**5. Summary and Conclusions**

Earthquakes can cause many simultaneous failures of components throughout WDSs, which result in very different and severe conditions compared to normal failure conditions that water communities usually deal with (e.g., single pipe failure). In this study, an economic, cost-constrained optimal design approach of a WDS was proposed to maximize seismic reliability. The network's seismic reliability is defined as the ratio of the available supply to the required water demand during stochastic earthquakes. The physical relationship between the earthquake intensity and the WDS components' vulnerability characteristics was defined and utilized for quantifying seismic reliability. To overcome the limitation of DDA in modeling earthquake failures, negative pressures were assumed to have realistic hydraulic calculations. Then, we investigated the seismic reliability improvement with respect to the economic investment in the system and the associated topological and pipe diameter changes. A traditional benchmark network, the Anytown network, was used to demonstrate the approach. Random earthquakes around the study network were generated for reliability quantification.

The results were quite different from what we generally observed from traditional reliability-based design (e.g., resilience-based design). First, allowing redundant small pipes in the system did not help improve seismic reliability. Those pipes cause frequent failures because of their low durability to earthquake forces. Second, having too-large pipes also degrades the system reliability during earthquakes. Compared to small pipes that are 152 mm to 305 mm, a big pipe (762 mm) has a lower failure probability; however, the failure's influence is very significant to the system once it fails. The large pipe's cross-sectional area will help release more water out of the system. Therefore, the first step to efficiently improve the WDS seismic reliability should be to identify the most appropriate pipe sizes for a system. For example, from the Anytown network, having a uniform 508 mm for all pipes provides the highest system reliability of 0.38 among seven uniform designs.

This study has several limitations that future research must address. First, this model is sensitive to correction factors for the pipe and the assumption of the opening area of the pipe under failure. Intensive sensitivity analysis should be conducted with experimental studies to simulate the most realistic failure behavior of WDS components. Second, this study only considers the pipe failures while pump, valve, tank, and reservoir failure can occur during an earthquake. Therefore, various failure types could be included in future studies. The proposed semi-PDA approach and EPANet can be replaced with a PDA-based network solver in order to simulate more realistic behavior of WDS under earthquake events. Third, while this study focuses on the system's reliability right after an earthquake occurs, post-earthquake recovery strategies should also be investigated to enhance the overall WDS's reliability/resilience. This could be found mostly in the context of operation and management. Fourth, the proposed semi-PDA approach and EPANet can be replaced with a PDA-based network solver in order to simulate more realistic behavior of WDS under earthquake events. Finally, interdependencies among multiple lifeline infrastructures (e.g., the water, power, transportation, and communication systems) can help improve and recover an individual infrastructure's reliability during an earthquake. Therefore, more efforts should be made to identify these interdependencies.

**Acknowledgments:** This work was supported by a gran<sup>t</sup> from The National Research Foundation (NRF) of Korea, funded by the Korean governmen<sup>t</sup> (MSIP) (No. 2013R1A2A1A01013886) and the Korea Ministry of Environment as "The Eco-Innovation project (GT-11-G-02-001-2)".

**Author Contributions:** Do Guen Yoo and Donghwi Jung carried out the survey of previous studies, analysis of proposed method, participated in the sequence alignment and drafted the manuscript. Joong Hoon Kim and Doosun Kang conceived the original idea of the study, and helped to write the final manuscript.

**Conflicts of Interest:** The authors declare no conflicts of interest.
