Civil
Engineering Point of View
Konstantinos Gkoumas*1, Francesco Petrini1,2, and Franco Bontempi2
[email protected], [email protected], [email protected] 1StroNGER srl, Italy
2Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Italy
Abstract: In the recent years, natural disasters are recognized to be the cause of considerable human and
socioeconomic losses, particularly in modern, infrastructure-dependent societies. For example, the 2011
earthquake and tsunami in Japan have been one of the most devastating disasters of the past decades. Likewise,
the Katrina hurricane in the US east coast in 2005. In this context, the concepts of “structural robustness” and
“resilience of urban areas” and “resilient community”, have gathered the attention of researchers. On top of that,
more recently, anti-fragile design came as an evolution of design for resilience (intended as the capacity to recover),
or for robustness (a main dimension of resilience, intended as the ability of a structure to withstand events without
being damaged to an extent disproportionate to the original cause). This study focuses on a modern approach in
disaster resilience - including anti-fragile design and structural robustness - providing insight for a preliminary
framework on important modelling aspects.
Keywords: resilience, robustness, antifragility, structural engineering, structural design, urban design.
Introduction
In his reference book Anti-fragile: Things That Gain
attribute of antifragility for systems (economic, social,
natural etc.), as a step forward from robustness and
resilience (Taleb 2012). While fragile systems suffer
or break from randomness and volatility, and resilient
systems have the characteristic to stay the same, anti-
fragile systems gain and grow stronger from
variability and stress (up to a certain point). Taleb
argues that instead of seeking to eliminate variability
(something that can be perceived as a “loser’s game”,
since variability and randomness are the rule and not
the exception in everyday life), it is better to live and
deal with it, and try to gain using different tactics.
In a different context, Italo Calvino, in his
touchstone fabulist novel The invisible cities (Calvino
1972), in a dystopian context (cities mostly represent
dystopian urban environments), finds reminiscence
and a sense of hope in fictional conversations between
a young Marco Polo and ageing emperor Kublai Chan.
Cities in his book represent complex historical
examples and imaginary possibilities, characterized by
their infinite complexity, their intensive urban
landscape, and their strong interactions between them
and their inhabitants. While some of them are utopian
models of success, the majority of them are left to their
destiny, being responsive to their purpose and to the
acts of their inhabitants. What emerges is the idea that
some cities are “invisible”, ever changing, with details
ready to be discovered (or left behind): in this sense,
people continue to live in the cities, albeit the
deficiencies or crisis situations. Calvino’s envisions
match Castoriadis’ thoughts on society (an inheritance
from Aristotle, Plato and Marx), well extending from
the physical objects of the city (Castoriadis, 1975).
The above two examples, provide a starting point
for discussions on the future of urban resilience
assessment for urban developments, considering the
complexity, the continuously changing aspects and the
multiplicity of situations that can occur. In fact, cities
and urban settlements tend to become more populated
and complex, with the introduction of structures and
infrastructures hardly imagined years ago (e.g. mega
skyscrapers, extreme long span bridges).
Resilience builds on concepts nowadays
corroborated in structural engineering design, such as
structural robustness, while resilient design is a
requirement for anti-fragile design, a new concept still
in its genesis. In the following sections, a series of
concepts, considerations and case studies are critically
introduced, as used in civil (structural in particular)
engineering.
Concepts
The paper builds on three interrelated concepts:
structural robustness
resilience
antifragility
These concepts, as will be discussed below, are
strongly connected.
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
Figure 1. Antrifragility, resilience and robustness
As figure 1 suggests, robustness can be
perceived as a complement of resilience, and resilience
as a complement of antifragility. In the same figure, a
timeline of significant events that led to the
development of the concepts is also shown. While
robustness refers to a single structure (or a series of
structures, especially when considering the case of
progressive or disproportionate collapse), antifragility
and resilience refer to a complex of structures in the
most wide sense, including issues well beyond
structural design. On top of that, antifragility, is a
novel concept, introduced only recently, that provides
a new insight in risk assessment methods in different
engineering and life science fields.
As stated before, these concepts are thoroughly
discussed in the book Anti-fragile: Things That Gain
from Disorder (Taleb 2012). Taleb states that “Anti-
fragility is beyond resilience or robustness. The
resilient resists shocks and stays the same; the anti-
fragile gets better”.
In the following three sections, robustness,
resilience and antifragility are discussed in the context
of Civil and Environmental Engineering (CEE).
Relevant references, examples and design ideas are
provided where possible.
Robustness
Robustness is a collective term that finds application
in different complex systems (e.g. biology, computer
science, economics and optimization) and implies the
capacity of α system to tolerate perturbations that
might affect the system’s functional body.
Structural robustness is a research topic
particularly relevant in the design and the safety
assessment of both new and existing structures. The
latter are prone not only to local failure due to
accidental or man-made attacks, but also due to long-
term material degradation (e.g. corrosion), bad design
or construction. Behind this attention, there is the
increasing interest from society that cannot tolerate
death and losses as in the past. This is more evident
after:
recent terrorist attacks (a series of terror attacks in
America and beyond, the deadliest being the
September 11, 2001 events);
recent bridge collapses due to deterioration or bad
design or bad construction (for example, the De la
Concorde overpass collapse in Montreal, 2006).
