1 Introduction

Disasters of any kind to water infrastructure cannot be clearly figured out or predicted before its occurrence. The increased risk due to terrorism is also a major concern for vulnerability of water distribution systems (Rasekh and Brumbelow 2014). Drinking water supply of a city can be seriously disrupted if its raw water resource is damaged by a flood or an earthquake. Such case happened in the state of Maharashtra in western India wherein the barrage built across the Ulhas River that supplies water to the Badalapur and Ambernath cities was damaged (Dahasahasra et al. 2006) due to flood. Figure 1a shows the barrage and its vertical lift gates before flood. The gates of the barrage were washed off due to unprecedented flood on July 26, 2005, as shown in Fig. 1b. When such raw water resource fails, unlike pipe failure, longer period is required for recovery and restoration of water supply. Therefore, to tackle such disaster, there is a need for preparation of action plans for recovery of drinking water supply.

Fig. 1
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Badlapur barrage—a raw water resource of drinking water

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Safety of drinking water of a city requires a comprehensive water safety plan. This plan must incorporate (Climatetechwiki.org) health-based targets, surveillance and the required outcomes. Surveillance should include system assessment, monitoring and management with effective communication. In flood-type disaster, marking the highest flood-level line is now made compulsory in Indian cities which are monitored in monsoon. If the flood is likely to cross this line, then the city administration communicates the warnings and further steps of evacuation are undertaken. Thus, the risk management of drinking water system of a city should include all the necessary action plans right from catchment of a raw water resource to consumer end. The system assessment comprehensive risk management can be made using the Pressure-Dependent Approach (PDA) in the planning.

While designing a water distribution system of a city, conventional methods are used for analysis which assumes a known nodal demand (Mohd Abbas et al 2014). Nodal pressures and pipe flows are then determined with respect to this known demand. It is presumed that the nodal pressures are always adequate to satisfy the demand at nodes (Tabesh et al. 2002) of the water distribution system (WDS). All the network solving algorithms such as Hardy-Cross, Newton–Raphson, and Global Gradient Method are based on this assumption (Bhave and Gupta 2006).

However, in disaster, when pressure-deficient conditions are formed, the traditional methods do not simulate the exact behavior of pipe network and give unrealistic results (Tabesh et al. 2002, 2014; Shiv Kumar and Prasad 2014; Moosavian and Jaefarzadeh 2013). Therefore, PDD analysis is important (Todini 2012; Tanyimboh 2008; Tanyimboh and Templeman 2010; Gupta 2015) in analyzing networks in such situations.

The objective of this paper is to describe a small hypothetical model that simulates the disaster condition because of failure of water raw water resource. A small water supply network is considered which is taken from the literature (Abdy Sayyed and Gupta 2013). This paper cited an incidence of failure of Badlapur barrage—just to highlight the fact that the city’s water supply can fail because of failure of its raw water resource. A PDD analysis of such simulated situation has been carried out using WaterGEMS software. Based on this analysis, the paper provides recovery assessment options to prepare action plans of water supply in such crisis conditions.

2 Problem Definition

2.1 Normal Scenario

A loop network is taken as it is from the literature (Abdy Sayyed et al. 2014; Ozger and Mays 2003). Pipes P-1 to P-21 and nodes J-1 to J-14 represent the network of City1, and one of its raw water resources is R1. Pipelines shown by P-23, P-24 and P-25; nodes J-15, J-16 and flow controlling valves FCV-1 and FCV-2 that regulate the flow to both the cities are added to the original network for simulation purpose. This arrangement represents the network of a City2 whose sole raw water resource is R2. Raw water resource R2 supplies drinking water to both City1 and City2. Node J-16 represents the distribution of City2. The water supply arrangement, when modeled, is shown in Fig. 2.

Fig. 2
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(Source: Mohd Abbas et al. 2014)

Definition model of water supply of two adjoining cities

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2.2 Disaster Scenario

Consider a hypothetical case (Fig. 2) wherein the raw water resource of a city gets damaged due to flood disaster like the one that has been described in Fig. 1. Now, let us consider a case when the raw water resource R1 of City1 gets damaged in the event of disaster. In this crisis scenario, only the raw water resource R2 must supply water to both the cities—City1 whose supply from raw water resource R1 is affected and the City2 which is solely dependent on raw water resource R2.

