Pipe and isolation valve failure-impact analysis and prioritization model for an urban water distribution network

The water distribution network (WDN) is a crucial infrastructure that provides safe and adequate drinking water to consumers at the tap level. It connects various demand nodes through pipelines and valves that are subject to frequent failures. Such failure leads to leakage, blockage, air pockets, cavitation, detachment, biofilm formation, faulty junctions, and corrosion (Duan et al. 2020; Guo et al. 2021). Further, failures can increase head loss, reduce water delivery, and deteriorate water quality, which leads to minimize system performance (Che et al. 2018; Beker & Kansal 2022). It can also cause water-hammer surges, which can have a negative impact on the WDN performance, operations, and the customers’ safety (Trabelsi & Triki 2020). To minimize the impact of failures on system performance, it is essential to identify and analyze the failures that have the greatest negative effect on the system. Understanding the effects of pipe and valve failures is also crucial for developing an effective maintenance program. Additionally, it is important to prioritize the most vulnerable pipes and valves in order to use limited operation and maintenance resources efficiently.

The failed pipe/segment can be isolated by closing the isolation valves surrounding the broken pipe for repair or replacement. Isolation valves serve to stop the spread of failure throughout the WDN and are essential in reducing the impact of a failure. Therefore, it is important to consider both pipe failure and isolation valves together, as they are interconnected. The failure impact can only be successfully limited to the damaged pipe if all nearby valves are operating correctly (i.e., if the reliability of the valves is 100%). However, previous research has demonstrated that valve reliability is frequently much lower (Jun et al. 2008). American utilities estimate that up to 40% of valves could become inoperable if they are not inspected, maintained, or replaced every 5 years (Baird 2011). In general, valve failure has received insufficient attention as only a few articles have focused on this issue in the past (Trietsch & Vreeburg 2005; Blokker et al. 2011; Liu et al. 2017).

The impact of pipe and valve failure is often evaluated based on system performance under failure likelihood (Jun et al. 2008; Blokker et al. 2011). However, it can be challenging to assess failure probability, as records of mean time to failure and mean time to repair are not consistently maintained or recorded. This study shifts the focus from understanding pipe and valve failure to understanding its impacts and consequences, regardless of the occurrence probability. Previous studies have used customer minute loss (CML), the average time a customer is without service, as a measure of performance to determine the most important valves (Trietsch & Vreeburg 2005; Blokker et al. 2011). Liu et al. (2017) used hydraulic performance indicators to analyze the direct impacts in the incident area and the indirect effects (in terms of pressure) under failure conditions. This study combines system characteristics (the number of isolation elements (NIE) and the number of affected customers (NAC)) and hydraulic performance (supply shortfall (SS)). These parameters are used to analyze the effects of component failure on the performance of the WDN and to evaluate the critical pipes and valves. In existing urban water distribution networks (WDN), operation, maintenance, and rehabilitation planning are essential. Previous studies have focused on prioritizing pipes for rehabilitation in WDNs, mainly based on general guidelines and empirical judgments (WRC 1989; K-Water 1995). Subsequent studies have suggested prioritization based on failure probability analysis using a degree of deterioration and regression (Kim et al. 2005; Shuang et al. 2017), economic feasibility analysis (Alvisi & Franchini 2006; Di Nardo et al. 2016), and relative importance analysis of failure (Yoo et al. 2014). Pipe deterioration and regression analysis methods are often used to estimate failure likelihood and require complex mathematical procedures based on extensive historical pipe failure data. However, obtaining such data in practice can be challenging, making it difficult to accurately assess the degree of deterioration (Așchilean & Giurca 2018). Similarly, regression and economic analysis methods also require large amounts of pipe failure data (Yoo et al. 2014). In recent years, several computer-aided software (such as Care-W by Saegrov 2005; CASSES by Cemagref 2008, and AWARE-P by AWARE-P 2012) and decision support tools (Large et al. 2014; Așchilean & Giurca 2018) have been developed for WDN rehabilitation. However, using these computer-aided software and decision support tools is costly and requires expertise, which can be a challenge, particularly in developing countries.

