An Assessment of Evacuation Shelter Operations and Spatial Distribution Characteristics of Disaster Relief Volunteers Under Large-Scale Earthquake Scenarios

Abstract

In large-scale seismic scenarios, the operational continuity of evacuation shelters is frequently compromised by limited governmental capacity, necessitating the strategic integration of Disaster Relief Volunteers (DRVs). Traditional assessments often rely on coarse regional aggregates, overlooking the critical spatial mismatch between volunteer availability and localized demand. In this study, a high-resolution, spatially explicit framework was developed to evaluate urban operational resilience in New Taipei City. Utilizing the TERIA platform, a nocturnal magnitude 6.8 Shanjiao Fault rupture was simulated, identifying that approximately 460,000 individuals would be affected, with shelter demand reaching 300,000—double the current capacity. Service areas were delineated using ArcGIS Network Analyst (Dijkstra’s algorithm) based on an 800 m walking threshold, further refined by a secondary assignment rule to redistribute “shadow demand” from peripheral populations. Quantitative analysis of the newly introduced “DRV shortfall” metric reveals that 74% of shelters (148/200) face concurrent spatial and manpower saturation. Notably, 42 analysis units lack resident volunteers entirely, with the most severe shortfall magnitude reaching 361 DRVs at a single “high-risk convergence node”. These results uncover a profound deficiency in urban disaster resilience driven by significant spatial mismatch. This research contributes a three-fold advancement: (i) the high-resolution coupling of volunteer residential data with dynamic demand patterns; (ii) the formalization of the DRV shortfall as a standardized metric for resource adequacy; and (iii) the formulation of a strategic policy framework for multi-shelter activation sequencing, “Support Hub” designation, and resource synchronization in hyper-dense urban environments.

1. Introduction

In the event of a large-scale seismic scenario, beyond the immediate risk of massive casualties, factors such as residential structural damage and traffic paralysis often lead to a significant number of individuals being stranded outdoors. Furthermore, a substantial population of “persons unable to return home” (including commuters, students, and tourists) emerges due to the suspension of transportation networks. Consequently, the establishment and operation of evacuation shelters become paramount. Such catastrophic events typically exhibit several characteristics:

(1)

A vast number of isolated and helpless individuals;

(2)

Extensive structural damage or destruction rendering buildings unusable;

(3)

Impact on urban underground spaces, significantly increasing rescue difficulty;

(4)

Strained capacity and resources of medical institutions;

(5)

Disruption of transportation infrastructure or severe compromise of traffic order;

(6)

Operational disruption of public agencies and critical infrastructure;

(7)

Widespread business closures and severe disruption of essential public services.

However, activating disaster relief sites is a complex undertaking. The simultaneous opening of multiple shelters can lead to operational difficulties if local government manpower is insufficient. These sites require diverse spatial configurations, ranging from large open spaces such as parks, plazas, and stadiums to indoor facilities such as gymnasiums, community centers, and school classrooms. According to established protocols [1,2], shelter management is typically structured into five functional sections: (1) Person-in-Charge (Manager), (2) Operations Section, (3) Logistics/Administrative Section, (4) Care Section, and (5) Security Section. The Manager holds overall command responsibility, coordinating with facility owners and autonomous community leaders, disseminating initial disaster information, and directing the various sub-units. The Operations Section focuses on evacuee registration, situational data collection, and liaison with the Emergency Operations Center. The Logistics Section manages placement, supply chain administration, and sanitation. The Care Section addresses the needs of the elderly, people with disabilities, and the mental health of evacuees. Finally, the Security Section maintains order and conducts patrols, requesting police intervention when necessary. In this structured framework, Disaster Relief Volunteers (DRVs) play an indispensable role.

Given their mandate to assist in shelter activation, local governments should integrate DRVs into their Human Resource Management strategies to ensure seamless operations. As public resources are finite, relying solely on governmental capacity is insufficient. Due to similarities in geography and disaster profiles (predominantly earthquakes and typhoons), Taiwan’s disaster management framework heavily references Japan’s Disaster Countermeasures Basic Act. The Japanese “Bousaisi” (DRVs) system operates on the principles of “Self-help, Mutual help, and Cooperation,” focusing on community-based resilience. A specialized category, the “Disaster Relief Care Volunteer”, emphasizes assistance, combining professional expertise with work experience to mitigate the inconveniences faced by vulnerable groups such as the elderly and persons with disabilities. Fundamentally, Taiwan’s system mirrors Japan’s emphasis on “Self-help” [3]. Rahman et al. [4] note that “While hardware-based mitigation is driven by administrative agencies, software-based countermeasures must target the general public.”