From a historical perspective, structural
robustness (and progressive collapse for that matter)
resilience
robustness
antifragility
timespacial complexity
spatialcomplexity
Ronan Point (1968)Building (5th Amendment) Regulations 1970
1960 1970 1980 1990 2000 2010
Seismic (Bruneau et al. 2003)Urban (MCEER, 2006)Ecological (Holling, 1973)
(TALEB, 2012)
Eurocodes (‘80s)
robustness (global)+resilience (local)
+resilience (social)
+antifragility (social)
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
came up first as a structural engineering concern just
after the collapse of the Ronan Point Tower, a
residential apartment building in Canning Town,
London, UK, in May 1968, two months following
initial occupancy of the building. Ronan Point was a
22-story building, with precast concrete panel bearing
wall construction. An explosion of natural gas from the
kitchen of a flat on the 18th floor failed an exterior
bearing wall panel, which led to loss of support of
floors above and subsequent collapse of floors below
due to impact of debris (Ellingwood 2002).
Subsequently to the Ronan Point apartment collapse,
building codes in many-countries have adopted
structural integrity or "robustness" provisions that may
be directly traced to the collapse (Pearson and Delatte
2005), starting from the “Fifth Amendment” to the UK
Building Regulations, introduced in 1970.
Even though a variety of terms has been used in
literature, robustness in structural engineering is
commonly defined as the “insensitivity of a structure
to initial damage” (Starossek and Haberland 2010).
The concept of robustness is strongly linked to the one
of collapse resistance, intended as the “insensitivity of
a structure to abnormal events” and progressive
collapse, defined as the spread of an initial local failure
from element to element, eventually resulting in
collapse of an entire structure or a disproportionately
large part of it ASCE 7-05 (2005). Starossek and
Haberland (2010) focus on the differences of
progressive and disproportionate collapse, concluding
that the terms of disproportionate collapse and
progressive collapse are often used interchangeably
because disproportionate collapse often occurs in a
progressive manner and progressive collapse can be
disproportionate.
Structural robustness assessment methods
A relevant issue related to the structural robustness
evaluation, is the choice of appropriate synthetic
parameters describing for example the sensitivity of a
damaged structure in suffering a disproportionate
collapse.
Eurocode 1 (EN 1991-1-7 2006) merely outlines
the issue of structural robustness in a qualitative
manner, stating that a structure should not be damaged
by events to an extent disproportionate to the original
cause.
Several authors provide a review of methods for
assessing structural robustness (Canisius et al. 2007,
Starossek and Haberland 2010, COST 2011, Sørensen
et al. 2012, Parisi and Augenti 2012, Cavaco et al.
2013).
Ellingwood and Dusenberry (2005), link the
progressive collapse probability P(F) to a chain of
probabilities, consisting in (i) the hazard of an
abnormal event P(H), (ii) the local damage as a
consequence of this hazard P(D│H), and (iii) the
failure of the structure as a result of the local damage
D due to H P(F│DH).
P(F)= P(F│DH)∙P(D│H)∙P(H) (1)
Baker et al. (2008) propose a probabilistic
framework for the robustness assessment, computing
both direct risk, associated with the direct
consequences of potential damages to the system, and
indirect risk, corresponding to the increased risk of a
damaged system. The latter corresponds to the
robustness of the system, since it can be assumed as a
risk from consequences disproportionate to the cause
of the damage. In their approach, a robust system is
considered to be one where indirect risks do not
contribute significantly to the total system risk.
IndDir
DirRob
RR
RI
(2)
The index takes values from 0 (if all risk is due
to indirect consequences) to 1 (if there is no risk due
to indirect consequences, thus, the system is
completely robust).
Biondini et al. (2008) propose a robustness index
(ρ) associated with the displacements of the system:
d
o
s
s (3)
Where s0 is the displacement vector, ║∙║ denotes
the Euclidian norm, and the subscript “0” and “d” refer
respectively to the intact and damage state of the
structure.
Izzuddin et al. (2008) propose a multi-level
framework for the progressive collapse assessment of
building structures subject to sudden column loss. The
proposed assessment framework utilizes three main
stages: (i) nonlinear static response of the damaged
structure under gravity loading; (ii) simplified
dynamic assessment to establish the maximum
dynamic response under sudden column loss; and, (iii)
ductility assessment of the connections. Within this
framework, they propose that the single measure of
structural robustness is the system pseudo-static
capacity, that is the maximum value of the nonlinear
static resistance for which the resulting maximum
dynamic displacement, is less than or equal to the
ductility limit. The comparison of the latter against the
applied gravity loading establishes the required limit
state.
Cavaco et al. (2013) consider robustness as the
measure of degree of structural performance lost after
damage occurrence, and propose the following metric
(Rd: Robustness Index).
1
0)(
d
dd dxxfR (4)
Where Rd indicates the area above the curve
defined by the normalized structural performance f
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
(given by the ratio between the structural performance
on the intact and damage states), subjected to a
normalized damage d (given by the ratio between
actual and maximum possible damage).
Nafday (2011) discusses the usefulness of
consequence event design, for extremely rare,
unforeseen, and difficult to characterize statistically
events (black swans). In this view, the author, with
reference to truss structures, proposes an additional
design phase that focuses on the robustness, the
damage tolerance and the redundancy of the structure.
This proposed metric consequence factorCif for the i-
th member is based on the evaluation of the
determinants of the normalized stiffness matrixes for
the undamaged and damaged structure and is defined
as:
N
i
Ni
fK
KC (5)
Where |KN| is volume of the geometrical shape
which is spanned by the vectors of matrix KN for
‘intact condition’ and |KNi | is similar volume under
‘damaged condition’ i.e., after the removal of the i-th
member.
What emerges from the above is the difference in
the approaches and indexes in literature towards the
structural robustness quantification. An overview is
provided in table 1.
