Comparative Study on Strategies for the Division of Earthquake-Proof Strengthening Segments to Reinforce the Reliability of Water Supply Systems

Abstract

It is very important to secure the sustainability of physical and non-physical social infrastructure facilities in the event of a disaster. The water supply network is particularly vulnerable to seismic damage, and so physical earthquake resistance is very necessary to adapt to or withstand disaster situations. This study evaluated various strategic methods to improve the reliability of water distribution network systems in the event of an earthquake disaster with a focus on structural earthquake-proofing methods for pipelines. For this purpose, three major flow-, diameter- and connection-hierarchy-based earthquake proofing strategies are proposed. We quantified the extent to which earthquake reliability improved after the strengthening of the earthquake-proofing of the pipeline segments, which had been divided based on the proposed strategies. The proposed methodology of dividing the pipeline segments for earthquake-proof strengthening was applied to the water supply system of the Republic of Korea and analyzed thereafter. As a result, it was confirmed that the associated costs and the extent of the improvement in the reliability of earthquake proofing for each strategy and scenario need to be precisely analyzed. Thus, it is necessary to execute strategic earthquake proofing of pipelines with medium size diameters and which occupy most of the length of a mainline, in order to simultaneously satisfy the reliability and cost efficiency of the relevant water supply. However, additional earthquake proofing for segments of a higher level of flowrate is required because a marked drop in overall reliability is caused if they are damaged. In addition, because the effect of an increase in reliability in comparison with the costs incurred is insignificant in the case of some low demand and small-diameter pipeline segments, it is reasonable to exclude earthquake resistance strategies for these sections. The proposed study results—determining the level of importance of each resistance method—can be utilized to make a combined plan for optimal earthquake-proofing strategies.

1. Introduction

Securing the sustainability of physical and non-physical social infrastructure facilities in the event of a disaster is very important. Research to evaluate the impact of damage to water pipe network systems began with a study to quantitatively analyze the risk of pipe failure, and many studies are still in progress [1,2,3]. Earthquakes are representative disasters that can cause multiple forms of damage to pipelines. Studies on earthquake disaster reliability evaluations of water supply systems (WSSs) can be divided into the development of new index-based reliability models and studies on the strengthening of the performance or resilience of earthquake-proofing. In the case of earthquake disaster reliability evaluation models, the extent of physical damage to the structures that compose a water supply system are categorized first. Then, the possibility of water supply prior to and following the occurrence of an earthquake is quantified and presented through hydraulic analysis in the event of an earthquake with a predefined magnitude [4,5].

Strengthening of the resilience of water supply systems to earthquakes can be approached through a wide range of structural or nonstructural formats [6]. Supplementing the structural and material earthquake proofing of structures such as pipelines or the strengthening of back-up functions such as the installation of separate emergency water storage tanks and cisterns can be referred to as structural approach methods. The establishment of emergency countermeasure plans to promptly cope with the occurrence of an earthquake, or collaborations with institutions and the establishment of strategies for the efficient arrangement of manpower and equipment for quick service restoration are representative of nonstructural approach methods. Among the various resilience enhancement methods, academic studies on the establishment of strategies for the efficient arrangement of manpower and equipment have been presented and carried out by various researchers since the 2000s [7,8,9,10,11,12,13]. In their latest study, Song et al. (2022) used a genetic algorithm to deduce and present optimal restoration strategies that consider the restoration of supply routes to important, prioritized facilities as well as aspects of changes in the demand pattern in evacuation shelters, hospitals and general end users following an earthquake with a genetic algorithm [13].

The techniques for strengthening facilities against earthquakes comprise a very important topic that can be used as an assertive measure to prevent and reduce earthquake damage. Kuwata and Takada (2003) stochastically analyzed the probability of water supply to very important hospital facilities to reduce casualties at the time of a large magnitude earthquake [14]. The possibility of damage to reservoirs, pipelines and buildings was computed, and the number of hospitals and hospital beds present in the WSSs was factored into the computation of the probability of the cessation of the functions of the hospitals. To increase the probability of water supply, the laying out of parallel pipelines and the means of constructing pipelines that are highly resistant to earthquakes were reviewed, as well as an analysis and presentation of the effects of the application of the corresponding methods on the enhancement of the probability of water supply. Some studies presented the means to improve the structural earthquake-proof performances of pipelines by considering the environment of the geological placement of the pipeline as well as a method of designing joints for pipelines that have strong earthquake-proof resilience to seismic waves [15,16,17]. Studies have been conducted to determine individual pipelines that need improvement using simulated annealing techniques, for when costs are limited [18,19]. Recently, as part of an evaluation of the methodology for calculating the disability priority of water pipes, the possibility of the destruction of multiple pipelines due to an earthquake was examined [20]. In addition, under conditions of a limited construction budget, single and multi-purpose optimization methods for maximizing the reliability of the WSSs in the event of an earthquake disaster were proposed and the results evaluated [21,22].