Several researchers have recently focused on the optimization, reliability-based design, and analysis of WDN that include isolation valves (Kim et al. 2019; Zischg et al. 2019; Fiorini Morosini et al. 2020; Giustolisi 2020). Zischg et al. (2019) used complex network analysis to evaluate and compare the valving of various WDNs by examining their dual topology. Their method enables a rapid comparison of different valve scenarios but does not offer a prioritization scheme for specific valves or segments. Hernandez & Ormsbee (2021) proposed a method for assessing segments that take into account the impact of the location of isolation valves in a WDN. In addition, a heuristic technique using graph theory concepts has been proposed to determine the optimal isolation valve placement in a WDN (Hernandez & Ormsbee 2022). However, previous research has primarily focused on identifying, designing, analyzing, and optimizing isolation valves in WDNs without ranking components or valves within the network. Only a few studies have focused on rehabilitation methods for valves.

Jun et al. (2008) proposed an approach for identifying critical valves and pipes based on its impact on the number of customers (NC). Liu et al. (2017) analyzed and suggested the prioritization of valves for replacement based on the failure effects such as supply shortages. However, these approaches rely on a single parameter, namely, the NAC or supply shortage. Abdel-Mottaleb et al. (2021) used the socio-technical attributes to identify the isolation valves. They proposed the use optimization model for this purpose. However, their method does not incorporate several important parameters and suggest any integration of proposed parameters. Overall, there are several gaps and limitations in previous studies on failure impact analysis and prioritizing pipes and valves in WDN. These include: (1) previous studies’ uses of extensive historical failure data to prioritize pipes and valves, which may not be true for future; (2) the lack of philosophy combining both pipes and valves in the analysis and its prioritization; and (3) the exclusion of both hydraulic and system property parameters in assessing the critical pipes and valves. Based on these limitations, this study proposes an impact-based prioritization model for the pipe and isolation valve repair/replacement in a WDN using the analytic hierarchy process (AHP). The proposed approach is demonstrated through a case study of a part of the Dire Dawa WDN in Ethiopia, the second-largest city in the country. The pipes and valves of the Dire Dawa city WDN are prone to failures, and its network performance is poor (Beker & Kansal 2021, 2023). The result of this analysis emphasizes the significance of pipes and valves in a network and offers a tool for decision-makers to optimize the operation and maintenance of the WDN with limited resources.

Dealing with a problem involving multiple perspectives and assessment criteria requires using aggregation techniques that can consider all the different issues at play. This problem can be addressed through multi-criteria decision-making tools (MCDT), which offer techniques to assist in decision-making in complex problems under high uncertainty and conflicting criteria. MCDT can be applied in situations involving multiple data types, interests, and perspectives (Wang et al. 2009). MCDT includes a variety of distinct approaches. The popularity of formalized decision-analytical tools for addressing complex problems has risen in recent decades. According to Tscheikner-Gratl (2016), MCDM tools can be divided into three categories: (1) value measurement models, which assign a numerical score to each alternative and weight w to each criterion to represent its importance (e.g., Weighted Sum Model, AHP); (2) Goal, aspiration, and reference level models evaluate the extent to which different options achieve predetermined goals or aspirations (e.g., TOPSIS); and (3) Outranking models, which compare each option pairwise on each criterion and determine which option has a stronger preference for each criterion (e.g., ELECTRE, PROMETHEE).