Table 1. Overview of robustness approaches
Robustness
Approach Index
property of the
structure or
property of the
structure and the
environment
static or dynamic
linear or non-
linear
deterministic or
probabilistic
Structural robustness and member based design
One of the authors of this paper proposed a simple
method for the robustness assessment (for additional
details see Olmati et al. 2013) on the basis of
considerations made in Nafday (2011). Focusing on
skeletal structures (e.g. trusses), current member-
based design in structural codes does not explicitly
consider system safety performance during the
structural design, while the level of safety in new
designs is usually provided on the basis of intuition
and past experience (Nafday 2008). On the other hand,
the Ultimate Limit State (ULS) of the Performance-
Based Design (PBD) requires that individual structural
members are designed to have a resistance (R) greater
than the load action (E), where both R and E are
probabilistically characterized (Stewart and Melchers,
1997).
The member-based design is summarized in the
following design expression, valid for a single
structural member:
0ER undamaged
d
undamaged
d (6)
where Rdundamaged and Ed
undamaged are the design values
respectively of the resistance and of the solicitation in
the undamaged configuration of the structure.
Concerning the commonly implemented standards this
equation is not respected with a probability of 10-(6÷7).
The method applied here aims to introduce an
additional multiplicative coefficient in the first term of
the Eq. (6): this is identified as the member
consequence factor (Cf), takes values within a range
from 0 to 1, and quantifies the influence that a loss of
a structural element has on the load carrying capacity.
Essentially, if Cf tends to 1, the member is likely to be
important to the structural system; instead if Cf tends
to 0, the member is likely to be unimportant to the
structural system. Cf provides to the single structural
member an additional load carrying capacity, in
function of the nominal design (not extreme) loads.
This additional capacity can be used for contrasting
unexpected and extreme loads.
0ER*)C1( undamaged
d
undamaged
d
scenario
f
(7)
Nafday (2011) provides Eq. (7) in a similar
manner, with the only difference being on the range
mean of Cf that is the inverse of the proposed one, so
the first term of Eq. (2) is multiplied directly by Cf.
Thus, in this case, the equation proposed in Nafday
(2011) has been slightly revised in order to fit with the
here proposed expression of the Cf - see both Eq. (7)
and Eq. (8). The structure is subjected to a set of
damage scenarios and the consequence of the damages
is evaluated by the consequence factor (Cfscenario) that
for convenience can be easily expressed in percentage.
For damage scenario is intended the failure of one or
more structural elements.
Considering the above, robustness can be
expressed as the complement to 100 of Cfscenario,
intended as the effective coefficient that affects
directly the resistance - see Eq. (8). Cfscenario is
evaluated by the maximum percentage difference of
the structural stiffness matrix eigenvalues of the
damaged and undamaged configurations of the
structure.
N1i
un
i
dam
i
un
iscenario
f 100)(
maxC
(8)
where, λiun and λi
dam are respectively the i-th
eigenvalue of the structural stiffness matrix in the
undamaged and damaged configuration, and N is the
total number of the eigenvalues.
The corresponding robustness index (Rscenario)
related to the damage scenario is therefore defined as: scenario
f
scenario C100R
(9)
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
Values of Cf close to 100% mean that the failure
of the structural member most likely causes a global
structural collapse. Low values of Cf do not necessarily
mean that the structure survives after the failure of the
structural member: this is something that must be
established by a non-linear dynamic analysis that
considers the loss of the specific structural member. A
value of Cf close to 0% means that the structure has a
good structural robustness.
Some further considerations are necessary. The
proposed method for computing the consequence
factors should not be used for structures that have high
concentrated masses (especially non-structural
masses) in a particular zone, and for structures that
have cable structural system (e.g. tensile structures,
suspension bridges).
The first issue is related to the dynamic nature of
a structural collapse, since Eq. (8) does not take into
account the mass matrix of the system that is directly
related to the inertial forces. It is possible to accept this
limitation only if the masses are those of the structural
members, thus distributed uniformly. Moreover, there
is no way to consider any dynamic magnification
phenomena with Eq. (8).
The second issue is related to the geometrical
non-linearity of cable structures. For such structures
the stiffness matrix is a function of the loads,
something not accounted for in the elastic stiffness
matrix. Moreover, for the nature of the elastic stiffness
matrix, eventual structural dissipative behaviors and
non-linear resistive mechanisms (e.g. catenary action)
are not taken into account.
In the authors’ opinion, the above limitations can
be accepted if the desired outcome is a non-
computational expensive method, since the Cf value
provides an indication of the structural robustness in a
quick and smart manner.
Therefore, the Cf as expressed in Eq. (8) can be
used primarily as an index to establish the critical
structural members for the global structural stability,
or to compare different structural design solutions
from a robustness point of view.
Resilience
The concept of resilience is present since the 70’s in
fields of study such as psychology and ecology. The
Merriam Webster dictionary defines resilience as “the
ability to become strong, healthy, or successful again
after something bad happens” (for individuals) or “the
ability of something to return to its original shape after
it has been pulled, stretched, pressed, bent, etc.” (for
objects or things).
The American Psychological Association (2014)
defines resilience as “the process of adapting well in
the face of adversity, trauma, tragedy, threats or
significant sources of stress - such as family and
relationship problems, serious health problems or
workplace and financial stressors. It means "bouncing
back" from difficult experiences.” Even though
psychological resilience is related to optimistic
attitude and positive emotionality, it relies, among else,
on adapting and on perspective, and some of the
methods for building resilience can be applied also in
other fields.
In ecological systems, resilience is defined as the
capacity of an ecosystem to respond to a perturbation
or disturbance by resisting damage and recovering
quickly (see for example, Holling 1973; Gunderson
2000; Gunderson and Holling 2002).
Even though resilience is domain-dependent
(that is, it relates to the specific context), there are
similarities in different fields and contexts.
