A compositional demand/supply framework to quantify the resilience of civil infrastructure systems (Re-CoDeS)

Abstract

Disaster resilience of civil infrastructure systems is essential to security and economic stability of communities. The novel compositional demand/supply resilience framework named Re-CoDeS (Resilience-Compositional Demand/Supply) generalizes the concept of disaster resilience across the spectrum of civil infrastructure systems by accounting not only for the ability of the civil infrastructure system to supply its service to the community, but also for the community demand for such service in the aftermath of a disaster. A Lack of Resilience is consequently observed when the demand for service cannot be fully supplied. Normalized resilience measures are proposed to allow for direct comparisons between different civil infrastructure systems at component and system levels. A scheme is introduced to classify component and system configurations with respect to their resilience. In addition to quantify the resilience of civil infrastructure systems, Re-CoDeS can be used to evaluate or design community risk mitigation strategies and to optimize post-disaster recovery.

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A compositional demand/supply framework
to quantify the resilience of civil infrastructure
systems (Re-CoDeS)
Max Didier , Marco Broccardo, Simona Esposito & Bozidar Stojadinovic
To cite this article: Max Didier , Marco Broccardo, Simona Esposito & Bozidar Stojadinovic (2017):
A compositional demand/supply framework to quantify the resilience of civil infrastructure systems
(Re-CoDeS), Sustainable and Resilient Infrastructure, DOI: 10.1080/23789689.2017.1364560
To link to this article: http://dx.doi.org/10.1080/23789689.2017.1364560
© 2017 The Author(s). Published by Informa
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SUSTAINABLE AND RESILIENT INFRASTRUCTURE, 2017
https://doi.org/10.1080/23789689.2017.1364560
A compositional demand/supply framework to quantify the resilience of civil
infrastructure systems (Re-CoDeS)
MaxDidier, MarcoBroccardo, SimonaEsposito and BozidarStojadinovic
Department of Civil, Environmental and Geomatic Engineering, Swiss Federal Institute of Technology (ETH) Zurich, IBK, Zurich, Switzerland
ABSTRACT
Disaster resilience of civil infrastructure systems is essential to security and economic stability of
communities. The novel compositional demand/supply resilience framework named Re-CoDeS
(Resilience-Compositional Demand/Supply) generalizes the concept of disaster resilience across
the spectrum of civil infrastructure systems by accounting not only for the ability of the civil
infrastructure system to supply its service to the community, but also for the community demand for
such service in the aftermath of a disaster. A Lack of Resilience is consequently observed when the
demand for service cannot be fully supplied. Normalized resilience measures are proposed to allow
for direct comparisons between dierent civil infrastructure systems at component and system
levels. A scheme is introduced to classify component and system congurations with respect to their
resilience. In addition to quantify the resilience of civil infrastructure systems, Re-CoDeS can be used
to evaluate or design community risk mitigation strategies and to optimize post-disaster recovery.
KEYWORDS
Resilience; civil infrastructure
system; recovery;
vulnerability
ARTICLE HISTORY
Received 6 November 2016
Accepted27 June 2017
© 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-
nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built
upon in any way.
CONTACT Max Didier didierm@ethz.ch
OPEN ACCESS
1. Introduction
Civil infrastructure systems (CISs), such as electric power
supply, telecommunication, gas, and water distribution
systems are the backbones of contemporary societies.
eir services, meeting certain quality standards, are
indispensable in daily life of modern communities. It fol-
lows that the CISs vulnerability to and their performance
aer disasters is of paramount importance to minimize
the adverse eects of such events. Systemic disaster risk
evaluation of CISs has attracted continuous attention in
the scientic literature in recent decades (e.g. Adachi &
Ellingwood, 2008; Cavalieri, Franchin, Buritica Cortes, &
Tesfamariam, 2014; Dueñas-Osorio & Rojo, 2011; Esposito
et al., 2014; Jayaram & Baker, 2010; Mieler, Stojadinovic,
Budnitz, Comerio, & Mahin, 2015; Pitilakis, Alexoudi,
Argyroudis, Monge, & Martin, 2006; Reed, Powell, &
Westerman, 2010; Song, Der Kiureghian, & Sackman,
2007; Wang, Au, & Fu, 2010).
Based on the National Infrastructure Advisory council
(NIAC, 2009) and on the US Presidential Policy Directive
21 (2013), the disaster resilience of a CIS can be dened as
the CIS’s ability to anticipate, absorb and adapt to events
potentially disruptive to its function, and to recover either
back to its original state or to an adjusted state based on
new post-event conditions. In fact, aer past disasters, it
has been observed that the post-event performance and
recovery of CISs has a remarkable impact on the resil-
ience of communities. CIS performance inuences the
coordination and the execution of emergency actions in
the direct aermath of a disaster, e.g. an earthquake, as
well as the long-lasting post-disaster recovery process of
a community. In particular, inability to meet the post-
event service demand induces indirect costs, such as those
related to business interruptions (e.g. due to persisting
power blackouts), that may exceed direct losses due to
physical damage to the components of the CISs.
ere is, thus, a growing need to quantify disaster resil-
ience. An extensive review and a categorization of a variety
of proposed resilience quantication measures are pre-
sented by Francis and Bekera (2014) and Hosseini, Barker
and Ramirez-Marquez (Hosseini, Barker, & Ramirez-
Marquez, 2016). A functionality-based model that cap-
tures the fundamental features of disaster resilience, e.g.
the losses (consequences of an event) and the recovery
process aer a disaster, is introduced by Bruneau et al.
(2003). A CIS functionality or performance measure, e.g.
the amount of service that an electric power supply system
or a water distribution system can supply to a community,
is tracked as it varies during the post-disaster recovery
process. e loss of resilience is dened as the cumulative
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2 M. DIDIER ET AL.
Many resilience quantication frameworks proposed
in literature impose the idealistic point of view that an
infrastructure owner’s or operator’s goal is to fully recover
the CISs back to their initial (or an improved) state as fast
as possible, and to quickly repair all (physical) damage
aer a disaster. e evolution of the community demand
is not considered or is considered implicitly (e.g. by track-
ing the water pressure in a water supply pipeline, or the
waiting time at a hospital). In the case of major disasters,
these approaches might have only limited validity. e
CISs do not exist in a vacuum: they are built to deliver a
service to a community. For this reason, the focus of a CIS
resilience assessment should be not only on the impact of
a disaster in terms of the loss of service or performance
of the CIS over time, but also on the ability of a CIS to
supply the time-varying community demand for its ser-
vices and to recover the supply/demand balance as fast as
possible for parts of or for the entire community. A CIS
resilience quantication framework needs, thus, to explic-
itly account for both the evolution of the supply (i.e. the
service supply capacity of the system) and the evolution
of the demand of the community and other CISs for its
services in the aermath of a disaster.
