Stochastic Design of Water Distribution Systems with Expected Annual Damages

This paper presents a stochastic design approach that quantifies the expected annual damages sustained by residential, commercial, and industrial users during low- and high-pressure hydraulic failures in a water network. The approach, which couples stochastic models of water demand, fire flow, and pipe breaks with Monte Carlo simulation, was used to solve part of the Anytown design problem. Results indicated that a significant proportion of low-pressure failures occurred during low-demand months in the last $10\text{years}$ of the planning period. The timing and spatial distribution of demands observed during failure differed significantly from the demands assumed in conventional design (maximum hour and maximum day $\text{demand}+\text{fire})$ . The results also indicated that including damages in design makes it possible to produce cost effective systems that yield a low level of expected annual damages. This gives force to framing the network design problem as a stochastic, multiobjective one to balance cost efficiency with system capacity/redundancy and provide a hedge against hard-to-anticipate temporal and spatial patterns of demand in networks.