Resiliency evaluation for the water distribution system considering earthquake scenarios for Indian case studies Open Access

Water distribution systems (WDSs) are made up of pumps, tanks, reservoirs, pipelines, and other components. All these components of the water distribution network (WDN) are susceptible to natural disasters and other human activities (Klise et al. 2017a). Earthquakes are the most dangerous natural disasters that can impact every part of a water system, from damaging underground pipes due to short-wave, higher-frequency earth motion to tank collapse caused by ground motion caused by a long wave frequency (Gholikandi et al. 2009; Choi & Kang 2020). Not only does an earthquake induce permanent ground movement but it also seriously damages underground pipes and the foundations of vital water systems. Water pipelines were typically not made to withstand the effects of earthquakes when they were first installed. The impact can range from minor leaks to catastrophic ruptures, leading to water contamination and loss of service. Repairing damaged pipes poses significant challenges due to factors such as the accessibility to affected areas, limited resources, and the complexity of the network.

The seismic analysis of WDNs heavily relies on peak ground velocity (PGV) for assessing the seismic vulnerability of underground pipelines. This dependence arises because the maximum horizontal strain induced in the soil by seismic waves is directly linked to the horizontal PGV (Bommer & Alarcon 2005). Various empirical studies have established robust correlations between the repair rate (RR) of pipelines during earthquakes, typically measured as repairs per kilometer of the pipeline, and PGV (Isoyama et al. 2000). The peak ground acceleration (PGA), affecting these structures is determined using equations that account for seismic wave attenuation. The facility will cease to function effectively and will be considered as having been destroyed. According to the ALA (American Lifelines Alliance (2001a, 2001b), the damage levels for water distribution pipelines are defined based on specific PGA and PGV thresholds. Marleni et al. (2022) developed a seismic vulnerability index for WDN.

PGA is a critical seismic parameter that measures maximum earthquake-induced ground shaking. High PGA can damage WDN, causing leaks, breaks, and service interruptions, affecting the water supply. Understanding and assessing PGA levels is essential for designing resilient systems in earthquake-prone areas, ensuring network durability. PGV is also vital in an earthquake's impact analysis on WDNs because it quantifies the speed of ground motion, offering insights into potential damage (Klise et al. 2017a). Using PGA, PGV, and RR evaluation data, Klise et al. (2017a) used a water network tool for resiliency (WNTR) determination of drinking water systems to disaster. Understanding and incorporating PGV data enhance network resilience and earthquake preparedness. The structural integrity of repaired infrastructure adds another layer of difficulty of restoring the water supply network to its original function demands, comprehensive planning, substantial resources, and efficient execution to mitigate the long-term consequences on public health and infrastructure resilience. Various methods have been adopted in past studies to evaluate the resilience of WDN based on damages, serviceability, and repair strategies of the water supply network after the earthquake impact (Klise et al. 2017a). Pitilakis et al. (2011) explore the systemic seismic vulnerability and risk analysis of urban systems, lifelines, and infrastructures. SYNER-G, the methodology employed, accounts for various factors including ground shaking intensity, geotechnical hazards like liquefaction-induced lateral spread, settlement, slope displacement, and fault rupture, as well as transient ground strain. Notably, stochastic seismic scenarios are integrated into the analysis to evaluate the systemic vulnerability of lifeline systems, such as WDN, by incorporating spatial correlation and cross-correlation of intensity measures across diverse locations. However, SYNER-G does present limitations, particularly concerning the transferability of its numerical simulation approach due to computational complexity, model intricacy, and the confined range of scenarios considered.

