In the Republic of Korea, multi-regional water supply pipelines were intensively laid during the rapid economic growth period; however, these pipelines are now aging. The cost of renewal of the aged pipelines would be enormous. Therefore, limited resources need to be distributed effectively in accordance with the priority of renewal. In this study, the risks involved in the multi-regional water supply pipeline of region K were calculated and assessed for setting the priority of renewal. The probability of failure of the pipeline was calculated through a quantification theory, and the effects of failure on the water supply pipeline were calculated by interpreting a pressure driven analysis. The risk considering the probability and consequence of failure comprehensively was found to be the largest at section A12. Three alternatives were considered for risk reduction, and the effect of each alternative on the risk reduction was analyzed. As a result, the construction of double piping by laying a new pipeline was found to be the most effective measure for risk reduction. The results of this study can be utilized as the basic data for establishing an investment plan for the renewal of the water supply pipeline and asset management plan.

## INTRODUCTION

In the Republic of Korea, multi-regional water supply pipelines were intensively laid during the rapid economic growth period between the 1970s and 1980s. Although those facilities made a great contribution to the development of Korea, they have been gradually deteriorating with time. As of 2013, it is expected that 1,381 km, which accounts for 27.17% of the entire multi-regional water pipes, will need renewal from 2014 to 2024. Further, the length of the pipe for renewal is expected to increase to 2,666 km, which accounts for 52.45% of the entire pipeline, between 2024 and 2034 (Koo *et al.* 2014). If an administrator allows water supply pipelines to age without appropriate countermeasures, the safety of the pipeline will be sharply decreased. Because the decreased safety can lead to water leakage, increased impacts of disasters, degradation of water quality and other relevant problems, there are concerns for the need of measures to reduce the risk of pipelines and increase safety (Kim *et al.* 2014). In particular, a majority of the multi-regional water supply pipelines consists of transmission pipelines with large diameters, which can cause large-scale accidents. In addition, the cost of renewal of the aged multi-regional water supply pipelines would be enormous. Therefore, limited resources need to be distributed effectively in accordance with the priority of renewal. To do so, the priority of renewal must be established (Park 2007).

To set the priority for renewal, the risk of failure of the water supply pipeline may be considered. Risk assessment methods can be categorized into connectivity/topological risk and hydraulic risk (Ostfeld 2004). The connectivity/topological risk is associated with the measurement of the probability that the components are not physically continuous in a fixed water pipe network. The hydraulic risk is related to the measurement of the probability that water cannot be supplied with consistent water quantity and pressure. Wagner *et al.* (1988) proposed an analytical methodology to evaluate the connectivity, and Goulter *et al.* (1990) defined system risk as the probability that a failure occurs in the system using dis-connectivity and the concept of topological risk. Al-Bahar (1988) classified risks into three categories as follows: risk events refer to inappropriate events (suspension accident, etc.) which are inherent to a system, uncertainty of risk factor refers to the probability of occurrence of risk factor (the failure rate of a pipeline), and the potential failure of risk factor refers to the results of an inherent accident (time spent on the repair of the pipeline, the level of consumption of water, redundancy, etc.). According to these, a risk event is defined by multiplying the uncertainty of the event by the potential loss or gain. The Environmental Protection Agency (EPA) (2012) also proposed a similar measure to calculate risk as Al-Bahar (1988), defining risk as the product of the multiplying probability of failure (PoF) and the consequence of failure (CoF) and proposed risk mitigation. Choi (2013) estimated the failure rate of a pipeline through logistics regression analysis and calculated risk by assessing the effect of failure on the pipeline in terms of water suspension quantity. Rahman *et al.* (2014) studied the PoF and a variety of influences of the failure to calculate risks of water supply pipelines in the subject region of their study. Further, they marked the result of the risks on a map. Choi *et al.* (2014) analyzed the water suspension using a fault tree analysis and estimated the amount of risk reduction when an administrator replaces the old pipe with a new one and connects it to the water district. Koo (2015) calculated the failure rate through safety rate and calculated shortage quantity on each demand node as the CoF to calculate risks.