The task before the administrator of the City1 is how to overcome this challenge and restore its water supply to the minimum life sustenance of the people living in it. The above small theoretical model is used to analyze and find a solution to the problem which can be generally applicable to the urban cities having more than one raw water resource.

3 Model Data

A hydraulic model simulating the problem discussed in Fig. 2 has been prepared using WaterGEMS software. The pipe and the junction data are shown, respectively, in Tables 1 and 2. Total water demand is 4146.4 m3/h as mentioned in Table 2 out of which, City1 gets 3146.4 m3/h water and City 2 gets 1000 MLD m3/h water in the normal scenario. To estimate the performance of a damaged water distribution network, as mentioned by Mani et al. (2013), hydraulic analysis is must.

Table 1 Pipe data
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Table 2 Junction data
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Three scenarios have been considered as defined below:

  1. 1.

    Normal Scenario—City1 and City2 get water, respectively, from the intact raw water resources R1 and R2

  2. 2.

    Disaster Scenario—When raw water resource R1 fails, pressure-deficient conditions are formed in the distribution system of City1

  3. 3.

    PDD Scenario—To analyze network in pressure-deficient conditions.

3.1 Scenario 1: Normal Scenario

As described above in the normal scenario, City1 and City2 get water, respectively, from raw water resources R1 and R2. The analysis has been made in steady-state condition using demand-driven approach. On giving the data, the model is run. Results of the flows and velocity in pipes and the pressures at each node in the pipe network of both the cities are observed. It is observed that the flows and velocity in pipes and pressures at nodes are adequate. After running the hydraulic model, the City1 is observed to get water of 3146.4 m3/h (2253.4 m3/h from raw water resource R1 and 893 m3/h from the R2) and the City2 gets 1000 m3/h from the raw water resource R2.

3.2 Scenario 2: Disaster Scenario

When the raw water resource R1 fails, both the cities—City1 and City2—should get water from the raw water resource R2 which is intact even in disaster. On running the hydraulic model with Demand-Driven Approach (DDA), it is observed that all the nodes in the pipe network of the City1 have negative pressures. In DDA, water demand at nodes is assumed as fixed (Tanyimboh and Templeman 2010; Suribabu and Neelakantan 2011). Hence, on raw water resource failure, irrespective of stoppage of flow from the raw water resource R1, the demand of the city remains the same, i.e., 3146.4 m3/h which the raw water resource R2 must satisfy. This demand is much more than the designed demand of 893 m3/h. Hence in DDA approach, the hydraulic grade line would come down below the ground elevation, and as a result the negative pressures are observed. Thus, the water will not reach the customer at all.

3.3 Scenario 3: PDD Scenario

Simulation results show that although in the event of disaster conventional DDA predicts no water flowing to the affected nodes of City1, some quantity of water reaches some of the nodes but with much less pressure. This observation agrees with the results of (Abdy Sayyed and Gupta 2013; Abdy Sayyed et al. 2014; Alemtsehay and Tanyimboh 2014). Thus, the pressure-deficient conditions are formed in the distribution system of City1. Hence, it is required to carry out the PDD analysis. Islam et al. (2014) stated that in PDD analysis, both nodal demand and pressure are considered simultaneously to obtain available flow, which is more realistic to actual conditions. Shirzad et al. (2013) also stated this fact. Therefore, in the present case, PDD analysis which is a robust and efficient approach of pressure-dependent demand model (Wu and Walski 2006; Walski et al. 2016) is used to quantify the amount of flow and pressure to take vital decisions regarding disaster mitigation plans.

The following PDD Relationship (Wu et al. 2006, 2009; Minakshi et al. 2014) is considered in the computation engine of the WaterGEMS software.

$$\frac{{q_{i} }}{{q_{ri} }} = \left\{ {\begin{array}{*{20}l} 0 \hfill & {P_{i} = 0} \hfill \\ {\left( {\frac{{P_{i} }}{{P_{ri} }}} \right)^{0.5} } \hfill & {P_{i} = 0 < P_{i} < P_{t} } \hfill \\ {\left( {\frac{{P_{t} }}{{P_{ri} }}} \right)^{0.5} } \hfill & {P_{i} \ge P_{t} } \hfill \\ \end{array} } \right.,$$
(1)

where Pi represents the calculated pressure at node i; qri is the requested demand or reference demand at node i; qi is the calculated demand at node i; Pri denotes the reference pressure that is required to supply full requested/reference demand; Pt is the threshold pressure above which the demand is independent of nodal pressure and 0.5 is the exponent of pressure demand function.