Zhao et al. (2015) presented a framework that compares the effectiveness of pipeline ductile retrofitting and network meshed expansion in enhancing resilience, providing valuable insights for decision-makers in the field. Yoon et al. (2018) proposed a comprehensive framework for assessing the seismic risk of urban WDN, including the estimation of ground motion and the evaluation of seismic fragility curves for different network components. Yoo et al. (2016) suggested an optimal layout for WDNs based on seismic reliability, defined as the ratio of available water quantity to the required demand during stochastic earthquakes. Massoud Tabesh et al. (2019) studied the risk analysis and management of WDNs in the face of earthquakes, modeling pipeline damage from seismic wave propagation and introducing a novel index to illustrate the impact of repairs on nodal pressures. Pasic et al. (2021) introduced eFRADIR-III, a framework for disaster resilience in communication networks, which builds upon previous models by incorporating advanced algorithms. Nikolopoulos et al. (2022) introduced a stress-testing framework for urban water systems that employs a source-to-tap approach for assessing resilience. Choi & Kang (2020) investigated the influence of valve layout on system serviceability during seismic damage restoration in WDN, identifying effective restoration strategies. Marasco et al. (2021) provided integrated platform to assess seismic resilience at the community level. Mazumder et al. (2021) explored into the critical realm of pipeline failure risk analysis, pioneering the utilization of data-driven ML algorithms as a promising alternative to traditional physics-based methodologies. Deploying a repertoire of ML algorithms, Mazumder et al. (2021) explored their efficiency in classifying pipelines according to their likelihood of failure. Fan & Yu (2022) proposed a reinforcement learning model to optimize the restoration sequence of WDN post-earthquake, considering evolving water demands and consumer needs. A few research gaps are identified after the literature review: (1) Existing methodologies lack in developing a comprehensive approach that integrates detailed seismic parameters modeling, fragility analysis, and resilience assessment, specifically tailored for WDN. (2) There is a lack of methodologies that provide detailed simulations of earthquake scenarios to accurately assess the impact on WDN. (3) Current approaches lack the use of fragility curves that reflect the vulnerability of WDN components to seismic events. (4) Lack of comparative analysis of earthquake impact WDN in different regions. (5) No applications in real case studies of Indian scenarios.

The main aim of the study is to assess the resiliency of WDSs to natural hazards like earthquakes in Indian scenarios using WNTR. Dawood et al. (2020) examined the realm of AI applied to the modeling of water pipe deterioration mechanisms, aiming to provide a thorough review of existing methodologies while charting out pathways for future research endeavors. Leveraging ML methods like ANN and Fuzzy Inference Systems, their study improved in water distribution network. Doorn (2021) delved into the realm of AI within the water domain, aiming to uncover avenues for its responsible deployment. Employing a systematic review methodology utilizing the ISI Web of Knowledge, Doorn (2021) meticulously sifted through a myriad of literature to pinpoint AI applications within water management while concurrently scrutinizing the ethical underpinnings intertwined with such endeavors. Earthquake scenarios are considered since WDSs are highly susceptible to damage. The impact of earthquakes on WDS is analyzed based on earthquake parameters, such as PGA and PGV and the number of pipes that need to be repaired per length of pipe. The damaged state of pipes in WDN is analyzed using a seismic fragility curve. The methodology and software used in this study are suggested by Klise et al. (2017a) which involves four steps: (1) To simulate earthquake scenarios by assigning hypothetical earthquake parameters including location, magnitude, and depth, based on historical earthquake data and proximity; (2) To apply appropriate ground motion prediction equations for determining PGV, PGA, and RR for various scenarios; (3) To generate the pipe fragility curve; (4) To utilize the fragility curve and PGA values to determine the major and minor damages of WDN components. Finally, the resiliency of WDN before and after the earthquake is calculated using the Todini resilience index (RI) against the earthquake.

In India, the effect of earthquakes on the WDN is a serious issue. Seismic events have a great impact on the water infrastructure. As a result, it creates disruptions in services and the cleaning process of water. When looking back at previous earthquakes, it is critical to understand the differences between earthquake intensity and magnitude – two concepts that are sometimes misinterpreted. The length of the earthquake is a measurement of the earthquake's magnitude that represents the elastic energy it released. A specific actual value on the Richter scale is used to identify it (e.g., magnitude 6.5 earthquake). The Indian seismic code (IS:1893-1984) categorizes regions into five seismic zones based on various aspects of ground motion such as ground acceleration, velocity, shaking duration, and frequency content. These zones, labeled I through V, correlate with different levels of seismic intensity on the MMI scale: from V or lower in Zone I to VI, VII, VIII, and IX or higher in Zones II through V, respectively. Millions of people in India's mountainous regions are at risk from high rates of seismic activity caused by the geodynamics of India's northward convergence beneath Eurasia. For this reason, Zone IV or V on the seismic hazard zone map designates northeastern and northern India. Large earthquakes (a magnitude of 7 or higher) that cause fault displacement can rupture the ground surface, but these ruptures also cause strong ground shaking, which can have secondary effects that damage infrastructure and cause earthquakes, which frequently cause more damage and fatalities. Water systems, which include pump stations, treatment facilities, tanks, reservoirs, and pipes, are all vulnerable to earthquakes and landslides. All parts of a water system are susceptible to earthquake damage, ranging from low-frequency shaking from farther away sources to tank collapse caused by high-frequency, brief period ground motions that break above-ground pipes. Currently, no study has been performed in Indian scenarios to determine the resiliency of WDSs to natural hazards such as earthquakes by modifying the code of WNTR. Two practical case studies are considered to evaluate the resiliency of WDSs of the National Institute of Technology (NIT) Kurukshetra, Haryana, and Bhuj, Gujrat, India, considering the vulnerability of WDSs to earthquake scenarios. Furthermore, the resiliency of WDN is evaluated before and after earthquake simulations which calculate the damage state of each pipe. After the earthquake, nonfunctional pipes are removed and RI is again calculated. For the NIT and Bhuj network, it is observed that the distance to the epicenter and earthquake parameters, such as magnitude, depth, epicenter, and interconnection of nodes and pipes of the network play an important role in estimating the severity of the damage. Furthermore, it is observed that the closer the location is to the earthquake's epicenter, the more the WDN's resilience is reduced. These changes indicate significant damage and reduced ability of the network to maintain water pressure and supply, emphasizing the need for a strong infrastructure in earthquake-prone areas.