A water supply pipeline system should be capable of supplying a certain level of water to the regions the pipeline affects, even during abnormal situations such as water leakage and pipeline failure. The situation in which a suspension cannot be used by consumers is regarded as a risk. Here, stochastic figures including uncertainty factors such as leakage and failure, the degree of damage caused by suspension, and redundancy to compensate for the damage in suspension accidents may be taken into consideration (Goulter 1987). That is to say, the stochastic figure for unstable supply of water to consumers as a result of various uncertainties, the effects of the damage caused by suspension time (required for repair of pipe, water consumption, etc.) and indexes including redundancy rates can be defined as water suspension risks.

In this study, therefore, the risks of multi-regional water supply pipelines of region K, which is the subject of this study, were calculated and assessed for setting the priority of renewal. The PoF of the water supply pipeline was calculated through a quantification theory, and the effects of the failure on the water supply pipeline were calculated by interpreting a pressure driven analysis (PDA). Three alternatives (replacement of the existing pipeline, increasing the level of retention time in a reservoir, and double piping by laying a new pipeline) were taken into consideration, and the effect of each alternative on the reduction of risk was analyzed.

## METHODS

### Study area

Multi-regional supply of K region . | . |
---|---|

Installation year | 1972–2001 |

Pipe type | steel pipe, ductile cast iron pipe |

Pipe diameter | 200 mm–900 mm |

Break history | 32 (from 1980 to 2013) |

Pipe length | 69.967 km |

Supply area and demand | KJ city (68,732 m^{3}/d) |

Multi-regional supply of K region . | . |
---|---|

Installation year | 1972–2001 |

Pipe type | steel pipe, ductile cast iron pipe |

Pipe diameter | 200 mm–900 mm |

Break history | 32 (from 1980 to 2013) |

Pipe length | 69.967 km |

Supply area and demand | KJ city (68,732 m^{3}/d) |

### Risk calculation method

#### PoF (quantification theory)

Quantification theory is a multi-dimensional data analysis method developed by Chikio Hayashi in the 1950s. In Japan, Hayashi's methods of quantification are well known and widely used in various fields, such as social and marketing surveys and psychological and medical research, where information is obtained mainly in the form of qualitative categories (Arai *et al.* 2009; Jiang *et al.* 2010). In particular, the quantification theory type II, a quantitative concept, is a statistical technique to find independent variables that can discriminate or describe the measured dependent variable to deduce a discriminant function. Further, similarly to a discriminant analysis, the quantification theory predicts the group of dependent variables to which new data will belong. Variables including the existence of a failure in a pipeline, the type of a pipeline, and laying environment cannot be quantitatively interpreted. Therefore, the quantification theory, which converts the variables of a qualitative concept to a quantitative one, was applied to calculate the failure rate of a pipeline.

The deduction of a discriminant function for the calculation of the failure rate of a pipeline by using the samples of the multi-regional pipeline and the failure history of region K was not useful for the deduction of statistical significance due to a small number of samples. In this study, therefore, the data of the multi-regional pipeline of the entire nation were utilized to deduce a discriminant function. The water pipelines were classified with respect to the changes in the installation year of the water pipeline, the types of pipes, pipe diameter, and topographic conditions. As a result, the water pipelines nationwide were classified into 8,170 groups. The history of failures that occurred on the pipeline for the last 34 years from 1980 to 2013 was used. The case with two or more failures was set to 1 and the case without failure occurrence was set to 0, because the pipeline with two or more failures was considered to be affected by only the laying environment rather than the construction or other conditions. There were 193 pipelines in which two or more failures occurred. The independent variables set to figure out dependent variables are listed in Table 2.