In this study, a novel compositional demand/sup-
ply disaster resilience quantication framework named
Re-CoDeS (Resilience – Compositional Demand/
Supply) is presented. Re-CoDeS is based on demand
and supply layers, dened locally for CIS components
and extended to the system level by a system service
model. Component variables, i.e. demand, supply and
consumption at a component, are dened rst. A Lack
of Resilience occurs when the service demand at a com-
ponent cannot be fully supplied. In a second step, the
demand, supply and consumption variables are dened
at a system level. Lack of Resilience at the system level is
computed using a compositional, bottom-up, approach,
i.e. by integrating the component states using a system
service model. Normalized resilience metrics, designed to
directly compare the resilience of dierent CISs, are pre-
sented. e supply reserve margin is proposed as metric to
assess the redundancy and robustness of a CIS, while the
notion of resilience time is proposed as a measure of the
resourcefulness and the rapidity of the recovery process.
A scheme is introduced to classify dierent component
and system resilience congurations with respect to their
post-disaster behavior. An application case study is used
to demonstrate the proposed framework and to indicate
that changes in the post-disaster demand due to recovery
eorts and population movements can also be considered
using the Re-CoDeS framework. Finally, the potential for
using the Re-CoDeS framework for post-event supply and
demand scenario analysis, as well as for optimization of
post-disaster recovery strategies is discussed. Specically,
CIS performance deciency aer a disaster with respect
to a pre-disaster level until full recovery of the tracked
metric. An example of the implementation of the model is
given by Cimellaro, Reinhorn and Bruneau (2010) for hos-
pitals. e concept is further extended in the PEOPLES
framework for evaluating resilience (Cimellaro, Renschler,
Reinhorn, & Arendt, 2016).
An approach to merge engineering and ecosystem
resilience is suggested by Cavallaro, Asprone, Latora,
Manfredi and Nicosia (2014). e spatial network layers
of CISs are extended with further nodes and links, repre-
senting the interactions of the CISs with the community
inhabitants, to form Hybrid Socio-Physical Networks
(HSPNs). en, a resilience metric is formulated as the
area under the curve that tracks the evolution of HSPN
communication eciency aer a disaster. is approach
allows assessing the capability of a system to recover, even
in a dierent conguration compared to the initial one.
A case study of the city of Acerra (Italy), considering the
road network and the building stock with its inhabitants
in case of earthquakes, is presented by Cavallaro, Asprone,
Latora, Manfredi, and Nicosia (2014). An application of
quantifying seismic resilience using HSPNs in a synthetic
city, composed of the building stock and dierent CISs,
is given by Franchin and Cavalieri (2014). A multi-stage
framework to measure the expected annualized resilience
of a CIS is proposed by Ouyang, Dueñas-Osorio and Min
(2012). Given the occurrence rate and the interdependence
of multiple hazards, the annual resilience of a given system
can be calculated for dierent hazard types, or a combi-
nation of them. e framework is tested on the power
transmission grid in Harris County (USA). e concept is
extended by Ouyang and Dueñas-Osorio (2012) towards
a time-dependent resilience metric dened over a given
time period. is resilience measure is given by the ratio of
the real and the target performance curves. e approach
allows to account for future system evolution, e.g. the inte-
gration of new technologies, which have a direct impact
on a system’s future characteristics and, thus, on its resil-
ience. e suggested resilience metric quanties dierent
dimensions of resilience (technical, organizational, social
or economic), depending on the chosen performance
indicators. Cavalieri, Franchin, Gehl and Kazai (2012)
and Franchin (2014) develop a model allowing to assess
the interactions between the physical damage state of
buildings and the post-disaster serviceability of CISs to
compute, for example, the displaced population. Cutler,
Shields, Tavani and Zahran (2016), Ellingwood et al.
(2016) and Guidotti et al. (2016) investigate and develop
algorithms and metrics for community resilience assess-
ment using the Centerville Virtual Community Testbed,
which is composed by several CISs whose failures have a
direct impact on community resilience.
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SUSTAINABLE AND RESILIENT INFRASTRUCTURE 3
the Re-CoDeS framework may serve infrastructure own-
ers and operators as well as community administrators
in their eorts to plan post-disaster community recovery
with the goal to minimize the impact of CIS service una-
vailability on the community.
2. Compositional demand/supply resilience
quantication framework (Re-CoDeS)
CISs are built to deliver a service to a community
(composed of its residential building stock, industries,
businesses and critical facilities) and to other CISs.
us, a CIS disaster resilience assessment needs to be
demand-oriented, based on the ability of a CIS to supply
the time-varying community demand for its services. e
compositional demand/supply resilience quantication
framework (Re-CoDeS) enables such CIS disaster resil-
ience assessment. e framework accounts for the impact
of a disaster on both the demand and the supply side of
the CIS-community system, and tracks the post-disaster
evolution of demand and supply at the component and
the system levels. e elements of the Re-CoDeS frame-
work are:
(1) e demand layer, used to model the evolution
of the CIS demand. e evolution of the demand
for CIS service depends mainly on the vulnera-
bility, the recovery and the individual demand
of the components of the demand layer (noted
by index i).
(2) e supply layer, used to model the evolution of
the CIS supply. e evolution of the supply of
CIS service depends mainly on the vulnerability,
the recovery and the individual service supply
of the components of the supply layer (noted by
index j).
(3) e system service model, regulating the allo-
cation (or dispatch) of the CIS service supply
in order to satisfy the demand of the consum-
ers. is model accounts, for example, for the
capacity limitations and interactions of dier-
ent CIS elements: the service supply system, the
distribution system and the transmission links
between the demand and the supply layers, the
technical functioning limits and control mecha-
nisms of the system, and the system or network
eects. It considers, thus, the topology of the
system, the operator service allocation policies,
and the possible supply distribution strategies.
2.1. Resilience at a component level
At a component (element, node or location) i of the
demand layer, the component Lack of Resilience, LoRi,
represents the amount of supply that cannot be provided
by the (damaged) CIS to cover the demand at compo-
nent i over a given period of time. is is the amount of
unsupplied demand or the supply decit. e following
variables are dened:
• e component demand, Di(t), is the total demand
of all consumers using the CIS service at compo-
nent i at time t. For example, in the case of a local
water well supplying water to a community, Di(t)
is the water demand of the consumers at time t; in
the case of an electric substation, Di(t) is the electric
power demand of the buildings and other facilities
connected to that substation at time t.
• e component available supply,
Sav
i
(
t)
, is the avail-
able service supply at component i at time t. For
example,
Sav
i
(
t)
is the water supply of a well or the
electric power available at a distribution substation
at time t.
• e component consumption, Ci(t), is the eective
consumption, i.e. the eectively consumed amount
of service by the consumers at component i at time
t. For example, Ci(t) is the consumed amount of
water at a well or the consumption of electric power
at a distribution substation at time t.
e consumption Ci(t) can match either Di(t) or
Sav
i
(
t)
.
