Resilience-based design (RBD) modelling of civil infrastructure to assess seismic hazards - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 269

different vulnerabilities P j ( D / H ) (because they belong to different structure
topologies, they are retrofi tted differently, etc.), might have reduced losses
at the community level with respect to group of buildings retrofi tted with
the same strategy, therefore having the same vulnerability level.
Another advantage of RBD with respect to PBD is that it considers the
community as a complex system where losses as well as the recovery process
are coupled dimensions involving several parameters that are not only
engineering parameters, such as drift and accelerations, but also other
parameters, such as socio-economic gender, age of the population, etc. In
addition, the recovery process becomes an integral part of the RBD process,
so it should be planned upfront.

11.3.1 RBD in structures

In the last decade, earthquake engineers have given more attention to
deformations during their analysis, and life safety, while less attention has
been given to socio-economic parameters. Nowadays, attention is shifting
toward the necessity to develop a damage-free structure using risk assess-
ment tools which should develop more robust structures against uncertain-
ties. Shorter recovery processes are possible at the building level if the
structural damage is minimal; otherwise it might take months to recover.
One of the options in order to achieve more resilient structures in face of
an earthquake is for example providing them with advanced technologies
such as self-centring capabilities with minimum residual deformations
which will allow a faster recovery process (e.g. Christopoulos and Filiatrault,
2006).

11.3.2 Defi nition of resilience

While the general defi nition of resilience is provided in the introduction of
this chapter, the index is illustrated graphically in Fig. 11.1 as the normalized
shaded area underneath the functionality function of a system Q ( t ) . Figure
11.1 depicts this as a non-stationary stochastic process and each ensemble
is a piecewise continuous function. Analytically, resilience is defi ned as

t +

∫

T OE LC

() =

()

Rr O t T d t [11.4]

TOT LC

t

OE

where Q TOT (t) is the global functionality of the region considered; T LC is the
control time of the period of interest; → is a position vector defi ning the
position P in the selected region where the resilience index is evaluated
(Cimellaro et al. , 2009, 2010a,c). The community functionality is the combi-
nation of all functionalities related to different facilities, lifelines, etc., for the
case when physical infrastructure resources and services are considered.