This section only includes a short overview, summary, and comparison of selected methods (AHP, TOPSIS, and ELECTRE family) that are reviewed, because these methods are well known and have been described in many publications (Tzeng & Huang 2011; Tscheikner-Gratl 2016). The ELECTRE (ELimination Et Choix Traduisant la REalite) family of outranking techniques used by 15.1% of publications regarding water and waste water (Kabir et al. 2014). It consists of seven distinct models (I, II, III, IV, A, IS, and TRI), each of which is descended from the original ELECTRE I. An outranking relation (i.e., mainly ELECTRE family) is a system for evaluating preferences that take into account three scenarios: preference, indifference, and incomparability (Govindan & Jepsen 2016). Despite the fact that it has advantages and several research works have been published (15.1% of publications regarding water and wastewater) (Kabir et al. 2014), ELECTRE has some limitations, including (a) its focus on selecting the smallest set of optimal alternatives rather than creating a ranking of alternatives from the best to the worst (Govindan & Jepsen 2016) and (b) the fact that the final results are sensitive to the vote threshold, making it unclear how to determine an appropriate threshold (Tzeng & Huang 2011).

The other MCDT (with a frequency of 1.9% (Kabir et al. 2014)) is the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method. This method involves finding a middle ground by selecting the best option that is closest to the optimal, or most ideal, solution and farthest from the inferior solution (Behzadian et al. 2012). However, both the positive and negative ideal solutions are hypothetical constructs. One advantage of using TOPSIS is that it only requires determining the weights of the various factors being considered, while the relative distances between the alternatives are based on both the weights and the range of the alternatives themselves. The disadvantage of TOPSIS is the requirement for vector normalization when addressing multi-dimensional problems (Kabir et al. 2014).

The AHP is the most used method in publications regarding water and wastewater (28.3% of publications related to water and wastewater (Kabir et al. 2014)) and is selected for this study. It is a widely applied approach for determining preferences or weights of importance for criteria and alternatives in various fields. Some advantages of this method include the ability to incorporate both qualitative and quantitative criteria, the structured decision-making process which enables traceability of the decision, and quality assurance through consistency indices. AHP has several advantages over other MCDA tools, such as flexibility, the ability to judge inconsistencies, the capability to incorporate both quantitative and qualitative factors provided through expert views, and the ability to classify them into a multi-criterion ranking (Kilinç et al. 2018). So that it was selected for this study.

Studies have suggested the automatic generation of segments and unintended isolation by applying a topological matrix using hydraulic characteristics and analyzing unintended segments in optimizing pipe rehabilitation using the valving system (Kao & Li 2007; Li & Kao 2008). In addition, Creaco et al. (2010) proposed a method for the identification of intended and unintended isolations based on a sequence of simplified hydraulic simulations. A recent study also involved the segmentation of a WDN by generating segments using WaterGEMS (Liu et al. 2017). This study adopted the automatic generation of segments and unintended isolation using the advanced WaterGEMS connectors in the 2021 version. The number of generated segments using WaterGEMS for a case study network for all four-valve configurations (explained in detail in the next section) is shown in Table 1.

The appropriate location of isolation valves near intersections of pipes is vital to improving the performance (reliability) of a WDN. As a rule-of-thumb, the location of a valve at an intersection can be categorized into two most common rules: the ‘N valve rule’ and the ‘N − 1 valve rule’ (Walski 2011). The N valve configuration involves installing two isolation valves in all pipes at both ends, as depicted in Table S1 in the Supplementary Material. In the N valve configuration, each segment contains a single pipe, and one segment is isolated from the network using two isolation valves installed at both ends of the pipeline (i.e., two isolation valves are required to separate a failed pipe). In addition to the N and N − 1 scenarios, the limited and original valve configurations are employed to assess the effects of pipe and valve failure on system performance. The limited valve configuration is based on the N − 1 valve configuration, with a few valves removed. The original valve configuration represents the actual number of valves installed in the existing WDN. Unfortunately, the actual number of valves in the case study WDN is less than the number of valves in the limited valve configuration used in this study (Table 1).

The performance of a WDN is affected by pipe and isolation valve failures, which is reflected by affected segment (Mugume et al. 2015). When an isolation valve is closed, a group of independent segments is created that is not connected to any source. The critical valve is not directly determined by the value of a performance index (PI), but rather by the change in the metric's value when the isolation valve goes from a working to a failed state. This paper utilizes system property indices and hydraulic performance indicators, such as the NIE, NAC, and SS, to analyze and quantify the effects of pipe and valve failures on system performance.