However, since this strengthening method is aimed at achieving an optimal design for the entire pipeline or at improving the individual pipelines of a WSS, it fails to consider the economic rationality and connectivity and water flow of the current system. In recent years, studies have been carried out on the setting of pipeline segments for which the improvement of earthquake-proof performance is needed to supplement the pipelines’ weaknesses. A methodology and set of procedures were proposed to determine the major pipeline sections (critical categories), while considering the frequency of earthquakes, key connection sections of water supply, and socio-economic ripple effects [23]. In addition, reliability evaluation was performed in the event of a soil disaster according to the seismic design of each section in consideration of the water supply path [24]. Moreover, the authors quantified the extent of improvement in reliability when earthquake proofing was executed for each water supply route of a WSS with various sources of supply and water supply routes. For this purpose, the critical path of the WSS of the Republic of Korea, that had experienced a previous high magnitude earthquake, was divided into nine categories and the reliability and earthquake proofing costs of the WSSs were computed and compared. As a result of the application of this study, it was confirmed that reliability and demand for water supply and earthquake proofing costs must be considered comprehensively in order to establish earthquake proofing strategies for the critical path.

However, this study has a limitation in that it only examined connectivity in accordance with the WSSs of the pipeline rather than in accordance with consistent standards (e.g., the determination of priority through hydraulic review based on pipeline flow rate) or through various methods that divide the entire system into nine segments for earthquake proofing. It is clear that the replacement of pipeline segments vulnerable to earthquakes with earthquake-proofed and corrosion-resistant pipes can reduce the damage arising from earthquakes and improve the network performance following an earthquake. However, if it is difficult to accurately determine the pipeline segments vulnerable to earthquake, it is essential to select strategic and efficient strengthening segments by reviewing various segment setting standards such as hydraulic and hierarchy aspects.

In this study, in relation to earthquake-proof design, an earthquake reliability evaluation was conducted based on a pipeline strengthening scenario—the typical strategy for WSSs. Based on the analysis results, we attempted to investigate a strategic route selection factor that can maximize seismic reliability. For this purpose, three major flow-, diameter- and connection-hierarchy-based strategies are presented to quantify the aspects of earthquake reliability that must be improved when strengthening the earthquake-proofing of pipeline segment categories based on the proposed strategies. The proposed methodology of the pipeline segment division for earthquake-proof strengthening was applied to the ‘A’ WSS of the Republic of Korea and then analyzed. Since the demand, extension and diameter of the pipeline are distributed very differently, the costs incurred in strengthening the segment were additionally reviewed for an objective comparison of the evaluation results and were comparatively analyzed along with the extent of the improvement of hydraulic performance.

2. Methods of Composing Strategic Earthquake-Proof Pipeline

2.1. Hydraulic Analysis Technique for Seismic Events

To quantitatively evaluate the reliability of the WSS during earthquakes, it is essential to apply the hydraulic analysis technique. In this study, the supply reliability of a WSS in the event of an earthquake is computed by operating the REVAS.NET model proposed by Yoo et al. (2016) [21]. The hydraulic analysis technique of water supply networks is divided into demand driven analysis (DDA) and pressure driven analysis (PDA). In DDA, all quantities supplied to the pipe network are considered as known values, and hydraulic analysis is performed on the premise that the quantity set is necessarily supplied. It is not possible to directly simulate the loss of water due to abnormal situations such as earthquake disasters and pipe breakage accidents, nor is it possible to simulate the decrease in water supply to consumers due to the consequent decrease in water pressure. In the case of an abnormal situation such as an earthquake disaster or in an area with a large amount of leakage, the supply and usage are not the same, so it is common to perform a PDA that can take into account changes in the supply and leakage depending on the water pressure. Recent models such as Water Network Tool for Resilience (WNTR [5]) and EPANET2.2 [25] support the PDA analysis function.

The REVAS.NET model uses the EPANET2 (2000) [26] source code, which is based on DDA. However, to solve the problem of DDA, it is supplemented by the application of quasi-PDA, which is calculated by repeatedly performing DDA and changing the available supply amount according to the derived pressure.

