Graph-based method for analysis of multiple pipe failures in water distribution networks

Critical infrastructures such as water, power, telecommunications, and transportation systems are an important part of human life in an urban environment, which are vulnerable to disasters, failures, asset forfeiture, and sabotage. The focus of this work is on water distribution networks (WDNs) including different hydraulic elements such as pipes, tanks, valves, and reservoirs to transport drinking water from central treatment plants or sources to consumers. Thereby, efficient identification of system parts in a WDN that are vulnerable to failures is important for efficient management and to provide high reliability. Therefore, often hydraulic simulations are applied, which are computationally intensive and impractical for large networks and multiple pipe failures.

In this study, a graph theory-based analysis is used to identify the critical elements (pipes) in a WDN based on "demand edge betweenness centrality (EBC^Q)". Therefore, the connectivity of the network based on spatial layout is modelled using a mathematical graph-based approach that represents the topology of the WDN and incorporates hydraulic factors to imitate hydraulic behavior. The mathematical graph consists of #N (vertices) connected by a set of #E (edges) corresponding to nodes and pipes respectively. The ratio of length and diameter is used as edge weight to determine the shortest path, and adds the demands of the nodes to obtain EBC^Q values for all edges in that path. In case of pipe failures, the corresponding edge is removed, and the EBC^Q of the new graph is calculated and compared with the maximum possible flow to find overloaded and affected edges. Thereby, single and multiple pipe failures are investigated with this method.

The method is applied to a benchmark case study and to a real network of an Alpine municipality in Austria. Furthermore, the results of the graph-based method are compared with the results from hydraulic modelling in terms of accuracy and computational time. The first results show only slight differences in the results of the graph-based method compared to those from hydraulic modeling.  Further, the graph-based method is able to identify the same order of critical pipes with low deviation compared to those from the hydraulic model. Additionally, the computational time and data requirements, in the calculation of pipe criticality by graph-based approach is significantly less compared to the hydraulic modelling method. This method is useful in disaster or contamination scenarios where many scenarios or combinations are required.

Funding: The project “RESIST” is funded by the Austrian security research programme KIRAS of the Federal Ministry of Finance (BMF).