The Failure Risk Analysis of the Water Supply Network
Abstract
:1. Introduction
2. Method for Assessing the Risk in Water Distribution Subsystems
- or a continuous random variable:
- for the discrete variable:
- Ci—an independent variable describing the specific loss value;
- P(C)—the probability of the adverse events in the interval [0,C];
- Pj—the probability, that a loss will result from an adverse event;
- i = 1, 2, …, n and C0 = 0;
- n—number of intervals describing the loss parameter C;
- j = 1, 2, …, m and P0 = 0;
- m—number of intervals describing the probability parameter P.
- Ci—hazard consequences (assumed depending on the type of water supply network, according to Table 1);
- Pj—hazard occurrence probability (assumed depending on the failure rate λ, according to Table 2);
- Vk—vulnerability to hazards (adopted on the basis of the risk factors, according to Table 3 and Formula (5)).
- i—point weight for parameter C, i = {1,2,3};
- j—point weight for parameter P, j = {1,2,3};
- k—point weight for parameter V, k = {1,2,3}.
- For the loss parameter Ci. Evaluation criteria were adopted depending on the number of inhabitants (LM) exposed to the possibility of a hazard resulting in a shortage or restriction of a water supply according to Table 1.
Point Weight (i) | Parameter Description (Inhabitants LM) |
---|---|
1 | 1–5000 |
2 | 5001–50,000 |
3 | >50,000 |
- For the probability parameter Pj the evaluation criteria i were adopted depending on the failure rate value λ of the water supply network or exceedances. Table 2 proposes a procedure for the evaluation of the parameter Pj depending on the range of the frequency of occurrence of a failure event or failure rate and the different types of water mains: mains (M), distribution (D), water supply connections (WC).
Point Weight (j) | Parameter Description | Range of Incidence Emergency Event/Exceedance fi [Event/a] | OR | λ [no. of Failures⋅km−1⋅a−1] | ||
M | D | WC | ||||
1 | unlikely | ≤0.1 | ≤0.3 | ≤0.5 | ≤1 | |
2 | medium probability | (0.1–2> | (0.3–0.5> | (0.5–1> | (1.0–2> | |
3 | likely | >2 | ≥0.5 | ≥1 | ≥2 |
- For the vulnerability parameter Vk. The vulnerability parameter is complex and its magnitude can be influenced by various factors depending on the technical conditions of the network itself (e.g., type of material), but also on the type of hazard under consideration, for which the risk is analyzed. Therefore, the procedure to value this parameter is complex. For this purpose, an original method for the analysis of this parameter is proposed. The VIM method is based on the identification of factors influencing the degree of vulnerability. The proposed method is based on the classification of vulnerability factors on the water supply network and the assignment of Ri ranking point values and wij point weights to them, followed by the calculation of the vulnerability index (VI) according to Formula (5). In the first step of the analysis, the factors that can affect the vulnerability of the network to a given type of failure (e.g., water pipe failure resulting in water leakage, secondary water contamination in the network, pipe leakage, fittings failure) should be identified.
- VI—vulnerability index;
- Ri—rank of ith risk factor (degree of importance);
- wij—weight jth of this factor;
- i = 1, 2 …, n;
- n—number of factors taken into account;
- j = 1, 2, 3.
- (0–1]—neglected,
- [2–3]—low importance,
- [4–6]—moderately important,
- [7–8]—important,
- [9–10]—very important.
Influencing Factor | Rank Ri | Weight of the Factor wij | ||
---|---|---|---|---|
Low = 1 | Medium = 2 | High = 3 | ||
Age of the water supply network | 9 | to 10 years | (10–30) years | >30 years |
Network material | 6 | plastics | steel | grey cast iron |
Hydrogeological factors influencing the network | 8 | good | average | bad |
Monitoring of the network operations | 5 | above standard comprehensive monitoring of the water distribution network through the measurement of water pressure and flow rates. possession of specialized equipment for detecting water leaks using acoustic methods, unrestricted 24-h communication with the public via a dedicated phone line, monitoring of water quality within the WDN through a protection and warning system | standard simplified monitoring of the water distribution network, primarily through pressure measurements, inability to promptly respond to minor leaks. periodic water quality testing within the water distribution network | none lack of monitoring of network and water quality |
Measures taken to prevent corrosion | 4 | full | standard | none |
Network location—including factors such as dynamic loads and density of underground components | 3 | small pipeline in the not urbanized areas | average pipeline in the street | big pipeline in the pedestrian traffic |
Hydraulic conditions within the network | 7 | good favorable working conditions of the water supply network: v = 1.0–1.5 m/s, water age < 24 h, smooth pressure regulation depending on hourly water consumption | average average conditions of waterworks network operation: network in mixed, v = 0.5–1.0 m/s, water age < 24–48 h, pressure regulation depending on hourly water consumption | bad unfavorable conditions of waterworks network operation: network in open system, v < 0.5 m/s, water age > 48 h, no pressure regulation depending on hourly water consumption |
Chemical stability of the water supplied by the network * | 8 | low water is chemically stable with the following parameters: Langelier saturation index IL = 0, or Ryznar index IR = 6.2–6.8, or Strohecker index Ist < 0.5) [73,74,75] | medium mild corrosion, does not produce protective CaCO3 layers, with the following parameters: Langelier Saturation Index IL = −3 to 4, or Ryznar Index IR = less than 8.5, or Strohecker Index Ist > 0.5, except when there is low susceptibility (Langelier Saturation Index IL = 0 and Ryznar Index IR = 6.2–6.8) and high susceptibility (Langelier Saturation Index IL = 3 to 4 and Ryznar Index IR = less than 5.5) [73,74,75] | high rapid corrosion, does not produce protective CaCO3 layers, with the following parameters: Langelier Saturation Index IL = −4 to −5, or Ryznar Index IR = more than 8.5 and less than 5.5 or Strohecker Index Ist > 0.5, or Langelier Saturation Index IL = 3 to 4, or Ryznar Index IR = less than 5.5, or Strohecker Index Ist > 0.5 [73,74,75] |
3. Characteristics of the Study Object
- Water intake and pumping subsystem.