Resilience has found application in the last years
in other fields (e.g. electronic and computer systems).
Maruyama et al. (2014), provide a taxonomy for
general resilience, focusing on four orthogonal
dimensions:
i. type of shock or perturbation
ii. target system
iii. phase of concern
iv. type of recovery
The same authors highlight strategies for
achieving resilience (through redundancy, diversity or
adaptability).
Davoudi et al. (2013) develop a conceptual
framework by drawing on three broad perspectives on
resilience, engineering, ecological and evolutionary.
Among their conclusions, they highlight the potential
transformative opportunities that emerge from change.
In the civil and architectural engineering field,
resilience is present through the notions of “resilience
of urban areas” and “resilient community”, as
introduced by the Multidisciplinary Centre for
Earthquake Engineering Research - MCEER (MCEER
2006). The approach has the potential to provide a
considerable contribution in lowering the impact of
disasters, and is implemented through the Resilience-
Based Design (RBD) for large urban infrastructures
(buildings, transportation facilities, utility elements
etc.), conceived as a design approach aiming at
reducing as much as possible the consequences of
natural disasters and other critical unexpected events
on the society. Something pursued by developing
actions that allow a prompt recovery of the
infrastructures (Bruneau et al. 2003; Renschler et al.
2010, Cimellaro et al. 2010, Cimellaro and Kim 2011).
Since then, several work focused on extending
the above. Franchin and Cavalieri (2015), focusing on
earthquakes, extend a previously developed civil
infrastructure simulation framework to the evaluation
of resilience, and introduce a new infrastructure
network-based resilience metric. Their model builds
on findings from Asprone et al. 2013, who introduce a
metric with reference to the ability of a whole system
to recover the full functional level, in terms of housing
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
reestablishment, existing prior to the event even if in a
new, different state.
There are different ways to measure resilience.
The most common way, is to focus on the area defined
by the system quality evolution over time (see for
example Bruneau et al. 2003). Looking at figure 2 (see
also Petrini et al. 2015), the events affecting the system
quality during its life, are identified in five phases of
the system life, specifically related to a discrete
occurrence of events:
i. historical. This is the starting point with a system
quality equal to Q0, indicating the initial quality at
a reference time (e.g. time zero). It depicts the
reference equality of the system at a time
reasonable “away” from the next phase.
ii. pre-event. In this phase, all the different
possibilities for improvement, or, the degradation
of the historical system state are represented. In
general, the system quality decreases with time due
to degradation. However, the system quality could
increase with a rate DQ/dt if there are renovation
projects, or even increase vertically (if new
infrastructures are inserted in the system).
iii. during the event. This phase starts with a (usually)
vertical (sudden) loss of quality. After that,
resilience measures take place and the quality
increases. It is important that this happens initially
with a rather high rate (depicting the system
response).
iv. aftermath of the event (recovery phase). In this
phase all possible measures take place aiming at
the recovery to the previous situation or even an
improvement. This depends on the goals set at a
community lever after the event, and on the basis
of political decisions.
v. long-run. In this phase the ordinary evolution of the
system takes place, with degradation effects,
eventual improvements, etc.
Figure 2. System quality or functionality over time with multiple events and responses
Considering the above, a series of issues arise
regarding resilience based design. The most important
is maybe the choice of hazard scenarios that can
influence resilience. The problem arises from the way
to consider multi hazard scenarios.
The multi-hazard scenario can manifest in the
following three different modalities (Petrini and
Palmeri 2012):
i. independent hazards, when different hazards affect
the structure independently. For example, in the case
of wind and earthquake hazard, they can be considered
as independent of each other because no mutual
interaction between the two hazards has the effect of
modifying the intensity of the corresponding actions.
These hazards can occur individually or
simultaneously.
ii. interacting hazards, when the actions produced on
a structure by different hazards are interdependent
(e.g., wind and wave hazards, or wind and windborne
debris hazards)
iii. hazard chains, when the effects of some hazards
modify sequentially the effects of other hazards. For
example, the actions on a structure due to windborne
debris can damage the structural envelope and
increases the vulnerability of the structure to strong
winds. The same applies for fire hazard after
earthquake.
In fact, it is a common understanding in
structural design, that different hazards (thus, different
loading schemes on the structure), have different
design requirements. For example, in the case of high-
rise building or long span bridges, and considering
wind and earthquake loading, the first is the one that
governs the structural design. Furthermore, optimizing
for one hazard, can have a counter effect on another.
All these, not considering complications arising from
standard serviceability limits.
Considering the above complexities, it is safe to
say that he concept of resilience implies
multidisciplinary aspects (Bosher 2008), and requires
dQ/dt fR(t)
dQR/dt
ΔQ
Q0
Pre-event During the event Aftermath of the event
SYSTEM QUALITY Q
TIME
Long-runHistorical
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
collaboration between different experts (e.g. urban
designers, ecologists, engineers, architects, social
scientists). Its definition is not univocal: a
straightforward one is the one given by Lindell (2010),
where a resilient community is defined as the one
having the ability to absorb disaster impacts and
rapidly return to normal activities. Furthermore, it has
been recognized that some infrastructures are critical
for resilience in the sense that they mostly contribute
to the response to disasters. In a Resilience-Based
Design, focus should be given to such infrastructures,
but no criteria have been established yet for
determining the role of different types of
infrastructures in the achievement of a resilient
response of an urban area to critical events.
Nowadays, urban resilience focuses on three
distinct threats (Coaffee, 2008):
climate change;
natural disasters; and,
terrorism.