The nodal demand and pressures in normal scenario with DDA approach are shown in Table 3. Pressures in the normal scenario are taken as required or reference pressures in the PDD analysis. Maximum value of this nodal pressure 50.26 m is taken as threshold pressure above which the nodal demand is independent of the nodal pressure.

Table 3 Nodal demand and pressures in normal scenario
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The PDD relationship as mentioned above (Eq. 1) has been set to all the nodes of the network in the respective alternative of the PDD scenario. It is now required to compute the available nodal flow at each node.

3.4 Analysis

As stated in scenario 1 (normal scenario), the City1 gets water at the rate of 3146.4 m3/h (2253.4 m3/h from raw water resource R1 and 893 m3/h from the raw water resource R2, and the City2 gets 1000 m3/h from the raw water resource R2. In the disaster scenario, i.e., when raw water resource R1 fails, the City1 would not get water from its raw water resource R1 but gets only a diminished quantity of 893 m3/h water from the raw water resource R2 which remains intact in disaster. The raw water resource R2 shall only be left to supply water to both the cities. In such situation, City2 gets its normal water but City1 would get less water depending upon the pressures at the nodes, thus forming pressure-deficient conditions.

3.5 The Strategy

The strategy to mitigate the disaster would be to identify the nodes in the distribution pipe network of the City1 that are affected due to its raw water resource (R1) failure. The main task would be to see how much City2 would curtail its own water and with that lessened quantity how much water City1 would get (recover) to sustain the life of its residents. The norm of per capita water in normal condition is 150 L (CPHEEO Manual 1999). This paper assumes that nearly 50% of this norm, say 70 L per capita, is required to sustain in the crisis. Thus, the quantum of water that the affected City1 gets from the unaffected raw water resource of City2 totally depends upon how much water the City2 can spare. Th following PDD scenarios are studied:

  • Scenario 1 City2 spares no water and City 1 gets only 893 m3/h of water.

  • Scenario 2 City2 spares 100 m3/h of water and City 1 gets (893 + 100) m3/h water.

  • Scenario 3 City2 spares 200 m3/h of water and City 1 gets (893 + 200) m3/h water.

  • Scenario 4 City2 spares 300 m3/h of water and City 1 gets (893 + 300) m3/h water.

  • Scenario 5 City2 spares 400 m3/h of water and City 1 gets (893 + 400) m3/h water.

  • Scenario 6 City2 spares 500 m3/h of water and City 1 gets (893 + 500) m3/h water.

Tankers The nodes that are having negative residual pressures are shown in Table 4. This means that such nodes will not get any water during crisis period. It is also observed that there are nodes which have enough nodal pressures. Water can be tapped from such nodes and can be supplied to the customers which are placed around the nodes having negative pressures. Some alternate arrangement will have to be made to supply water to the customers. From such nodes, water can be supplied by containers, called tankers, which are specifically designed for this task and fabricated to meet an urgent need. A special delivery point called as tanker fed spots shall be created to tap the water from these nodes.

Table 4 Result of nodal demand and nodal pressures
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3.6 Introduction of Interlink

To create above PDD scenarios, interlink (pipe P-27) is introduced between systems of City1 and City2, as shown in Fig. 3. The interlink joins the node J-1 and J-15 of City1 and City2, respectively. Care is taken to see that interlink from City2 joins with transmission system of City1 at the entrance of its distribution system where pipe size is bigger.

Fig. 3
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Introduction of interlink between systems of City1 and City2

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The hydraulic model is run for PDD analysis. The results of nodal demand and pressures are shown in Table 4.

