the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Jan 2026
A Process-Based Four-Stage Framework for Seismic Resilience Assessment of Urban Water Distribution Networks through Multi-Attribute Metrics
Abstract. Urban water distribution networks are critical lifelines whose seismic resilience is essential for maintaining daily functions and post-disaster service continuity. However, most existing studies focus on seismic-induced functional failures and short-term recovery, while neglecting pre-disaster preparedness and long-term adaptation – two stages that fundamentally shape the overall resilience trajectory. Conventional assessments typically rely on single-dimensional hydraulic or network indicators, which tend to be one-sided and error-prone. These limitations hinder a comprehensive understanding of WDN behavior across different seismic disturbance stages, yielding only coarse performance judgments that offer limited guidance for diagnosing vulnerabilities or planning effective resilience enhancement and retrofit strategies. To address these limitations, this study proposes a process-based four-stage seismic resilience framework that explicitly incorporates preparedness, robustness, recoverability, and long-term adaptation, capturing the full evolution of WDN performance during seismic events. A multi-attribute indicator system integrating topological homogeneity, energy redundancy, pipeline fragility, hydraulic service performance, and recovery efficiency is developed to enable refined stage-specific assessment. An adaptation index (ACI) is further introduced to quantify the integrated improvement achieved by different retrofit strategies. Applications to the Jilin and Mianzhu WDNs demonstrate clear stage-dependent resilience disparities and provide actionable guidance for optimizing seismic resilience enhancement. Application to the Jilin and Mianzhu WDNs demonstrates the framework's applicability and reveals clear stage-dependent resilience disparities, which provide scientifically grounded guidance for optimizing seismic resilience enhancement in urban WDNs.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-5830', Anonymous Referee #1, 04 Feb 2026
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RC2: 'Comment on egusphere-2025-5830', Jürgen Mey, 09 Apr 2026
Review for „A Process-Based Four-Stage Framework for Seismic Resilience Assessment of Urban Water Distribution Networks through Multi-Attribute Metrics” by Miao et al. submitted to NHESS
In this contribution the authors develop a method to comprehensively assess the resilience of water distribution networks (WDN) to earthquakes. They start with an introduction into the topic including the definition of resilience and its dimensions, present examples where such an approach (multi-stage assessment) was previously applied to other network infrastructures, refer to previous work on WDN resilience assessment and identify their shortcomings. They propose a further refinement of the indicator-based method, where a fourth stage is accounted for, that represents the long-term response to earthquake hazard. For each of the four stages, pre-disaster, in-disaster, post-disaster and this long-term enhancement stage, they define the metrics preparedness, robustness, recoverability and adaptation, respectively. These metrics in turn depend on specific, quantifiable properties of the WDN e.g. geometry, pipe strength/diameter, energy reserves and recovery time.
They apply their method to two example WDNs under the assumption of damaging earthquakes and demonstrate how it can highlight shortcomings of these WDNs and guide optimal retrofitting measures.
The study is well designed, and I could follow the line of thought. It may be helpful to state in the beginning that this study is a theoretical work that would need verification or proper field testing before it could be fully evaluated. I recommend publication after minor revisions.
I have several suggestions for improving e.g. the readability detailed in the line comments below.
Specific comments:
L15: WDN need to be defined before its first use
L22: What does ACI stand for?
L23-27: Repetition
L66: WDN should be defined in the abstract or in the title already
Table1: This table needs more horizontal separators to see which equations belong where. No definition of variables etc! Without this the eqs are of little use. Their font is too small.
L109: What do you mean by “actual earthquake processes”?
L109-110: By only adding a fourth stage, does the proposed approach really solve this issue?
L116-117: “entire seismic process of water distribution networks” I don’t understand this. Suggest rephrasing.
L136-137: Since you include the robustness during the EQ event, it should read “before, during and after an earthquake”.
L1411: what is meant by “developing seismic codes”? computer code? emergency procedures?
L157: “several seconds to hours” à rather days and even weeks in case of larger earthquakes
L165-166: Do you mean maps of supposed peak ground acceleration etc are used in these simulations?
L179-180: You wrote this sentence already at the end of the previous paragraph.
L181: WDN recovery rate needs to be defined somewhere, suggest to add here a reference to the equation where it is defined.
L195: I guess you only modelled these upgrades rather than actually employing them.
Fig:1: Second panel, interior graphics of the circle is to small. Panel 3 needs more explanation/description. Key needs to be larger. Where is the variable description?
L200: “assessment of WDNs” ? word missing?
Fig.2: first box starting with “Input”: The repair rate should logically be part of the recovery phase, right? I guess it should rather be renamed to damage rate here.
Is SSIQ a usual abbreviation for this variable? If not, I suggest a single letter abbreviation.
L232-233: Here you should offer some justification.
L235: I strongly suggest to replace the term “repair rate” with “damage rate” when you want to quantify the damage of the pipeline network. By the way, technically speaking the use of the term “rate” implies some form of time dependency in its definition, which is not the case here.
L242: Please add the used correction coefficients.
L250-252: How do you justify this assumption?
Fig.3: Fonts could be larger. What is Qbleak?
L271: “n” I suggest to use a differnt index variable because you already used n for the number of damages above.
L272: “which can be determined according to actual conditions and managers’ requirements.” Please specify.
L279: Here you use damage rate. Keep consistency in variable naming.
L293: “NEI” Here and elsewhere, why using these multi-letter abbreviations? What is Qreg?
L295: “NEI represents the energy index considering pipeline diameter uniformity” is this the Todini index?
L306: “”damage rate” à time should be part of its definition if its a rate, right?
