*4.3. Random Designs*

Finally, random designs that satisfy pressure requirements are generated from the proposed model to confirm the aforementioned conclusion. Figure 9 shows the profiles of seismic reliability and resilience of many random designs. We can clearly see that there is an inflection point around the total cost of 23 M USD and seismic reliability around 0.4, after which the overall seismic reliability decreases (Figure 9a). Because the total cost is a direct function of the pipe diameter, this plot indicates that installing large pipes does not always guarantee an increase in seismic reliability. The printed solutions are all suboptimal solutions that are dominated by the Pareto solutions found in Figure 7. On the other hand, installing large pipes resulted in an upward trend in resilience (Figure 8b).

**Figure 9.** (**a**) Seismic reliability of randomly generated solutions (**black dot**) and Pareto solutions shown in Figure 7 (**blue diamond**) and (**b**) resilience of the same random designs.

Under normal failure condition, having more additional paths and installing large pipes throughout the system are beneficial with respect to system reliability (*i.e.*, ability to supply required quantity of water) and redundancy (*i.e.*, level of pressure redundancy). However, we observed this does not apply under earthquake failures. Earthquake deforms WDS components and their original function. Once failed under earthquakes, large pipes, which can deliver large volume of water under normal condition, help accelerate water loss out of the system. This study was the first attempt to take into account such irregular hydraulic behavior in the WDS modeling and design and highlight the need to find the optimal pipe layout considering the system's performances under the two different states.