• 1. Peak ground velocity: The PGV is the velocity of the seismic waves generated below the ground surface in m/s.

• 2. Peak ground acceleration: The PGA is the acceleration of the seismic waves generated below the ground surface. It is represented as the multiplier of acceleration due to gravity (9.81 m/s²).

• 3. Repair rate: RR is defined as the number of pipes to be repaired per kilometer length of pipe which is typically measured as repairs per kilometer of the pipeline.

• 4. No damage: This level signifies that the water distribution pipelines undergo no significant damage. The PGA limit for no damage is typically below 0.1 g (where ‘g’ represents the acceleration due to gravity), and the PGV limit is generally less than 2 m/s.

• 5. Minor damage: Minor damage signifies some structural impairment to the pipelines, such as leakages or cracks on the pipeline surface, but they are in working condition and no need for the replacement of pipelines. The PGA threshold for minor damage ranges between 0.1 and 0.2 g, while the PGV limit is typically in the range of 2–5 cm/s.

• 6. Major damage: Major damage indicates the failure of the water distribution pipelines, including leakages and breakages of the pipelines. The PGA threshold for the major damage is usually above 0.2 g, and the PGV limit exceeds 5 cm/s.

WNTR is a Python-based package designed for simulating and analyzing the resilience of WDNs (Klise et al. 2017a). It offers extensive capabilities to create, modify, and simulate water networks, particularly focusing on resilience and response strategies under various disruptive scenarios. WNTR features are as follows:

• (1) Model generation and modification

• • • Creating models: WNTR allows users to generate water network models either from scratch or by importing existing EPANET-formatted network input files (INP files).

  • • Editing models: Users can modify network structures by adding or removing components (e.g., pipes, pumps, and tanks) and altering component characteristics, such as size, roughness, or operational settings.

• (2) Simulation of disruptive incidents:

• • • Incident scenarios: WNTR can simulate various disruptive incidents, such as the damage to infrastructure components (tanks, valves, and pumps), pipe leaks, power outages, and contamination events. This helps in understanding the impact of such incidents on water distribution.

  • • Response and repair: The tool includes the ability to add response strategies, such as leak repair, retrofitting pipes, power restoration, and the use of backup generators. These simulations help in planning and optimizing repair and mitigation strategies.

• (3) Hydraulic and water quality simulation:

• • • Hydraulics: WNTR can perform pressure-dependent demand and demand-driven hydraulic simulations. This flexibility allows for accurate modeling under various operational conditions, including low-pressure scenarios.

  • • Water quality: The tool also supports simulations related to water quality, including the spread of contaminants through the network, helping to assess the safety and security of water supplies during and after incidents.

• (4) Probabilistic simulations and resilience metrics:

• • • Fragility curves: WNTR uses fragility curves to model the probabilistic failure of network components under different stress conditions, such as earthquakes or severe weather events.

  • • Resilience assessment: The tool computes various resilience metrics, including hydraulic, water quality, security, and economic metrics. These metrics provide a comprehensive view of the network's ability to withstand and recover from disruptions.

  • (5) Integration and custom analysis:

  • • Python ecosystem: WNTR is compatible with several scientific computing packages in Python, such as NetworkX, Pandas, Numpy, Scipy, and Matplotlib. This integration allows users to perform custom analyses and visualize the results effectively.

  • • Interactive graphics and animations: The tool can generate interactive graphics and network animations, aiding in the visualization and communication of simulation results.

  • (6) Applications in different scenarios:

  • • Disaster scenarios: Defining and simulating disaster scenarios, such as power outages and pipe leaks, to study their effects and develop mitigation strategies.

  • • Stochastic simulations: Running stochastic simulations to understand the range of possible outcomes and their probabilities is crucial for risk assessment and planning.

