Resilience-Based Repair Strategy for Gas Network System and Water Network System in Urban City

Abstract

In resilience-based frameworks, optimizing the repair strategy and approaches is important for the recovery of the function of gas network systems (GNS) and water network systems (WNS). According to the resilience quantification results of GNS and WNS for a real example urban city in China, the potential impact of utilizing different repair sequences and repair/replacement approaches was investigated. First, a Monte Carlo simulation-based method was proposed to search for the optimal repair sequence according to the skew of the recovery trajectory (SRT). Under high seismic intensity conditions, the significant difference between the repair sequence corresponding to maximum SRT and minimum SRT indicates that choosing the optimal repair sequence is important in the enhancement of repair efficiency, especially when the pipelines have experienced serious damage. We also discussed the parallel repair strategy, which is more consistent with the practice, and can greatly improve the recovery efficiency compared with the single pipeline repair strategy under large damage conditions; however, under minor damage levels, the parallel repair strategy may result in a certain degree of redundancy. Next, three different repair approaches were thoroughly compared, including the point-by-point repair approach, whole pipeline replacement, and hybrid repair approach. At the condition of high seismic intensity (e.g., macroseismic intensity IX), the resilience curves for the hybrid repair approach and the pipeline replacement approach are overall similar and take less time and economic cost than the point-by-point repair approach. However, when the seismic intensity is low, the point-by-point repair approach is most efficient and has the shortest recovery time. Therefore, the choice of repair approach should be determined by stakeholders based on the specific pipeline’s damage situation. Finally, we calculated the joint resilience curves by allocating different weight factors to GNS and WNS, to represent the proportion of water and gas supply that contributes to community resilience.

1. Introduction

As critical infrastructures, the gas network system (GNS) and water network systems (WNS) play important roles in ensuring the normal operation of modern societies. Earthquake disasters can have significant consequences on GNS and WNS, which are spatially distributed networks composed of numerous interconnected and interacting components [1,2]. Due to the connectivity of the network, failure or leakage in one pipeline can affect the function of the system in the region. In other words, small disturbances may trigger cascading failures and cause large-scale consequences [3,4]. Hence, not only does the direct resulting disaster need to be paid attention to, like the explosion caused by gas leakage, measuring the function recovery process of the network system is also quite important.

The concept of resilience refers to the ability of a system to minimize disruption and return to normal function after a disaster [5,6,7,8]. A broad quantification framework was proposed by Bruneau et al. [5] to evaluate the seismic resilience. Resilience could be defined in four interrelated dimensions: technical, organizational, social, and economic. In this study, we focus on the technical dimension, which refers to the ability of physical components of the system to operate normally after earthquake events [5,9]. Research interest in the technical dimension of the resilience of infrastructures has led to the development of various frameworks and models in systemic approaches [10,11]. Some researchers have studied the dynamic behavior of water supply systems by modeling it with system dynamics [12], others have formulated network-by-network theory focusing on system redundancy as a significant factor in water supply resilience [13,14,15]. Qualitative approaches such as expert judgments have also been adopted by researchers to quantify infrastructure resilience [16]. In Ref. [17], the failure risk analysis of WDN systems had been carried out using hydraulic models on real field data. The index of “Average Time of Water Not Supplied” was proposed to represent the time in which the water supply does not meet the requirements of the users. In Ref. [18], a method was proposed to measure the failure risk of water pipes in terms of water supply safety. Generally, the failure ratio of the physical unit of the system was used to measure the performance of the system, or it was measured based on various complex network physical performance indicators [19].

The earthquake loss of resilience, RL, is usually defined using Equation (1) [20]:

$$RL=\underset{t_0}{\overset{t_1}{\int }}\left[100-Q\left(t\right)\right]dt$$

(1)

It was measured by the expected degradation in performance function of the system, Q(t), over a time period t₀ to t₁, where t₀ represents the time when the earthquake occurred and t₁ refers to the time when the infrastructure returns to the pre-event state. The seismic resilience is defined with robustness (ability to maintain a certain level of service after earthquake events), rapidity (recovery speed), redundancy (substitutable components within the system), and resourcefulness (availability of resources).

