Underground water infrastructure is essential for life in cities. The aging of these infrastructures requires maintenance strategies to maintain a minimum service level. Not all elements are equally important for the functioning of the infrastructure as a whole. Identifying the most critical elements in a network is crucial for formulating asset management strategies. The graph theory is presented as a means to identify the most critical elements in a network with respect to malfunctioning of the system as a whole. As opposed to conventional methods, the proposed method does not rely on iterative hydraulic calculations; instead, the structure of the network is taken as a starting point. In contrast to methods applied in practise, the results are independent on the chosen test-load. Because of the limited calculation effort, the method allows the analysis of large networks that are now, for practical reasons, beyond the scope of methods applied so-far.

Drinking water distribution networks (WDNs) are a crucial infrastructure for life in cities. Deterioration of this ageing, and partly hidden from view, infrastructure can result in losses due to leakage and an increased contamination risk. To counteract this, maintenance strategies are required to maintain the service level. Information on the most critical elements of a WDN, with respect to the functioning of the system as a whole, is essential for prioritising maintenance or rehabilitation activities. In this study a Graph theory based method is developed and applied for efficiently identifying the most critical elements. The main advantage of this method is that it avoids the need to perform elaborate hydrodynamic model calculations. Instead, the structure of the network is the main starting point. The results show that the structure of the network is more decisive than the hydraulics with respect to the criticality of the system’s performance as a whole. Results depict that the suggested approach is applicable not only to the main (primary) network, but also to the capillaries which are normally beyond the scope of the traditional methods applied so-far because of the complexity of the networks and the required calculation time.

Urban drainage systems are composed of subsystems. The ratio of the storage and discharge capacities of the subsystems determines the performance. The performance of the urban water system may deteriorate as a result of the change in the ratio of storage to discharge capacity due to aging, urbanisation and climate change. We developed the graph-based weakest link method (GBWLM) to analyse urban drainage systems. Flow path analysis from graph theory is applied instead of hydrodynamic model simulations to reduce the computational effort. This makes it practically feasible to analyse urban drainage systems with multi-decade rainfall series. We used the GBWLM to analyse the effect of urban water system aging and/or climate scenarios on flood extent and frequency. The case study shows that the results of the hydrodynamic models and the GBWLM are similar. The rainfall intensities of storm events are expected to increase by approximately 20% in the Netherlands due to climate change. For the case study, such an increase in load has little impact on the flood frequency and extent caused by gully pots and surface water. However, it could lead to a 50% increase in the storm sewer flood frequency and an increase in the extent of flooding.

Urban water systems are composed of subsystems (gully pots, storm sewers and surface water), each with its own system dynamics. Engineers balance the functioning of the systems based on storage and discharge capacity of the subsystems. The load on, and capacity are influenced by e.g. ageing, urbanization, climate change. Consequently, the performance of and demand put on subsystems varies over time, potentially resulting in disturbances in the balance between the storage and discharge capacity of the subsystems. The Graph Based Weakest Link Method (GBWLM) is developed to analyse the behaviour of urban water systems to identify potential limitations due to deterioration, and/or changes in load. The proposed GBWLM is based on the structure of the networks. In addition, Graph theory is applied as alternative for series of hydraulic calculations. The GBWLM allows for an integrated performance assessments of urban water systems using multi-decades rainfall series. The results are sufficiently accurate to be able to determine the extent and frequency of urban flooding in order to compare the performance of the subsystems for various degrees of available discharge capacity. Keywords Criticality, flow paths analysis, Graph theory, linearised hydrodynamics, urban water systems, Weakest Link Method Highlights 1. Method for the analysis of urban water systems based on Graph theory 2. The use of linearised hydrodynamics in flow path analyses