The NIE is the number of valves needed to successfully isolate an incident area (segment), representing property-related parameters and the characteristics of the segments. Isolation elements in the model can include different types of valves, such as isolation valves, pressure-reducing valves (PRVs), flow control valves, etc. In reality, pressure/flow control devices cannot be used as isolation devices, but isolation valves often accompany them. The NIE can characterize the difficulty of shutting off valves when isolating an incident part; as more isolation valves are needed to separate the problematic area, more time and cost are required for placement and operation.

SS is an indicator that quantifies the hydraulic performance response of a system to a failure event. Liu et al. (2017) defined SS as the difference between demands and water supplied for all node demands during an incident/pipe failure in the entire network. This indicator accounts for the demand that is not met when the isolated segment is out of service due to pipe failure. SS includes (1) water loss due to nodal disconnection from the source and (2) loss of water supply due to insufficient nodal pressure (Liu et al. 2017). Pressure-dependent demand (PDD) analysis measures a system's performance when some network components are abnormal. Consequently, researchers have used PDD analysis to evaluate existing WDN and pipe design (Wu & Walski 2006; Giustolisi et al. 2008; Creaco et al. 2022). Studies proposed a mathematical function that shows the relationship between outflow and pressures (Wagner et al. 1988; Fujiwara & Ganesharajah 1993; Gottipati & Nanduri 2014). In this study, the gradient approaches for the PDD model proposed by Wu & Walski (2006), integrated into the modeling framework of WaterGEMS, are used to estimate PDD.

Multi-criteria decision analysis (MCDA) is a technique that considers all variables or factors that potentially impact a problem and attempts to quantify the impact of these variables on the issue. Researchers have proposed various weighing approaches to provide weight for each PI. Among these, the Analytic Hierarchy Process (AHP), equal weights methods, least mean square, ordered weighted averaging, analytical network approach, etc., are frequently used (Wang et al. 2009). AHP is the most familiar MCDM tool for formulating weights for various comparative indexes and has been used in several WDN studies (Dwivedi & Bhadauria 2014; Ataoui & Ermini 2015a, 2015b; Kilinç et al. 2018). Therefore, AHP is selected and used to determine each parameter weight in this paper. In general, AHP involves three main steps, as described below.

The relative importance of each index is estimated using the standard scoring values proposed by Saaty (2000). The intensity scale has nine standard score values ranging from one (1) for equally important to nine (9) for extremely strong important, as shown in Table 2. Ten experts from various fields (four researchers, three practitioners or water utility operation and maintenance workers, and two assistant professors) participated in deciding the weightage of each index using the AHP method. Their opinions are gathered through online google sheet questionnaires. Experts were asked to respond to questions such as ‘how important are the indices compared to each other’ to determine their superiority among each other based on the criteria shown in Table 2. Comparison matrices (size: 3 × 3) are created and used for the further calculation to provide weights to each index.

Once the comparison matrix (priority vector) is formed, the next step is to compute the weights, which normalize the eigenvector of the matrix. In this study, priority vectors are calculated based on the judgment matrix using the geometric mean, which is reported as simple to implement (Ataoui & Ermini 2015a, 2015b). The weights determined are normalized with a scale of 0–1, as shown in Table 3.

The random index (RI) depends on the number of comparative indexes (n) and the RI from the RI table (Table S2 in Supplementary Material). For this study, the obtained consistency ratio (CI) is 0.0373, which is less than the acceptable value of 0.1 (Saaty 1980), indicating that the calculated priorities are reliable. If the CI is not approved, decision-makers' judgments must be repeated until they are consistent. Once the CI is approved, the weights reflect the importance of each index.

