The arrangement and maintenance of isolation valves are key for resilience management of water distribution systems (WDSs). As the density of isolation valves is often much lower than the desirable level in practice, addition of new valves to existing WDSs has been reported in literature. However, optimization of the placement of new valves has been based on the risk of pipe failure and the assumption of full functionality of existing valves in the prior research, which is insufficient for resilience management of WDSs against unexpected system failures. A framework built on graph theory is proposed in this study for the optimization of placement of new valves based on resilience assessment and by considering potential failures of existing valves. The framework is applied to a real-life WDS, which demonstrates its effectiveness in identifying the vulnerable sections of existing systems and the significant, non-linear impacts of valve failure in degrading system performance.