Abstract
The consideration of isolation valves and segments is essential for evaluating the water service and resilience of water distribution systems when shutdowns are required under pipe failure. However, little work has been done on assessing the resilience response and intervention based on segments. This study investigates the impact of intervention (valve density and protection of critical segment) and response (recovery time and recovery sequence) on system resilience taking valve layout into consideration. An algorithm to identify segments based on the graph theory is proposed. Resilience is quantified using the satisfactory rate of the water supply demand. Critical segments are ranked based on resilience analysis. The resilience evaluation method is applied to a case study network. It is found that valve optimization can significantly reduce the number of valves without considerably decreasing the resilience performance. Valve density and the protection of critical segment can reduce the severity of pipe failure, while efficient recovery response can reduce the severity and shorten the duration of pipe failure simultaneously. The criticality of segments depends on the segment location and hydraulic interdependency among segments.
HIGHLIGHTS
The evaluation of resilience response and intervention based on valve segments is carried out for understanding the performance of water distribution systems under pipe failure.
A segment identification method is proposed to identify all segments simultaneously for visualization and resilience analysis.
Segment criticality and recovery sequence are subject to network topology and hydraulic interdependency among segments.
Graphical Abstract
INTRODUCTION
With the corrosion and aging of pipes in water distribution systems (WDSs) coupled with the impact of man-made damages or earthquakes and other natural disasters, it is inevitable that the pipes will rupture and fail, resulting in the interruption of water supply services. To maintain adequate levels of water service, water utilities should formulate preparedness to improve emergency response before disruption, and scheme to schedule repair sequence of broken pipes after their failure is detected, in which priority must be given to critical pipelines due to the limited labor forces (He & Yuan 2019).
After a pipe is broken, it needs to be isolated for repair or replacement. The broken pipe is usually modeled by changing its status from open to closed during the repair period. This assumes that there are two isolation valves at both ends of each pipe (‘N Valves’ layout where the number of valves is equal to the linked pipes at a junction), and many research methods adopted this valve configuration for simplification (Diao et al. 2016; Liu & Lansey 2020). However, due to financial constraints, the number of valves is limited in practice. That means in order to isolate a broken pipe, several adjacent valves are selected to be closed to form an isolated set of pipes as a segment, which was first introduced by Walski (1993). It is clear that the application of segment is more practical and accurate in modeling pipe failure (Walski 2020).
The regular valve placement rule is ‘N − 1 Valves’, which means the number of valves is one less than linked pipes. And there are also some general guidelines for valve placement in WDS (AWWA 1986; MOHURD 2018), for example, the Ten State Standards (GLUMRB 2012) suggests that a sufficient number of valves should be provided on water pipes to minimize inconvenience and health hazards during maintenance. The interval of valves can be different according to different clustering of water demand. Rules of thumb are often used to guide the placement of valves. For example, at least two valves should be installed at the T-joint, three valves should be installed at the cross-section, and no more than four valves should be placed for pipe section isolation.
During the early introduction of segment, segment identification is a tedious manual process. Then several segment identification methods are proposed later. The computation of topological matrix with valves was used without knowledge of graph theory (Creaco et al. 2010; Giustolisi & Savic 2010). Many other researchers used graph theory searching methods. The general way to represent a valve in a water distribution network (WDN) is by using a short link. Then node-node adjacency matrix can be constructed. Zhuang et al. (2013) used the depth-first search (DFS) method for identifying the segment, the searching process will continue until all the boundary valves of a segment are identified. Hernandez & Ormsbee (2021b) used a link-node incidence matrix to identify the segments and segment adjacency matrix to find unintended secondary isolations. Gao (2014) applied valve pair to represent the valve and improved the Warshall algorithm to compute node transitive closure sets to identify all segments at a time. Weber et al. (2020) disconnected all the valves in WDN and searched the connected components using DFS to find all the segments.
Now that the layout of valves is important, the impact of valve quantity and location on the hydraulic performance of WDS needs to be investigated. Hwang & Lansey (2021) investigated the impact of valve density on a realistic network's service metrics; they found that the number of valves can be reduced to more than 50% of N − 1 rule without significant negative impacts, and when the number of valves is similar to the pipes, good engineering judgment is sufficient for valve placement without using optimization. Some researchers also analyzed the impact of valve failure on system performance (Jun et al. 2007; Liu et al. 2017). Except for engineering experience to place valves, Giustolisi & Savic (2010) proposed the multi-objective optimal design of valve systems by minimizing the number of isolation valves and the total undeliverable demand. Creaco et al. (2010) compared different objectives for valve placement and stated that the most appropriate objective functions are the total cost of valves and weighted average demand shortfall. Giustolisi (2020) optimized isolation valves to minimize the risk of disconnection and unintended isolations of segments.
