4.1.3. Results for Scenario 3: Fire Flow

Figure 6 and Table 6 show the correlation between reliability indices and hydraulic measures according to the application of Scenario 3. In Scenario 3, node-assigned fire flow causes increment of flow and head loss along a specific flow path from the source to the node at which the fire occurred. As seen in Figure 6 and Table 6, overall, the correlation coefficients in Scenario 3 are less than those of the other two abnormal scenarios.

**Figure 6.** Scatter plots of Scenario 3 (*x*-axis—Reliability index; *y*-axis—Hydraulic measure). The plots highlighted in yellow show high correlation coefficient of 0.95 or higher.


**Table 6.** Correlation coefficients for Scenario 3.

Note: The values highlighted in yellow indicate high correlation coefficient of 0.95 or higher.

**Ser2 0.97 0.97 0.97** 0.91 0.90 0.88 0.94 0.92 **0.97**

Overall, the hydraulic indices (RI, MRI, and API) and mixed hydraulic index (NRI) show higher correlations (*R* values are in the range of 0.90–0.99) compared to other indices (in the range of 0.76–0.91). It is interesting to observe that RRI shows strong correlation with Red2 and Rob2 under Scenarios 1–3 (*R* values are always ranged in 0.94–0.98). It should be noted that Red2 and Rob2 measure the minimum pressure at critical nodes and RRI represents the resilience of the network while maintaining the minimum required head.

The topological indices (AD and NE), entropic index (FE), and a hydraulic-gradient based mixed index (PHRI) show relatively low correlation with the measures under the fire-flow scenario; none of them yield a correlation coefficient of greater than 0.95.