The initial functionality loss of GNS and WNS after an earthquake was determined by the vulnerability of the network under the hazard event [5], while the indirect loss due to downtime is long-term and more important for GNS and WNS as mentioned. To measure the rapidity and efficiency of road network system recovery, total recovery time (TRT) and the skew of the recovery trajectory (SRT) were proposed by Zhang et al. [21]. The SRT is defined to describe the shape of the recovery curve and measure the efficiency of different repair strategies. GNS and WNS are large-scale network systems with complicated spatial distributed structure and have two kinds of damage: pipeline rupture and pipeline leakage. In addition to repairing the pipelines as soon as possible to restore them to the original state before damage, the resilience recovery process, like the repair sequence, repair resource allocation strategy, and choice of repair/or replacement of pipelines also play vital roles. TRT and SRT are both significantly affected by the repair strategy or approaches when resources for post-disaster recovery are limited and could be used collectively to identify the optimal post-event repair scheduling for the network recovery.

In pipelines network repair practice, we need to consider four issues: (1) For the specific pipeline network and seismic intensity, the overall repair time regarding different repair sequences is the same if the corresponding damage rate and total repair resource are fixed. However, the resilience recovery trajectory varies between different repair sequences. An efficient recovery trajectory comes with lower SRT value, indicating that the function loss would be largely be restored in the early stage and also facilitate the function recovery of other dependent infrastructures. (2) Multiple rupture points exist in the pipelines of network after the earthquake event. In repair practice, a unit of repair resource is assumed to be allocated to repair all the rupture points of one damaged pipeline before continuing to repair another damaged one. (3) In order to recover the function of the lifeline system quickly, multiple units of repair resources or teams would be deployed in the different damaged pipelines in practice. The repair time cost by different repair units varies with the number of rupture points in different pipelines. Therefore, the concept of “parallel repair strategy” would be utilized in this study to reflect this real repair process of GNS and WNS. (4) The resilience of a single lifeline system, like GNS or WNS itself, is not enough to measure the overall post-event function recovery process of a community or a region of a city. Joint resilience considering the importance weight of multiple lifeline systems would be discussed in this study.

In this paper, GNS and WNS in an urban city of China were taken as an example to thoroughly investigate the impacts of repair sequence and repair/replacement approaches regarding different macroseismic intensity. According to the skew of the recovery trajectory (SRT), a Monte Carlo simulation-based method was proposed to search the optimal repair sequence. Parallel repair strategy and single pipeline repair strategy were compared. Then three different repair approaches, including the point-by-point repair approach, the whole pipeline replacement, and hybrid repair approach, were thoroughly compared under different conditions.

2. Resilience Quantification of the Pipeline Network Considering Parallel Repair

2.1. Resilience Metrics and Measurement of Restoration Efficiency for GNS and WNS

For GNS and WNS, the resilience-based performance metrics of a network could be defined in different ways as reviewed. In this study, we focus on the resilience definition in technique dimensions, which is more closely related to the performance of the network and not significantly influenced by other factors, like population and dependency of other social facilities.

Specifically, it was defined in two different ways:

Case 01, the gas or water flow (or volume) was considered to measure the performance of network, as defined in Equation (2).

$$Q_1\left(t\right)=\frac{1}{D_W}{\displaystyle \sum _{\omega \in W}{d}_{\omega }\left(t\right)}$$

(2)

where W represents the set of all source demand point pairs in the network; ω represents any point pair in set W; D_W represents the total water and gas flow (volume) of the network; $d_{\omega }\left(t\right)$ is the volume of the point pair.

Case 02, the length of pipelines was utilized to the performance of network, as defined in Equation (3).

$$Q_2\left(t\right)=\frac{1}{N_W}{\displaystyle \sum _{\omega \in W}{\mathsf{\lambda }}_{\omega }\left(t\right)}$$

(3)

where N_w is the total length of pipe network in set W; ${\mathsf{\lambda }}_{\omega }\left(t\right)$ is the length of the pipeline for connected ω point pairs at time t.