The EPANET software was used to create the input file of the WDN model of the study area with all the components, such as nodes, pipes, and tanks. For the nodes, the elevation and base demands at each node are introduced. Similarly, for the pipes, diameters, lengths, and coefficient of roughness, and for the tanks, the data, such as maximum and minimum water level, diameter, and minimum volume, are incorporated. The backdrop image was georeferenced using geographic information systems (GIS) coordinates of WDN components to obtain the actual Universal Transverse Mercator (UTM) which is to be used for the simulation of earthquake scenarios.

• 2. Simulate earthquake scenarios

An earthquake's location, magnitude, and depth are assigned in a pre-planned hypothetical scenario. The values for these attributes could be selected at random or, as in this study, according to the understanding history of previous earthquakes and their distance. In this study, a tool WNRT is used to simulate an earthquake scenario.

• 3. Model seismic wave attenuation

The next step is to assign appropriate ground motion prediction equations (Equations (2) and (3)) to describe the weakening of seismic waves. The primary factors considered in this step are topography, location, and the characteristics of the simulated earthquake. Then expressions for PGV, PGA, and RR values for various scenarios are entered which are distributed over the length of the pipes and calculated for every scenario. The PGV, PGA, and RR variations along each pipe are generated using Equations (2)–(4), respectively.

• 4. Generation of a pipe fragility curve

A pipe fragility curve was generated to evaluate the damaged state of pipes in the WDN in the study area based on the PGA and RR.

• 5. Assess damage along WDN pipes

Using the fragility curve and PGA values, the damaged state of WDN components was generated along the length of the pipe of the WDN: major, minor, and no damage.

• 6. Seismic resilience analysis of WDN

In the next step, repair strategies are adopted by assuming many crews, members per crew, and time to fix one leak.

• 7. Steps for earthquake impact evaluation

• • •

    Distance to epicenter – Based on the assumed epicenter, the distance of each pipe from the epicenter (R) values is calculated using the WNTR python package. Assuming that the earthquake occurs in zone IV of the seismic region in India which has an average magnitude of the intensity of the earthquake (M) and thus assumed as ‘7’.

  • •

    Calculation of PGA and PGV – Considering the values of distance to the epicenter (R) and assumed M in Equations (2) and (3), PGV and PGA of each pipeline of WDN are evaluated.

  • •

    Calculation of RR – Considering the evaluated PGV of each pipe, the RR of pipes of WDN, due to the earthquake impact, is evaluated using Equation (4).

  • •

    Damage state of the components – Using the PGA and fragility curve generated by WNTR, the damage state is determined by selecting a uniform random variable which can be used to assign the damage state for the PGA of each pipe. The damage states are classified as major, minor, and no damage.

  • •

    Calculation leakage demand – The leakage demand is calculated by generating leak holes in the pipes for each major and minor damaged pipe in the center of the pipes. The leak hole diameters for majorly damaged and minorly damaged pipes are 25% of the pipe diameter and 10% of the pipe diameter, respectively.

  • •

    Calculation of RI – The RI of the WDN before earthquake impact is calculated. By using the damaged state of pipes results, the unfunctionable pipes are removed and the RI is evaluated for the WDN after an earthquake impact.

Based on the repair strategy and the damaged state of the components, the leakage demand and Todini reliance index of the WDN over time were obtained. Using Todini RI, the resiliency of WDN before and after an earthquake will be calculated to evaluate the resilience of WDN against an earthquake.

Using the WNTR, the resiliency of WDS is determined by simulating the effects of earthquakes on WDS, considering variables such as system integrity, earthquake magnitude, available resources, and repair tactics. The fragility curve is generated using WNTR and is then used to predict the major and minor damages in the components of WDN. Earthquake scenarios are simulated with hypothetical parameters, applying ground motion prediction equations, and generating pipe fragility curves; they evaluate WDN components' damage and resilience against earthquakes.

Ground motion is the reason for the WDN's post-earthquake damages. To estimate damages to a WDN, fragility curves, defined in terms of ground motion functions, are frequently utilized (Klise et al. 2017a). In this case, fragility curves are statistical instruments that forecast the likelihood that, in the event of a seismic excitation, a component will reach or surpass a specific damage state. Tanks, pumps, and pipes are examples of WDN components that may have varying degrees of damage, such as major, minor, and no damage at all. A particular kind of fragility curve, called an empirical fragility curve, can be created using a sizable database of earthquake features and their damages to WDN components. The fragility curves shown in ALA are an illustration of this kind of curve (ALA (American Lifelines Alliance 2001a, 2001b)). PGV and RR are employed to estimate the damages to underground pipes, while PGA is utilized in the case of tanks and pumps. Pump failure and leaks in tanks and pipes are examples of damage to network components. Fragility curves are used to define the risk of damage for each tank, pump, and pipe. Four damage states are included in the fragility curves for tank leakage diameter; for moderate it was 0.05 m, severe was 0.25 m, very severe was 0.5 m, and extreme it was 1 m. For pipelines, minor damage denoted a severe leak whose leak diameter ranges between 0.01 and 0.05 m and a major leak whose leak diameter ranges between 0.05 and 0.15 m. Leaks are placed to the pipe's midpoint and limited such that they would not fill more than 75% of the pipe's diameter (Klise et al. 2017a).

