Modelling of sensitivity

An elementary component is a material component for which an elementary damage function has been modelled. These elementary damage functions result from the interpretation of the answers given by the surveyed damage experts.

We define the sensitivity of an elementary component as its propensity to change state when affected by a flood.

For each elementary component, several states are defined, including at least the “normal” one, and some possible deteriorated states. By default, elementary components are considered to be in the “normal” state, which accounts for their current level of dilapidation. When a flood occurs, elementary components can be impacted, which modifies their state. Two parameters of flood intensity are considered to define the exact conditions in which a state modification occurs: the water depth and the duration of submersion. The exact conditions in which a flood modifies the state of an elementary component are defined relatively to this elementary component, not to the whole building. For instance, an electronic component is “destroyed” if the relative water depth is positive, “wet” if in presence of water that does not touch it. For some elementary components, the damage experts explained that the change of state is not certain and they defined it as a stochastic variable. For some elementary components, the damage experts also indicated a relation between the flood intensity (defined by the combination of water depth and duration of submersion) and either the probability of a change of state or the intensity of the change of state. The intensity of the change of state refers to the difference between the normal state and the deteriorated state. It is a coefficient comprised between 0 and 1. For instance, some elementary components with mechanical, electrical or electronic pieces can be slightly to highly damaged depending on the water depth.

For a given elementary component, each deteriorated state is associated to an action necessary to come back to the “normal” state. This action has some characteristics that may depend on the nature of the elementary component:

• a cost;
• a quantity of elementary components on which the action must be performed, if the elementary component can be divided into smaller parts. For instance, a quantity is indicated for the actions associated to the walls or wall coatings.

The coefficients that describe the intensity of a change of state are used to adjust the costs of the actions that need to be done to go back to the normal state by taking into account the severity of deterioration.

Elementary components that have the same sensitivity to floods but for which the costs of the actions can differ are grouped in what we call a category of vulnerability. This categorization was given by the experts. It enables the addition of elementary components on which the experts were not specifically interviewed. For instance, all electronic devices belong to the same category of vulnerability. Thus, we only need to know the replacement cost of any electronic device to produce its elementary damage function.