Resilience (engineering and construction)

The first influential quantitative resilience metric based on the functionality recovery curve was proposed by Bruneau et al.,[6] where resilience is quantified as the resilience loss as follows.

${\displaystyle R_{L}=\int _{t_{0}}^{t_{f}}[100\%-Q(t)]dt}$

where ${\displaystyle Q(t)}$ is the functionality at time ${\displaystyle t}$; ${\displaystyle t_{0}}$ is the time when the event strikes; ${\displaystyle t_{f}}$ is the time when the functionality full recovers.

The resilience loss is a metric of only positive value. It has the advantage of being easily generalized to different structures, infrastructures, and communities. This definition assumes that the functionality is 100% pre-event and will eventually be recovered to a full functionality of 100%. This may not be true in practice. A system may be partially functional when a hurricane strikes and may not be fully recovered due to uneconomic cost-benefit ratio.

Resilience index is a normalized metric between 0 and 1, computed from the functionality recovery curve.[7]

${\displaystyle R={\frac {\int _{t_{0}}^{t_{h}}Q(t)dt}{t_{h}-t_{0}}}}$

where ${\displaystyle Q(t)}$ is the functionality at time ${\displaystyle t}$; ${\displaystyle t_{0}}$ is the time when the event strikes; ${\displaystyle t_{h}}$ is the time horizon of interest.

Thomas Tredgold was the introduced the concept of resilience in 1818 in England.[8] The term was used to describe a property in the strength of timber, as beams were bent and deformed to support heavy load. Tredgold found the timber durable and did not burn readily, despite being planted in bad soil conditions and exposed climates.[9] Resilience was then refined by Mallett in 1856 in relation to the capacity of specific materials to withstand specific disturbances. These definitions can be used in engineering resilience due to the application of a single material that has a stable equilibrium regime rather than the complex adaptive stability of larger systems.[8][10]

In his paper Resilience and Stability of Ecological systems (1973), C.S. Holling first explored the topic of resilience through its application to the field of ecology. Ecological resilience was defined as a "measure of the persistence of systems and of their ability to absorb change and disturbance and still maintain the same relationships between state variables."[11] Holling found that such a framework can be applied to other forms of resilience. The application to ecosystems was later used to draw into other manners of human, cultural and social applications. The random events described by Holling are not only climatic, but instability to neutral systems can occur through the impact of fires, the changes in forest community or the process of fishing. Stability, on the other hand, is the ability of a system to return to an equilibrium state after a temporary disturbance. Multiple state systems rather than objects should b studied as the world is a heterogeneous space with various biological, physical and chemical characteristics.[12]

• Urban resilience