Modelling Network Vulnerability conditions in MIKE+

Water Distribution (WD) networks are exposed to a wide range of structural, environmental and operational factors that may compromise their functionality. Among these factors are progressive aging and deterioration of pipeline materials, changes in the geotechnical and hydrological conditions of the surrounding soil, and external disturbances like construction activities nearby the WD infrastructure. These stressors increase the likelihood of pipe failures, including burst and leakages. Failures like these disrupt the service continuity of drinking water but also increase the risk of water pollution, increase water losses and can lead to major potential problems such as erosion, subsidence and ground collapse near the faulty infrastructure. 

Due to the uncertain nature of these types of failures, the evaluation of the system vulnerability must be based on mathematical model accounting the network failure distribution. MIKE+ provides a modelling technique to rank the pipes based on the importance, risk and plan accordingly rehabilitation tasks, known as the “Network Vulnerability Tool”

The Network Vulnerability Tool bases the analysis on different indicators such as, the Todini Index, the Connectivity Index, the Node Reachability Index and the Pipe Criticality Index.

• The Todini Index is a measure of how well a WD network can deal with failures like pipe breaks, pump failures or high demand conditions, basically an index of the system resilience capabilities. 

• The Connectivity Index describes if the system has sufficient alternative paths for the water to flow, if one pipe breaks can the water still go through another pipe path. A low index presumes that the system may have many dead ends, a higher value on the other side indicates that there are multiple loops. 

• The Node Reachability Index ponders if water can reach every node (user) in the network if a pipe failure occurs. The index indicates how many nodes can be supplied even after failures. If this index is low, it indicates that there are many isolated areas in the network, a higher value indicates that many nodes are connected. A high reachability indicates that the model keeps serving a large amount of people, showing how widespread a water outage can be.

• The Pipe Criticality Index gives an idea of how important each pipe in relation to the entire system response to pipe failures is. In other words, some pipes matter more than others, a pipe is critical if many users depend on it, if there are few alternatives to this pipe and/or if a failure in this pipe causes big pressure drops. 

In MIKE+ the Pipe Criticality (“C”) is computed as an average performance of these indicators: Pipe flow criteria (P1), Service pressure criteria (P2), Water demand criteria (P3), Pipe length criteria (P4) and an optional User defined criterion (P5).  Values close to one (1) correspond to optimal indicators for the first four indicators, the User defined indicator (P5) is not included in the combined indicator “C”:

       C (pipe i) = Average (P1+P2+P3+P4) (pipe i),

How to run the Vulnerability Analysis in MIKE+?

In MIKE+ this tool must be activated as the Network Vulnerability found under “Special Analysis” of the Water Distribution, see Fig. 1. 

Fig. 1 - WD Modules, Special Analysis

The Water Distribution model must run without computational or hydraulic errors under extended period conditions to analyze multiple time step levels. Within the Network Vulnerability Tool, the user is required to define the minimum service pressure, the time horizon of the analysis and the spatial extent of the network.  See Fig. 2.

These results will be available after running the analysis: undelivered flow per pipe on volume units (for all levels) Q, number of nodes with insufficient service level (SumNodes), demand or total water volume (for all levels) (SumDemand), total pipe length where the service is insufficient (SumLength), as well as the previously explained performance indicators.

The results are presented as a table and can be added to the map as additional layers.  See Fig. 3. 

Conclusion  

The following table summarizes the purpose and assessment of each index. These indicators look at different aspects of resilience in the system.  

See Table 1.  

A strong water network should have many paths (Connectivity), should reach most users after a failure takes place (Reachability), should not depend on a few pipes (low criticality) and should have extra pressure (Todini).  A reliable system will have high indexes for all these four indicators. 

The Water Network Vulnerability should provide answers to questions like:

“Do we have backups?”

“Who still gets water during failure events?”

“Which parts of the network must not fail?”

This tool provides a comprehensive framework for decision-makers to evaluate the robustness and vulnerability of water distribution networks under critical failure conditions or program which pipes must be inspected more often, which ones should be replaced first and prioritize which infrastructure must be protected.