Post-Earthquake Resilience Assessment of Water Distribution Network:

"The increased number of disruptive events have increased concerns on the resilience assessment of infrastructure systems. This paper presented a post-earthquake resilience assessment method of water distribution network (WDN) based on the extended period simulation. The post-earthquake resilience of WDN is defined as its joint ability to resist the earthquake hazards, absorb the initial damage, and recover to the normal operation. The pipe leaks and breaks generated by earthquake are modeled as emitters and virtual reservoirs, respectively. The supplied nodal flow is calculated by the WDN hydraulic model using a pressure driven demand (PDD) model. The post-earthquake recovery process is simulated by a discrete event simulation (DES) model. Under the limited recovery resources, two recovery strategies are proposed and discussed. According to the definition of the post-earthquake resilience of WDN, the post-earthquake resilience index (RI) is the accumulation of functionality from the occurrence time of an earthquake until full recovery of the WDN (shaded area in Figure 1), which can be calculated by Equation (1). At each time step, the functionality of the WDN is calculated by the percentage of the water demands that are satisfied by the WDN, and the percentage of the working pipe length. Where Qi(t) is the supplied flow calculated by pressure driven demand model at node i at time t, Qi *(t) is the demanded flow at node i at time t; m is the number of nodes in the WDN; L(t) is the sum of working pipes length at time t, L*- is the sum of all pipes length; w1 and w2 are the adjustment coefficients, w1 = w1 =0.5; t0, t1 and t2 are the time when earthquake occurred, when the functionality of the WDN recovered 90% and when the functionality of the WDN recovered 100%, respectively. The post-earthquake resilience index is calculated according to the extended period simulation of the WDN. The extended period simulation of the WDN is executed utilizing the PDD model. For each time step, the statuses of recovery crews are checked from a schedule obtained by the DES model. The statuses of pipes are also updated once they are isolated, repaired or replaced, or reopened. In the DES model, key elements include entities, variables, and events (Cagnan et al, 2004). In this study, the pipes and the recovery crews are modeled as entities, the statuses of the pipes and the crews are modeled as variables, the recovery activities (e.g., isolation, reparation or replacement) are modeled as events. Table 1 lists the entities, variables and events in the DES model. Figure 2 shows a simple example of water distribution network and its damage scenarios. In the example WDN, there are two recovery crews. Table 2 lists the illustrative activities and their time duration. As a damaged pipe should be isolated before its reparation or replacement, activity 1 should be assigned before activity 2. An activity sequence could be {1,3,2,4}, for example. The crews’ statuses changed from available to unavailable, when the activity 1 and the activity 3 are assigned to the crew 01 and the crew 02, respectively. When the activity 1 is finished, the status of crew 01 changed from unavailable to available. Repeat the above steps, until all activities are finished. The crews schedule is shown in Table 3. Under limited resources, the recovery activity sequence plays a crucial role in WDN recovery process (Ouyang et al, 2012). Two types recovery strategies of the activity sequence are proposed: 1) the activity sequence is determined according to the pipe hydraulic importance. 2) the activity sequence is determined according to an optimization model, in which the optimization goal is maximum the post-earthquake resilience index, the optimization variable is the activity sequence, and the genetic algorithm is used to solve the optimization model."