3.7 Improvement in Nodal Flow and Nodal Pressures in Network of City1

When the disaster struck the raw water resource of City1, its water supply is totally hampered as shown in the Scenario 2. The residents of the City1 must get some relief, say bare minimum quantity of water to sustain their lives, otherwise law-and-order situation as stated by Dahasahasra (2009) could prevail. Thus, the objective of better management of disaster would be to improve the supply and pressures at the nodes of the affected network of City1. This is achievable when the City2 spares some water by sacrificing its normal water supply to some affordable level to City1. For simulation of this situation, it is proposed to study the improvement in the nodal flow and pressures in City1 while restricting the nodal flow of the distribution pipe network of City2. The supply to City2 has been reduced from initial value of 1000 m3/h, to 900, 800, 700, 600 and 500 m3/h, and the simultaneous improvement in nodal flows and nodal pressures of City1 has been observed, as shown in Figs. 4 and 5.

Fig. 4
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Improvement in nodal flow of City1 with reduced supply of City2

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Fig. 5
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Improvement in nodal pressures of City1 with reduced supply of City2. (Note: Unit of the pressure is water head in m)

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Critical observations from Figs. 4 and 5 are:

  1. 1.

    Flows in normal scenario at nodes J-5, J-7 and J-8 are maximum (Fig. 4); however, in disaster scenario the same flows at these nodes have been reduced substantially. This is due to the decreased nodal pressures (Fig. 5) at these nodes.

  2. 2.

    Flows in normal scenario at nodes J-4 and J-6 were less (Fig. 4) when compared with flows in disaster scenario; however, the same flows at these nodes have been increased now in disaster scenario. This is due to the increased nodal pressures at these nodes.

  3. 3.

    Thus, nodes J-4 and J-6 can provide water for probable tankers in the disaster scenario.

3.8 Recovery

Daily supply to City1 is 3146.4 m3/h. Assuming water supply share of 150 Liters per Capita per Day (LPCD), population of City1 is 503424. The partial recovery of water supply of City1 in disaster condition is shown in Table 5.

Table 5 Recovery of water supply of City1
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3.9 Action Plan

Based on the results of PDD analysis as shown in Table 5, action plans for recovery of water supply of the affected City1 are required to be prepared. Table 5 illustrates how much City2 should curtail its water and with this limited water how much recovery would be possible in the water supply of City1in crisis.

3.10 Planning for Tankers

From PDD analysis, it is observed that pressure at some nodes is zero (shown bold values in Table 4), and thus water would not reach these nodes in crisis condition. Disaster management plan requires identification of no pressure or very low-pressure area of distribution system of the affected City1. The pressure contours are shown in Fig. 6.

Fig. 6
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Pressure contours identifying low-pressure areas of City1

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Now, consider a case in which City2 can spare just 100 m3/h to the affected City1. In this scenario, the nodes J-10, J-11, J-12 and J-13 (Fig. 6) do not get water because of negative pressure and the city administration would have to deploy 259 tankers (assuming a tanker with 10,000 L capacity) with two trips each. These tankers can be filled from the nodes of J-4 and J-6 which are having enough pressures even during pressure-deficient condition that can supply water to the striving nodes. The analysis thus provides a ready reckoner to the concerned Urban Local Body to take an amicable decision.

4 Conclusions

Safety of drinking water of a city requires a comprehensive water safety plan which should be prepared with assessment of risks in the system, monitoring and management with effective communication. The risk management should include all the necessary action plans right from catchment of a raw water resource to consumer. While making the system assessment, comprehensive risk management can be made using the Pressure-Dependent Demand (PDD) approach in the planning. When the disaster strikes, there is a possibility of damage to the raw water resource that supplies drinking water to the city. Action plan for recovery of water supply should be prepared for the cities whose locations are in the adjoining area. In the event of such disaster, it is possible to recover and restore water supply (partial) of the affected city to the minimum life-sustaining level (say, 70 LPCD) by introducing an interlinking pipeline from the adjoining city’s water supply. While restoring water supply of the affected city, pressure-deficient conditions are formed. Using PDD analysis, behavior of both the cities—donor (unaffected) and receiver (affected)—has been analyzed. The analysis of the small representative network presented in the paper gives a broad idea/concept which can be further used to frame a methodology for preparing a necessary disaster management action plan of the partial recovery of water supply.