In this study, PDA and quasi-PDA, which are known to be more reasonable than DDA, were used for earthquake disaster simulation, and the difference in results was analyzed in advance. Water supply reliability ($S_s$) deduced with the operation of REVAS.NET can be computed by using Equation (1).

$$S_s=\frac{Q_{Available demand}}{Q_{Requried demand}}\times 100\%$$

(1)

Here, Q_{Available demand} signifies the quantity of water that can be supplied to the entire water distribution network system following an earthquake, while Q_{Required demand} signifies the quantity of water demanded by the WSSs in normal situations and $S_s$ signifies quantification of the supply capability of the total water distribution network system immediately following an earthquake. These values have a range of 0~100%. A value closer to 0 signifies that the quantity of water that can be supplied after an earthquake is smaller in comparison with that supplied normally prior to the earthquake, while a value closer to 100% signifies that the water supply is harmonious.

As shown in

Table 1. Comparison of water supply reliability ($S_s$) according to the hydraulic analysis method.

Case	$\mathbf{Water}\mathbf{Supply}\mathbf{Reliability}\left({\mathit{S}}_{\mathit{s}}\right)$
	Quasi-PDA	PDA
Case 1 (M = 5)	66.4	75.7
Case 2 (M = 7)	42.8	45.4

, cases 1 and 2 represent situations where earthquakes of magnitudes of 5 and 7, respectively, occurred in the water supply system of a medium-sized city in Republic of Korea. The improved version of the REVAS.NET model was programmed as shown in Figure 1 and, additionally, performed PDA. Table 1 shows the results of calculating the water supply reliability according to the two hydraulic analysis (quasi-PDA and PDA) methods.

When examining the water supply reliability values in cases 1 and 2, it can be confirmed that the water supply reliability during to earthquake disasters is relatively large when the methodology with hydraulic pressure analysis is used compared with the hydraulic analysis method installed in the existing model. That is, when quasi-PDA is applied, more conservative reliability is calculated compared with PDA. As explained above, the quasi-PDA model is a method by which to solve the excessive negative pressure problem that can occur in a single DDA model by repeatedly performing it. Nevertheless, since quasi-PDA is based on the DDA model, it can be said that it has limitations and disadvantages. Therefore, it can be said that the PDA model derives more realistic results than the quasi-PDA. However, since the PDA model also has a step of inputting parameters with uncertainty, it is not appropriate to say that the PDA method is unconditionally correct and that quasi-PDA is incorrect. In terms of the relative evaluation of scenario-based outcomes, it can be seen that both quasi-PDA and PDA can be used for the relative comparison of strategies for strengthening seismic reliability.

The simplified operation method and methodology of REVAS.NET proposed in this study are as follows. First, secure the pipeline network information (pipeline diameter, etc.) to which the model is to be applied. Second, compute the level of vulnerability for each compositional element. Third, stochastically compute the earthquake simulation. In this study, the location of the earthquake was generated based on the location of the actual past occurrence of an earthquake. Fourth, determine the status of system compositional elements after the earthquake and create a hydraulic analysis model based on the status determined. The reliability of the system is computed by repeating the aforementioned processes with Monte Carlo simulation. In this study, 100,000 simulations were run to secure the reliability of the results. In addition, presume that the segment deduced in accordance with the various segment division strategies (flow-based end-user-oriented, pipeline diameter-oriented and connection-hierarchy-based supplementation of the earthquake-proof performances of pipelines) has been earthquake-proofed and then repetitively execute the aforementioned processes. The presumption that earthquake proofing has been achieved signifies that there is no occurrence of abnormal damage such as leakage or breakage of earthquake-proofed pipelines in the event of an earthquake. We assumed that an earthquake-resistant pipe that could operate sufficiently would be used under conditions associated with the largest earthquake magnitude (M = 7) applied in this study. The earthquake resistance of pipes can be implemented by utilizing pipes and joints that are resistant to earthquakes. Lastly, compute the water supply reliability ($S_s$, System Serviceability) and costs of earthquake-proof strengthening for each strategy deduced in accordance with the operation of the model, and analyze their effects for each strategy. Detailed issues related to earthquake-proof strengthening strategies and costs are presented in the next section.

2.2. Method of Strategic Segment Division of Earthquake-Proof Strengthening of WSS

The methodology established in this study for the evaluation of water supply capabilities related to the composition of strategic earthquake-proof pipelines of water distribution network systems is presented in Figure 2. To establish a means of earthquake-proof design, three methodologies and various scenarios were established.