Regarding threats from natural hazards in
particular, Resilience-Based Design focuses on
possible outcomes from threats such as heat waves,
droughts and flooding, earthquakes, tsunamis, solar
flares, etc. The complexity arises from the possible
occurrence of multiple hazards (eventually as a
consequence of each other).
Antifragility
Very briefly (Taleb and Douandy 2013), fragility is
related to how a system suffers from the variability of
its environment beyond a certain preset threshold
while antifragility refers to when it benefits from this
variability. In other words, systems range from fragile
(degrading with stress), to robust (unchanged by
stress), to antifragile (improving with stress).
Antifragility builds on a previous work of Taleb
on Black Swans, very rare events that lie in the tails of
distributions, and often beyond a specific sample
range.
Taleb (2007) states:
What we call here a Black Swan (and capitalize
it) is an event with the following three attributes.
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. Second, it
carries an extreme 'impact'. Third, in spite of its outlier
status, human nature makes us concoct explanations
for its occurrence after the fact, making it explainable
and predictable.
I stop and summarize the triplet: rarity, extreme
'impact', and retrospective (though not prospective)
predictability. A small number of Black Swans explains
almost everything in our world, from the success of
ideas and religions, to the dynamics of historical
events, to elements of our own personal lives.
It is a common perception that Black Swans (and
X-Events for this matter – see Casti, 2012) have
changed the designers perception after the shocking
events of September 11.
To reconnect with what stated before, simply put,
fragility and antifragility mean potential gain or harm
from exposure to something related to volatility. This
“something”, as Taleb states (see, Keating 2013),
belongs to the extended disorder family (or Cluster):
(i) uncertainty, (ii) variability,(iii) imperfect
incomplete knowledge, (iv) chance, (v) chaos, (vi)
volatility, (vii) disorder, (viii) entropy, (ix) time, (x) the
unknown, (xi) randomness, (xiii) stressor, (xiv) error,
(xv) dispersion of outcomes, (xvi) “unknowledge”
(this one as an antonym for knowledge).
A challenge remains on how to quantify
antifragility. Even though, fragility is rather easily
measured (or better, compared) using metrics, and the
use of fragility functions is common nowadays, this is
not the case for antifragility.
Aven (2015), on the basis of Taleb’s work,
suggests using the notion of “asymmetry”, that is, the
idea that if a random effect has more upside effects that
downside effects, is antifragile. Otherwise, it is fragile.
The idea is to measure the harm induced by shock: if
it gets higher as the intensity of the shock increases,
the system can be considered as fragile. Otherwise
(that is, if the harm is relatively low - what could be
called a beneficiate to the system) the system is
antifragile. This concept has dissimilarities with the
conceptual idea that “robustness” lies between
fragility and antifragility (in this case, somehow
antifragility coincides with a “dynamic” robustness),
however, it is a simple way to qualitatively describes
something otherwise difficulty quantifiable.
Johnson and Georghe (2013) focus on the
antifragility assessment of complex adaptive systems,
and provide a case study on smart grid electrical
systems, using a series of analytical criteria that
characterize the system as fragile, robust or antifragile.
In their case, the antifragility criteria met coincide with
issues arising from positive outcomes of inducing
stressors and learning from mistakes. This is not
something uncommon. Since the start of the
millennium, there have been attempts to induce
(controlled) stressors in systems in order asses their
resilience. This is the case of Amazon GameDay
project, with similar efforts from google and others
(see Robbins et al. 2012). In this sense, a system can
become antifragile, since, it grows stronger from each
successive stressor, disturbance, and failure, in a
“lessons learned” manner. The more frequently failure
occurs, the more prepared the system and organization
become to deal with it in a transparent and predictable
manner (Tseitlin 2013).
What should be clear is that antifragile design
(and this is also the case for resilient based design)
spans a wide area of topics, wider than commonly
implemented methods for risk assessment and
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
instruments, with decisions taken on the basis of
scenarios and good judgement.
The profound understanding of a number of
concepts, some common, some other borrowed from
other fields (e.g. financial science, psychology) is
necessary in order to pursue antifragility in the design,
especially within a risk analysis framework.
Even though it is impossible to comment on all
(figure 3), some of these concepts are explained below
Figure 3. Tag cloud of pertinent terms in risk analysis, resilience-based and antifragile design
multi-hazard (design). Natural hazard types have
very different characteristics, in terms of the spatial
and temporal scales they influence, hazard
frequency and return period, and measures of
intensity and impact (think for example earthquake
and strong wind). The (rarity) of the contemporary
presence of such hazards is accounted in structural
limit state design (and this is the case for
uncorrelated hazards). However, some hazards are
a consequence of others (e.g. an earthquake may
trigger landslides or fire, whereas a wildfire may
increase the probability of future landslides – see
Gill and Malamud 2014). A "multi-hazard" design
approach that pursues to identify all possible
natural hazards and their interactions or
interrelationships is nowadays essential (Petrini
and Palmeri 2012).
black swan. The term was first introduced by Taleb
(2001). Other similar terms have been introduced
in the recent years (“known unknowns”, X-Events,
etc.) to describe rare events, with extreme impact,
and retrospective.
halo effect. A cognitive process in which the global
evaluation of something or someone can influence
one’s response to other attributes or the impression
of one attribute shapes the impression of another
independent attribute. In risk analysis it can lead to
wrong judgement.
gambler’s fallacy. The (mistaken) belief that, if
something happens more frequently than normal
during some period, it will happen less frequently
in the future, or that, if something happens less
frequently than normal during some period, it will
happen more frequently in the future. It arises from
the erroneous belief that small samples must be
representative of the larger population. As in the
previous case, it can lead to misjudgment.
synchronicity. A term coined by Jung (1960) to
express a concept about acausal connection of two
or more psycho-physic phenomena, that is, the
"timing together" of otherwise "unrelated" events.