If it is not possible to cover all of the demand at compo-
nent i at time t, the consumption is equal to the available
supply. However, if the available supply is sucient, the
consumption is equal to the demand. us:
Given the above denitions, LoRi is dened as
where
⟨
⋅
⟩
is the singularity function that returns 0 for neg-
ative arguments, or the argument otherwise. e start and
the end time of the resilience assessment are denoted as
t0 and tf, respectively. Equation (2) is valid as long as the
available supply at element i at time t is known and can be
strictly delimited, i.e. eects of other system elements are
accounted for, negligible, or the available supply is inde-
pendent of and not inuenced by other parts of the sys-
tem. e demand/supply concept at the component level is
qualitatively shown in Figure 1. SRi(t) is the supply reserve
margin at component i at time t, dened as the dierence
between the available supply and the demand at element
i at time t (i.e.
SRi
(
t
)=
Sav
i
(
t
)−
Di
(
t)
). SRi(t) can be inte-
grated over a given time period to obtain SRi, as shown in
Figure 1.
TR
i
is the component resilience time, dened as the
duration of time during which a supply decit is observed.
(1)
Ci
(t)=min
(
S
av
i
(t),D
i
(t)
)
(2)
LoR
i=
t
f
∫
t
0⟨
Di(t)−Sav
i(t)
⟩
dt =
t
f
∫
t
0(
Di(t)−Ci(t)
)
dt
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4 M. DIDIER ET AL.
Note that 0≤ Ri ≤ 1. In particular, Ri=1 corresponds
to a fully resilient component whose demand Di(t) can
always be completely covered aer the event, and Ri=0
corresponds to full lack of resilience of a component for
which none of the demand Di(t) can be covered at any
time aer the event.
2.2. Resilience at a system level
At a system level, a Lack of Resilience, LoRsys, occurs
when the demand exceeds the available supply of service
at any component of the system over a given period of
time. e following variables are dened:
• e system demand,
Dsys(t)
, is the total demand for
the services of a CIS at time t. It is dened as the
aggregate sum of all component demands,
Di(t)
:
where I is the total number of components of the
demand layer of the system.
• e system consumption,
Csys(t)
, is the total service
consumption in the CIS. It is dened as the aggre-
gate sum of all component consumptions, Ci(t):
Note that, regardless of the chosen discretization of the
demand layer, the consumption can in no case exceed
the demand. For example, a hospital that is connected
to the electric power supply system, but that has also an
emergency power generator, still poses a well-dened
(5)
D
sys(t)=
I
∑
i=1
Di(t)
,
(6)
C
sys(t)=
I
∑
i=1
Ci(t)
.
Depending on the scope and the duration of the CIS
disaster resilience assessment, dierent values for t0 and
tf can be chosen. e start of the resilience assessment,
t0, is oen set to the moment of occurrence of a disaster.
e end of the resilience assessment, tf, can theoretically
be set to innity. For practical reasons, e.g. for strategic
planning of the system operator, nancial, or insurance
aspects, tf might be set to the moment when the demand
or the supply attain again their pre-disaster levels, tf,D and
tf,S, respectively (see Figure 1), or the moment when the
supply again meets the demand, tR, or to the lifespan or
the lifecycle of the system.
To obtain a dimensionless Lack of Resilience metric
in the [0,1] range that makes it possible to compare the
resilience of dierent components of the same or dier-
ent CISs, the obtained LoRi is divided by the cumulative
service demand over the resilience assessment period,
t
f
∫
t0
Di(t)
dt
. Such normalization is used because the pro-
posed denition of resilience is demand-oriented: namely,
if all of the demand can be supplied all of the time, no Lack
of Resilience is observed, if no demand is satised at any
time, the normalized value of the Lack of Resilience is 1.
e normalized metric for the Lack of Resilience at node
i,
̂
LoRi
, over the resilience assessment period t0≤t≤tf, is,
therefore, given by:
e resilience Ri of the component i, over a time period
t0≤t≤tf, is, nally:
(3)
̂
LoR
i=
∫
t
f
t0
⟨
Di(t)−Sav
i(t)
⟩
dt
∫tf
t
0
Di(t)dt
=
∫
t
f
t0
(
Di(t)−Ci(t)
)
dt
∫tf
t
0
Di(t)dt
(4)
Ri
=1−
̂
LoRi
Figure 1.Lack of Resilience at the component level.
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SUSTAINABLE AND RESILIENT INFRASTRUCTURE 5
system) is produced or made available at the dierent sup-
ply components, j∊{1,J}. e second step is the distribution
of service to the individual demand components, i∊{1,I}
according to the system service model. e relationship
between component available service supply at a compo-
nent i of the demand layer,
Sav
i
(
t)
, and the system supply
capacity,
Sc
sys
(
t)
, is not trivial. e available service supply
at a component of the demand layer can be represented as:
where φ is the system service model. Demand layer com-
ponent loss at a demand component i at time t,
Sloss
i
(t
)
, is
the loss of service occurring in the distribution of service
to that component of the demand layer due to the char-
acteristics of the system service model and losses due to
disaster-caused or environmental stressor damage to the
demand component. For example, service losses can be
incurred due to the technical functioning of the system (e.g.
capacity limitations, transmission losses) or due to the sys
-
tem dynamics imposed by the allocation/dispatch strategy
of the system service model (e.g. grid stability measures in
an electric power supply system to prevent cascading fail-
ures or an overload of parts of the system). Similarly, losses
due to damage to the distribution systems caused by the
disaster or because of aging, corrosion or wear and tear of
a demand layer component can be quantied using
Sloss
i
(t
)
.
(8)
Sav
i(t)=𝜑
(
S
c
1(t)…S
c
J(t),C1(t)…CI(t),D1(t)…DI(t)
,
Sloss
1
(t)…Sloss
I
(t)
)
demand to a node because its consumption is lim-
ited by the demand of its equipment. Consequently, if
the entire hospital demand is supplied by the electric
power supply system, it does not present any demand
to the emergency power system and vice versa.
• e system supply capacity,
Sc
sys
(
t)
, is the total ser-
vice supply capacity of the entire CIS at time t. It can
be dened as the aggregate sum of all component
supply capacities,
Sc
j
(
t)
:
where J is the total number of components of the sup-
ply layer of the CIS, and
Sc
j
(
t)
is the supply capacity
of supply node j at time t. Specically,
Sc
j
(
t)
corre-
sponds to the actual maximum supply capacity of that
component, reduced by the supply layer component
losses, such as losses due to disaster-caused damage,
losses due to long term environmental stressors (e.g.
aging, corrosion) or losses due to maintenance inter-
ventions at the supply component.
e distribution of the system supply capacity
Sc
sys
(
t)
to
the (oen) geographically disjoint demand components
depends on the nature and on the topology of the CIS and
on the system service model. is distribution process is
qualitatively shown in Figure 2. In the rst step, the service
of a CIS (e.g. electric power in an electric power supply
(7)
S
c
sys(t)=
J
∑
j
=1
Sc
j(t)
,
Figure 2.Scheme to determine the supply, demand and consumption quantities.