As shown in Figure 4, the NIE increases as the valve density decreases. In normal conditions, only a small number of valves are needed to isolate a segment, but the number of additional valves required significantly increases in the event of a valve failure. In a WDN with fewer valves, a larger number of isolation valves must be used to isolate the problematic area, which leads to longer valve operation times and a higher risk of valve failure. Table 5 displays the changes in the isolation elements for four-valve configurations in two states. On average, nearly three valves are needed to compensate for a valve failure in a limited valve configuration. Additionally, the number of valves required to isolate the failed segment in the inoperable valve scenario increases by 103% compared to the operable valve scenario for the original valve configuration (Table 5). The NIEs required to isolate a segment from the network for maintenance purposes differ among the valve configurations, and the impact of valve failure can be minimized by increasing the number of isolation valves in the WDN, as indicated by Table 5. As indicated in Table 5, the NIE is higher for the valve failure condition compared to the valve working scenarios.

The statistical results of the average NAC for all valve configurations before and after an isolation valve failure are shown in Table 6. The NAC is higher for the failed valve scenario compared to the operable valve scenario; the difference between them increases as the valve density decreases. For the original valve configuration, the NAC increased by 360 in the single valve failure state compared to the operable valve conditions (Table 6). There is significant variation in the NAC for both operable and inoperable valve conditions among all valve configurations, and the differences increase as the valve density decreases.

Additionally, the failure of the segments disconnected by these critical valves would result in a high SS in the system. However, isolating several valves on the main transmission line can lead to increased pressure variations that may cause hammer surges in the pipe. To address these issues, it is important to apply water-hammer protection methods such as installing a pressure regulator, reducing fluid velocity in the pipes, using slow-closure faucets, and implementing start-up and shut-down procedures on an existing installation.

The average values of SS before and after a single isolation valve failure are shown in Table 7 for the four-valve configuration. The results show that the SS increases as the valve density decreases. Significant variation exists in the failed valve scenarios for all valve configurations, indicating that an isolated segment when a single valve fails can have a greater impact on the WDN than operable valves. This suggests that an outage of a segment when a single valve fails can result in significantly more impact than shutting down a segment with operating valves (more than three to four times higher in this case). Table 7 shows the average SS for all valve configurations before and after an isolation valve failure. There is significant variation between the operable and inoperable states of the valve for all valve configurations. Generally, the impact of the SS increases as valve density decreases, and a smaller number of valves in the WDN may increase the risk of valve failure.

Figure 7(b) shows the impacts of each pipe failure on water customers (in terms of NAC indices) due to isolated and unintended segments. The results show that a single pipe failure can result in a significant number of pipes being out of service when the valve density adjacent to the failed pipes is too small, especially in the limited and original valve configuration scenarios (Figure 7(b)). This can cause many customers to be forced out of service. Furthermore, in the original valve configuration (Figure 7(b)), when a single pipe fails, the additional pipes in the segment are out of service. This means that the failure of one pipe in the segment can lead to the isolation or disconnection of additional pipes in the same segment. In contrast, in the N valve configuration, almost all pipes are isolated by two adjacent valves when they fail, so the impacts are limited to only the failed pipes and a small NC would be out of service, resulting in low effects on system performance

The results in Figure 7(c) show the impacts of pipe failures on the four-valve configuration based on SS. Like NIE and NAC indices, pipes in WDN have different impacts (based on SS) when they fail. The degree of impact depends on the density of valves installed near the pipe. The results in Figure 7(c) revealed that as the number of valves increases, the effects of pipe failure on SS decrease and vice versa. Therefore, for the limited and original valve configuration, when the number of valves is relatively lower than in the N and N−1 scenarios, a single pipe failure causes a high system SS in the WDN. The degree of impact depends on the location of the pipes and the number of isolation valves near the failed pipe. Additionally, the original valve configuration is more adversely affected by pipe failure compared to the other valve configurations for all indices. The impacts of pipe and valve failure can be reduced by increasing the number of isolation valves around critical pipes and valves, although this may come at the cost of additional valves and a reduction in their impacts.