Currently, researchers have begun to evaluate the impact of segments on the performance of WDS. Liu et al. (2017) investigated the impact of isolation valves failure on segments size and demand shortfall, and they found that a higher density of isolation valves leads to less impact of valve failure. Abdel-Mottaleb & Walski (2021) developed a method to identify critical segments based on a reachability matrix without hydraulic calculations. Hernandez & Ormsbee (2021a) proposed four different performance metrics to evaluate the loss of junction demands and fire flows when segments are isolated based on the location of actual valves in a real WDS. Weber et al. (2020) proposed a segment-based vulnerability method to evaluate the vulnerability of segments and the whole WDS against a single pipe burst, and the degree distributions of the segment graph were analyzed and showed that the segment graph is close to a random graph which is robust against random pipe burst. They also found that WDSs are similar to the scale-free networks in terms of their vulnerability with some critical segments and the rest of the segments are slightly vulnerable.
Reliability (Gheisi et al. 2016), vulnerability (Weber et al. 2020) or criticality analysis (Ayala-Cabrera et al. 2019) only considers the impact of service decline after pipe failure but does not consider how the service level changes during the recovery process. More recently, resilience has gained increasing attention because resilience can directly describe the whole variation process of service capacity of WDS from failure to recovery (Figure 1). Bruneau et al. (2003) defined resilience as the size of the expected system performance degradation in quality from reduced time to recovery, which reflects the capability of the infrastructure to recover from failure to normal level from a more comprehensive perspective. It has four stages of resisting, absorbing, recovering and adapting (Shin et al. 2018; Shuang et al. 2019), among which the essential feature is recovering that distinguishes resilience from other performance indicators. The resilience of WDS can be improved by enhancing robustness, redundancy, resourcefulness, and rapidity (Lansey 2012). Zhuang et al. (2013) implemented a framework for the resilience analysis considering the impact of adaptive pump operations and isolation valve locations. Zhang et al. (2020) optimized repair scheduling of damaged pipes to improve the resilience of a postdisaster WDS. Liu et al. (2020) discussed different pipe recovery strategies in enhancing the resilience. He & Yuan (2019) took minimizing system loss as an objective to optimize scheduling repair sequence.
While many intervention measures have been proposed to increase resilience stated above, only limited studies focused on resilience evaluation, which is a basis to understand resilience and a prerequisite to enhance resilience. Diao et al. (2016) proposed the global resilience analysis (GRA) method to evaluate the resilience of WDS under different stress magnitudes (different combinations of pipe failure), but segment was not applied in pipe failure. More recently, Atashi et al. (2020) used GRA to analyze the impact of segments on the resilience of WDS based on three different isolation valve configurations (N valve, N− 1 valve, and limited valve). The change of the position of the isolation valve significantly affects the resilience of WDS. Critical pipes and sections also change with different valve configurations. Intervention measures to enhance resilience, for example, adding isolation valves in crucial parts, can be considered, but the arrangement of limited valves is only based on the rule of thumb, without any optimization measures, and the resilience recovery is simplified.
In this paper, the whole process of failure–isolation–recovery of WDS under various pipe failure stress is analyzed by considering different valve configurations. A segment identification method is proposed to identify all segments simultaneously. By visualization of the segment-valve graph (SVG), valve placement can be optimized. Resilience metrics are presented in terms of satisfactory rate of the water supply demand based on pressure-dependent analysis. The analysis of factors affecting system resilience and segment criticality are also studied. The major contribution of this study is in applying segment-valve topology for analyzing the impact of resilience response and intervention on system resilience and segment criticality.
METHODOLOGY
In the following sections, segment identification and hydraulic simulation under pipe burst are mainly based on open-source packages including Water Network Tool for Resilience (WNTR) (Klise et al. 2018) and NetworkX (Hagberg et al. 2008). The WNTR is an open-source Python package designed to help water utilities investigate the resilience of WDSs to hazards and evaluate resilience-enhancing actions. WNTR provides a flexible platform for modeling destructive events and repair strategies in WDS, including the option of simulating burst events, and low pressure in pressure-driven analysis (PDA), which are used for resilience metrics calculation in this study. The powerful function of WNTR as an open-source tool has been well applied and demonstrated in this paper. It is suggested that readers get more detailed information in this review (Klise et al. 2018).