- Water treatment subsystem.
- Water transmission subsystem.
- Water storage subsystem.
- Water distribution subsystem (water supply network with utilities).
- Accident events causing losses on a small scale, but occurring relatively frequently. These types of events include failures of the water distribution network and water supply connections, failures of individual devices.
- Emergency events causing medium-scale losses that occur relatively rarely. These include failures in water mains, incidental contamination in the source of intake water.
- Catastrophic events that occur relatively rarely but cause significant losses.
- Adverse events in the water distribution subsystem can therefore be divided into:
- Failures of water supply lines and fittings (e.g., material defects, corrosive soil, too high pressure, age of the pipes).
- Secondary water pollution in the water supply network.
- Failures of water supply pumping stations.
- Incidental events, i.e., contamination of water sources, failures of water treatment plants, water contamination in network water supply tanks.
- Action of forces of nature (droughts, landslides, rainfall).
- Actions of third parties (acts of vandalism, terrorist and cyberterrorist attacks).
- The effects of the above-mentioned events are:
- Interruptions in water supply or its complete lack.
- Secondary contamination of tap water.
- Loss of safety of water consumers due to consumption of poor quality water.
- Financial losses related to the purchase of bottled water, medical costs.
- Water losses and financial losses incurred by the water supply company related to network flushing, network disinfection, costs of repairing failures, lack of water sales.
- Compensation paid to water consumers.
- Washing out of the bottom layer of the substrate due to the action of water flowing from the damaged pipe, which results in unsealing of subsequent sections of the network.
- Loss of trust in the water recipient–water supplier relationship.
- Preliminary stage (research preparation).
- Analysis of the structure of facilities and the process of their operation and functioning.
- Obtaining and verifying operational data.
- Processing the collected data and determining reliability characteristics objects.
- Use of processed data (research results).
- Main line No. “0”, with a diameter ranging from Φ 1200 to 800 mm, made of steel.
- Mains No. “1” and No. “2”, both with a diameter of Φ 400 mm, constructed from steel and cast iron.
- Pipe line No. “3”, also with a diameter of Φ 400 mm, made from a combination of steel and cast iron materials.
4. Results
4.1. Failure Analysis of Water Supply Network
- the mains consist of pipes with diameters ≥ 300 mm;
- the distribution network consists of tpipes with diameters of 90–280 mm.
4.2. Analysis of the Chemical Stability of Water
4.3. Failure Risk Analysis of Water Supply Network
4.3.1. Case One Assumes Failure on the Main, Diameter Φ 400 Made of Cast Iron
- main water supply pipe located in the southern part of the city, Φ 400 mm made of cast iron;
- according to the Table 2, the value of the P parameter has been assumed at P = 1 because, based on the number of failures recorded in 2020, i.e., <20 failures per year, the failure frequency parameter has been assumed as fi ≤ 0.1 events/year;
- according to Table 1, the value of the C parameter has been assumed at the level of C = 2;
4.3.2. Case Two Assumes the Failure of the Distribution Network Pipe, Diameter Φ 90 Made of PE Plastic
- water distribution pipe located in the south-western part of the city, Φ 90 made of PE plastic;
- according to Table 2, the value of the P parameter has been assumed at P = 1 because, based on the number of failures recorded in 2020, i.e., <20 failures per year, the failure frequency parameter has been assumed as fi ≤ 0.1 events/year;
- according to Table 1, the value of the C parameter has been assumed at the level of C = 1;
5. Conclusions and Perspectives
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Point Weight (k) | Value of VI |