Leakage modeling holds significant importance in the analysis of WDSs, and the WNTR presents a comprehensive approach to tackle the dynamic changes resulting from leaks. Substantial alterations in network hydraulics, stemming from leaks, can significantly affect system efficiency and water loss. WNTR offers a sophisticated platform to explicitly model water loss due to valves. The toolkit employs a flexible strategy to simulate leaks occurring at various points within the distribution system, from the moment a leak initiates until the affected area is isolated by repair crews. This segments the pipe into two parts and introduces a junction between these newly formed pipe segments. In the case of pipe breaks, the original pipe is replaced with two new junctions, each associated with a leak. Two additional pipes connect these junctions to the network, but notably, they remain unconnected, preventing any flow between the originally linked junctions as per the original pipe configuration.

The network consists of 113 junctions with specific demand patterns. These junctions are all at an elevation of 251 m mean sea level (MSL) and demands ranging from 0.144 cubic meters per day (CMD) (e.g., J38) to 16.884 CMD (e.g., J17). It consists of two tanks. One tank is located at an elevation of 24 m from ground level, with an initial water level of 3.1 m, a minimum level of 3 m, and a maximum level of 3.2 m. It has a diameter of 7.72 m and a minimum volume of 150 m³. The other tank is located at an elevation of 20 m from ground level, with an initial level of 3.3 m, a minimum level of 3 m, and a maximum level of 3.5 m. It has a diameter of 9 m and a minimum volume of 225 m³. These pipes connect the junctions and the storage facilities with varying lengths and diameters, ensuring efficient water distribution. For example, Pipe L1 connects J1 and J2 with a length of 145.25 m and a diameter of 100 mm. The largest pipe mentioned, L10, connects J8 to J112 with a diameter of 300 mm and a length of 26.94 m. The layout of the NIT Kurukshetra network is shown in Figure 3.

Distance to Epicenter – The epicenters from USGS historical data shown in Table 1 are far away from the WDN of NIT. Because of this reason, three epicenters are selected hypothetically for the analysis based on the distance from the NIT Kurukshetra such as 2.5, 5, and 7.5 km, respectively. Other earthquake parameters are kept the same for every epicenter which is the depth of focus (10 km) and magnitude (M_w = 7). Based on the assumed epicenter, the distance of each pipe from the epicenter (R) values is calculated using the WNTR python package. The spatial representation of the distance to epicenter is shown in Figure 4.

• (1) Calculation of PGA and PGV

Using the values for the distance to the epicenter (R) and the assumed magnitude (M) in Equations (2) and (3), the PGV and PGA for each pipeline in the WDN are evaluated and are shown in Supplementary Figures S1(a) and S1(b), respectively, for the simulated earthquake.

• (2) Calculation of RR

Based on the evaluated PGV for each pipe, the RR of WDN pipes due to earthquake impact is calculated using Equation (4). The RR of the WDN of NIT Kurukshetra is shown in Supplementary Figure S1(c) ranging from 0.00032 to 0.00035 repairs/m.

• (3) Damage state of the components

Using the PGA and fragility curve generated by WNTR, the damage state of each pipe is determined by selecting a uniform random variable, which helps to assign the damage state for the PGA of each pipe. Damage states are major, minor, or no damage. A total of 16 pipes are found to have minor damage, and four pipes are found to have major damage. Supplementary Figure S1(d) shows the damaged state of NIT Kurukshetra.

• (4) Calculation leakage demand

The leakage demand is determined by creating leak holes in the center of each major and minor damaged pipe and is shown in Supplementary Figure S1(e), which illustrates the leakage demand of the WDN of NIT Kurukshetra. Repairs are assumed to begin 5 h after the earthquake and are completed within 80 h.

• (5) Calculation of RI

The RI of the WDN before the earthquake impact is calculated. Using the damaged state of pipes, nonfunctional pipes are removed, and the RI for the WDN is evaluated after the earthquake impact. The RI values before and after the earthquake for major and minor damaged pipes of the WDN of NIT Kurukshetra are calculated.

The results of WDN of NIT Kurukshetra Network are given in Table 2.