Segment identification
When the water supply pipeline fails, the practical way to isolate the damaged pipe is by cutting off the connection between the damaged pipe section and the surrounding pipe section by closing the adjacent valves. The isolation segments can be determined by the SVG based on segment identification. SVG is widely used in valve layout and related segment analysis of WDS (Huang et al. 2020; Abdel-Mottaleb & Walski 2021). The main challenge to identify the segments is the identification efficiency, which depends on the dimension of adjacency matrix. The existing identification methods represent a valve by way of adding two new nodes and one link on a pipe, which increases the size of adjacency matrix greatly. In this paper, it is supposed a valve is placed close to one node of a pipe only by adding one new node and a short link, as shown in Figure 2. The reasons for using short links instead of valves are as follows: first, the operation is simple, which can be completed in only two steps: adding virtual nodes and short pipes, and the working properties are easy to control; and opening and closing of valves can be simulated by setting the open and closed status of short links. Secondly, it will not interfere with the hydraulic simulation compared with the simulation of real valves. The actions of real valves often affect the system performance to some extent. This kind of adverse effect can be avoided by short links, which is helpful to accurately analyze the relationship between valve arrangement and system performance. Besides, the segment identification method proposed in this paper employs open-source library, which reduces the difficulty of programming compared with some commercial software.
As shown in Figure 3(a), a simple WDS is used to illustrate the flowchart of the proposed segment identification method, and the details of the method are given as follows:
Step 1. Load water distribution network in WNTR (Figure 3(a)).
Step 2. Identify all the pipes with valves in network.
Step 3. Modify the network topology by adding one new node for each pipe with valve and one short link close to either node of the pipe as valves using the ‘split_pipe’ function of WNTR (Figure 3(b)).
Step 4. Store the modified network in adjacent matrix.
Step 5. Close all valves virtually by deleting short links in matrix automatically by setting the corresponding elements zero (Figure 3(c)).
Step 6. Identify node clusters as segments using NetworkX (Figure 3(d)).
Step 7. Traverse each segment to find all boundary valves. If only one connecting node of the candidate valve is found in the connected subgraph, it can be concluded that this valve is the boundary valve of this valve segment. While if both nodes are in the valve segment, the candidate valve is judged as not a boundary valve.
Step 8. For each valve, find the adjacent segments linked to the valve.
Step 9. Plot the SVG by setting segments as nodes and valves as links (Figure 3(e)) using NetworkX.
It is noted that all the identification procedures are executed automatically. In this paper, the location of segments can be tuned manually in order to visualize the SVG with similar space layout to the original network.
Flowchart of segment identification: (a) a simple WDN; (b) valve layout; (c) remove the valve; (d) segment partition; and (e) SVG.
Flowchart of segment identification: (a) a simple WDN; (b) valve layout; (c) remove the valve; (d) segment partition; and (e) SVG.
Optimal isolation valves design
SVG proposed in this paper cannot only be used to describe the isolation segments formed by isolation valves intuitively, but also be applied to optimize the arrangement of valves by visualizing the valve layout, especially avoiding the tree branch segments and valve redundancy.
For the tree branch segment (Figure 4(a)), both upstream and downstream segments can only be connected by routine segment between them. When the upstream region is damaged following isolation measures, the water supply service of the downstream segments will be lost entirely, which will seriously reduce the resilience of the WDS. In order to cope with this problem, this paper considers changing the location of isolated valves to increase the connectivity of segments. One solution is to have multiple connections among the different segments so that the unexpected water supply of other segments caused by an isolation in the accident site can be avoided, as shown in Figure 4(c). However, for the branch pipe network, there will inevitably be a branch segments structure. For this situation, more valves can be arranged in the distribution pipes, which can avoid reducing the regional water supply after the distribution pipes are broken and need to be isolated.
SVG optimization solutions: (a) problem of tree branch segments; (b) problem of segment with parallel valves; and (c) solution to tree segments and parallel segments.
SVG optimization solutions: (a) problem of tree branch segments; (b) problem of segment with parallel valves; and (c) solution to tree segments and parallel segments.
During the SVG optimization process, there is a very common phenomenon that the valves are connected in parallel. Some situations are unavoidable due to the loop network structure, but in some circumstances, this may be caused by the large size of segment, being that there are more valves connected between the segment and the surrounding segments, which increases the degree of maintenance difficulty. Therefore, this situation should be eliminated by changing the position of the valves. For example, as shown in Figure 4(b), it can be seen that the covered area of segment S3 is obviously larger than S2 and S1, and there are two valves between S2 and S3. Valves can be added to divide the original segment S3 into two segments to improve connectivity (Figure 4(c)).
Compared with the original valve layout, the SVG has the merits of direct viewing, and being easy to understand and to use in engineering practice for network analysis. For example, the segment graph can be built in the segment topology matrix. The degree of different segments can be calculated by summing the elements along each row or column of the matrix. It can be observed that different valve placements will have different degree distribution even if the number of valves is the same by comparison with Figure 4(a) and 4(b). Moreover, by adding more valves, the average degree of segments will increase (Figure 4(c)).
During the valve optimization based on SVG, more valves will reduce problems regarding large segment areas, parallel valves, or tree branch segments. But it is difficult to find a way to reduce the number of valves. Therefore, it is suggested in this paper that the minimum number of valves should be adopted at the beginning of valve placement, then according to the existing problems, other valve places can be determined appropriately.