In risk analysis, can be used to develop a broad
view of phenomena otherwise standardized in
clusters.
apophenia. Although the term has its basis in
psychiatry (used to describe early stages of
schizophrenia), it is nowadays intended as the
experience of seeing meaningful patterns or
connections in random or meaningless data. In risk
analysis it is linked with statistical errors, while a
positive effect, can be the added resourcefulness in
scenario planning.
dependability. It is concisely defined as the grade
of confidence on the safety and on the performance
of a system (see Sgambi et al. 2012 for a
dependability framework in the civil engineering
field). This is a qualitative definition that
comprehensively accounts for several properties,
which, even though interconnected, can be
examined separately. Robustness is a dependability
attribute.
bias (see also selection bias). In risk analysis, it is
important to select unbiased data, group, people,
etc. Experts are often biased towards expected
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
results and (non deliberately) drive their results.
See also cherry picking, suppressing evidence, or
the fallacy of incomplete evidence
self-deception (also subjective validation). The art
of convincing and validating oneself. Can prove to
be negative in risk brainstorming activities.
swarm effect. It is the collective behavior that
emerges from a group of social insects (or humans,
for what matters). Through this effect, people may
group together, share the same influences and drive
towards the same goal or beliefs. The swarm effect
has a strong effect on political decisions that
influence infrastructure planning and maintenance,
thus, influence resilience.
retrospectiveness. It is an attribute of black swans,
and helps explain facts after their occurrence. To
make a simple case, everyone after 7/11 considers
the possibility of an airplane impact on strategic
structures (something less rare in the 60’s and 70’s
- considering also nuclear plants construction) but
faded afterwards.
mindfulness (collective). Another concept from
human behavior, essentially to “live as if you were
living for the second time and have acted wrongly
the first time as you are about to act now” (see also
mindful management – Weick and Sutcliffe 2007).
Robustness, resilience and antifragility connection
It is important to link the above three concepts in the
field of study of interest (in this case, principally civil
and structural engineering), and highlight their limits
and dependencies.
structural robustness relates to a single structure or
complex of structures. In this sense, it stays well
above the concept of structural resistance (referred
to a part of the structure or a structural element),
but it is limited to a (even though large) structural
system. In this sense, we can talk about the
structural robustness of a high-rise building, a
bridge, a hospital etc.
resilience is a much more complex term, that
relates to broader systems (also socio-economic)
well beyond structural measures. In civil
engineering and architecture, we talk about the
resilience of urban developments, even cities, or,
depending on the threat consequences, even at a
state level.
antifragility is very recent term that can find
application in the risk assessment of complex
systems. Even though initial applications are at the
material level, the challenge is to adopt the concept
for complex urban developments. In fact, it would
be interesting to see cities, urban developments and
structures not only recover, but also grow stronger
after adverse events (floods, earthquakes, terrorist
attacks).
Concluding, antifragile design has the potential
to become a major issue in the imminent future, as has
been the case for resilience-based design. Since the
recent introduction of the term by Taleb, there are few
or none references in literature (especially concerning
urban design or civil and architectural engineering in
general). The point is that, although advances in
technology are rapid, these are initially reserved either
in special fields (e.g. space engineering, where budget
is not always the primary concern) and soft computing
(e.g. A.I. – Artificial Intelligence), where changes in
system tactics can be fast and cost efficient.
Although difficult to provide details, some
preliminary considerations for future antifragile
design can be made.
For example, self-healing materials, developed
originally for space mission applications, provide a
typical example. Such materials could heal damage
upon detection, thus, providing extra safety and
performance. But what if materials could do more than
heal damage? What if they could adapt for strength:
borrow from areas of less stress to fortify areas under
more stress? What if materials could grow in strength
in response to stress, similar to how muscles build
strength? (Jones 2014).
Another aid will come from novel technologies
implemented nowadays for security or Structural
Health Monitoring.
Case studies
The authors provide two brief case studies on
structural robustness and resilience assessment. The
cases, are not exhaustive, but serve as example to
elucidate some point. The readers are referred to the
specific references for additional details.
Case study 1: robustness assessment of a steel
truss bridge
This section provides a case study of robustness
assessment of a steel truss bridge (for more details see
Olmati et al. 2013). The bridge is the I-35 West Bridge
in Minneapolis. The I-35 West Bridge was built in the
early 1960s and opened to traffic in 1967. The bridge
spanned across the Mississippi River, Minneapolis and
it was supported on thirteen reinforced concrete piers
and consisted of fourteen spans. Eleven of the fourteen
spans were approach spans to the main deck truss
portion. The total length of the bridge including the
approach and deck truss was approximately 580 meter
(1,907 feet). The length of the continuous deck truss
portion which spanned over four piers was
approximately 324 meter (1,064 feet). The elevation of
the deck truss portion of the bridge is shown in figure
4.
The deck truss portion of the bridge was
supported on a pinned bearing at Pier 7 and roller
bearings at the other three supports. The main bridge
trusses were comprised of built-up welded box and I-
sections sandwiched by gusset plates at each panel
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
point. The collapse which occurred on August 1st 2007
was probably due to a combination of the temperature
effect, roller bearings condition, and increased gravity
loads on the bridge prior to collapse. For this
functionally non-redundant bridge the initial buckle at
the lower chord member close to the pier and local
plastic hinges in the member resulted in global
instability and collapse (Malsch et al. 2011).
The bridge has been thoroughly studied by
Brando et al. (2010) focusing on the issues of
redundancy, progressive collapse and robustness.
