Design for Robustness, Resilience and Anti-Fragility in the Built and Urban Environment: Considerations from a Civil Engineering Point of View

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



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





Tamkang University

National Chiao Tung University

Feng Chia 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.

17

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)

18


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

19


(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)

20


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

21


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

22


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

23


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

24


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

25


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

26


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

27


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

28


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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