• 1. The distance to the epicenter

Figure 4 illustrates how far earthquake shock waves traveled to reach various components. These simulations help us understand how the waves impacted a complex network structure by depicting the spatial distribution of PGA and PGV for a specific earthquake scenario. Fragility curves for pipes are employed to determine the level of damage based on the PGA value. This information assists in identifying the damaged state of each pipe, facilitating decisions on repair or replacement during post-earthquake maintenance. The RR of pipes within the WDN increases progressively from the epicenter's location, as observed from the simulated results. Through component simulation, it becomes possible to identify major and minor damages based on the damage state of the components. Following the earthquake, it is assumed that the repair crew took 5 h to identify damaged components. Damaged pipes in a minor state are repaired, while those significantly damaged are replaced.

• 2. PGA and PGV

PGA and PGV are critical parameters in understanding the seismic impact on WDN pipelines and are shown in Supplementary Figures S1(a) and S1(b), respectively. PGA values range from 0.435 to 0.450 g, while PGV values range from 1.35 to 1.45 m/s. Higher PGA and PGV values generally indicate more severe ground shaking and potential for pipeline damage. For example, Pipe L93 experienced a PGA of 0.445767 g and a PGV of 1.397602 g, which are among the highest values recorded, suggesting significant ground motion at that location.

• 3. Repair rate

The RR of pipelines (Supplementary Figure S1(c)) is directly influenced by both PGA and PGV. According to the results, higher PGV values are associated with increased repair rates. For instance, Pipe L93 with a PGA of 0.445767 g and a PGV of 1.397602 g has an RR of 0.000337497, indicating substantial stress on the pipeline due to seismic activity. Conversely, pipes with lower PGA and PGV, such as Pipe L1 (PGA = 0.432819 g, PGV = 1.310746 m/s), have a lower RR of 0.000316519, indicating less damage. This correlation suggests that both PGA and PGV must be considered when assessing the vulnerability and repair needs of pipelines after an earthquake.

• 4. Damage state

Analyzing the relationship between RR, damage state, PGA, and PGV provides a comprehensive understanding of earthquake impacts on pipelines. Pipelines with higher PGA and PGV values typically show higher RR and more severe damage states. For example, Pipe L13, with a PGA of 0.438955 g and a PGV of 1.350681 m/s, has an RR of 0.000326163 and a damaged state classified as a major leak. This contrasts with Pipe L3, which has a PGA of 0.433364 g and a PGV of 1.314212 m/s, resulting in a lower RR of 0.000317356 and a minor leak damage state. The simulation shows that even slight increases in PGA and PGV can significantly impact the RR and damage severity. Pipes L30, L31, and L34 have approximate PGA values of 0.440 and PGV values of 1.360 and show higher RRs as 0.000328777, 0.000328534, and 0.000328213, respectively, and minor leak damage states.

• 5. Leakage demand

The leakage demand (Supplementary Figure S1(e)) is associated with major and minor damage to the pipe. The colored lines represent the leakage in damaged pipes in WDN after the earthquake. A list of leakage demands of each major or minor damaged pipe is generated in order to prioritize the repair or replacement of pipelines in WDN. The earthquake impact simulation of the WDN reveals significant data on leakage demand in relation to PGA, PGV, RR, and damage states. Among the analyzed pipes, various levels of damage and subsequent leakage demands are observed. Pipes L132 and L137 experienced major leaks with corresponding PGA values of 0.454015 and 0.453720 g, resulting in high leakage demands of 1.233814 and 1.229550 m³/s, respectively. In contrast, most of the pipes, such as L3, L4, L30, L31, and others, suffered minor leaks with lower PGA values and consequently lower leakage demands ranging from 0.086355 m³/s to 0.541939 m³/s. RR varied across the pipes but generally remained consistent within minor or major leak categories. This simulation underscores the critical impact of seismic events on WDN, emphasizing the need for targeted mitigation strategies based on specific pipeline vulnerabilities identified through such analyses.

• 6. Todini resilience index

Before the earthquake, a WDN had an RI of 0.032663. After the earthquake, the RI values decreased at different locations, depending on their distance from the epicenter. At location 1, 10 km away, the RI dropped to 0.022648. At location 2, 5 km away, it further decreased to 0.02233. The biggest drop was at location 3, only 2.5 km from the epicenter, where the RI fell sharply to 0.00507. This shows that the closer the location is to the earthquake's epicenter, the more the WDN's resilience is reduced. These changes indicate significant damage and the reduced ability of the network to maintain water pressure and supply, emphasizing the need for strong infrastructure in earthquake-prone areas.