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6 M. DIDIER ET AL.
i.e.
S
c
sys(t)≠
I
∑
i=1
Sav
i(t
)
. Instead, the system supply capacity
is dened by Equation (7), considering the supply layer.
Given the above denitions and constraints, the sys-
tem Lack of Resilience for the investigated CIS, LoRsys, is
dened as the sum of the Lack of Resilience of the compo-
nents of the demand layer over a time period t
0
≤t≤t
f
, i.e.
which can be written as follows:
e normalized Lack of Resilience on a system level,
̂
LoRsys
,
over a time period t
0
≤t≤t
f
, is obtained by dividing Equation
(10) by the aggregate CIS demand over the same time period:
e resilience Rsys of a CIS, over a time period t0≤t≤tf,
is therefore:
Note that 0≤Rsys≤1. e compositional demand/supply
concept on the system level is shown in Figure 3. SRsys(t)
is the system supply reserve margin, dened as the dier-
ence between supply capacity and demand on a system
level (i.e.
SRsys(t)=Sc
sys(t)−Dsys (t)
). SRsys(t) can be inte-
grated over a given time period to obtain SRsys, as shown
in Figure 3.
TR
sys
is the system resilience time. e proposed
Lack of Resilience measure follows conceptually the orig-
inal resilience measure proposed by Bruneau et al. (2003)
in that it represents the (normalized) area between supply
and demand evolution curves.
(9)
LoR
sys =
I
∑
i=1
LoRi
,
(10)
LoR
sys =
I

i=1
tf
∫
t0Di(t)−Sav
i(t)dt
=
I

i=1
tf
∫
t0Di(t)−Ci(t)dt
=
tf
∫
t
0
Dsys(t)−Csys (t)dt
.
(11)
̂
LoR
sys =
I
i=1LoRi
I
i=1∫tf
t0Di(t)dt
=I
i=1∫tf
t0Di(t)−Sav
i(t)
dt
I
i=1∫tf
t0Di(t)dt
=
∫tf
t0Dsys(t)−Csys (t)dt
∫tf
t0
D
sys
(t)dt
(12)
Rsys
=1−
̂
LoR
sys
e system service model φ depends on three main
elements: the technical functioning of the CIS, the topol-
ogy of the CIS, and on the dispatch/allocation strategy of
the CIS operator. e technical functioning represents the
physics laws that govern the generation and distribution
of the CIS service. For example, ow balance equations
govern the service ow in utility networks such as elec-
tric power, water supply and gas networks. e dispatch
strategy of the operator includes both the technical deci-
sions aimed at minimizing the damage to the distribution
network (e.g. due to overpressure or high currents) and
prevention of cascading failures, and the strategic deci-
sions for supply allocation to dierent components of the
community (e.g. hierarchical dispatch of services based
on a set of critical consumers, especially during phases of
service decit or system breakdowns). e complexity of
the system service model φ is inuenced by the scale of
the resilience analysis and the modeling and the discre-
tization of the demand and supply layers. A ner granu-
larity from the functional component level down to the
sub-components (e.g. the sub-components of an electric
substation or the individual consumers connected to a
substation) increases the complexity of the analysis. e
art of modeling is in nding the right balance between
the complexity of φ and the scale of the problem. e
selection of the scale depends mainly on the accuracy
of the available data and the scope of the analysis. For
example, in case of a lack of high resolution spatial data
of a pipeline system, the geometry of the network needs
to be simplied. On the other hand, to model the service
delivered, for example, by a gas distribution network to the
buildings, not only the serviceability of the stations and
the pipes of the medium- and low-pressure network needs
to be considered, but service delivery also depends on
small diameter pipes that connect the low-pressure pipes
to individual buildings. ese pipes should, thus, be con-
sidered in the model. Examples of Re-CoDeS employed
at dierent scales (national and city level) are provided
by Didier, Grauvogl, Steento, Ghosh, and Stojadinovic
(2017) and Didier, Baumberger, Tobler, Esposito, Ghosh
and Stojadinovic (2017).
erefore, the component available service supply,
Sav
i
(
t)
,
depends on the demand at the component itself, the losses
in the distribution of service and in the demand layer, the
consumption at other connected components, the supply
capacity of the supply components and the system service
model. It is dened on the component level:
Sav
i
(
t)
of dier-
ent components are, generally, not additive on the system
level, i.e. the system supply capacity
Sc
sys
(
t)
is not the simple
sum of the component available service supply quantities,
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SUSTAINABLE AND RESILIENT INFRASTRUCTURE 7
at the same time. e supply reserve margin can also be
normalized by the demand to assure comparability across
dierent components or systems.
On the component level, the normalized supply reserve
margin of a component i at time t,
̂
SRi
(
t)
, is dened as:
On the system level, the normalized supply reserve
margin at time t,
̂
SRsys
(t
)
, is dened as:
If
̂
SRsys
(t)≥
0
, or
̂
SRi
(
t
)≥
0
, the system or the demand
component i have a supply reserve. If a service is not avail-
able at all at the system level or at the demand component
level, then
̂
SRsys
(t)=−
1
, or
̂
SRi
(
t
)=−
1
.
Using the supply reserve margin, the robustness of a
CIS is dened as:
where t0 is the start of the resilience assessment dened
above. ese normalized resilience measures can be used
to compare the redundancy and robustness of dierent
CIS components or to compare dierent CISs.
2.3.2. Resilience time
e system resilience time,
TR
sys
, is dened as the total
duration of the aggregate service decit, i.e. when
Csys(t)<Dsys (t)
(Figure 3). Equivalently, the component
(14)
̂
SR
i(t)=
Sav
i
(t)−D
i
(t)
D
i
(t)=
Sav
i
(t)
D
i
(t)−
1
(15)
̂
SR
sys(t)=
Sc
sys
(t)−D
sys
(t)
D
sys
(t)=
Sc
sys
(t)
D
sys
(t)−
1
(16)
r
sys =min
t

SRsys(t)
SR
sys
t0

Observe that:
e denition of the system resilience is, thus, not a naïve
extension of the component resilience denition. Instead,
using Equations 8, 9 and 10, it accounts consistently for
system dynamics, interdependencies and losses. ese
may not be identied if the system-level supply
Sc
sys(t)
and
demand D
sys
(t) are used in a simple extension of Equation
2, giving the last element of Equation 13. In fact, such an
approach results in an underestimation of the actual Lack
of Resilience of the CIS.