---|---|
1 | <100 |
2 | 101–160 |
3 | >160 |
Risk Level | Point Range |
---|---|
Accepted | 1–8 |
Controlled | 9–18 |
Unacceptable | 19–27 |
Statistical Characteristics | Diameter | |||||||
---|---|---|---|---|---|---|---|---|
100 | 110 | 150 | 160 | 200 | 225 | 250 | 280 | |
Std. Dev. | 8.85 | 2.57 | 7.14 | 2.17 | 3.02 | 1.19 | 3.61 | 0.45 |
Median | 31.00 | 5.00 | 27.00 | 5.00 | 7.00 | 0.00 | 8.00 | 0.00 |
Avg. value | 32.55 | 5.64 | 25.00 | 5.00 | 6.64 | 0.82 | 8.18 | 0.27 |
Variance | 78.25 | 6.60 | 50.91 | 4.73 | 9.14 | 1.42 | 13.06 | 0.20 |
perc. 0.25 | 25.50 | 4.00 | 18.50 | 4.00 | 4.50 | 0.00 | 6.50 | 0.00 |
perc. 0.55 | 33.00 | 5.00 | 28.50 | 5.00 | 7.00 | 0.50 | 9.00 | 0.00 |
perc. 0.75 | 38.50 | 7.00 | 30.50 | 5.00 | 7.50 | 1.00 | 11.50 | 0.50 |
Statistical Characteristics | No. of Failures | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Diameter | ||||||||||
300 | 315 | 325 | 350 | 400 | 450 | 500 | 600 | 800 | 1200 | |
Std. Dev. | 2.02 | 1.07 | 0.77 | 1.71 | 7.02 | 0.39 | 3.51 | 0.29 | 0.45 | 0.29 |
Median | 2.00 | 0.00 | 0.00 | 3.00 | 20.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
Avg. value | 2.91 | 0.64 | 0.64 | 2.73 | 20.55 | 0.18 | 2.82 | 0.09 | 0.27 | 0.09 |
Variance | 4.08 | 1.14 | 0.60 | 2.93 | 49.34 | 0.15 | 12.33 | 0.08 | 0.20 | 0.08 |
perc. 0.25 | 2.00 | 0.00 | 0.00 | 1.00 | 14.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
perc. 0.55 | 3.00 | 0.00 | 0.50 | 3.50 | 21.50 | 0.00 | 2.00 | 0.00 | 0.00 | 0.00 |
perc. 0.75 | 4.00 | 1.00 | 1.00 | 4.00 | 24.00 | 0.00 | 4.00 | 0.00 | 0.50 | 0.00 |
Statistical Characteristics | No. of Failures | |||||
---|---|---|---|---|---|---|
Material | ||||||
Steel | Galvanized Steel | Grey Cast Iron | PE | PCV | AC | |
Std. Dev. | 32.51 | 7.44 | 18.17 | 5.12 | 2.93 | 1.30 |
Median | 62.00 | 34.00 | 87.00 | 29.00 | 15.00 | 2.00 |
Avg. value | 77.09 | 35.64 | 89.55 | 28.00 | 15.64 | 2.36 |
Variance | 1056.81 | 55.32 | 330.25 | 26.18 | 8.60 | 1.69 |
perc. 0.25 | 55.00 | 30.00 | 80.00 | 23.50 | 14.00 | 1.50 |
perc. 0.55 | 74.50 | 35.50 | 90.50 | 29.00 | 16.00 | 2.50 |
perc. 0.75 | 94.50 | 42.00 | 105.50 | 31.50 | 18.00 | 3.50 |
Influencing Factor | Weight of the Factor wij | Rank Ri |
---|---|---|
3 | 9 | |
Network material: grey cast iron | 3 | 6 |
Good hydrogeological factors influencing the network | 1 | 8 |
Above standard monitoring of the network operations | 1 | 5 |
No measures taken to prevent corrosion | 3 | 4 |
Average dynamic loads and average density of underground utilities | 2 | 3 |
Good hydraulic conditions within the network | 1 | 7 |
Low susceptibility for the chemical stability of the water supplied by the network | 1 | 8 |
Influencing Factor | Weight of the Factor wij | Rank Ri |
---|---|---|
Age of the water supply network: 10–30 years | 2 | 9 |
Network material: plastic | 1 | 6 |
Good hydrogeological factors influencing the network | 1 | 8 |
Above standard monitoring of the network operations | 1 | 5 |
Standard measures taken to prevent corrosion | 2 | 4 |
Low dynamic loads and low density of underground utilities | 1 | 3 |
Good hydraulic conditions within the network | 1 | 7 |
Low susceptibility for the chemical stability of the water supplied by the network | 1 | 8 |
Type of Failure/Risk | P | C | V | r |
---|---|---|---|---|
Failure of the main | 1 | 2 | 1 | 2 |
Failure of the distribution network | 1 | 1 | 1 | 1 |
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Tchórzewska-Cieślak, B.; Pietrucha-Urbanik, K.; Piegdoń, I. The Failure Risk Analysis of the Water Supply Network. Water 2023, 15, 3815. https://doi.org/10.3390/w15213815
Tchórzewska-Cieślak B, Pietrucha-Urbanik K, Piegdoń I. The Failure Risk Analysis of the Water Supply Network. Water. 2023; 15(21):3815. https://doi.org/10.3390/w15213815
Chicago/Turabian StyleTchórzewska-Cieślak, Barbara, Katarzyna Pietrucha-Urbanik, and Izabela Piegdoń. 2023. "The Failure Risk Analysis of the Water Supply Network" Water 15, no. 21: 3815. https://doi.org/10.3390/w15213815