Variable . | Category . | Condition . | Number of group . | Ratio of group (%) . | Length (km) . |
---|---|---|---|---|---|

Installation year | Installation 1 | Before 1983 | 1,019 | 12.47 | 487.42 |

Installation 2 | 1983–1993 | 1,448 | 17.72 | 732.11 | |

Installation 3 | 1993–2003 | 2,635 | 32.25 | 2,216.08 | |

Installation 4 | After 2003 | 3,068 | 37.55 | 1,544.69 | |

Pipe type | Type 1 | Steel pipe | 4,114 | 50.36 | 2,756.40 |

Type 2 | Iron pipe | 3,341 | 40.89 | 1,889.89 | |

Type 3 | Others | 715 | 8.75 | 333.99 | |

Coating | Coating 1 | Epoxy | 2,807 | 34.36 | 1,951.40 |

Coating 2 | Enamel | 1,325 | 16.22 | 829.79 | |

Coating 3 | No coating | 4,038 | 49.42 | 2,199.10 | |

Pipe diameter | Diameter 1 | Below 500 mm | 2,186 | 26.76 | 1,062.87 |

Diameter 2 | 500 mm–1,000 mm | 2,309 | 28.26 | 1,495.40 | |

Diameter 3 | 1,000 mm–1,500 mm | 1,777 | 21.75 | 1,096.20 | |

Diameter 4 | 1,500 mm–2,000 mm | 1,015 | 12.42 | 661.19 | |

Diameter 5 | Above 2,000 mm | 883 | 10.82 | 664.63 | |

Pipe length | Length 1 | Below 250 m | 3,928 | 48.08 | 306.19 |

Length 2 | 250 m–500 m | 1,103 | 13.50 | 396.90 | |

Length 3 | 500 m–750 m | 755 | 9.24 | 466.42 | |

Length 4 | Above 750 m | 2,384 | 29.18 | 3,810.78 | |

Topography | Topography 1 | Road | 2,413 | 29.53 | 1,648.49 |

Topography 2 | Land | 4,968 | 60.81 | 2,732.16 | |

Topography 3 | River or others | 789 | 9.66 | 599.63 | |

Depth | Depth 1 | Below 1.5 m | 1,503 | 18.40 | 651.28 |

Depth 2 | 1.5 m–2.0 m | 2,030 | 24.85 | 1,330.53 | |

Depth 3 | 2.0 m–2.5 m | 1,943 | 23.78 | 1,341.41 | |

Depth 4 | 2.5 m–3.0 m | 1,150 | 14.08 | 776.88 | |

Depth 5 | Above 3.0 m | 1,544 | 18.90 | 880.18 |

Variable . | Category . | Condition . | Number of group . | Ratio of group (%) . | Length (km) . |
---|---|---|---|---|---|

