TV WPN -Theory of Vulnerability of Water Pipe Networks Theory of Vulnerability applied to the identification of failure cenarios in water networks Demos
Theory Vulnerability Theory
In the context of this work, vulnerability has been defined as the disproportionateness of the failure consequences in relation to the initial damage. This definition is fundamental for the understanding of the TVWPN (Theory of Vulnerability of Water Pipe Networks).

Following this idea, a WPN (Water Pipe Network) is vulnerable when a small damage demand leads to a disproportionately large WPN failure.

A key concept in the proposed approach is to consider a system as a set of interacting objects. The objects are arranged in layers, connected and interacting in a specific way.

At the lowest level, a graph model represents the system in terms of nodes and links. In a WPN system, the nodes are the joints and the links are the pipelines.

The basic theoretical concepts of the TVWPN are: WPN primitive cluster (i.e. the pipelines between the adjacent nodes), WPN branch cluster (group of two or more pipes and respective nodes), WPN reference cluster (i.e. it is a storage tank (or other supply source) which is the cluster from which the WPN is separated for the total failure scenario to occur), WPN ring (i.e. an abstract way of representing a WPN), well formedness (i.e. measure of the quality of the WPN form), nodal connectivity, WPN deteriorating event (i.e. it may be the damage that results from any type of action which causes the loss of the capacity to supply good quality water to a location, it may be the collapse of a pipe line, an obstruction or even the degradation of water quality), WPN damage demand (E) (i.e. it is considered, at this stage, as a measure of the effort required to cause a deteriorating event in the WPN which is proportional to the strength capacity of a pipeline), relative damage demand (Er), separateness (φ), WPN vulnerability index (γr-).

These concepts have been defined and implemented in the TVWPN by making a direct extrapolation from the reciprocal concepts used in the structural vulnerability theory.
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