Burst simulation
As a typically complex and interconnected system, the urban water supply network covers a large area, and therefore inevitably faces natural disasters and man-made destruction during operation, which leads to pipes being easily broken. The damage types are mainly divided into background leakage and burst. Background leakage is relatively small and has a lower impact on the pipe network than burst. Therefore, this paper mainly focuses on burst. In the WNTR package, burst is simulated by breaking the burst pipe and adding two unconnected junctions and a new pipe; one of the new junctions is connected to the original pipe, and the other is connected to the new pipe with the same diameter, roughness and state as the original pipe (Figure 5). This is a complete pipe destruction simulation, and water will flow out of the two new nodes. Burst parameters and duration can be set to these nodes.
In WNTR, the break point can be added to any position of the pipe, and different outlet areas can be set to simulate the damage degree of a pipe. The focus of this paper is to analyze the characteristics of the valve isolation of the pipe network, so burst position and parameters are fixed. The burst position is at the midpoint of the broken pipe, and the duration of burst is given in the case study.
Pressure-driven analysis
The traditional demand-driven analysis (DDA) simulation method supposes the nodal demands are fixed and unchanged no matter how the pressure varies. Therefore, DDA can provide reliable simulation results under normal conditions, however, under pressure insufficient conditions caused by pipe burst or other accidents, the results of DDA will deviate greatly from the actual situation.
PDA makes up for the deficiencies of DDA mentioned above, and it is based on the pressure-demand relationship that water demands are calculated as the function of pressure. PDA is very suitable for analyzing the performance of pressure insufficient WDN under different extreme damage scenarios; in addition, it can analyze different types of water demand, such as user-based water demands or burst outflow. Experience shows that the PDA simulation method is more accurate, numerically stable, effective in calculation, and apt to implement, and it is well applied in real pipe network, especially in extended period simulation scenarios (Mahmoud et al. 2017).
Resilience metrics
Resilience is used to evaluate the performance changes of WDSs facing disasters, so various resilience performance evaluation indexes can be used for resilience analysis. Zhang et al. (2020) proposed six resilience metrics to measure the resilience of postdisaster WDS, including restoration time of critical customers, rapidity of system recovery, functionality loss, average time of consumers without sufficient water service, and number of consumers without sufficient service for a given time period and water loss. Diao et al. (2016) presented different metrics for three accidents, which are demand-supply shortage for pipe failure, nodes with pressure deficiency for firefighting, and contaminated water supply for substance intrusion. Meng et al. (2018) used five resilience metrics including time to strain, duration, failure magnitude, failure rate, and severity under pipe failure; they also tried to find topological metrics of resilience, but results show that topological attribute metrics alone are not sufficient for measure resilience of WDSs. From the above studies, we can see that most resilience metrics are related to hydraulic performance because hydraulic attributes directly refer to the basic functions of WDS, which is to supply sufficient water to consumers; therefore, water supply satisfactory rate (functionality reachability) and unsatisfactory rate (functionality loss) are reasonable metrics to quantify network resilience, and they are used in this paper to evaluate the resilience of WDS. Water quality is not considered in this paper, and it can be easily incorporated in future resilience analysis. The whole process of resilience evaluation from failure to isolation and recovery is simulated in this paper. In particular, the change of water supply satisfactory rate under different valve densities is investigated. The impact of valve isolation on the segment with pipe failure and other segments is analyzed.
In the formula, SLA is the resilience loss of WDS. A is the resilience strength of the pipe network during the accident. EA is the expected resilience under normal conditions.
Among them represents the water demand in the isolated segment;
are the expected and actual water demand in the low-pressure segments, respectively.
CASE STUDY
In this paper, the Net3 pipe network in EPANET2 is taken as an example to analyze the resilience of the water supply pipe network. Net3 has 91 nodes, 115 pipes, two water sources, three water tanks, and two pumps. Hydraulic parameters of Net3 under pipe burst conditions are obtained for resilience analysis, with PDA applied to solve the burst network.
Fourteen pipes were randomly damaged when analyzing the impact of valve density, recovery duration and sequence, and preparedness measures on system resilience. In the last subsection, one pipe in each segment was randomly damaged in turn when segment criticality is analyzed with regard to resilience.
When assigning maintenance strategies, researchers have different settings for recovery time and resources. For example, Klise et al. (2017) started maintenance 12 h after the earthquake, and five people were assigned to repair pipes, two people repaired water tanks, one person repaired water pumps, and one person was responsible for firefighting. Three different standards were given to get different maintenance scenarios, and different repair times were given to each component.
In this study, although the real situation should be simulated in detail, the simplification of the complex real situation should be considered at the same time, and the repair should be made immediately after the damage. It is assumed that there is only one maintenance team, a broken pipe is repaired immediately after it is isolated, and the time spent on the journey is neglected. Since the target of this paper is only for pipelines, it does not involve other components such as water tanks and pumps.