Installation year | Installation 1 | Before 1983 | 1,019 | 12.47 | 487.42 |

Installation 2 | 1983–1993 | 1,448 | 17.72 | 732.11 | |

Installation 3 | 1993–2003 | 2,635 | 32.25 | 2,216.08 | |

Installation 4 | After 2003 | 3,068 | 37.55 | 1,544.69 | |

Pipe type | Type 1 | Steel pipe | 4,114 | 50.36 | 2,756.40 |

Type 2 | Iron pipe | 3,341 | 40.89 | 1,889.89 | |

Type 3 | Others | 715 | 8.75 | 333.99 | |

Coating | Coating 1 | Epoxy | 2,807 | 34.36 | 1,951.40 |

Coating 2 | Enamel | 1,325 | 16.22 | 829.79 | |

Coating 3 | No coating | 4,038 | 49.42 | 2,199.10 | |

Pipe diameter | Diameter 1 | Below 500 mm | 2,186 | 26.76 | 1,062.87 |

Diameter 2 | 500 mm–1,000 mm | 2,309 | 28.26 | 1,495.40 | |

Diameter 3 | 1,000 mm–1,500 mm | 1,777 | 21.75 | 1,096.20 | |

Diameter 4 | 1,500 mm–2,000 mm | 1,015 | 12.42 | 661.19 | |

Diameter 5 | Above 2,000 mm | 883 | 10.82 | 664.63 | |

Pipe length | Length 1 | Below 250 m | 3,928 | 48.08 | 306.19 |

Length 2 | 250 m–500 m | 1,103 | 13.50 | 396.90 | |

Length 3 | 500 m–750 m | 755 | 9.24 | 466.42 | |

Length 4 | Above 750 m | 2,384 | 29.18 | 3,810.78 | |

Topography | Topography 1 | Road | 2,413 | 29.53 | 1,648.49 |

Topography 2 | Land | 4,968 | 60.81 | 2,732.16 | |

Topography 3 | River or others | 789 | 9.66 | 599.63 | |

Depth | Depth 1 | Below 1.5 m | 1,503 | 18.40 | 651.28 |

Depth 2 | 1.5 m–2.0 m | 2,030 | 24.85 | 1,330.53 | |

Depth 3 | 2.0 m–2.5 m | 1,943 | 23.78 | 1,341.41 | |

Depth 4 | 2.5 m–3.0 m | 1,150 | 14.08 | 776.88 | |

Depth 5 | Above 3.0 m | 1,544 | 18.90 | 880.18 |

The size of the data of contrasting groups should be the same for the reliability of the discriminant analysis (Kim *et al.* 2013). To set the same size of data groups, systematic sampling was used. Further, it was applied after transforming the scale type variables including installation year, length of the pipeline, and depth to ordinal data. When the sample was selected, a random number table was utilized. Meanwhile, for the independent variable, which is to be included in discriminant, only a statistically significant variable was selected through a stepwise method. SPSS ver. 21.0 (IBM) was employed for statistical analysis. When the statistical analysis was conducted through a stepwise method, generally used in many cases, 0.05 of significant probability of F value, which includes variables in discriminant function, and 0.10 of significance probability of F value, which eliminates variables from discriminant function, were used (Koizumi *et al.* 2012).

The Wilk's lambda test, used to test the significance of the discriminant function, employing chi-squared distribution and Box's M with a corresponding F statistic, is a procedure for testing homogeneity of variance and covariance. These two tests were used to determine the validation of the discriminant analysis (Katos 2007).

The results of the discriminant analysis estimate a discriminant score, which determines where independent variable should belong according to the dependent variable groups. In this study, the discriminant score for the estimation of a qualitative result was converted to a quantitative failure rate to calculate the risk quantitatively. The failure rate was calculated through the discriminant score deduced from each pipeline and regression analysis between failure rates of each pipeline.

#### CoF (PDA)

The hydraulic analysis of a pipe network can be divided into two techniques according to the major subject to be interpreted: demand driven analysis (DDA) and PDA. DDA is used as a basic principle for most of the commonly used pipe network analysis programs such as EPANET. This is the method for the calculation of the head loss of each node under the assumption that the water demand of each node is always satisfied. In the case of the normal status of the water supply system, the application of DDA is not problematic. However, if the water demand increases rapidly due to fire or insufficient hydraulic pressure of each node because of a pipeline failure, an unrealistic problem, in which negative pressure is calculated, may occur. If the hydraulic pressure of the node decreased, a demand shortage would occur. PDA is the method to calculate node runoff considering the node's hydraulic pressure. Unlike DDA, which calculates node head under an assumption that water demand of the node is always satisfied, the PDA calculates the water supply according to the changes in the hydraulic pressure of the node. Further, the amount of water supply available and head would be obtained at the same time (Mays 2003). In other words, PDA is a method for the calculation of the amount of water available in an actual node in accordance with head-nodal outflow relationship (HOR).

*et al.*(1988) in the form of a power function was used as a basis for the PDA module of the WaterGEMS model.

Even if the required amount of water is not supplied during the repairing time, the required water can be supplied for certain times using the holding quantity in a reservoir or water storage. The suspension quantity was calculated by considering ease quantity, i.e., the holding quantity of the reservoir or water storage at the demand break point of the multi-regional water supply pipeline of region K. Table 3 lists the time required for the repair corresponding to the pipe diameter utilized in this study (K-water 2015). At this point, an additional five hours were added for the calculation of the time required to repair a failure, assuming that additional repair time would be required for road excavation if the pipe is laid beneath the road. Table 4 lists the demand of water and holding quantity of the reservoir or water storage.