2.3. Other resilience metrics
2.3.1. Supply reserve margin and robustness
e supply reserve margin, as dened in Section 2.1 at the
component level, and in Section 2.2 at the system level, can
be used as a measure of the redundancy of the CIS (the
extent to which components or systems are substitutable)
and of the robustness of the CIS (the strength of its com-
ponents or systems). ese two properties of a resilient
system were dened by Bruneau et al. (2003). For example,
a supply reserve could be used to substitute (completely or
in part) for the loss of supply due to disaster-induced dam-
age to some supply layer components of the CIS. However,
the actual supply to the demand layer components also
depends on the transmission system and the system ser-
vice model. erefore, it is possible to observe a Lack of
Resilience at a system level while having a supply reserve
(13)
LoR
sys(t)=
I

i=1
LoRi
=
tf
�
t0
Dsys(t)−Csys (t)dt ≥
tf
�
t0
Dsys(t)−Sc
sys(t)

dt
.
Figure 3.Lack of Resilience at the system level.
Downloaded by [ETH Zurich] at 05:25 12 September 2017

8 M. DIDIER ET AL.
or the system,
̂
TR
i
and
̂
TR
sys
correspond to the unavailability
of the component or the system over its lifetime. ese
normalized resilience measures can be used to compare
the resourcefulness and the rapidity of dierent CIS com-
ponents or dierent CISs.
2.4. Component and system resilience-related
congurations
Changes in both the community service demand and the
CIS service supply are expected aer a disaster. e ability
of a CIS to supply its services oen decreases, depend-
ing on the vulnerability of its components. However, the
CIS can be designed, or extraordinary measures may be
taken, to increase the supply of its service aer a disaster.
On the other hand, the community component and sys-
tem demand for services may drop, remain constant or
increase and vary signicantly during the post-disaster
recovery period depending on the recovery eorts and
movements of the population. e proposed Re-CoDeS
framework is designed to account directly for the changes
in component and system supply and demand, and to
consistently quantify the arising Lack of Resilience. Such
quantication depends on magnitudes and rates of change
of the demand, supply and consumption, and, thus, on a
myriad of factors.
e Re-CoDeS framework makes it possible to classify
CIS-community component and system congurations
based on the states of the component variables Di(t) and
Sav
i(t)
, and the system variables Dsys(t),
SC
sys
(t
)
and Csys(t),
dened above. Note that every conguration can lead to
good or bad performance, i.e. a smaller or larger Lack
of Resilience. However, some congurations, like the
anti-fragile conguration (i.e. an increase in post-disas-
ter demand and supply), are less prone to a large Lack
resilience time,
TR
i
, is dened by the total duration of the
local service decit, i.e.
Ci(t)<Di(t)
at a given component
i (Figure 1). When a sequence of disaster events is of con-
cern (e.g. a series of aershocks following the main seis-
mic event), the resilience time is dened as the sum of the
partial resilience times, i.e.
TR
sys =
∑
k
T
R
sys,
k
, and
TR
i=
∑
k
T
R
i,
k
,
where k is the number of partial resilience times and
TR
i,k
and
TR
sys
,
k
are the k-th partial component and system
resilience time, respectively (Figure 4). e addition of
partial resilience times can be applied if demand drops
repeatedly below the consumption, for example, due to
a varying recovery speed of demand and supply.
TR
i,k
are
only additive for the given component i and should not
be added across dierent components. Instead, the system
resilience time,
TR
sys
, should be used to characterize the
system behavior.
e resilience time can be used as measure of the
resourcefulness (the capacity to mobilize resources to
achieve goals) and the rapidity (the capacity to achieve
goals in a timely manner) of recovery of the CIS, as
dened by Bruneau et al. (2003). e component and
system resilience time can be normalized, for example,
by the duration of the resilience assessment, (tf−t0):
where
̂
TR
i
is the normalized component resilience time of
component i, and
̂
TR
sys
is the normalized system resilience
time. If
(
tf−t0
)
is set to the lifetime of the component
(17)
̂
T
R
i=T
R
i
t
f
−t0
(18)
̂
T
R
sys =T
R
sys
t
f
−t
0
Figure 4.System resilience time
TR
sys
in the case of two consecutive disastrous events.
Downloaded by [ETH Zurich] at 05:25 12 September 2017

SUSTAINABLE AND RESILIENT INFRASTRUCTURE 9
population), whereas the supply available at the
component increases. While a Lack of Resilience is
not likely to occur, such conguration leads to an
(oen unnecessary and inecient) increase in the
supply reserve margin,
SRi(t)
. For example, due to
large donations, large reserves of food and cloth-
ing were generated and wasted aer the 2010 Haiti
earthquake and the 2012 hurricane Sandy (Fessler,
2012).
• Fragile conguration:
Di(t)>Di(t0)ΛSav
i(t)≤Sav
i(t0)
,
t>t0. A simultaneous increase in service demand
and decrease in service supply is likely to result in a
Lack of Resilience. Components of the telecommu-
nication system or elements of the transportation
systems are likely to exhibit such fragile congu-
ration during the post-disaster emergency phase.
For example, in the aermath of the 2011 Tohoku
earthquake, local telecommunication demand is
indicated to have increased up to 8 or 10 times the
normal demand (ASCE, 2011). Even if the telecom-
munication system remains fully functional (i.e. no
loss of resilience is observed in a resilience frame-
work evaluating only the functionality of the CIS),
it may have diculties to meet the post-disaster
demand at all demand layer components.
• Anti-Fragile conguration:
Di(t)>Di(t0)ΛSav
i(t)>Sav
i(t0)
,
t>t0. An increase of both the demand and the sup-
ply compared to their pre-disaster levels may still
of Resilience, while others, like the fragile conguration
(i.e. an increase in post-disaster demand and a decrease
in post-disaster supply), are more likely to result in a
large Lack of Resilience. Analysis of the CIS-community
component and system congurations is, therefore, an
important step in a resilience evaluation and optimiza-
tion procedure.
2.4.1. Component resilience-related congurations
Four possible relations between demand and supply at the
component level, shown in Figure 5, dene four types of
component resilience-related congurations:
• Classical conguration:
Di
(t)≤D
i(
t
0)
∧S
av
i
(t)≤S
av
i(
t
0)
,
t>t0. In the classical component conguration, the
components of the supply and the demand layers
are vulnerable to the disaster (e.g. components of an
electric power supply system and buildings of the
community building stock are simultaneously dam-
aged during a disaster). Consequently, component
demand and supply both decrease aer the disaster,
and a Lack of Resilience may occur, depending on
the magnitude and the rate of the demand and sup-
ply decrease. A majority of CIS-community system
components is expected to belong to this perfor-
mance category.
• Inecient conguration:
Di(t)≤Di(t0)ΛSav
i(t)>Sav
i(t0)
,
t>t0. In some cases, component demand decreases
(e.g. due to fatalities or temporary reallocation of
Figure 5.Component resilience-related configurations: (a) Classical; (b) Inefficient; (c) Fragile and (d) Anti-Fragile.
