## 3 Seismic Resilience  
In this section, seismic resilience is considered with a new development that is necessary to include interdependencies. In particular, seismic resilience has been object of several contributions, such as [32; 33; 34; 35; 36]. In this this regard, [PERSON]. [37] proposed an adaptive and compositional modelling framework to model the resilience by examining the effectiveness of the rapid-response. In addition, [PERSON]. [38] investigated the impacts of repair sequence and repair/replacement approaches regarding different macroseismic intensity by proposing a Monte Carlo simulation-based method to select search the optimal repair strategy. In [39], a novel seismic resilience assessment method for urban systems has been proposed based on post-earthquake loss (casualties and functionality loss) and recovery time by applying the analytical hierarchy process.  
Traditionally, resilience was defined at the beginning of 2000 by [32]. In addition, [PERSON]. [40] defined resilience as the ability to maintain or restore the flows, which are important ways of approaching community resilience. The traditional formulation by [23] implemented in [24] quantifies the seismic resilience as:  
\[\mathrm{SR}=\int_{\mathrm{t_{EE}}}^{\mathrm{t_{DE}+RT}}\frac{\mathrm{Q(t)}}{ \mathrm{RT}}\mathrm{dt} \tag{1}\]  
where  
\(\mathrm{t_{DE}}\) is the time of occurrence of the earthquake \(\mathrm{E}\),  
\(\mathrm{RT}\) is the repair time (RT) that is necessary to recover the original functionality,  
\(\mathrm{Q(t)}\) is the recovery function that describes the recovery process necessary to return to the pre-event level of functionality and may be represented in 1D as in Figure 2.  
Figure 1: (**a**) Failure typology 1: Cascading effect (E: Earthquake, Ii: Infrastructures). (**b**) Failure typology 2: Common cause (E: Earthquake, Ii: Infrastructures).  
In literature, different types of recovery functions were proposed and depend on many variables (such as community preparedness and available resources) with disparities among different geographic areas, in the same community or state and showing different rates and quality of recovery [41]. In particular, Ref. [23] proposed linear formulation that can be applied with no information, Ref. [42] proposed exponential, while [43] trigonometric.  
However, these formulations cannot account for the interaction of the different systems that necessarily interact each other. In other words, the definition of seismic resilience needs to consider issues that may not be easily quantified, but are often the most significant [40]. Therefore, it is important to keep in mind that seismic resilience needs a multidisciplinary approach and requires a holistic point of view. In this regard, Ref. [40] considered the lessons from the Christchurch disaster by proposing six categories: time, money, resources, governance and management, social community and business community. The conclusions insisted on the fact that community resilience needs to consider two aspects: (1) the flows between the community and its surrounding environments; and (2) the community resources (commercial, capital, human, social, physical and information) [40]. In other words, the community needs to be considered as a system with many correlated interdependencies, and thus the definition of resilience must quantify at the same time several dimensions.