Diameter (mm) . | <350 . | 400 . | 450 . | 500 . | 600 . | 700 . | 800 . | 900 . |
---|---|---|---|---|---|---|---|---|

Time (h) | 10 | 11 | 11 | 12 | 13 | 14 | 15 | 16 |

Diameter (mm) . | <350 . | 400 . | 450 . | 500 . | 600 . | 700 . | 800 . | 900 . |
---|---|---|---|---|---|---|---|---|

Time (h) | 10 | 11 | 11 | 12 | 13 | 14 | 15 | 16 |

Water supply area . | Water demand (m^{3}/d)
. | Holding quantity of reservoir (m^{3})
. | Water supply area . | Water demand (m^{3}/d)
. | Holding quantity of reservoir (m^{3})
. |
---|---|---|---|---|---|

SD1 area | 2,515 | 750 | D industry | 3,577 | 7,000 |

SH area | 23,929 | 7,000 | D hospital | 151 | 160 |

S industry | 6,405 | 6,000 | D dormitory | 2,782 | 2,500 |

HC area | 3,000 | 1,375 | DM area | 5,664 | 2,500 |

YJ area | 1,032 | 940 | Y apartment | 771 | 1,035 |

SW area | 1,706 | 1,140 | N apartment | 290 | 585 |

SD2 area | 6,148 | 3,113 | DB area | 5,640 | 3,330 |

AJ area | 3,005 | 2,000 | IW area | 2,177 | 1,700 |

Water supply area . | Water demand (m^{3}/d)
. | Holding quantity of reservoir (m^{3})
. | Water supply area . | Water demand (m^{3}/d)
. | Holding quantity of reservoir (m^{3})
. |
---|---|---|---|---|---|

SD1 area | 2,515 | 750 | D industry | 3,577 | 7,000 |

SH area | 23,929 | 7,000 | D hospital | 151 | 160 |

S industry | 6,405 | 6,000 | D dormitory | 2,782 | 2,500 |

HC area | 3,000 | 1,375 | DM area | 5,664 | 2,500 |

YJ area | 1,032 | 940 | Y apartment | 771 | 1,035 |

SW area | 1,706 | 1,140 | N apartment | 290 | 585 |

SD2 area | 6,148 | 3,113 | DB area | 5,640 | 3,330 |

AJ area | 3,005 | 2,000 | IW area | 2,177 | 1,700 |

## RESULTS AND DISCUSSION

### Result of risk assessment

#### PoF

#### CoF

For the threshold pressure of water demand break point for the PDA analysis, 39.1 m, a hydraulic pressure for consumers indicating the minimum pressure at normal conditions, was applied. If the pressure head of the water demand break point is higher than 39.1 m, the entire water demand can be supplied. In addition, if the pressure head is between 0 and 39.1 m, only parts of the water demand can be supplied by a power function. Further, if the pressure head of the water demand break point is less than 0 m, the required water cannot be supplied.

Table 5 lists the predicted water suspension quantity during the failure repair in case of a failure on each of the 232 multi-regional water supply pipelines of region K, which indicates the sum of suspension quantity at each demand break point. The results of the estimation of suspension quantity indicate that over 10,000 m^{3} of suspension occurs if a failure occurs in zones A and B. Because suspension quantity is different for failures occurring in time with low and high water consumptions, the average suspension quantity is indicated. The results of the calculation of risk with comprehensive considerations of the PoF and CoF are shown in Table 5. As shown in Table 5, CoF is 0 in systems F, G, H, I, J, K, L, and N, and the risk is also calculated as 0. It is possible to satisfy the water demand during repairing time even if a failure occurs in the water pipelines because the small pipe diameter of the system does not require much time to recover and the reservoir in the system has abundant average water capacity.

System ID . | Pipe length (km) . | PoF (failures/km/yr) . | CoF (m^{3}/failure)
. | System risk (m^{3}/yr)
. |
---|---|---|---|---|

A | 5.027 | 0.0608 | 17,921 | 5,477 |

B | 6.799 | 0.0460 | 11,118 | 3,477 |

C | 8.196 | 0.0565 | 2,133 | 988 |

D | 2.601 | 0.0712 | 74 | 14 |

E | 5.889 | 0.0529 | 430 | 134 |

F | 7.461 | 0.0529 | 0 | 0 |

G | 4.088 | 0.0736 | 0 | 0 |

H | 2.702 | 0.0437 | 0 | 0 |

I | 0.562 | 0.0230 | 0 | 0 |

J | 3.575 | 0.0564 | 0 | 0 |

K | 8.287 | 0.0646 | 0 | 0 |

L | 5.226 | 0.0658 | 0 | 0 |

M | 4.757 | 0.0526 | 264 | 66 |

N | 2.727 | 0.0797 | 0 | 0 |

System ID . | Pipe length (km) . | PoF (failures/km/yr) . | CoF (m^{3}/failure)
. | System risk (m^{3}/yr)
. |
---|---|---|---|---|