Downloaded by [ETH Zurich] at 05:25 12 September 2017

10 M. DIDIER ET AL.
to experience a Lack of Resilience due to a disaster than,
for example, fragile congurations with similar pre-dis-
aster supply reserve margins.
e second set of system resilience-related congu-
rations includes four special congurations (Table 1), as
follows:
• Reserve-Margin conguration (Figure 6(e)): ese
systems usually have a supply reserve margin
designed to absorb increases in the system demand
and can avoid or minimize the Lack of Resilience.
is ability depends, for example, on the size of the
supply reserve margin, possible redundancies in
their transmission system, and ecient service dis-
patch strategies. Such a conguration can be found,
for example, in nuclear energy facilities where the
high-consequence low-probability events justify a
substantial (but costly) system reserve margin.
• Cli-Edge conguration (Figure 6(f)): A cli-edge
conguration is usually observed in systems where
either critical components (especially of the trans-
mission system) are vulnerable and dicult to
repair, or where damage may cascade to otherwise
undamaged components exacerbating a possible
system Lack of Resilience. Such systems experi-
ence cli-edge failures because of non-redundant
designs, inecient system service models, or poor
recovery strategies. A simple example of such a sys-
tem is a two nodes system, consisting of a supply
node (source) and a demand node (sink) connected
via a single highly vulnerable link. e supply
node, for example a health care facility, is designed
in a way to increase its supply capacity in case of
a hazardous event, since an increase in the service
demand due to injuries is expected. However, the
facility can only be reached by a highly vulnerable
link, in this case a bridge that was damaged by the
earthquake. It is, thus, not possible to access the ser-
vices of the hospital anymore.
• Inadequate conguration (Figure 6(g)): ese CISs
do not satisfy the demand of the community before
the disaster, even despite possibly large supply
reserve margins. A likely cause of such system per-
formance is poor system design and maintenance,
result in a Lack of Resilience, depending on the size
of the pre-disaster component supply reserve mar-
gin and on the magnitude and rate of demand and
supply increase. However, if the increase in sup-
ply matches or exceeds the increase in demand, no
Lack of Resilience is observed. An example of such
conguration are health care facilities that set up
temporary beds and improvised emergency rooms,
and, thus, increase the supply of their service to
meet an increased post-disaster demand. Such per-
formance is classied as anti-fragile, adopting a
concept introduced by Taleb (2012). Here, this con-
cept is used to identify components that (resource-
fully) adapt aer a disaster to minimize the Lack of
Resilience. Anti-fragility should be a target design
objective for the critical components of disaster-re-
silient CISs.
2.4.2. System resilience-related congurations
Resilience-related performance categorization of compo-
nents is based solely on the comparison between com-
ponent demand
Di(t)
and available supply
Sav
i
(
t)
, since
component consumption cannot exceed its demand
(Equation (1)). However, at the system level, demand
Dsys(t)
and supply capacity
SC
sys
(t
)
are not sucient to cate
-
gorize the post-disaster performance of a CIS-community
system. As was observed when LoRsys was dened above,
it is necessary to account for the changes in the system
consumption, Csys(t) (Equation (6)), as complexity can
arise e.g. due to the topology or the nature of the system
service model of the CIS. Eight possible CIS-community
system resilience-related congurations are listed in Table
1 and shown in Figure 6.
e system resilience-related congurations are
grouped into two sets. e rst set includes the four
CIS-community system congurations equivalent to the
four resilience-related component congurations. Again,
a Lack of Resilience may occur in any conguration,
independently of their supply reserve margin. However,
some systems, for example, those with an anti-fragile
resilience-related conguration, have desirable defense-
in-depth features. ey are usually more capable of e-
ciently redistributing the service supply and are less prone
Table 1.System resilience-related configurations.
Sc
sys
(t
)
Dsys(t)
Csys(t)
Conguration
Set I (a)
Sc
sys
(t)
≤
Sc
sys
(t
0)
Dsys(t)
≤
Dsys(t0)
Csys(t)
≤
Csys(t0)
Classical
(b)
Sc
sys(t)>
Sc
sys(t0)
Dsys(t)
≤
Dsys(t0)
Csys(t)
≤
Csys(t0)
Inefficient
(c)
Sc
sys
(
t
)
≤
Sc
sys
(
t0)
Dsys(t)>Dsys (t0)
Csys(t)
≤
Csys(t0)
Fragile
(d)
Sc
sys
(t)
>
Sc
sys
(t
0)
Dsys
(
t
)
>Dsys
(
t0)
Csys
(
t
)
>Csys
(
t0)
Anti-Fragile
Set 2 (e)
Sc
sys
(t)
≤
Sc
sys
(t
0)
Dsys(t)>Dsys (t0)
Csys(t)>Csys (t0)
Reserve-Margin
(f)
Sc
sys
(t)
>
Sc
sys
(t
0)
Dsys(t)>Dsys (t0)
Csys(t)≤Csys (t0)
Cliff-Edge
(g)
Sc
sys
(t)
>
Sc
sys
(t
0)
Dsys(t)
≤
Dsys(t0)
Csys(t)>Csys (t0)
Inadequate
(h)
Sc
sys
(t)
≤
Sc
sys
(t
0)
Dsys(t)≤Dsys (t0)
Csys(t)>Csys (t0)
Under-Designed
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SUSTAINABLE AND RESILIENT INFRASTRUCTURE 11
reactivation of two idled hydrocarbon fuel electric
power generation plants and the use of local emer-
gency power generators to increase the service sup-
ply (Didier, Grauvogl et al., 2017).
2.5. Illustrative example
e proposed Re-CoDeS framework is demonstrated on
the task of quantifying the resilience of an electric power
supply system of a virtual community. e aim of the
example is to demonstrate the application of the Re-CoDeS
framework in an academic setting. A more elaborated
application of the Re-CoDeS framework using a virtual
CIS-community system is illustrated in Didier, Esposito, &
Stojadinovic (2017). In addition, the Re-CoDeS framework
was used to analyze the resilience of the electric power sup-
ply system in Nepal (Didier, Grauvogl et al., 2017) and of
the water distribution system and the cellular communica-
tion system of the Kathmandu Valley (Didier, Baumberger
et al., 2017) aer the 2015 Gorkha earthquake. Resilience
evaluation of more complex, but still virtual systems is
presented in Didier, Sun, Ghosh, & Stojadinovic (2015).
Systems with agent-based recovery models, still employing
with the distribution components of the system
unable to execute the CIS service dispatch. Another
cause may be high transmission losses, resulting in
a pre-disaster supply decit. Examples for such a
conguration are systems with some supply facili-
ties that may only be available during emergencies
and at a high cost (e.g. emergency power genera-
tors). While they remain unused in normal situa-
tions, system operators might decide to use these
supply facilities in the case of a disaster in order to
increase the supply and limit the Lack of Resilience
aer an event.