Impact of valve density on resilience
MOHURD (2018) in China stipulates that isolation valves required for self-maintenance and accident maintenance should be considered for water pipelines. When sudden incidents such as pipe rupture and damages occur, the valves should be closed quickly to stop water supply and emergency repair should be organized (MOHURD 2013). It can be seen that when valves need to be closed under the conditions of operation and maintenance of the WDS and emergency repair, sufficient valves must be met to reduce the isolation impact on the water supply service. Walski et al. (2006) suggested that to minimize the adverse effects on the whole system and regional user service, it is necessary to install isolation valves with higher density because the higher the density of valves, the smaller the impact of isolation measures on the resilience of the WDS after pipe section damage, but the cost of valve construction and management limits the number of valves to a great extent. Therefore, it is an indispensable step to reduce the influence of the valve isolation segment on the performance of the WDS by rationally optimizing the valve layout.
Hwang & Lansey (2021) analyzed the impact of valve density ranging from 0.5 to 2 on the network performance. The results show that when the valve density exceeds 0.8, it may not be necessary to optimize the valve position. Although optimization tools can be used to improve the valve layout scheme, the incremental benefits may be small. Moreover, when the valve density is greater than 0.7, the isolation effect will be enhanced by adding valves. Atashi et al. (2020) considered the impact of limited valves with a valve density of 0.45 on system resilience. However, the above two studies did not consider the optimization of valve position for limited low-density valves. The former adopted the method of average distribution, while the latter set valves only by experience. In this paper, valve placement is improved by optimization with the help of SVG.
Figure 6 shows the original network and three different valve layouts with valve densities of 2, 1, and 0.365 corresponding to 230, 115, and 42 valves, respectively. The valve density of 2 means that valves are arranged at both ends of each pipe (‘N Valves’). The valve density of 1 is designed to arrange a valve at the end of each pipe, and the valve density of 0.365 is the optimized valve arrangement. Furthermore, the average node degree of segments is calculated by means of adjacency matrix, as shown in Section 2.2. The average degree of SVG in three cases are 2.17, 2.41, and 3.12, respectively. With the decrease of valve density, the average node degree of SVG will increase. For the valve density of 0.365, the average degree is obviously higher than that of 2.55 (Walski et al. 2006) and 2.25 (Weber et al. 2020). The possible reason is that the valve density is relatively low and optimization is not used in the two studies.
In this paper, the isolated segment is used as the unit to analyze the pipe failure, aiming to simulate and analyze system performance from damage to recovery. In order to simply analyze the impact of valve density on resilience, a short-time recovery scheme under ideal conditions is adopted. It is assumed that 14 pipes have failed when pipe burst occurred at 9:00. At 12:00, the staff simultaneously closed the valves for repair and opened after repair at 14:00. The simulation time step is 1 h, and the total simulation duration is 42 h. Finally, the resilience performances of three valve densities are obtained, as shown in Figure 7. Obviously, the smaller the number of valves, the greater the drop of the water supply satisfaction curve, which means lower the resilience performance of the WDS and more serious resilience loss.
The statistic results of three scenarios with 230, 115, and 42 valves are summarized in Table 1. The unsatisfied rates of system water supply demand in three scenarios are 19.5, 21.2, and 22.9%, respectively. Taking Scenario 1 as a reference, the number of valves in Scenario 2 decreased by 50%, and the resilience loss increased slightly by 1.7%; the valve decreased by 81.7% for Scenario 3, while the resilience loss increased only by 3.4%. Therefore, when we consider the actual situation of the pipe network, the number of valves is far less than the ideal situation. Reasonable valve optimization can significantly reduce the number of valves and save the installation cost of valves without considerably decreasing the resilience performance. In the next sections, analysis and discussions are based on the valve layout of Scenario 3.
Statistic results of Net3 under three kinds of valve density
Valve placement . | Number of valves deployed . | Valve density . | Average degree of segment graph . | Number of closed valves . | Unsatisfied rate of the water supply demand (%) . |
---|---|---|---|---|---|
Scenario 1 | 230 | 2 | 2.17 | 14 | 19.5 |
Scenario 2 | 115 | 1 | 2.41 | 35 | 21.2 |
Scenario 3 | 42 | 0.365 | 3.12 | 35 | 22.9 |
Valve placement . | Number of valves deployed . | Valve density . | Average degree of segment graph . | Number of closed valves . | Unsatisfied rate of the water supply demand (%) . |
---|---|---|---|---|---|
Scenario 1 | 230 | 2 | 2.17 | 14 | 19.5 |
Scenario 2 | 115 | 1 | 2.41 | 35 | 21.2 |
Scenario 3 | 42 | 0.365 | 3.12 | 35 | 22.9 |
Impact of recovery time on resilience
Taking the placement with 42 valves as an example, the Net3 network is divided into 26 isolated segments by the 42 valves, as shown in Figure 8. The segment graph drawn by NetworkX only has the simple connection relationship and cannot reflect its actual position; therefore, it is necessary to manually fine-tune the layout of SVG diagram to make it consistent with the real pipe network layout. It can view the SVG clearly and help to understand the impact analysis of segment resilience.