Studies have been conducted in order to assess the
effect of the collapse of specific structural components
(Crosti and Duthinh 2012), while Crosti et al. (2012)
performed non-linear dynamic analysis on specific
damage scenarios.
For computing the consequence factors and the
robustness index of the structure for the selected
damage scenarios a FE model of the structure is
necessary.
Figure 5 shows the three-dimensional FE model
of the I-35 West Bridge built using the commercial FE
solver Sap2000® (Brando et al. 2010).
Both shell and beam finite elements are used in
the FE model. The bridge superstructure and both the
deck girders and beams are built using beam elements,
while, the concrete deck is modeled using shell
elements. Moreover, contact links connect the deck
with both the deck girders and beams.
In accordance with the original blueprints of the
I-35 West Bridge (MnDOT 2012), standard and non-
conventional beam cross sections are implemented in
the model.
Figure 4. Bridge overview (edited from MnDOT
2012).
Figure 5. 3D FE model of the I-35 West Bridge
From this model, a simplified (plane) FE model
is extracted and is adopted for computing the structural
stiffness matrix in both the damaged and undamaged
configurations. This choice has mostly to do with
computational challenges in computing the stiffness
matrix for the full model.
The method applied in this study aims at
increasing the collapse resistance of a structure, by
focusing on the resistance of the single structural
members, and accounting for their importance to the
global structural behavior consequently to a generic
extreme event that can cause a local damage.
The expression of the consequence factor
provided by Eq. 8 refers to the eigenvalues of the
elastic stiffness matrix. The choice to use a simplified
model is also justified and feasible since Eq. 8 is
independent from the mass of the structure. Eq. 8 is
also independent from the loads, so the loads in the FE
model are not considered. Only a single lateral truss of
the bridge is considered, and a set of damage scenario
is selected (figure 6).
Figure 6. Lateral truss of the bridge and selection of
damage scenarios.
The damage scenarios for this application are not
cumulative, so only a single member is removed from
the model for each damage scenario. In this
application the scenarios chosen focus on the area
recognized as initiating the collapse according to
forensic investigations (Brando et al. 2013).
With the aim of increasing the structural
robustness of the bridge, and in order to test the
sensitivity of the method proposed, an improved
variation of the structural system is considered. In this
case, (figure 7) the updated bridge truss is a hyper-
static steel truss structure. Figure 8 shows the results
of both the original and the enhanced structural
schemes, under the same damage scenarios.
Figure 7. Updated lateral truss of the bridge and
selection of damage scenarios.
The proposed robustness index (based on the
member consequence factor Cf) captures both the lack
of robustness of the I-35 W Bridge, and its robustness
enhancement as a consequence of increasing the
redundancy of the structure.
3 Span Continuous Trusses – 1,064 ft
Pier 7 Pier 6
North
Pier 8 Pier 5
6
7
21
3
4
5
6
7
2
1
3
4
5
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
Figure 8. Damage scenario evaluation.
Generally speaking, it can be observed that the
case-study bridge shows a low robustness index. This
is because it is (internally) statically determined. From
the analysis of the bridge in its original configuration
and for the chosen damages configurations, a
consequence factor of 0.77 has been computed for the
DS7 and, consequently, a robustness index of 0.23 is
obtained.
The redundant bridge configuration (figure 7)
certainly shows an insensitivity to the internal damage
scenarios (number 1, 2 and 3). This option can be
considered as a global improvement of the structural
system. The previous strategies can be adopted
simultaneously: i) the designer sizing of the elements
can be affected by the robustness index by using Eq.
(2); and ii) the structural scheme can be changed (also
on the basis of the Cf values) in order to increase the
robustness. In this case, both local and global solutions
provide improvements to the structural system.
Case study 2: resilience assessment of an aqueduct
The case study is a sub-system of a regional-scale
network representing the large-scale infrastructure
formed by an urban development and a strategic
infrastructure supporting the urban development in
terms of energy and water supplies (see Ortenzi et al.
2013, also for the developed framework). The
analyzed sub-system is the strategic infrastructure,
which can be represented as a node of the regional
scale network but also as a network at a smaller scale.
The first step consists in representing the
infrastructure as a system network. The system is
composed by a soil slope retained by two sheet pile
walls, a hydroelectric power station and a conduit (all
these placed uphill). As stated before, the
infrastructure is important because provides electric
power by the hydroelectric power station and water
sources by the conduit and the successive distribution
system. The process of representation of the
infrastructure as a network system is depicted in figure
9, where the main components of the system are
individuated. A finite element model has been
developed for each component of the sub-system. In
this study only the numerical results obtained from the
analysis of the upper retaining wall are present.
Figure 9. Representation of the infrastructure as a
network systemHazard and failure scenario analysis
Even if, in general, the hazard analysis must be
conducted in a multi-hazard philosophy, in the present
case the earthquake is considered as single acting
hazard.
The use of fault trees is an excellent and
synthetic way to represent all the possible failures of a
system. A preliminary investigation aims at identifying
the possible scenarios in terms of service (electrical or
hydraulic) interruption or single system element
collapse as represented in figure 10.
Consequently, the previous identified scenarios
can be specified with a fault tree analysis, carried out
in this case with the avail of appropriate flowchart as
the one represented in figure 11.
Figure 10. Schematization of the service
interruptions.
This diagram starts with the hypothesis that an
action causes failure of one of the system components
(WU in this case). Starting from this initial failure, a
number of additional (subsequent or contemporary)
failures can occur, depending on the logical and
physical connections between the elements. Each of
the possible combinations between these failures can
be connected with the service interruption scenarios
previously identified. In the specific case of figure 10,
it has been assumed that the failure of HY and CU can
be represented as cascade effects depending on the
previous failure of some other elements (WD and HY
respectively).