The goals of this study include establishing the segment division strategies for the improvement of earthquake-proof performances as the operational scenario, executing supply capability evaluations for each scenario, and comparatively evaluating the results for each strategy. Three major segment division strategies for earthquake proofing were established as illustrated in Figure 3, which is a schematization of the water distribution network system in the format of a simple model. The large red circle signifies a high-demand end user, while the blue circle and black lines represent junctions with average demand and pipelines, respectively.

The strategies established in this study are illustrated in

Table 2. Strategy for earthquake-proof strengthening of a water distribution network system.

Earthquake- Proof Strengthening Strategy No.	Method of Establishing the Strategy	Detailed Issues
1	In the order of demand of the supply line to high-demand end user	Strengthen the pipelines connecting the largest-demand nodes
		Earthquake-proof strengthening in the order of demand
2	In the order of pipeline diameter size	Commence earthquake-proof strengthening in three stages by classifying the diameter of the pipelines of the corresponding system (in the case of the ‘A’ system in Republic of Korea, apply by classifying into 700~1500 mm, 200~600 mm and 0~150 mm segments)
3	Based on river ranking	Apply the method of assigning generalized ranking to tributaries and main stream in accordance with their relative locations (in the case of the ‘A’ system of Republic of Korea, it is divided into primary and secondary segments for application)

and are classified into three categories. The first strategy divides the earthquake-proof strengthening segments based on the scale of the demand. The demand of the consumer has different distributions for each system. There are high-demand end users that consume large quantities of water in a majority of WSSs and strengthening the supply lines against earthquakes for these high-demand end users can contribute to the enhancement of reliability. Therefore, the execution of earthquake-proof strengthening was considered a foremost priority to make sure that water supply to the junctions with the largest demand is possible. Moreover, earthquake-proof strengthening was executed sequentially in the order of the size of demand, and this approach is set as Strategy 1. The second strategy executes earthquake-proof strengthening in the order of the size of the pipeline diameter. Since a larger pipeline diameter means the transfer of water with greater flux, it is meaningful to perform earthquake proofing for pipeline segments with greater flux. Lastly is to use the stream order method proposed by [27]. Stream order refers to the allocation of ratings to the tributaries and mainstream according to the relative locations of streams. In this study, ratings of river improvement were set for the applicable water distribution network system with the establishment of a strategy for the execution of earthquake-proof strengthening in the order of waterways with a higher rating. At this time, it is presumed that pipelines established by the strategy do not undergo destruction regardless of an earthquake of any magnitude. For example, in the event of the application of the methodology under the presumption of Strategy 1 (pipeline connecting the water source to a high-demand end user), the supply pipeline extending to the high-demand end user will never be destroyed.

2.3. Evaluation of Costs of Earthquake-Proof Strengthening for Each Strategy

The cost of replacement of earthquake proofing pipelines applied in this study is illustrated in

Table 3. Cost of replacement of seismic performance pipes [16].

Pipe Diameter (mm)	Earthquake Resistant Japanese Ductile Iron Pipe (USD/18 ft)
	Bare Cost without Backfill Cost	Total Cost with Backfill Cost
101.6	103.58	108.07
152.4	94.57	99.72
203.2	151.62	157.45
254	196.61	203.11
304.8	259.94	267.14
355.6	303.16	311.07
406.4	316.50	325.13
457.2	412.80	422.17
508	423.10	433.22
609.6	474.25	485.91

. It is important not only to evaluate reliability in accordance with the strategies proposed above, but also to compute and analyze the economic costs of replacing pipelines. Table 3 is proposed by Shahandashti and Pudasaini (2019) and illustrates the costs of an earthquake-proof pipe with a length of 18 ft [16]. Lee et al. (2020) formulated and presented a regression equation based on the data of Table 3, since there is a need to compute the costs of earthquake-proof pipelines with various diameters with Equation (2) [24]. Similarly, this study computed the economic costs of earthquake-proof strengthening for each strategy by using the proposed regression equation and then used the results to analyze and compare the outcomes of earthquake-proof reliability evaluation.

$$C_R=0.8392D-0.0536$$

(2)

Here, C_R is the pipe replacement cost derived by the regression equation. D denotes the pipe diameter.