• Under-Designed conguration (Figure 6(h)): Such
CISs are not adequately designed, have an inecient
or costly supply distribution or have, for example,
been damaged in recent disasters such that they
are not able to execute pre-disaster CIS service dis-
patch without failure (e.g. black- or brown-outs in
the electric power supply system). An example for
this conguration is the electric power supply sys-
tem in Nepal, which was under-designed before
the 2015 Gorkha earthquake, with its supply per-
formance deteriorating further despite a temporary
Figure 6.System resilience-related configurations: (a) Classical; (b) Inefficient; (c) Fragile; (d) Anti-Fragile; (e) Reserve-Margin; (f ) Cliff-
Edge; (g) Inadequate; and (h) Under-Designed.
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12 M. DIDIER ET AL.
(due to damage to the building stock and displacement of
the population), and three links are broken (Figure 7(a)).
Seismic fragility functions can be used to determine the
expected damage to the components (e.g. Didier, Esposito
& Stojadinovic, 2017 or Didier, Grauvogl et al., 2017).
e disaster-induced damage is absorbed during the rst
6days. At t=6days, the connection between nodes j=1
and i=4 is repaired. e demand at node i=1 recovers
during this period (some people are, for example, allowed
to return to their homes aer a safety evaluation) and the
demand at node i= 4 increases, compared to the pre-
event level due, for example, to relocation of the popu-
lation from other damaged locations. At t=9days, the
connection between nodes j=1 and i=1 is repaired and
a part of the supply capacity lost at supply node j=1 is
recovered (repairs of the generator are nished). Finally, at
t=12days, the supply system recovers back to its pre-dis-
aster capacity. Simultaneously, the demand at the dier-
ent nodes continues to gradually recover. is process is
tracked for 60days. e evolution of the metrics at the
system level and at the demand and supply layer compo-
nents is shown in Figure 7(b–f). e values of the dierent
resilience metrics over time can be found in Table A1.
While the demand layer nodes i=2 and i=3 do not
experience any Lack of Resilience, despite the drop in
the available supply at both nodes, a Lack of Resilience is
observed for the demand layer nodes i=1 and i=4. e
resilience-related post-disaster behavior of these nodes is
classied into the classical conguration. At node i=1,
which is completely disconnected from the network, there
is no supply available at all during the rst 9days aer the
the Re-CoDeS framework for resilience evaluation, are pre-
sented in Sun, Didier, Delé, & Stojadinovic (2015).
e virtual CIS (Figure 7(a)) comprises 2 supply layer
nodes (e.g. hydropower plants,
j∈{1, 2}
) and 4 demand
layer nodes (e.g. small cities,
i∈{1, 2, 3, 4}
) connected
by links. e system service model is based on a simple
dispatch strategy: demand node i=1 is served rst, until
its local demand is satised, demand node i=2 is served
second, and so on, until either all the demand at all the
demand nodes is satised, or the system supply capacity is
entirely distributed. Losses due to capacity limitations of
the transmission lines, and the electricity ow restrictions
are not considered, but can be included using models pro-
posed by Pires, Ang, & Villaverde (1996) and (Modaressi,
Desramaut, & Gehl (2014). us, the available supply at
a demand node is:
is dispatch strategy (system service model) is used
to distribute the electric power supply both pre- and
post-disaster. Possible occurrence of network discon-
nects and formations of network islands are considered
by applying the adopted dispatch model to the dierent
formed network components.
At time t0, the system is shocked by an earthquake. In
this scenario, one supply layer node becomes partly dam-
aged, the demand at several demand layer nodes decreases
(19)
S
av
i(t)=
⎧
⎪
⎨
⎪
⎩
Sc
sys(t),for i =1
Sc
sys(t)−
i−1
∑
1
Ci(t),for i >
1
Figure 7.Virtual CIS-community (a) system topology before and after a disaster, results; Lack of Resilience evaluation for (b) the system
and (c–f) the demand nodes 1 through 4.
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SUSTAINABLE AND RESILIENT INFRASTRUCTURE 13
the port. However, while the port was rebuilt to its full
pre-disaster capacity, container transshipments cargo
trac gradually decreased to about 10% of pre-disaster
levels as it was switched to other ports (Chang, 2010).
Another example of changes in both demand and supply
occurred in the regional gas supply network aer the 2009
L’Aquila earthquake. e gas pipe network was modied
in response to a new set of needs: inaccessible zones were
bypassed, the gas network in L’Aquila downtown was com-
pletely replaced, missing links added, and temporary or
new urbanized areas connected (Esposito, Giovinazzi,
Elefante, & Iervolino, 2013). e topology and the oper-
ation of the L’Aquila gas network changed so signicantly
in the aermath of the 2009 earthquake that a compar-
ison to the pre-disaster state was rendered meaningless.
ese examples illustrate the need to take the evolution
of both the post-disaster demand and supply explicitly
into account. However, the mere balance of supply and
demand at a low level does not necessarily mean that the
CIS-community system recovery process is satisfactory
or over.
e Re-CoDeS framework is also able to account for
dierent recovery priorities and rates of recovery of vari-
ous CIS-community system congurations (e.g. the elec-
tric power supply system may recover in a few days, while
the built inventory may require signicantly more time
to recover its functions). is makes it possible to use the
Re-CoDeS framework to optimize post-disaster recovery
by minimizing the Lack of Resilience under resource and
time constraints, while simultaneously accounting for the
pre-disaster planning and preparedness, disaster mitiga-
tion and recovery management actions, and possible new
post-disaster supply and demand patterns. e ability to
account for the future evolution of the demand, as well as
for the evolution of the supply, makes it possible to extend
the Re-CoDeS framework beyond the recovery phase to
plan optimal allocation of sparse resources and nancial
means to better prepare for the next disaster.
Major challenges include the development of improved
models of the evolution of post-disaster service demand
and the consideration of eects of interconnectivity and
interdependence of the investigated CIS with other CISs.
For example, models to estimate the evolution of the
post-disaster service demand have been proposed for the
electric power supply system (Didier, Grauvogl, Steento,
Broccardo et al., 2017) and the cellular communication sys-
tem and the water distribution system (Didier, Baumberger
et al., 2017). Further research may also address possible
implications of population movement related to a (tempo-
rary) inability to occupy otherwise undamaged buildings
due to the lack of CISs services (Franchin, 2014). Such
population movement leads to an interdependency of the
evolution of the demand at dierent demand components.
disaster. e available supply at node i=4 is not sucient
to cover the increased demand during the rst 6days. Note
that although there is a system supply reserve before and
aer the disaster, a system Lack of Resilience is observed at
the same time. is is due to the topology of the damaged
system, the prioritization of the recovery actions, and the
dynamics of demand caused by population movement.
e example shows that although the supply is higher
than the demand on a system level at every moment, i.e.
t
f
∫
t0⟨
Dsys(t)−Sc
sys(t)
⟩
dt =
0
, dierent nodes have a supply
decit and there is a Lack of Resilience at the system level,
LoR
sys =
I
∑
i=1
LoRi>
0
. erefore, Equation (13) holds. It is
interesting to note that a recovery strategy prioritizing
the recovery of the links, as opposed to the recovery of
the supply nodes, would minimize the Lack of Resilience
for this virtual CIS-community system in this scenario.