37
59
42 4535 38
23
63
41
58 5565 62
77
0
20
40
60
80
100
1 2 3 4 5 6 7
Rob
ust
nes
s %
Damage Scenario
Cf max Robustness
83 87 88
5360
86
64
17 13 12
4740
14
36
0
20
40
60
80
100
1 2 3 4 5 6 7
Ro
bu
stn
ess
%
Damage Scenario
Cf max Robustness
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
Numerical analyses
Only the numerical analyses related to the problem of
stability of non-homogeneous slope with retaining
walls and tie-beams are presented in this study. The
numerical analysis of the upper and lower retaining
walls (WU and WD) is carried out. Structural elements
of the wall are:
An upper sheet pile ϕ 1000 retaining wall with a
variable height from 1 to 8m from the upper layer
surface and a total height variable from 7 to 13 m.
This retaining wall has 2 tie-beams lines with 160
KN pre-tension, on 2 different levels:
upper level: 26 tie-beams with 6/10’’ strands
of area of 387 cm2 with total length 20 or 22
m;
lower level: 16 tie-beams with total length
32m.
A lower concrete sheet pile ϕ 1000 retaining wall
with a variable height from 10.55 to 12.55m over
the upper layer surface and a total height variable
from 15 to 17 m. This retaining wall has 4 tie-
beams lines with 160 KN pre-tension, on 4
different levels.
C25-30 grade concrete is used while the steel is
S235 grade. Both steel and concrete are modeled by
multi-linear constitutive laws.
The Mohr-Coulomb soil model has been adopted
and three different soil layers are present in the slope.
Two load cases are considered: i) gravity load
(g); ii) combination of the gravity load (g) and
horizontal seismic load (0.2g).
The soil slope stability analysis is carried out
using the strength reduction method, where the
strength characteristics of the soil gradually decrease
by the application of an increasing strength reduction
factor (SRF) and by maintaining a constant load. The
two-dimensional Finite Element model of the retained
slope is shown in figure 12. The model is made by
shell elements, where horizontal restrains are used for
lateral boundaries, and lateral and vertical restrains are
used for the bottom border.
The safety factor (FOS) of the slope is defined as
follows:
f
FOS
(10)
Where, under an axial stress of intensity σn:
tann
c (11)
fnfc
f tan (12)
SRF
c
fc (13)
SRFf
(14)
The slope is considered collapsed when the
analysis do not reach the convergence with the
maximum number of the considered iterations (10000)
(Popa and Batali 2010). At the failure it can be
assumed that FOS = SRF.
The effects of the degradation of the structural
materials have been investigated by carrying out a
number of analyses considering different strength for
the structural materials. In particular, the concrete has
been degraded from class C25/30 to C12/15, while the
steel has been degraded by decreasing the cross-
sectional area of the reinforcements to the 50% and
75% of its original value.
Figure 11. Schematization of the failure scenarios.
Figure 12. FE model of the slope with coordinates of
the nodes.
Figure 13. Effect of the deterioration of the structural
materials.
Results are shown in figure 13 in terms of SRF
values at the triggering of the first plasticity in the
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Fourth International Workshop on Design in Civil and Environmental Engineering, October 30-31, 2015, NTU
retaining wall. From the same figure, it is evident that
the steel degradation has a prominent role in the
quality of the slope retaining system.
Considerations on the system resilience
With the aim of providing a qualitative ranking of the
different failure scenarios the two extreme cases of the
figure 11 are considered (see figure 14) identified as
case 1 and case 2. The losses are classified in direct
and indirect.
The first case presents only a direct loss related
to the collapse of the upper retaining wall. Therefore,
the associated cost is due to the retaining wall repair.
The second case presents:
as direct losses, the collapse of both retaining walls,
the collapse of the hydroelectric power station and
the collapse of the upper conduit. Therefore, the
associated cost is due to their repair.
as indirect losses, the loss of hydroelectric power
and the loss of water flow from upper conduit.
Therefore, the associated cost is due to the lack of
power and water supply distribution to the users.
The recovery function is considered linear.
Figure 14. Considered failure scenarios.
Figure 15. Schematic representation of resilience
evaluation.
For qualitative evaluation purposes, each one of
the above defined losses are associated to an unitary
segment in the decay of the quality function, while the
slope of the recovery function is considered as directly
proportional to the losses.
In figure 15, the loss of quality of the
infrastructure in the two cases under the above-
mentioned assumption is shown. In the same figure,
the area “a” represents the loss of quality due to
degradation effects, while the areas “b” and “b+c”
represent the additional loss of quality corresponding
to case 1 and case 2.
Conclusion and reflections
The authors’ intention is to review recent
developments, together with corroborated research,
focusing on new trends in the resilience-based design.
Major events have major effects on a community scale
and drive the public opinion towards new demands.
This is how concepts such as those treated in this study
surfaced and became popular research topics.
Resilience-based design became a hot topic in the last
10 years, after major catastrophic events with extreme
impact occurred on a community scale.
Nevertheless, issues remain to be solved. There
are no resilience standards, and even resilience metrics
are somehow difficult to implement. On top of that, the
novel concept of antifragility can have a major
influence the resilience-based design.
Acknowledgements
This study presents methods, considerations and
results, developed in the last years principally by the
research group www.francobontempi.org. It is
partially supported by StroNGER s.r.l.
(www.stronger2012.com) from the fund “FILAS -
POR FESR LAZIO 2007/2013 - Support for the
research spin-off”.
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