3. Reliability Evaluation of Earthquake Strategy

3.1. Subject Regions

The industrial WSS of City A, a representative industrial city in the Republic of Korea, was selected as the subject region for the application of the methodology proposed in this study (Figure 4). There was an earthquake with a magnitude of 5.0 in its vicinity in 2016, but there was no damage to the WSS. The subject region is a city situated on the southern seashore and has a higher probability of an earthquake in comparison with any other regions in Republic of Korea. In addition, this region is situated in the close vicinity of the circum-Pacific earthquake belt with a high probability of earthquake.

Total demand of the corresponding system is 102,036 m³/day (CMD) with a total of 12 junctions with demands of more than 1500 CMD. Accordingly, 12 lines to be strengthened were composed in the order of the demands under Strategy 1 presented in Table 2. More detailed information is given in the next section. The total length of the pipeline is 27.60 km, composed of 204 junctions and 210 pipelines. In this study, water supply reliability evaluation was not considered for the emergency supply pipeline and the average water pressure of the corresponding system was 15.07 m, thereby maintaining appropriate water pressure for water supply.

3.2. Results of Segment Division According to Earthquake-Proof Strengthening Strategies

Results of the application of segment division strategies for the subject region are schematized in Figure 4. The strategy for strengthening the earthquake-proofing in sequence was determined by dividing the segment that supplies water to the 12 junctions with demand of more than 1500 CMD first. A supply line for each junction established was assigned with a scenario number as illustrated in

Table 4. $S_s$ results for each strategic earthquake strengthening.

Strategy No.	Scenario No.	Demand (CMD)	${\mathit{S}}_{\mathit{s}}$	Increase Rate	Rank
Entire system		102,036	84.87	-	-
1	1	37,100.66	91.54	6.67	3
	2	27,145.22	89.72	4.85	4
	3	9672.53	86.02	1.15	6
	4	8584.7	85.96	1.09	7
	5	6629.41	85.35	0.48	8
	6	5917.98	85.09	0.22	10
	7	3715.73	85.12	0.25	9
	8	2309.87	84.98	0.11	13
	9	2274.75	85.01	0.14	12
	10	2065.18	84.91	0.04	16
	11	1776.3	84.97	0.1	14
	12	1681.14	84.74	−0.13	17
2	1	-	92.96	8.09	2
	2	-	86.35	1.48	5
	3	-	84.94	0.07	15
3	1	-	95.62	10.75	1
	2	-	85.03	0.16	11

. Figure 5a illustrates the corresponding junctions, with a red color signifying the junction with the largest demand (37,100 CMD). Therefore, a total of 12 scenarios were composed in detail with the presumption that water supply is possible without destruction of the pipelines that correspond to each of the scenarios under any circumstances whatsoever. After that, the lines supplied to the 12 consumers, each selected in the order of demand, were individually simulated to be unconditionally reinforced.

The status of Strategy 2 is given in Figure 5b. The detailed scenario distinguishes three major situations. The first scenario is to execute earthquake proofing for pipeline diameters in the range of 0~150 mm, while the second and the last scenario execute earthquake proofing for pipeline diameters in the ranges of 200~600 mm and the largest diameter of 700~1500 mm, respectively. The pipelines with diameters in the ranges of 0~150 mm, 200~600 mm and 700~1500 mm have total lengths of 8719.48 m, 5817.37 m and 13,794.97 m, respectively.

The status of Strategy 3 is given in Figure 5c and classification into a total of two rankings in accordance with the rule of assigning river ranking of [25] was possible. It was found that the primary and secondary segments have lengths of 17,389.81 m and 10,942.01 m, respectively.

3.3. Application Results

3.3.1. Results of Water Supply Reliability ($S_s$, System Serviceability)

To generate random epicenters, a two-by-two grid was created and laid on the study network. The rectangular boundary of the grid is defined by the four end nodes: north, south, east, and west as shown in Figure 6. In other words, a total of nine intersections occur according to the two-by-two grid, and it is assumed that earthquakes occur equally at the nine intersections. A total of 100,000 earthquakes are generated, and a consistent number of earthquakes are assigned at each intersection of the grid.

Currently, the supply capability of the entire system without an earthquake-proof design after the occurrence of a magnitude 7.0 (M7) earthquake is found to be 84.87%. This means that 15.13% of the total supply cannot be used by consumers in the event of a magnitude 7.0 earthquake. Even in the event of a relatively high magnitude earthquake, the pipeline of the existing system is found to have high supply capabilities.