In fact, the system supply capacity is, at each time step of
the analysis sucient to cover the demand in the system.
However, the service supply cannot be distributed to all
the demand nodes.
3. Discussion and applications
e proposed Re-CoDeS disaster resilience quantica-
tion framework accounts for a dynamic adaption of the
post-disaster demand and supply to indicate that a Lack
of Resilience of the CIS-community system occurs only
when the desired demand of the community cannot be
fully supplied by the CIS. is is in contrast to other disas-
ter resilience quantication frameworks that focus mostly
on CIS supply and oen suppose that it will recover back
to the pre-disaster state to aect a full recovery of the
CIS-community system.
e Re-CoDeS framework can be used to model the
CIS resilience in disaster scenarios where entire regions
might be destroyed or become uninhabitable, leading to
displacements of population and relocation of economic
activities to other geographic locations. In such a context,
the focus on the full recovery of CIS service to the pre-
event level is misplaced because the community using the
services does not exist anymore. A prominent and extreme
case of such decreasing and/or disappearing demand is
Pompeii (Italy) aer the 62 AD Pompeii earthquake and
the volcano eruption in 72 AD. Instead, the CISs in the
newly populated areas need to be upgraded to meet the
increased demand levels. Such CISs may also exhibit a
Lack of Resilience, but at post-disaster supply and demand
situations that are very dierent from the pre-disaster sit-
uations. Another illustration of the eect of permanently
changed demand is the Port of Kobe aer the 1995 Kobe
earthquake. Many resources have been allocated to rebuild
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14 M. DIDIER ET AL.
(SNSF) SCCER SoE Project; the European Community FP7
STREST Project [grant number 603389]; and the Swiss Federal
Institute of Technology (ETH) Zurich. e authors gratefully
acknowledge this funding.
Notes on contributors
Max Didier is a PhD Candidate at the Chair of Structural
Dynamics and Earthquake Engineering at the Institute of
Structural Engineering (IBK) of the Swiss Federal Institute of
Technology (ETH) Zurich. His research interests are in design
and evaluation of earthquake-resilient communities and ele-
ments of the built infrastructure.
Marco Broccardo is a postdoctoral researcher at the Swiss
Competence Center for Energy Research–Supply of Electricity
(SCCER-SoE) of the Swiss Federal Institute of Technology
(ETH) Zurich, and at the Institute of Structural Engineering
(IBK) of ETH Zurich. His research is in probabilistic uid-in-
duced seismic analysis, resilience analysis, stochastic dynamics
and structural reliability methods.
Simona Esposito is an Earthquake Specialist at Swiss Re
Management Ltd. She worked as postdoctoral researcher
at University of Canterbury, New Zealand, and at the Swiss
Federal Institute of Technology (ETH) Zurich. She is an expert
in probabilistic seismic risk and resilience analysis of complex
infrastructure systems, seismic regional hazard and spatial cor-
relation of ground motion.
Bozidar Stojadinovic is a professor and Chair of Structural
Dynamics and Earthquake Engineering at the Institute of
Structural Engineering (IBK) of the Swiss Federal Institute
of Technology (ETH) Zurich and the Chair of the ETH Risk
Center Steering Committee. His research interests are in
design and evaluation of earthquake-resilient communities
and elements of the built infrastructure, dynamic behavior of
structures and structural elements, and hybrid simulation of
structural response to dynamic loads.
ORCID
Max Didier http://orcid.org/0000-0003-4231-2961
Simona Esposito http://orcid.org/0000-0003-4558-4671
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Disclosure statement
e methods, results, opinions, ndings and conclusions pre-
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SUSTAINABLE AND RESILIENT INFRASTRUCTURE 17
Appendix
Table A1.Resilience metrics tracked in the illustrative example.
LoR1(t0,t)
stands for
t
∫
t0⟨
D1(t)−Sav
1(t)
⟩dt
;
C(t),D
(t),S
c(t),S
av(t)
in [MW];
LoR(
t
0
,t
)
in [MWd];
R
[−],
̂
LoR1
(t
0
,t
)
[−].
t
<
t0
t=t0
t=3
days
t=6
days
t=9
days
t=12
days
t=20
days
t=30
days
t=60
days
Components
D1(t)
50 10 10 20 20 30 30 40 40
D2(t)
70 50 50 50 50 50 50 60 60
D3(t)
90 80 80 80 80 80 80 80 90
D4(t)
40 40 50 50 50 50 50 50 50
Sc
1(t)
200 120 120 120 180 200 200 200 200
Sc
2(t)
100 100 100 100 100 100 100 100 100
Sav
1
(
t)
300 0 0 0 280 300 300 300 300
Sav
2
(t
)
250 120 120 220 260 270 270 260 260
Sav
3
(t
)
180 100 100 170 210 220 220 200 200
Sav
4
(t
)
90 20 20 90 130 140 140 120 110
C1(t)
50 0 0 0 20 30 30 40 40
C2(t)
70 50 50 50 50 50 50 60 60
C3(t)
90 80 80 80 80 80 80 80 90
C4(t)
40 20 20 50 50 50 50 50 50
LoR1(t0,t)
0 30 60 120 120 120 120 120
LoR2(t0,t)
0 0 0 0 0 0 0 0
LoR3(t0,t)
0 0 0 0 0 0 0 0
LoR4(t0,t)
0 60 150 150 150 150 150 150
̂
LoR1
(
t0,t)
0 1 1 1 0.67 0.29 0.17 0.06
̂
LoR2
(
t0,t)
0 0 0 0 0 0 0 0
̂
LoR3
(t
0
,t
)
0 0 0 0 0 0 0 0
̂
LoR4
(t
0
,t
)
0 0.50 0.56 0.36 0.26 0.15 0.10 0.05
R1(t0,t)
1 0 0 0 0.33 0.71 0.83 0.94
R2(t0,t)
1 1 1 1 1 1 1 1
R3(t0,t)
1 1 1 1 1 1 1 1
R4(t0,t)
1 0.5 0.44 0.64 0.74 0.85 0.90 0.95
System
Dsys(t)
250 180 190 200 200 210 210 230 240
Sc
sys
(t
)
300 220 220 220 280 300 300 300 300
Csys(t)
250 150 150 180 200 210 210 230 240
LoRsys(t0,t)
0 90 210 270 270 270 270 270
̂
LoRsys
(t
0
,t
)
0 0.17 0.19 0.16 0.12 0.07 0.04 0.02
Rsys(t0,t)
1 0.83 0.81 0.84 0.88 0.93 0.96 0.98
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