A | 5.027 | 0.0608 | 17,921 | 5,477 |

B | 6.799 | 0.0460 | 11,118 | 3,477 |

C | 8.196 | 0.0565 | 2,133 | 988 |

D | 2.601 | 0.0712 | 74 | 14 |

E | 5.889 | 0.0529 | 430 | 134 |

F | 7.461 | 0.0529 | 0 | 0 |

G | 4.088 | 0.0736 | 0 | 0 |

H | 2.702 | 0.0437 | 0 | 0 |

I | 0.562 | 0.0230 | 0 | 0 |

J | 3.575 | 0.0564 | 0 | 0 |

K | 8.287 | 0.0646 | 0 | 0 |

L | 5.226 | 0.0658 | 0 | 0 |

M | 4.757 | 0.0526 | 264 | 66 |

N | 2.727 | 0.0797 | 0 | 0 |

#### Risk assessment and prioritization of renewal

The PoF and CoF refer to the weighted averages of the calculated values of each section within the pipelines for the length of the pipelines. System risk can be seen as suspension quantity risk for an entire line.

The priority of renewal can be set in accordance with the order of the quantitative risk of failure of each pipeline zone. At this point, the pipelines predicted to have no risk and the ones inducing tolerable risk were excluded from the priority. Then, the results of the prioritization of renewal are listed in Table 6.

Rank . | Section ID . | Individual risk (m^{3}/yr)
. | Rank . | Section ID . | Individual risk (m^{3}/yr)
. |
---|---|---|---|---|---|

1 | A12 | 1,251 | 15 | B20 | 150 |

2 | B3 | 1,039 | 16 | B19 | 131 |

3 | A11 | 987 | 17 | B2 | 121 |

4 | A5 | 795 | 18 | B15 | 119 |

5 | A7 | 763 | 19 | C1 | 114 |

6 | B21 | 582 | 20 | A2 | 92 |

7 | A10 | 566 | 21 | A6 | 87 |

8 | A9 | 425 | 22 | C2 | 79 |

9 | A3 | 413 | 23 | B2 | 73 |

10 | B12 | 344 | 24 | C3 | 66 |

11 | B17 | 259 | 25 | C4 | 62 |

12 | B14 | 214 | 26 | C5 | 57 |

13 | B22 | 161 | 27 | C6 | 56 |

14 | B7 | 158 | Others | Tolerable risk |

Rank . | Section ID . | Individual risk (m^{3}/yr)
. | Rank . | Section ID . | Individual risk (m^{3}/yr)
. |
---|---|---|---|---|---|

1 | A12 | 1,251 | 15 | B20 | 150 |

2 | B3 | 1,039 | 16 | B19 | 131 |

3 | A11 | 987 | 17 | B2 | 121 |

4 | A5 | 795 | 18 | B15 | 119 |

5 | A7 | 763 | 19 | C1 | 114 |

6 | B21 | 582 | 20 | A2 | 92 |

7 | A10 | 566 | 21 | A6 | 87 |

8 | A9 | 425 | 22 | C2 | 79 |

9 | A3 | 413 | 23 | B2 | 73 |

10 | B12 | 344 | 24 | C3 | 66 |

11 | B17 | 259 | 25 | C4 | 62 |

12 | B14 | 214 | 26 | C5 | 57 |

13 | B22 | 161 | 27 | C6 | 56 |

14 | B7 | 158 | Others | Tolerable risk |

### Alternatives for risk mitigation

If pipeline A12, which was estimated to be the top priority for renewal through risk assessment, was replaced with a new one, the PoF would be reduced from 0.0937 breaks/km/yr in the current level to 0.0718 breaks/km/yr, decreasing about 382 m^{3}/yr of risk. Further, if all pipelines in system A were replaced, the entire system risk would be decreased from 5,477 to 2,761 m^{3}/yr. The changes in the type and diameter of pipes, if any, when replacing the existing pipelines with new ones, may cause a hydraulic problem. Therefore, the existing pipelines were replaced on the assumption that new water pipelines should have the same type and diameter as the previous ones.