Results of the evaluation of the supply capabilities of the three earthquake-proof segment division strategies in the event of an earthquake are given in Table 4 and Figure 7. Strategy 1 is composed of 12 scenarios. All the scenarios selected junctions with demands of more than 1500 CMD and Scenario 1, which is for the largest end-user, displayed the highest supply capability (91.54%). This means that the end-user will lose only 8.46% of the water normally supplied by the system even when a magnitude 7.0 earthquake occurs. However, it can be confirmed that with a gradual drop in the demands of the corresponding junction, the supply capabilities also decrease correspondingly. In particular, in the event of the application of earthquake proofing for the line that supplies water to the junction with the lowest demand, supply capability (84.74%) lower than that prior to the earthquake-proof strengthening resulted. This means that there is uncertainty that the value of two decimal places can change in the simulation model. In addition, the implications of the results presented in Table 4 are that Strategies 1–12 do not show any improvement at all, despite our consideration of the uncertainty of the simulation model. A pipeline reinforced by Strategies 1–12 is part of a secondary network, if the existing pipe is damaged by an earthquake, the effect of reinforcement is lost.

These results signify that, although strengthening of earthquake-proof pipelines based on the demands of the end user could be a good strategy, the effect of an increase in water supply reliability in comparison with the costs incurred may not be significant in the event of the application of earthquake proofing for a supply line with a lesser demand than that with a higher demand.

Strategy 2 was applied by dividing the pipeline diameters into three segments, with the result that the strengthened earthquake-proofing of all pipelines with diameters in the range of 700~1500 mm displayed the highest supply capabilities (92.96%). In addition, the scenarios for the diameters in the ranges of 200~600 mm and 0~150 mm displayed supply capabilities of 86.35% and 84.94%, respectively. From the perspective of the overall ranking with considerations for all strategies and scenarios, the strengthening of the pipelines with larger diameters was found to be a good strategy for strengthened earthquake-proofing. However, from a realistic perspective, strengthening all the pipelines with corresponding diameters is not realistic. Therefore, there is a need for additional economic analysis in accordance with the pipeline diameter and length and this is presented in the next section.

Lastly, Strategy 3 comprises scenarios in which the pipeline network is divided into a primary and a secondary network by applying the river ranking method proposed by [29]. First, in executing earthquake-proof strengthening for pipelines that correspond to primary river ranking, the supply capability was 95.62%, thereby illustrating the highest water supply capability among all strategies. This was determined to be the result for the majority of the compositional elements of the systems corresponding to the primary pipeline.

3.3.2. Results of Evaluation of Economic Value

In the previous section, $S_s$, in accordance with each strategy, was analyzed. Since earthquake reliability is determined by diameter, length, demands, etc. of the pipeline, there is a need to additionally consider the economic costs from a realistic perspective. Therefore, this study computed the costs of earthquake-proof strengthening for each strategy and an earthquake reliability result evaluation was undertaken.

Table 5. Results of pipeline replacement costs necessary for strategic strengthening of earthquake-proofing.

Strategy No.	Scenario No.	Costs of Pipeline Replacement ($ ‘000)	Rank	Proportion Compared to Entire Pipeline Replacement (%)
Entire system		2166.87	-	100
1	1	696.04	13	32.12
	2	561.36	11	25.91
	3	493.21	8	22.76
	4	835.3	15	38.55
	5	551.2	10	25.44
	6	488.04	7	22.52
	7	424.37	5	19.58
	8	512.25	9	23.64
	9	348.82	4	16.10
	10	611.23	12	28.21
	11	737.31	14	34.03
	12	431.29	6	19.90
2	1	1833.24	16	84.60
	2	256.12	3	11.82
	3	77.52	1	3.58
3	1	2059.14	17	95.03
	2	107.73	2	4.97
Average		648.48	Average	29.93

and Figure 8 illustrates the costs of earthquake-proof strengthening in accordance with each strategy. For the computation of the costs of earthquake-proof strengthening, the regression equation presented in the methodology above was utilized.

First, in the case of Strategy 1, Scenario 4 was found to incur the highest costs of earthquake-proof strengthening. This signifies that the corresponding pipelines are the longest and include a lot of pipelines with large diameters. On the other hand, Scenario 1 was found to have costs ranked at fifth in spite of its highest demands.