As proposed by Zhang et al. [21], TRT and SRT were utilized to measure the rapidity and efficiency of the network recovery. The TRT is the time required for the network to be restored to its pre-hazard functionality level, while the SRT is defined to capture the characteristics of the recovery trajectory that relate to the restoration efficiency of different repair strategies considered. The concept of these two metrics is illustrated in Figure 1.

TRT is the time required for the system to recover to its functional level as defined in Equation (4).

$$\mathrm{TRT}=t_k-t_0$$

(4)

where t_k is the time when the system performance is fully recovered, and t₀ is the time when the system performance starts to recover. As shown in Figure 1, TRT is not enough to evaluate the efficiency of network repair strategies. For example, four restoration schedules have the same value of total recovery time, TRT, while the recovery trajectories as a function of time varies significantly, indicating different efficiency of recovery. It is obvious that schedule 4 is more efficient that the other three schedules in the early stage.

To represent different efficiency of restoration, SRT is defined as the skew of the recovery trajectory, which is the centroid of the area below the recovery trajectory (from t₀ to t_k) with respect to t = t₀ follows:

$$\mathrm{SRT}=\frac{{\displaystyle {\int }_{t_0}^{t_k}Q\left(t\right)\cdot \left(t-t_0\right)dt}}{{\displaystyle {\int }_{t_0}^{t_k}Q\left(t\right)dt}}\approx \frac{{\displaystyle {\sum }_{i=0}^k{t}_{i}Q\left(t_i\right)}\Delta t}{{\displaystyle {\sum }_{i=0}^{k}Q\left(t_i\right)}\Delta t}$$

(5)

where Q(t) is the system performance metric as defined in Equations (2) and (3). A large value of SRT indicates that the restoration process is not efficient, like the case in schedule 1, as illustrated in Figure 1. The SRT value of schedule 4 is the smallest among them, indicating it is the most efficient performance restoration process.

In most of the current study, the single pipeline repair strategy was adopted in the evaluation of resilience, that is, one unit of repair resource is allocated to one pipeline, then reallocated to another one when the function of this pipeline is restored. This single pipeline repair strategy is convenient in computation, while it is quite different from reality. In repair practice after earthquake events, a certain number of research teams, or units of resource, were allocated by companies or governments to multiple damaged pipelines at the same time. Hence, this paper uses the parallel emergency repair strategy to represent this repair process; that is, several units of resources are allocated to different damaged pipelines. When the damaged pipeline is repaired by one of the resources, it was released to repair another damaged pipeline. At most one maintenance resource is allocated to each pipeline until the whole repair process is completed. The parallel emergency repair strategy adopted is more consistent with the practice and could reduce the maintenance cost of multiple repair teams.

2.2. Search of Optimal Repair Sequency Based on Monte Carlo Simulation

If we have an attenuation of ground motion intensity measures for the studied region, like the widely used one in seismic safety evaluation work in China [22], the damage condition of the GNS could be determined by the empirical relationship with PGV (peak ground velocity) and PGD (peak ground displacement). This relies on the determination of the earthquake source mechanism of hypothesis earthquake scenario. Another efficient way is determining the total number of rupture points by the empirical relationship between the average earthquake damage rate and total length of the urban gas pipeline [23]. This could be derived from post-event field investigation. Then all rupture points can be randomly assigned to each pipeline by Monte Carlo simulation. In our study, PGV and PGD was not utilized to represent the ground motion input because we did not find suitable GMPE for this region, and the macro seismic intensity is used to define the corresponding damage condition [24]. The pipelines damage matrix was established accordingly, which includes the number of rupture points of the damaged pipeline network, the number or units of the repair resources, and the allocation sequence of the repair resources. The damage matrix is updated with time using the parallel repair strategy. The recovery process is finished until the number of rupture or leakage points in the pipeline damage matrix is updated to zero. The repair unit time could be predefined as a fixed value according to stakeholders or using Poisson distribution to estimate the value (Hazus-mh2.1) [25]. Finally, resilience-based performance metrics Q(t) of the GNS and WNS was determined in two different ways, according to Equations (2) and (3).