To minimize their impact on system performance during maintenance, it is necessary to prioritize the order of valves and pipes, which is reflected by three indices: NIE, NAC, and SS. Further, to use limited resources effectively, it is preferable to prioritize the maintenance/rehabilitation of the most vulnerable valves and pipes. The rehabilitation priority order for individual valves and water pipes is determined using a PS, which is based on the integration of the three indices using the AHP technique.

The proposed prioritization model has the additional advantage of ranking valves as a group rather than individually, which can save time in maintenance. Grouping the valves by priority allows for efficient use of limited resources and helps prioritize maintenance/rehabilitation efforts. The isolation valves are divided into four priority groups based on their PS values. Figure 8 shows the four priority groups and their locations based on their PS. It can be seen that valves connecting the tank to the main line and located on the main pipeline are in the highest priority class for repair/replacement, as their failure significantly impacts system performance, particularly in terms of supply shortages.

Additionally, valves with high SS values, which significantly affect the final PS, are also included in the highest priority group. Figure 8 also shows that valves located in commercial and high-density population areas are included in this group. In contrast, valves located in the tertiary pipeline and regions with lower population density, particularly in residential areas, are in the lowest priority group and have the least impact on system performance. Based on the obtained PS values, it is recommended that valves in the highest priority group be given the highest priority for maintenance and repair/replacement.

In making decisions on rehabilitation for the WDN, each pipe is considered, and repairs can be prioritized based on the calculated PS. The prioritization model has two main advantages: its flexibility to local conditions and its ability to adjust criteria based on water network indices, which can improve the accuracy of WDN rehabilitation plans. The model's ability to facilitate group decision-making, including evaluating expert opinions in planning WDN rehabilitation, is another benefit. This capability allows for calculating weights for each parameter in the decision-making process.

Table 9 lists the 10 most crucial pipes that received high-priority orders for repair or replacement based on prioritization scores calculated using the AHP method. The ranking of each water pipe is determined by integrating three indices in this study. The water pipelines in Table 9 generally had high PS values due to the significant influence of the SS parameter, which had high weighting values of 0.63 according to the survey result. The impact of pipe failure resulting from high SS values contributed to the high PS values for the top 10 pipes. However, the effect of the NIE index on the final PS is relatively lower compared to the others.

This study presents a method for assessing the impacts of pipe and isolation valve failures on system performance and identifying the most critical valves in the WDN using a set of metrics. It suggests a novel approach for prioritizing pipe and valve repair or replacement. The component that causes the highest difference in system performance is recommended on the highest priority as it is the most critical one for the WDN. System performance is evaluated using three indicators, i.e., the NIE, the NAC, and the SS. Prioritization scores (PS) for each pipe or isolation valve are assessed through the integration of these three elements using the AHP. The priority is assigned on the basis of the integrated score for maintenance purposes. The following specific conclusions are made using the WDN of Dire Dawa City WDN of Ethiopia:

• The impact of any failure is less severe as more isolation valves are installed in the network, and vice versa. The trade-off between the cost of repair/replacement and the placement of isolation valves must be considered.

• Most important/critical valves and pipes are those having the source or connecting large parts of the network with a single inlet.

• The critical isolation valve and pipes are highly related to network layout and valve topology.

• In the case study, isolation valves (V19, V29, V66, V26, and V42) and pipes (P89, P109, P110, P112, P115, and P117) have the highest priority score. The failure of these valves/pipes has a significant effect on the system's performance and should be repaired/replaced in the first instance.

• The system SS is the most important parameter among the other system performance parameters (with a weight of 0.63) in finalizing the rehabilitation scenario.

This study has certain limitations as well. For example, the study considers only the single failure at a time assuming that multiple failures have low probability. The multiple link failure condition is an area of future research and will be addressed separately in some other work. Further, the study has not considered the perspective of the physics and geometry of the network which will be discussed in the future.

The authors are grateful to the Dire Dawa Water supply and Sewerage Authority (DWSSA) in Ethiopia for providing data. In addition, the first author acknowledges the support of the Ethiopia Ministry of Education for sponsoring him to pursue a Ph.D. program at IIT Roorkee.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.