In this section, it is assumed that 14 pipes are damaged and need to be isolated for repair. Because some damaged pipes are very close to each other, it is supposed they are isolated together for maintenance convenience. Therefore, the small segments including damaged pipes merge into large segments referred to as C1, C2, C3, C4, and C5. The basic information is given in Table 2, and the layout is shown in Figure 9. It is noted that this is also the repair sequence for the five segments in this section.
Basic information of five segments
Segment . | Segment merged . | Maintenance pipeline quantity . | Number of closed valves . | Total length of pipes under 42 valves (m) . | Distance from water source (m) . | Expected demand in normal state (m3/s) . | Actual water demand after failure (m3/s) . | Output water flow in normal state (m3/s) . | Output water flow after failure (m3/s) . |
---|---|---|---|---|---|---|---|---|---|
C1 | 7, 13, 14 | 3 | 10 | 350 | 133 | 5.51 | 4.81 | 1.61 | 1.47 |
C2 | 11, 15, 25 | 3 | 11 | 325 | 244 | 2.62 | 2.35 | 1.57 | 1.41 |
C3 | 17, 18 | 4 | 9 | 162 | 382 | 6.02 | 4.25 | 0.53 | 0.41 |
C4 | 19, 21, 24 | 3 | 9 | 310 | 506 | 15.36 | 11.06 | 0.31 | 0.10 |
C5 | 3 | 1 | 2 | 349 | 234 | 1.23 | 1.093 | 0 | 0 |
Segment . | Segment merged . | Maintenance pipeline quantity . | Number of closed valves . | Total length of pipes under 42 valves (m) . | Distance from water source (m) . | Expected demand in normal state (m3/s) . | Actual water demand after failure (m3/s) . | Output water flow in normal state (m3/s) . | Output water flow after failure (m3/s) . |
---|---|---|---|---|---|---|---|---|---|
C1 | 7, 13, 14 | 3 | 10 | 350 | 133 | 5.51 | 4.81 | 1.61 | 1.47 |
C2 | 11, 15, 25 | 3 | 11 | 325 | 244 | 2.62 | 2.35 | 1.57 | 1.41 |
C3 | 17, 18 | 4 | 9 | 162 | 382 | 6.02 | 4.25 | 0.53 | 0.41 |
C4 | 19, 21, 24 | 3 | 9 | 310 | 506 | 15.36 | 11.06 | 0.31 | 0.10 |
C5 | 3 | 1 | 2 | 349 | 234 | 1.23 | 1.093 | 0 | 0 |
According to the number of damaged pipes in each segment, the isolation maintenance duration is mainly determined. In actual engineering projects, different damaged pipes are not only related to pipe diameter and damage severity, but also closely related to geographical location, weather conditions, and maintenance resources. In some practical cases, the maintenance duration of a pipe varies, so this study considers three different maintenance time plans of 1, 3, and 6 h for each pipe. And the isolation of each segment takes 3 h for all three maintenance plans. The detailed plans are given in Table 3.
Three recovery schemes with different recovery durations
Duration . | C1 . | C2 . | C3 . | C4 . | C5 . | System unsatisfied demand (m3/s) . |
---|---|---|---|---|---|---|
Short | 12–18 h | 18–24 h | 24–31 h | 31–37 h | 37–41 h | 12.60 |
Medium | 12–24 h | 24–36 h | 36–51 h | 51–63 h | 63–69 h | 23.69 |
Long | 12–33 h | 33–54 h | 54–81 h | 81–102 h | 102–111 h | 40.14 |
Duration . | C1 . | C2 . | C3 . | C4 . | C5 . | System unsatisfied demand (m3/s) . |
---|---|---|---|---|---|---|
Short | 12–18 h | 18–24 h | 24–31 h | 31–37 h | 37–41 h | 12.60 |
Medium | 12–24 h | 24–36 h | 36–51 h | 51–63 h | 63–69 h | 23.69 |
Long | 12–33 h | 33–54 h | 54–81 h | 81–102 h | 102–111 h | 40.14 |
Figure 10 shows the performance variation of different maintenance durations. Clearly, long maintenance duration results in long time duration of low performance of WDS and low level of water service (Table 3). We can conclude from these results that water companies should adopt advanced repair methods and required resources to shorten the maintenance duration and improve system resilience.