Another issue we need to take in to account is that the restoration of a single lifeline system itself cannot reflect the overall function recovery process of a city or community. This paper will utilize different the weight coefficients for different lifeline systems and establish the combined resilience curve. The weight could be predefined by users or stakeholders, depending on which life system is more important in the current stage. As the time to repair a single rupture point or leakage point of different lifeline systems is different, this paper uses the interpolation method to combine the two curves.

The resilience qualification and repair process of GNS and WNS based on Monte Carlo simulation are summarized as follows:

Step 1: Predefining the ground motion input parameters (seismic intensity [26] for the specific region), pipeline network information (including the pipeline length, spatial distribution, material, and so on), and repair resources (including the number of unit repair resource and corresponding repair unit time).

Step 2: According to the seismic intensity and the empirical relationship between damage rate, the total number of rupture points for the whole pipeline system is calculated.

Step 3: Rupture points are randomly assigned to each pipeline using Monte Carlo simulation methods.

Step 4: The repair resources are randomly assigned to the damaged pipeline.

Step 5: Update the pipeline damage matrix and calculate the corresponding repair time. Obtain the resilience curve of the studied pipeline network system over time.

Step 6: Repeat steps 3 to 5 for N times to obtain N_sim repair conditions and find the optimal repair strategy using values of SRT and TRT.

The proposed procedure is shown in the flowchart of Figure 2.

3. Resilience Quantification for GNS and WNS of Urban Example City

3.1. Basic Network Information

In this paper, a typical urban city in central China is taken as an example case. The city has a population of around 4 million [27]. We choose it as a typical city for the following reasons: (1) The central dense distribution of the GNS and WNS is the common pipelines layout for many urban cities in China. (2) It is not a very big city, like Shanghai, in which there is more than one pipeline cluster and centroid. It is also not like the small cities in the western region, in which the layout of GNS and WNS are simple. Figure 3 shows the spatial distribution of the network of gas and water supply system in this city. The total length of the city’s medium-pressure natural gas pipeline is 338.12 km, and the number of pipelines studied in this case is 46. The material of PE (polyethylene) was utilized in most of the pipelines with 90 mm to 315 mm pipe diameter, while thickened straight seam-welded steel pipes or seamless steel pipes were used for special locations (such as pipelines under bridges), with 150 mm to 400 mm pipe diameter [28]. The total length of water supply pipelines is 312.56 km, with 7653 pipelines, including PE, cast iron, and cement pipes with different pipe diameters. Considering the calculation efficiency and cost, the original network was simplified in this study with the main layers of the WNS retained. Based on the process as shown in the flowchart of Figure 2, technical dimensional resilience was qualified for GNS and WNS in this example city at seismic intensities ranging from Ⅶ to Ⅸ.

3.2. Search Optimal Repair Sequency for GNS and WNS

According to the procedure illustrated in Section 2, we firstly calculated two kinds of performance metrics for the studied GNS and WNS, considering the gas/water flow (or volume) and pipeline length, respectively, as in Equations (2) and (3). The empirical relationship between the damage rate and macroseismic intensities [29] was defined in Ref. [27], which was derived from pipeline damage investigation data in China’s historical earthquake events, like the 2008 Wenchuan earthquake event.

Next, the repair process of different repair sequences was simulated using the flowchart as illustrated in Figure 2. After determining the total number of rupture or leakage points of pipelines according to the empirical damage rate, they are randomly assigned to individual pipelines to obtain a matrix of pipelines that need to be repaired. In this study, a total number of 10,000 random repair sequences were generated and the optimal repair sequence was determined with a minimum value of SRT. For comparison reasons, this paper discusses and compares both the parallel repair strategy using multiple units of repair resources and the traditional single-resource repair strategy. It is assumed there is one and only one unit of repair resource is allowed to be allocated to one pipeline. Multiple repair resources can repair different damaged pipelines separately at the same time. Considering the different total number of pipelines in GNS and WNS, 10 units of repair resources were allocated for GNS and WNS.