The WDN of Bhuj City is shown in Supplementary Figure S2 which is used to calculate the resilience of WDN considering earthquake scenarios. Google Earth Pro was used to get the backdrop image to design a WDN for the analysis. The UTM coordinates of the backdrop image of Bhuj City can also be extracted from Google Earth Pro to simulate the WDN for the Bhuj earthquake. There are 116 junctions (e.g., J1–J116) in the network with elevations ranging from 92 to 102 m MSL. The network includes two tanks (T1 and T2). The system is interconnected by 196 pipes, such as L1 to L196. All pipes are listed as open, ensuring full operability in the simulation. The location of the epicenter was noted with a latitude of 28.36° N and a longitude of 70.28° E with depth of focus of 24 km and a magnitude of Mw 7.7, as per the India Meteorological Department (IMD). The epicenter of the earthquake was located approximately 10 km northeast of Bachau City in the Kutch district of Gujarat, with a focal depth of 24 km by the IMD. The impact of the earthquake was felt in Kashmir in the north, Kanyakumari in the south, and Nepal and Calcutta to the northeast. Among the worst-hit areas were Bachau, Bhuj, Anjar, Rapar, Gandhidham, and Kandla City in the Kutch district.

• (1) Distance to epicenter – The location of the epicenter was noted at a latitude of 28.36^o N and a longitude of 70.28^o E with a depth of focus of 24 km and a magnitude of 7.7, as per the IMD. Supplementary Figure S3 illustrates the distance from the epicenter of the earthquake to the components of the WDN. The spatial representation of the distance to the epicenter is shown in Supplementary Figure S3.

• (2) Calculation of PGA and PGV

• Considering the values of distance to the epicenter (R) and assumed magnitude (M) in Equations (2) and (3), the PGV and PGA for each pipeline in the WDN were evaluated. Supplementary Figure S4(a) and S4(b) displays the resulting PGA and PGV, respectively. The PGA ranges from 0.372 to 0.378 g, while the PGV ranges from 1.48 to 1.54 m/s for the simulated earthquake.

• (3) Calculation of RR

• Based on the evaluated PGV for each pipe, the RR of WDN pipes due to earthquake impact is calculated using Equation (4). The RR for Bhuj, as shown in Supplementary Figure S4(c), ranges from 0.00035 to 0.00037 repairs/m.

• (4) Damage state of the components

• Using the PGA and fragility curve generated by WNTR, the damage state of each pipe is determined by selecting a uniform random variable. This variable helps assign the damage state for the PGA of each pipe, categorized as major, minor, or no damage. A total of 15 pipes had minor damage, and nine pipes had major damage. The damage state of the WDN in Bhuj is shown in Supplementary Figure S4(d).

• (5) Calculation leakage demand

• The leakage demand is determined using Equation (5) by identifying leak points in pipes that have suffered major and minor damages within the network's core. Bhuj's WDN is illustrated in Supplementary Figure S4(e). Repair work is estimated to commence 5 h after the earthquake and be completed within 97 h.

• (6) Calculation of RI

• The RI of the WDN is computed prior to the earthquake. Subsequently, nonfunctional pipes, based on their damage states, are excluded, and the RI is reassessed post-earthquake. Following the earthquake in Bhuj, pipes experiencing major and minor damage are removed, and the RI is recalculated, revealing a value of 0.011151 before and after the earthquake.

• The study of the relationship between PGA and PGV is crucial for understanding the dynamics of earthquake impact on WDN, as shown in Supplementary Figures S4(a) and S4(b). The minimum PGA recorded was 0.3707 g, the average PGA was 0.3745 g, and the maximum PGA was 0.3784 g. Correspondingly, the minimum PGV was 1.4712 m/s, the average PGV was 1.5012 m/s, and the maximum PGV was 1.5324 cm/s.

• A comparison of PGA and PGV across different pipelines shows a consistent increase in PGV with increasing PGA. For instance, Pipe L1 with a PGA of 0.371512 g had a PGV of 1.477032 m/s, while Pipe L100 with a higher PGA of 0.376922 g exhibited a PGV of 1.520553 m/s.

• The RR (Supplementary Figure S4(c)), indicative of the frequency of required maintenance or repairs, also varies with PGA. The minimum RR observed was 0.0003553 repairs per meter, the average RR was 0.0003625 repairs per meter, and the maximum RR was 0.0003700 repairs per meter. Pipes with a higher PGA tend to have a higher RR. For instance, Pipe L76 with a PGA of 0.377166 g had an RR of 0.000367453 repairs per meter, whereas Pipe L3 with a lower PGA of 0.370722 g had an RR of 0.000355372 repairs per meter.

