Resilience and Vulnerability Analysis for Restoration After Tsunamis and Floods: The Case of Dwellings and Industrial Plants - Post-Tsunami Hazard: Reconstruction and Restoration - page 234

where: F R (.) = Resilience function of the system during the reference period T ref ;
V = total volume of the system; T ref = duration or reference period for recovery;
t = instant ranging between the occurrence of the disaster and T ref ; D(.) = damage
value (vulnerability) ranging within [0..1]; ʦ r (.) = recovery evolution function, and
ˇ r (.t) = “resilience capability and availability” function which depends on availability
of resources (internal or external) and the capacity to react adequately, such as past
experience, knowledge and readiness to react.
As resilience depends intimately on the loss of utility functions, the vulnerability
and fragility functions (i.e. damage, D) should be accurately modeled for each
potential hazard.

16.2.1.5 Resilience: Practice and Illustration

For the purpose of illustration, selected cases are discussed (Fig. 16.2 ):

- The instant t d,f = 2 [time units, in years for instance ] as an occurrence of the
triggering hazard, and t ref = 4 [time units, in years for instance ] as the reference
duration time during which the system has to recover its required capacity,
- The minimal threshold below which the system is considered as having failed
and being out of service is supposed to be F r,min = 0.2,
- The optimal value above which the system is considered as being extra resilient
is supposed to be F r,adm = 0.8,
- The system is considered resilient and still in service when its resilience
function values range within the interval [F r,min .. F r,adm ] during the reference
period [t d,f ..t ref ].
Thus, the final state of the system can be as follows (Fig. 16.2 ):

- The system is resilient in case of non-worsening conditions,

- The system is not resilient for any post-disaster evolution conditions since the

residual capacity is such that the system can never recover.

- The system is resilient and gains in capacity due to the limited amount of damage

and adequate strengthening after the reconstruction process.

16.2.1.6 Discussion

Measuring system resilience is a complex process and its objectivity relies on:

- An adequate and accurate choice of relevant values of the threshold F r,min , and

optimal value F r,adm

- Idem for the definition of reference period [t d,f ..t ref ] for recovering the expected

utility functions

- The volume of the system, its internal and external interactions

- Forms of post-disaster recovery or worsening functions