Impact of recovery sequence on resilience
On the assumption of 3 h isolation for each segment and 6 h for each pipe to be repaired, C1, C2, C3, C4, and C5, respectively, contain 3, 3, 4, 3, and 1 damaged pipes, and the corresponding isolation maintenance time is 21, 21, 27, 21, and 9 h, respectively. In this study, four different recovery sequences are compared according to the following strategies: output water quantity from segment (a), water demand within segment (b), distance from water sources (c), and combination of segment C1 as first and remaining segments sorted by water demand (d). The four recovery sequences and results are shown in Table 4.
Four recovery sequences
Sequence . | 1th . | 2th . | 3th . | 4th . | 5th . | Resilience loss rate . | Burst flow (m3/s) . |
---|---|---|---|---|---|---|---|
a | C1 | C2 | C3 | C4 | C5 | 57.38 | 26.83 |
b | C4 | C3 | C1 | C2 | C5 | 81.87 | 77.22 |
c | C1 | C5 | C2 | C3 | C4 | 62.01 | 16.69 |
d | C1 | C4 | C3 | C2 | C5 | 81.02 | 56.84 |
Sequence . | 1th . | 2th . | 3th . | 4th . | 5th . | Resilience loss rate . | Burst flow (m3/s) . |
---|---|---|---|---|---|---|---|
a | C1 | C2 | C3 | C4 | C5 | 57.38 | 26.83 |
b | C4 | C3 | C1 | C2 | C5 | 81.87 | 77.22 |
c | C1 | C5 | C2 | C3 | C4 | 62.01 | 16.69 |
d | C1 | C4 | C3 | C2 | C5 | 81.02 | 56.84 |
When carrying out isolation maintenance, the isolation of one segment will affect the water flow into or out of other segments, especially if the upstream segment is isolated, the water in the downstream segments will be cut off directly. For example, when C1 is isolated, all the downstream segments will be cut off, resulting in the phenomenon that the water demand quickly becomes zero, as shown in Figure 11(a), 11(c), and 11(d). When C2 is isolated, there is no water flowing to the downstream C3 and C4, which leads to a substantial reduction in the water satisfaction rate of the system. If downstream segments are isolated unintendedly by close of the upstream segment, the burst in the downstream segments will drop to zero, which are shown in Figure 12(a), 12(c), and 12(d). Considering this fact, it can provide a helpful reference for the reduction of system burst flow after the pipe network is destroyed, so the system burst flow is added as reference when analyzing the isolation sequence. The corresponding burst in the four recovery sequences is given in Table 4.
Among the four recovery strategies, recovery strategies based on output water quantity from segment (a) and distance from the water source (c) show better performance in Table 4. Moreover, their resilience curve trends are very similar (Figure 11). The unsatisfied rate of water supply in strategy (a) is slightly lower than that of strategy (c), but the water burst in strategy (c) is much less than that in strategy (a). The only difference between (a) and (c) is the recovery priority of C5. There is only one damaged pipe in C5. However, C5 is at the end of network, which is only affected by C1. No matter whether the remaining segments are isolated or not, they cannot lead to a cut-off of C5. Therefore, C5 in strategy (a) is repaired at the last time, so it has a long duration of water burst. C5 in strategy (c) is ranked second for maintenance, and the water burst stops when C1 starts to be separated, so the total water burst of the system in strategy (c) is greatly reduced.
However, strategies (b) and (d) show very poor performance, especially in resilience (Table 4). Both of them are based on the principle of water demand, but the only difference is the maintenance sequence of C1, which is closest to the water source and has the largest output water. In strategy (d), C1 is put first for maintenance, while strategy (b) is only based on the quantity of the water demand. Although C1 as the most important segment is repaired first, it still shows the same poor resilience as (b). But the water burst is lower than that of (b). The reason may be that C4 is located in the downstream of WDS, output flow after failure is only 0.1, as shown in Table 3. It has a small impact on other regions, even if repair priority is given to this segment, it will hardly have any beneficial effect on other segments upstream. For example, when C4 works normally again, and then it is the turn to isolate and repair C1 or C2, the downstream is still in a state of almost no water. Therefore, it is not an appropriate choice to judge the importance of segments by water demand. It will depend more on the output water volume and location of segments.
Protection of critical segment on resilience
According to the resilience analysis in Section 3.3, it can be concluded that C1 is an extremely critical area, and pipes damaged in this area will cause the significant deterioration of system resilience. Therefore, this study deems that during the design or operation and maintenance stage of the pipe network, it is necessary to increase manpower and resources to protect C1 from damage to ensure that no pipeline leaks or only slight leaks occur in this segment before the major disaster. For example, only one pipe in this segment is damaged by the disaster after the key protection compared with the original C1 with three damaged pipes. Figure 13 is obtained by hydraulic simulation; at this situation, it was found that the resilience curve of the pipe network did not suffer from the complete cut-off, and the burst flow was also significantly reduced.