If the holding quantity is increased by enlarging the size of the reservoir in the current system, the redundancy will be increased as well, and therefore, the risk will be reduced. In pipeline A12, which showed the highest level of risk, the holding quantity of the reservoir that needs to be increased to reduce the risk is as follows. If the holding quantity of the reservoir is as described in Table 7, the risk of failure of any pipeline of multi-regional pipelines of region K was found to be tolerable.

. | Holding quantity of SD1 reservoir (m^{3})
. | Holding quantity of SH reservoir (m^{3})
. | Holding quantity of SD2 reservoir (m^{3})
. | A12 risk (m^{3}/yr)
. |
---|---|---|---|---|

Before increase | 750 | 7,000 | 3,113 | 1,251 |

After increase | 2,000 | 21,000 | 5,000 | 49 |

. | Holding quantity of SD1 reservoir (m^{3})
. | Holding quantity of SH reservoir (m^{3})
. | Holding quantity of SD2 reservoir (m^{3})
. | A12 risk (m^{3}/yr)
. |
---|---|---|---|---|

Before increase | 750 | 7,000 | 3,113 | 1,251 |

After increase | 2,000 | 21,000 | 5,000 | 49 |

On the other hand, in the case of the construction of double piping by laying new pipes with the same pipe size in zones A, B, and C, a certain level of water suspension would occur due to the hydraulic pressure in some zones. However, the level of risk would be tolerable. In conclusion, when compared with the replacement of existing pipes with new ones and the increase in the reservoir size, laying of additional pipes with the same sizes as the existing ones in zones A, B, and C would have the largest risk reduction.

For the multi-regional pipeline of K, the utilization of all measures for risk reduction is the most effective way to prevent risk despite the failure on any pipeline. However, because of the high cost of implementation, the most practical measure needs to be utilized.

## CONCLUSIONS

In this study, the risk of failure was calculated for the multi-regional water supply pipelines of region K. From the results, the priority of renewal was set for each risk, and the measures for the risk reduction were proposed.

For the PoF, the quantification theory type II converts the qualitative results to the failure rate of a pipeline. The discriminant formula, which was constituted by utilizing the data from the national multi-regional water supply pipelines, resulted in 81.1% hit ratio. Further, the regression equation, which indicates the discriminant score and failure rate, was obtained. The results obtained from the application of the regression formula of the failure rate to the multi-regional water supply pipelines of region K indicated that the zones N, G, and D have the highest failure rates. The CoF was calculated by the amount of water that cannot be supplied in case of failure using the PDA. For this analysis, the threshold pressure was set as a minimum hydraulic pressure of the demand break point for a normal condition. During the repair of a failed pipeline, the results of the PDA and the average holding quantity of the reservoir were considered to calculate suspension quantity. In the case of a failure in zone A of the multi-regional pipeline of region K, the effect of failure was found to be the largest. The risk considering the PoF and CoF comprehensively was found to be the largest in section A12. Meanwhile, the case where 80% of the daily average water consumption can be supplied was defined and expressed as the tolerable risk.

Further, as alternatives to reduce the risk, the replacement of a certain pipeline with a new one, increasing the holding quantity of reservoir until a tolerable level of risk is achieved, and the construction of double piping by laying a new pipeline were proposed. As a result, the construction of double piping by laying a new pipeline was found to be the most effective measure for the risk reduction. In particular, the construction of double piping with the same pipe size as that of the existing pipelines of zone A, B, and C would result in a tolerable risk of failure of the entire region K. Therefore, this measure was inferred to be suitable.

Finally, it would be possible to utilize the results of this study as the basic data for the establishment of an investment plan for the renewal of water supply pipelines and asset management plan.

## ACKNOWLEDGEMENT

This study was funded by the Korean Ministry of Environment (MOE) as ‘Public technology program based on Environmental Policy (2014000700001)’.