In the case of Strategy 2, the costs increase in the order of scenarios with larger pipeline diameter. Because a smaller number of pipelines is included in the system with decreases in the pipeline diameter, the costs also decrease. As a result of the application of the river ranking method, an increase in the number of pipelines corresponding to the primary rank induces an increase in costs. An average of 648,480 USD is needed to improve the supply capability in comparison with that of the existing system, which corresponds to 29.93% of the cost of the total replacement of the pipelines. As a result, in terms of the cost of pipeline replacement, Scenario 3 of Strategy 2, which is earthquake proofing of pipelines with the smallest diameter, obviously incurred the lowest costs. Since earthquake resistance requires a lot of cost, economic efficiency must be clearly considered. However, it is clear that economic costs must be invested at a level that guarantees the effect of earthquake resistance at a certain level.

3.4. Comprehensive Evaluation

Comprehensive results in accordance with $S_s$ and costs of the earthquake-proof strengthening of pipelines are illustrated in

Table 6. Results of $S_s$ value and pipeline replacement costs in accordance with strategies.

Strategy No.	Scenario No.	${\mathit{S}}_{\mathit{s}}$ (%)	Rank (a)	Costs of Pipeline Replacement ($ ‘000)	Rank (b)	Total (a + b)	${\mathit{S}}_{\mathit{s}}$	Rank (c)
Overall system		84.87	-	2393.38	-	-	-	-
1	1	91.54	3	696.04	13	16	0.958	1
	2	89.72	4	561.36	11	15	0.864	2
	3	86.02	6	493.21	8	14	0.233	6
	4	85.96	7	835.3	15	22	0.130	8
	5	85.35	8	551.2	10	18	0.087	10
	6	85.09	10	488.04	7	17	0.045	12
	7	85.12	9	424.37	5	14	0.059	11
	8	84.98	13	512.25	9	22	0.021	14
	9	85.01	12	348.82	4	16	0.040	13
	10	84.91	16	611.23	12	28	0.007	16
	11	84.97	14	737.31	14	28	0.014	15
	12	84.74	17	431.29	6	23	−0.030	17
2	1	92.96	2	1833.24	16	18	0.441	5
	2	86.35	5	256.12	3	8	0.578	3
	3	84.94	15	77.52	1	16	0.090	9
3	1	95.62	1	2059.14	17	18	0.522	4
	2	85.03	11	107.73	2	13	0.149	7

and Figure 9. First, based on the 12 scenarios of Strategy 1, Scenario 1 was deduced as the strategy capable of achieving the most efficient supply rate from the perspective of $S_s$. However, if the cost aspect is to be considered, its final rank is 16, and it thereby lags in the ranking markedly among the scenarios of the corresponding strategy. For example, Scenario 2, which is ranked the second based on $S_s$, incurs lower costs in comparison with the first ranked scenario, and is thereby ranked first from the perspective of costs. As illustrated, there are limitations to the realistic perspective when evaluating the system only on the basis of earthquake reliability. Resultantly, a local autonomous government with the capability to earmark sufficient financial resources will execute earthquake-proof strengthening based on $S_s$. However, it is deemed that other local autonomous governments need to establish plans for earthquake-proof strengthening based on this economic analysis and analysis of the strategic method of pipeline strengthening.

In the case of Strategy 2, which established scenarios based on the pipeline diameter, there was no change in the ranking even when economic analysis was considered, as the number of pipelines with a small diameter is relatively very small. In addition, it was found that the scenario for mid-range diameters of 200~600 mm has the highest rating among all strategies and scenarios. This is deemed to reflect the characteristics of a system in which the pipeline with the corresponding diameter handles the transportation of the majority of the water supplied to the end users.

Lastly, of the scenarios of Strategy 2, which was based on river ranking, Scenario 2 was found to secure a much higher total rank. This was deemed to be the result of the very low costs it incurred, though it displayed a very low increase rate from the perspective of $S_s$. Ultimately, as illustrated in Table 6, the strategies for earthquake-proof strengthening for each pipeline need to be decided by comprehensively considering the reliability of the water supply in the system, supply quantity for each segment, the cost of the realization of earthquake proofing, etc. Reliability of WSSs in the event of an earthquake is greatly affected not only by the demand of the route that imparts direct effect but also the physical characteristics of the subject segment (distribution of diameter, length, and connectivity of pipeline). In addition, although the costs of the installation of earthquake-proof steel pipe increases with increases in the pipeline diameter, the reliability of earthquake-proof strengthening also increases at a very fair proportion in accordance with the pipeline diameter. Therefore, there is a need to establish earthquake-proof strengthening strategies by considering the economic values and in accordance with the distribution of the pipeline diameter given. However, according to the results deduced above, the rankings can change as the result of even a small increase in $S_s$ if very low cost is incurred. Accordingly, it is deemed that additional relevant study is necessary in the future. Looking at the $S_s$ rate of increase in cost, Scenario 1-1 was the highest. This means that it recorded the last rank in terms of cost, but as a result, showed the highest efficiency. However, in the case of Scenario 3, it can be seen that its overall ranking fell, which means that the efficiency is relatively low when seismic reinforcement is performed locally.