The resilience curves for GNS under macroseismic intensity Ⅶ, Ⅷ, and Ⅸ were illustrated in Figure 4. To illustrate the impact of different repair sequences, the resilience curves corresponding to the maximum and minimum SRT values among 10,000 simulation sequences were compared. Although the individual resilience curve for different repair sequences was not plotted, it should be noted that different repair sequences would lead to different recovery trajectories. Randomly choosing repair sequences would lead to the relative slow recovery of the gas supply while choosing the optimal repair sequence would lead to earlier gas supply recovery in more regions of the community. A significant difference was observed between the recovery trajectory with maximum SRT and minimum SRT value. With the increasing of the ground motion intensity, the difference is more obvious, indicating that choosing the optimal repair sequence is more important in damage earthquake events. The recovery trajectory with minimum SRT is treated as the optimal repair sequence among all the simulation results. In Figure 5, Case 01 and Case 02 refer to the resilience qualification metrics using gas flow and the length of pipelines as indexes, respectively, as defined in Equations (2) and (3). The overall trend of the resilience curve for Case 01 and Case 02 is similar, but the optimal repair sequence is different under different macroseismic intensities.

The above example is a case where the repair resources are well stocked and enough for repair. However, when the pipeline damage caused by earthquake is severe and the repair resources are limited due to the budget or other reasons, attention needs to be paid to how the limited resources can be allocated to realize an efficient recovery trajectory. In our future work, we would focus on the search for optimal repair sequence with the constraint of repair budget and other resources.

Similar to GNS, this study further discussed the resilience curves of WNS regarding macro seismic intensity VII, VIII, and IX as illustrated in Figure 6. Due to a large number of pipelines in WNS, this paper considers the extreme damage situation form of WNS pipelines, i.e., at most one rupture point per pipeline. In this case, only one unit of repair resource is assigned. It could be observed that 7000 h were spent for IX degrees of intensity under parallel repair strategy, 3500 h and 1200 h to 100% recovery for Ⅷ and Ⅶ degrees of intensity. The increasing trend of resilience curve is similar to GNS, while the WNS resilience curve is not the stepwise shape and is more linear. The difference between recovery trajectory with maximum SRT and minimum SRT is not obvious as for GNS. This is mainly because the number of water pipelines is far more than gas pipelines in the target area for a given macroseismic intensity, therefore the impacts of different repair sequences are not as significant as in GNS.

4. Impact of Utilizing Different Repair or Replacement Approach

In post-earthquake repair practice, there are three repair approaches usually adopted: one is directly replacing the damaged pipeline with new ones, another is repairing the rupture points of the damaged pipelines one by one. Hereafter we propose a third approach called hybrid repair/replacement method, which is combination of these two approaches, that is, part of the pipelines were replaced while some pipelines were repaired. With the limit of budget of stakeholders, the potential economic cost is utilized to determine which pipelines to replace or repair in the hybrid approach.

When a pipeline is damaged, the repair cost [30] Co is calculated as follows, consisting of both replacement of the existing pipelines and point-by-point repair cost.

$$Co={\displaystyle \sum _{i=1}^{N_r}{C}_i}\left(D_i,L_i\right)+{\displaystyle \sum _{j=1}^{N_j}{C}_j}\left(D_j,L_j\right)$$

(6)

where N_r is the number of pipelines to be repaired for rupture points; C_i (D_i, L_i) is the cost of replacing pipeline i with pipeline j, the length and diameter are indicated with L and D, and N_j is the number of new pipelines to be replaced; and C_j (D_j, L_j) is the cost of installation of new pipeline j.