L311: RR has already been defined above.
L313: this is not the right eq. reference
L321: “Qreg” à definition should come at the first usage. It would be good to have the units also defined for the other variables.
L342: WDN has already been defined
L359-360: Just put the variables in parentheses to the description above the eqaution, then you could delete this senteence.
L363: I guess this study doesn’t actually enhance the resilience of the WDN but is rather modelling the enhancement, right? Please clarify.
L365: suggest replacing “implemented” with “modelled”
Fig.4: check grammar and spelling e.g. “topology” not “topological” of WDN, “peak” instead of “pack”
L388: whats the population size of Jilin?
General comment: please consider adding a table where all variables are listed i.e. with abbreviation, name and unit.
L391: “simplification” à Please specify.
L415-417: This is only true for the Jilin WDN. In Mianzhy there are several nodes in the center that are equally important. But more importantly, why are the nodes directly attached to the sources so unimportant? If they are damaged the entire system shuts down.
Fig.7: This is completely counterintuitive. Nodes at the periphery shouldn't be that important. Am I missing something? It would help when you write in the caption again what Vi and MCB are. The “seismic fortification intensity” has not been defined.
L422: “seismic hazard analysis” à is this coming from official estimates or is this a randomly chosen PGA field? Are there seismogenic faults in the vicinity of these WDNs that have been studied?
I suggest replacing “the effect of spatial incoherence of the” with “ a spatially varying”.
L424: “ground motion field” do you mean PGA?
L427: wrong equation ref. it is actually eq 11.
General comment: I suggest to use more active language and simpler sentences.
L431: This implies that you assume the other correction factors to be equal, right? You should state this here.
L434: earthquake magnitudes, better separate the caption from the text in the manuscript.
Fig.10: text in figure is too small.
L465-467: But this is only true for the jilin WDN, because the Mianzuhn WDN reaches more than 0.95.
Fig.11: suggest to color code the lines like the bars
Fig.12: does it make sense that the µ+sigma curves all go beyond 1?
L482: Do you mean modelled?
Table2: “The key pipelines” instead of “The pipelines of key pipelines”.
Fig13: What is the red curve in the background?
Fig:16: What is grouth rate?
Citation: https://doi.org/10.5194/egusphere-2025-5830-RC2
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- 1
This manuscript proposes a four-stage framework (preparedness, robustness, recoverability, adaptation) for assessing seismic resilience of urban water distribution networks (WDNs). The authors integrate topological, energy-based, and hydraulic indicators into a multi-attribute system and apply it to two case study networks in China. While addressing an important research gap by incorporating pre-disaster preparedness and long-term adaptation stages, the manuscript suffers from significant methodological and presentation issues that require substantial revision.
Major Comments
1. Unclear Novelty
The abstract and introduction fail to clearly articulate what specific problem this work addresses and how the proposed framework advances beyond existing three-stage approaches. The abstract is vague about implications, and the first clear statement of the research problem appears only in lines 108-115. The manuscript reads as a pipeline of existing procedures rather than a coherent methodological advancement. Novel elements, if present, are obscured by technical details.
2. Methodology
The seismic hazard analysis (Section 3.1.1) is inadequately described. It remains unclear whether a proper PSHA was conducted or merely a simplified scenario calculation. Using only the Toro et al. (1997) ground motion model is inconsistent with state-of-the-art practice. Figure 8 presents scenario calculations, but Figure 2 mentions PGA sampling without specifying the approach. The fragility model terminology is also problematic, as the described approach differs from standard seismic fragility conventions.
3. Indicator weighting
The framework employs multiple indicators at each stage but assumes equal weights when computing aggregate resilience (Section 5.1). This assumption is unjustified, as indicators likely have unequal importance depending on network characteristics and stakeholder priorities. A sensitivity analysis exploring alternative weighting schemes is strongly recommended.
4. Adaptation quantification
Equations 16-17 introduce enhancement coefficients without explaining their derivation or calibration. The Adaptation Confidence Index (ACI) is mentioned but not adequately highlighted in results. Meanwhile, Section 5.1 introduces a Resilience Index not discussed in the methodology, creating confusion about the evaluation approach.
5. Statistics
The 200 Monte Carlo iterations lack convergence analysis justification. The case studies present limitations: both networks use only cast iron and plastic pipelines, and the Jilin WDN is small (27 nodes). Despite referencing the 2008 Wenchuan earthquake, there is no reference to the observed damage in the Mianzhu network and no comparison with the results.
Editorial quality comments
The introduction is excessively long with extended historical examples (lines 31-47) that could be condensed. Section 2 should be shortened and integrated into the introduction, as it duplicates contextual material. The manuscript contains redundant passages (e.g., lines 175-180 repeating recoverability definition; lines 22-25 repeating information). Figure 1 contains too many visual elements overwhelming the reader. Terminology is inconsistent ("renovation" versus "retrofit"; "seismic fortification intensity" undefined).
Minor Comments
Literature review lacks critical analysis of cited works. Equation 1 could be omitted. Figure 13 caption incorrectly references only Jilin WDN when showing both networks. The Gini coefficient formulation (Eq. 8) should be verified against standard forms. Provide a reference for the Gini coefficient or specify that it is a novelty.
Recommendation
The authors must: (1) clearly articulate the novel contribution beyond combining existing procedures; (2) consider a sensitivity analysis for indicator weighting; (3) clarify the seismic hazard analysis methodology; (4) check Monte Carlo convergence; (5) explain adaptation coefficient derivation; (6) substantially restructure Sections 1-2 for conciseness; and (7) consider validation against real earthquake data.