Resilience and burst flow of the system after the protection of segment C1.
Therefore, in the design and operation of the pipe network in the future, reasonably adding protective measures in segments close to water sources or with large output water flow will have significant effects on reducing the damaged severity.
Segment criticality
Due to the large size of WDS, subsystem analysis is widely used for water distribution management and supply zone decomposition. Huang et al. (2017) identified critical influence regions based on transient wave propagation. In this section, we are analyzing the resilience of each segment under pipe burst in turn to investigate the criticality of different segments.
In addition to the factors of pipe burst, the emergency response after pipe burst is also one of the main factors affecting the system's resilience, which mainly includes identifying the pipe burst segment, closing the isolation valves, and repairing the failed pipeline. This study assumes that the pipe burst occurs at 9:00 am. The staff arrive at the site immediately after the pipe damage and close the isolation for maintenance at 12:00 noon. There is only one maintenance team to repair the broken pipe and the maintenance work is completed at 24:00. The total simulation time of this work is 48 h.
When we implement isolation measures for the segment containing the damaged pipe, users in the isolated segment will not be able to get any water supply service. The impact of the isolated segment on other segments will be considered, for example, it will have adverse consequences such as low pressure, or even disconnection to water sources. The impact of segments on system resilience is shown in Figure 14. The interest in the black of the histogram represents the resilience reduction caused by water cut-off in the isolated segment. In contrast, the interest in the white represents the resilience reduction of other segments induced by the low pressure of the isolated segment.
The top 10 segments with high criticality with regard to the resilience impact of the WDS are divided into three levels of I, II, and III, as shown in Figure 15. We can observe that the essential segments of the WDS are mainly concentrated on the transmission pipes connecting the water sources to the downstream Segment 22. And more specific analyses on regional resilience are as follows:
- (1)
Segment 13 has the most significant impact on the resilience of the network, which means that when the segment is damaged, it will bring severe resilience losses to itself and other segments. The reason is that it is located on the main water supply path of two water sources, and the water demand in this segment is also ample. The failure of this segment will cause consumers within this segment to lose service and lead to water shortage in the up- and downstream segments due to severe low pressure. Therefore, it is necessary to strengthen the management of Segment 13 in daily operation and maintenance to enhance the resilience of the WDS.
- (2)
It is found that segment location and topological structure are two critical factors affecting other segments. For example, as far as Segment 7 is concerned, the demand is minimal. However, it is located near the water sources and on the main water supply path, and it has a significant impact on other segments. In addition, Segments 15, 16, and 17 also have small demand, but still have a significant impact on other segments because of their complex topology.
- (3)
The segment with large demand does not always have repair priority. For example, Segment 19 has a large amount of water flowing through it and covers essential users, but it is at the end of the water supply, so it has little impact on other segments. Instead, it is restricted by upstream segments. Therefore, it can be suggested that after the WDS is damaged, early isolation and early maintenance can be adopted for routing segments, which is beneficial to reduce the adverse impact on the system's resilience.
CONCLUSIONS
This paper presents a resilience evaluation method using a segment-valve topology. An algorithm is introduced that is capable of identifying segments by taking into account isolation valves. A resilience metric is developed for use in the analysis of the impact of segments on system resilience and the interaction among segments.
The SVG is generated using the graph theory. The proposed SVG can be obtained readily with the free application instead of commercial software for real WDSs with large sizes. Compared with the valve layout in WDS, SVG has the merits of direct viewing, is easy to understand, and easy to use. SVG is used to analyze the topology of segments and the impact of the segments isolation on the system resilience. Moreover, according to the SVG, valve optimization layout is discussed in this paper.
A resilience evaluation framework of the WDS under pipe failure considering actual valve arrangement is put forward, covering four resilience stages of WDS from damage to recovery. PDA is used to simulate pipe burst and valve shutdown. The resilience metric based on the hydraulic functionality of WDS is put forward. It is found that this method can effectively analyze the resilience of the damaged water supply pipe network.
Valve density and the protection of critical segments can reduce the severity of pipe failure while efficient recovery response can reduce the severity and shorten the duration of pipe failure simultaneously.
Based on the framework for pipe network resilience evaluation, the importance of isolated segments is graded and ranked. It is concluded that the pipe network topology is also one of the crucial factors affecting resilience, except for the part with large water volume and main water supply path.
In future research, an intelligent optimization algorithm should be considered to optimize the valve layout based on the proposed segment identification method. The interaction among segments needs deep investigation to understand the hydraulic interdependency for future maintenance. Future research can expand on the current study by considering water quality in system resilience.
ACKNOWLEDGEMENT
The research reported in this paper was supported by the Key Research and Development Program of Hebei Province (No. 21375401D), which is greatly acknowledged.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.