Taking the GNS as an example, the cost for the whole pipeline replacement and point-by-point repair method is determined based on the low-end cost standard proposed by Boyce and Bried [31], assuming replacement and horizontal directional drilling using burst methodology. The money inflation rates in the period 1998–2021 were taken into account. The installation cost of a new pipeline is $14.80/m ($14.80 per meter of pipe) and the point-by-point repair cost is $6.50 per rupture or leakage point. Given the damage condition of the pipelines under different macroseismic intensity, the optimal percentage of pipelines to be replaced or repaired in the hybrid approach was determined according to Equation (6). Given macroseismic intensity Ⅶ–Ⅸ degrees, the costs of three different repair approaches were compared in Figure 7. It could be observed that the hybrid repair approach comes with the lowest cost compared with other two approaches for all three seismic intensity situations. The cost of replacing new pipelines increases slowly with seismic intensity, followed by the hybrid repair approach, but the point-by-point repair cost increases significantly with intensity. The point-by-point repair cost is less than the cost of replacing new pipelines at VII degrees of intensity, while the cost of replacing a new pipeline is less than the cost of point-by-point repair at Ⅷ degrees of intensity, indicating that the cost of replacing new pipelines is much lower than point-by-point repair when the damage is serious. With the increase in macroseismic intensity, the advantage in cost regarding the hybrid repair method compared to the replacement of a new pipeline is gradually decreasing. This is also due to the fact that the greater the damage, the advantage is less significant for the point-by-point repair method, and almost all damage is repaired by replacing the pipeline with a new one. We use a similar analysis schedule to compute the cost of repairing the water network. The results indicated that due to the large number of the pipelines in WNS, and the water network mostly uses short pipe strings, the cost of repairing the pipelines is significantly lower than replacing with a new one. Therefore, only the GNS was discussed next for different repair approaches.

Then we will discuss the impact of utilizing three different repair approaches on resilience curves. The time cost for the whole gas pipeline replacement is defined as [32]:

$$T=\frac{2}{5}{L}^2\sqrt{D}$$

(7)

The pipeline length and diameter are represented with L and D.

The comparison between results for macroseismic intensities Ⅶ, Ⅷ, and IX degrees are shown in Figure 8. Under the seismic intensity of IX degrees, time costs of the hybrid repair approach are the smallest and also come with the lowest value of SRT, indicating the highest repair efficiency; then is the pipeline replacement approach and point-by-point repair approach. The results of this case show that at high seismic intensities, IX degrees, when there are more rupture points in the pipe network, the choice of hybrid or replacement repair systems is much more resilient than point-by-point repair. For macroseismic intensity VII degrees, the point-by-point repair approach is the most efficient method and takes the shortest time, and the replacement repair approach is the least efficient method. This suggests that the point-by-point repair approach is preferable to the hybrid repair approach and replacement approach when the damage is slight or moderate at low intensities.

5. Resilience Qualification of Combined Pipeline Networks

In this section, we would discuss the combined resilience curve considering the different contribution of GNS and WNS for the function of the community or region. The combined resilience curve of GNS and WNS using single resource repair strategy for macroseismic intensity VII, Ⅷ, and IX degrees were plotted in Figure 9. The damage rate and repair time for these two different lifeline systems vary significantly, therefore we need to interpolate their resilience curves and combine them by assigning different importance weight factors. We will discuss several combinations of weights factors regarding GNS and WNS: 0. 3/0.7, 0.4/0.6, 0.5/0.5, 0.6/0.4, and 0.7/0.3. For brevity, we only discuss the optimal repair sequence with minimum SRT values among Monto Carlo simulations as determined in Section 3.2. Different combinations of weight factors and corresponding resilience recovery curve are compared. The larger the weight of GNS is assigned, the increasing slope of the recovery curve is slower. For high seismic intensity conditions, VIII and IX degrees, because GNS is seriously damaged, the initial function Q(0) is close to zero and the increasing slope is steep. For comparison, the combined resilience curves using a parallel repair strategy were plotted in Figure 10. It can be found that the recovery curve of the joint resilience curves under different combinations of weights shows a stepwise longer period during the final restoration phase, which refers to the period of water network restoration. The phenomenon holds true for both single repair strategy and parallel repair strategy.