Figure 9 is the result of the formulation of the curve equation for each strategy. In the case of Strategy 1, it is composed of junctions with similar construction costs and induces a rapid but gradual improvement in $S_s$. In the case of Strategy 2, there is almost the same inclination as the pipeline diameter increases and it thereby results in an increase. Although the pipeline diameters were classified into three segments in this study, it is deemed that more appropriate results can be deduced if earthquake-proof design is conceptualized based on more detailed segmentations. Lastly, in the case of Strategy 3, it has an intermediate inclination in comparison with other strategies. Although this has a limitation in that there were only two rankings, it is deemed to be a strategy that is worthy of consideration if more various rankings exist. As a result of their application, it was confirmed that there is a need to closely analyze the extent of improvement of reliability as well as the costs of earthquake proofing for each strategy and scenario in order to secure the water supply reliability of the water distribution network system in preparation for the occurrence of an earthquake. That is, in order to simultaneously satisfy the reliability and cost-efficiency of the water supply, it is essential to execute earthquake proofing for pipeline segments with mid-range diameters. However, since a substantial drop in reliability will be caused if some of the segments of pipelines that supply water with very large flowrate are damaged, it is necessary to execute additional earthquake proofing for these segments.

4. Conclusions

In this study, various strategic methods to improve the reliability of water distribution network systems at during earthquake disasters were considered, with a focus on structural earthquake proofing methods for pipelines, and these methods were evaluated. For this purpose, an approach was undertaken that was based on three new strategies that used the REVAS.NET model to compute earthquake reliability via the reflection of hydraulic characteristics. These three strategies were established based on demand, diameter and connection-hierarchy, and were applied by segregating scenarios in accordance with the given situations for each strategy. The proposed strategies and scenarios were applied to the industrial WSS of the Republic of Korea with an analysis of the effects of each strategy on the reliability of water supply in the event of an earthquake. In conclusion, it is not only necessary to comprehensively consider reliability but also the supply capacity of the pipeline of the corresponding system and the costs of earthquake-proof strengthening to secure the reliability of the water supply of water distribution network systems in preparation for the occurrence of earthquakes. Moreover, there is an essential need for a template by which to make an approach based on various strategies. As a result of their application, it was confirmed that there is a need for close analysis of the costs of earthquake proofing and the extent of improvement of the reliability for each strategy and scenario in order to secure the reliability of the water supply of water distribution network systems in preparation for earthquakes. Though it is essential to execute earthquake proofing of pipeline segments with mid-range diameters to simultaneously fulfill the reliability and cost efficiency of water supply, a substantial drop in reliability will be caused if some of the segments of pipelines that supply water with very large flowrate are damaged, thereby making it necessary to execute additional earthquake proofing for these segments. In addition, because the effect of an increase in reliability in comparison with the costs incurred in the case of some low demand and supply pipeline segments—or those with a small diameter—is insignificant, earthquake proofing of such segments must be excluded. However, small-diameter pipelines are more likely to be destroyed by earthquakes. Therefore, it is necessary to consider seismic reinforcement by comprehensively considering parameters such as the possibility of destruction. It is anticipated that the results of this study may be used in the establishment of more specific and practical preliminary strengthening strategies in preparation for earthquakes that could occur in the future. This study may be used as such because the diversified strategies were evaluated for a single district rather than for the individual pipeline of a water distribution network system or an entire system. However, since this study was limited to a simple comparison of the economic costs and to the strategies of reliability of water supply in the event of earthquake, there is a need to more assertively analyze the weighted value of the reliability during an earthquake. This needs to be secured by the assigning of a weighted value for the economic value, one that the corresponding local autonomous government can consider for the purpose of a more detailed comparative analysis in the future. In addition, there is a need to add analysis that includes key routes under diversified situations under which the end-user is affected by a discontinuation of the water supply from their water distribution network system. Basically, based on the methodology and evaluation results presented in this study, it is necessary to prepare a plan that can simultaneously optimize the economic evaluation results and the reliability of supply through earthquake resistance, for multiple purposes. In addition, in order to generalize the degree of reliability improvement according to the cost of the three seismic performance improvement methodologies presented in this study, it is necessary to derive analysis results for more combinations.