• This trend indicates that higher ground acceleration leads to more frequent repairs, likely due to the increased mechanical stress on the pipelines. For example, pipes experiencing PGA around the average value of 0.374566 g (e.g., Pipe L20) have RR close to the average, at 0.000363596 repairs per meter.

• The damage state of the pipelines ranged from no damage to minor and major leaks as shown in Supplementary Figure S4(d). Pipes with a higher RR and a higher PGA and PGV are more likely to exhibit damage. For instance, Pipe L13 had a major leak with a PGA of 0.373262 g, a PGV of 1.491185 m/s, and an RR of 0.000360091 repairs per meter. Similarly, Pipe L34, also with a major leak, had a PGA of 0.376082 g, a PGV of 1.513580 m/s, and an RR of 0.000365499 repairs per meter.

• Pipes with minor leaks also showed higher values of these parameters than undamaged pipes. Pipe L4, with a minor leak, had a PGA of 0.370765 g, a PGV of 1.471629 m/s, and an RR of 0.000355369 repairs per meter.

• Leakage demand, influenced by RR and damage states, correlates with both PGA and PGV IS, as shown in Figure S4(e). Notably, major leaks tend to correspond with higher leakage demands, as evidenced by pipe IDs L34, L132, L137, and L190, which exhibit the highest leakage demands of 0.932360, 2.839439, 3.035572, and 0.960914, respectively. These pipes all have PGAs within a narrow range (approximately 0.37–0.38 g) but suffer major leaks, suggesting that even minor variations in PGA can result in substantial differences in leakage when the damage state is severe. Conversely, pipes with minor leaks generally show lower leakage demands, even with similar PGA values. For instance, L95 and L100, with PGAs around 0.377, show minimal leakage demands of 0.042934 and 0.028637 m³/s, respectively. This pattern indicates the critical role of the damage state in dictating leakage demand; while repair rates remain relatively low and consistent, the transition from minor to major leaks marks a substantial escalation in leakage, indicating that mitigation efforts should prioritize reducing the incidence of major leaks to control leakage demand effectively. Higher seismic forces result in greater repair needs and a higher likelihood of leaks, impacting the network's efficiency and necessitating more robust design and maintenance strategies to mitigate earthquake effects. The results of WDN of NIT Kurukshetra Network are given in Table 3.

• Before the earthquake, Todini RI of Bhuj's WDN was 0.018541. The earthquake damaged several pipes, disrupting the water supply and reducing the pressure needed to deliver water to the nodes. Since the WDN's resilience depends on maintaining adequate pressure at each node, the post-earthquake RI dropped to 0.011151. This indicates that the network's resilience significantly decreased due to the earthquake's impact.

This study mainly focuses on the determination of the resiliency of WDSs to natural hazards like earthquakes for two real-life case studies of India using the software WNTR. The data for two real case studies are collected and the network is then modeled in the EPANET and WNTR compatibility mode. The practical network of NIT Kurukshetra in the Haryana district and the Bhuj network in the Gujrat district are considered for earthquake impact analysis where the damage state of each pipe is evaluated before and after earthquake impact which are then classified as major and minor damage, respectively. The distance to the epicenter and earthquake parameters, such as magnitude, depth, and epicenter, play an important role in these simulations. Based on the results of case studies, it is evident that seismic fragility analysis plays a crucial role in understanding and mitigating the impact of earthquakes on WDNs. When comparing the results of the simulation of the earthquake impact of WDN of NIT and Bhuj, it is observed that even the slight change in magnitude (M_w = 7 in NIT, M_w = 7.7 in Bhuj) gives greater earthquake impact on WDN and that would give more damage quantitively.

In the NIT Kurukshetra network, 16 pipes have a major damage, and four pipes have a minor damage. In the Bhuj network, nine pipes have major damage and 15 pipes have minor damage. Based on those results, leakage demands and RI values are calculated for the networks before and after earthquake impact. In the NIT Network, even with higher PGA and RR, only minor damages occur due to the complexity of pipes connected in the WDN of NIT, which also affects the damage rate and repair strategy. The results highlight that minor damages are predominant in these scenarios, highlighting the need for efficient post-earthquake response strategies. Thus, the critical impact of seismic events on WDN is necessary to emphasize the need for targeted mitigation strategies based on specific pipeline vulnerabilities identified after earthquakes and damages. In this way, this study highlights the significance of timely identification and repair of damaged components of WDSs to restore water serviceability. Furthermore, the fragility curves generated provide valuable insights into the vulnerability of pipes, aiding in the development of mitigation strategies and infrastructure improvements. Thus, using the WNTR tool and conducting rigorous seismic fragility analysis, water utilities can better prepare for and respond to seismic events, ensuring the resilience and reliability of WDSs in the face of natural disasters.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.