The simulation in our study is based on real pipeline network data from the example city, and the number and deployment method of GNS and WNS varies significantly. The WNS is deployed with sections, and there are more than 7000 pipelines considered in our study. On the other hand, the GNS is deployed with separate pipes, and only 46 pipelines were studied. Therefore, the damage states of GNS and WNS differ greatly. For example, under the same intensity IX degree, according to the utilized empirical relationship of damage rate, a total number of 1514 and 2197 rupture points were generated for gas and water supply pipelines, respectively. The intact water supply pipelines occupy a high proportion because of the large total number of pipelines in the WNS, while the initial Q(t) is almost zero, and a large number of rupture points in a particular pipeline leads to a period of time to be repaired before the function of the system start to recover.

6. Conclusions

From the resilience quantification results of GNS and WNS for a real example city in China, the potential impacts of utilizing different repair sequences and repair/replacement approaches were investigated.

First, we proposed a Monte Carlo simulation-based method to search the optimal repair sequences according to the value of SRT of recovery trajectory. For GNS, the results indicated that the different repair sequence would lead to various recovery trajectories. A significant difference was observed between the recovery trajectory with maximum SRT and minimum SRT values, especially when the damage is severe in high seismic intensity conditions. On the other hand, the WNS resilience curve is not of a stepwise shape like in GNS, and the difference between the recovery trajectory of various repair sequences is not obvious as for GNS. This is mainly because the number of WNS pipelines is far more than the GNS pipelines, therefore the impacts of repair sequences are not as significant as in GNS. The results indicated that choosing the optimal repair sequence is important in the enhancement of repair efficiency, especially when the pipelines had experienced serious damage. The proposed parallel repair strategy is more consistent with the reality practice and can greatly improve the recovery efficiency under large damage conditions comparing with the single pipeline repair strategy; however, under minor damage levels, parallel repair may cause a certain degree of redundancy.

Three different repair approaches were analyzed, including the point-by-point repair approach, whole pipeline replacement, and the hybrid repair approach. At high seismic intensity conditions (e.g., macroseismic intensity IX), the resilience curves for the hybrid repair approach and the pipeline replacement approach are similar and take less time and economic cost than the point-by-point repair approach. However, when the seismic intensity is low, the point-by-point repair approach is most efficient and has the shortest recovery time. Therefore, the choice of repair method should be determined by stakeholders based on the specific pipelines damage situation. Since the same situation is defined according to the relationship between damage rate and the seismic intensity, our results are not influenced by the specific layout of the GNS and WNS. Therefore, our conclusion could be applied in other cities with similar scale.

The combined resilience curve considering the GNS and WNS was discussed and compared by assigning different weight factors. Since the damage rate and unit repair time for these two different lifeline systems vary significantly, the recovery time and the shape of the resilience curve are constrained by both GNS and WNS. The combined resilience qualification could comprehensively represent the total restoration process for both water and gas supply system. The proposed framework can be applied to other lifeline systems, such as power supply networks, railways and roads, and other pipeline-type critical infrastructures. In our study, individual critical infrastructures can be assigned different weights if different types of lifelines systems were added, although determination of the weight value still needs to be further investigated.

Although this work discusses thoroughly the repair method and corresponding impact on resilience of GNS and WNS, it was limited to the resilience metrics defined using technique dimension. For the technical dimension, network connectivity, network shortest distance, and other indexes of the WNS and GNS could also be used. It is worth noting that the connectivity of the GNS and WNS is not measured in the same way, because the GNS system could not work with leakage while the WNS could. Future work would focus on the combination of more lifeline systems, like the power system, and including more resilience metrics in organization or social dimensions. The organizational seismic resilience can be measured as the proportion of gas/water users before and after the earthquake, reflecting the process of change in the connectivity performance of the gas/water network. The social and economic dimensions are concerned with the social and economic impacts of the disruption of the WNS and GNS. The range of the seismic GNS and WNS consequences can be measured as the number of users experiencing water and gas deficit. Then the social dimension of seismic resilience can be measured as the proportion of unaffected population before and after the earthquake, reflecting the impact of the gas/water network as a social infrastructure on the population of the society. Furthermore, if the seismic damage is severe and the repair lasts for a long time, then the corresponding long-term economic and social loss is not negligible and could be also utilized as resilience metric, such as the displacement of the population and the reduction of the Gross Regional Product.