In Taiwan, DRVs serve as primary assistants in local disaster mitigation. They are expected to establish communication channels with neighboring volunteer groups and agencies to facilitate information flow and autonomously promote disaster preparedness within families, communities, and workplaces. By identifying local disaster potentials and vulnerabilities, they enhance community risk awareness. During an event, they act as a liaison for information sharing and evacuation guidance, assisting agencies in rapid response and shelter activation. Post-disaster, they support recovery efforts and facilitate the integration of external resources, serving as a bridge between the public sector, rescue units, private enterprises, and the citizenry to minimize impact and accelerate regional recovery. Therefore, the spatial relationship between shelter locations and the distribution of DRVs directly influences operational efficiency and maintenance capacity. Investigating this spatial distribution to formulate actionable management strategies and optimize resource allocation serves as the primary motivation for this study. The most critical mission of these volunteers is assisting in shelter operations following a large-scale earthquake, particularly when accommodating those with damaged homes or the “unable to return home” population. To this end, in this study we pursue the following three objectives:

To examine the current spatial distribution of DRVs and analyze the spatial attributes of evacuation shelters—including facility type, capacity, and geographic location—to inventory regional shelter capacity and human resources; to utilize TERIA (Taiwan Earthquake Impact Research and Information Application) simulations to address the critical challenges of multi-site shelter activation, employing distance-based analysis to delineate service areas and the corresponding volunteer density; and to evaluate high-vulnerability areas with severe capacity and manpower shortages by synthesizing volunteer distribution data with simulated evacuation demands, thereby assisting local governments in the formulation of robust disaster prevention and mitigation plans. In addition, the research provides an integrated resilience assessment framework with spatially explicit manpower assessment. This study also advances the current disaster management literature by establishing a high-resolution spatial coupling between the residential distribution of DRVs and site-specific shelter demands. Unlike traditional assessments that treat human resources as regional aggregates, here we introduce a spatially explicit model that identifies the spatial mismatch between volunteer availability and localized evacuation pressure.

Furthermore, we formulate a strategic policy framework for the simultaneous activation and sustained operation of multi-nodal shelter systems under extreme seismic uncertainty. By demonstrating that 74% of shelters face concurrent spatial and manpower saturation, we identify systemic failure points in current centralized response protocols. The contribution lies in the derivation of a resource-synchronization model, advocating for targeted DRV recruitment and pre-deployment strategies that prioritize identified “shortfall nodes” rather than mere administrative density, thereby enhancing the overall functional resilience of the urban sheltering network. In summary, the contribution of this work is three-fold: (i) high-resolution spatial coupling of volunteer residential data with dynamic seismic demand patterns; (ii) formalization of DRV shortfall as a standardized metric for human resource adequacy; and (iii) a strategic policy framework for multi-shelter activation sequencing, Support Hub designation, and resource synchronization in hyper-dense urban environments.

2. Materials and Methods

The spatial scope of this research primarily encompasses densely populated districts with aging building stocks in New Taipei City (as illustrated in Figure 1). Data for spatial analysis is derived from the roster of DRVs provided by the National Science and Technology Center for Disaster Reduction (NCDR), using mailing addresses as the primary geospatial basis. The geospatial localization of DRVs was achieved through a rigorous geocoding of mailing addresses. Utilizing the ArcGIS Pro 3.6 Address Locator coupled with the Taiwan Ministry of the Interior’s residential database, the process achieved a 98% success rate. To ensure analytical precision, only records with point-at-address accuracy were included, while non-geocodable entries were excluded to avoid spatial bias. This granular localization provides the necessary fidelity for modeling pedestrian movement within the 800 m service catchments. Furthermore, relevant information on evacuation shelters is retrieved from the Open Government Data Portal, with the source datasets managed and provided by the National Fire Agency, Ministry of the Interior.

2.1. Taiwan Earthquake Impact Research and Information Application (TERIA) Platform

The Taiwan Earthquake Impact Research and Information Application (TERIA) platform, developed by the National Science and Technology Center for Disaster Reduction (NCDR), is a dedicated platform for seismic impact assessment. The platform’s spatial data infrastructure is structured upon a 500 m × 500 m grid system, wherein each grid cell integrates multi-domain datasets, including building stock, population density, the vulnerability of transportation networks (roads and bridges), utility lifelines (power and water supply systems), and critical infrastructure. Although the primary spatial outputs are generated in Shapefile (SHP) format, the platform also supports .csv and .kml formats to facilitate diverse analytical applications.

Operationally, TERIA requires the input of seismic source parameters—either point source or fault models—alongside specifications for earthquake magnitude and focal depth. Once the simulation is executed, the outputs can be queried directly within the platform or exported into a Geographic Information System (GIS) for advanced spatial analysis and layer overlay operations. To ensure alignment with the seismic source configurations specified in the New Taipei City Regional Disaster Prevention and Protection Plan, this study utilizes the TERIA platform to simulate a magnitude 6.8 earthquake along the Shanjiao Fault, with a designated focal depth of 15 km [5]. This deterministic configuration is heavily necessitated by the profound structural complexities and time-dependent strain accumulation observed across Taiwan’s active fault systems. As demonstrated by foundational geological investigations into Taiwan’s major fault damage zones, such as the Chelungpu fault system, tectonic fractures exhibit highly non-linear, time-dependent deformations and complex stress relaxation behaviors over seismic cycles [6]. Due to these continuous geomechanical stresses, predicting the exact temporal trigger of a major urban rupture remains highly uncertain, making a high-consequence deterministic rupture along the Shanjiao Fault the most scientifically responsible stress test baseline for municipal civil defense and resource allocation planning. Ultimately, this worst-case scenario simulation is designed to estimate short-term evacuation and sheltering demands across various districts in New Taipei City, thereby providing a quantitative baseline for shelter activation strategies. Based on this large-scale seismic scenario, this paper proposes a comprehensive policy framework for multi-site shelter management amid the inherent uncertainties of extreme events, systematically integrating these simulation results with the geographical distribution of DRVs via spatial overlay to enable a holistic assessment of the region’s localized emergency response capacity.

2.2. Network Analyst

Network analysis is a well-established spatial methodology predicated on network-based cartography and graph theory. A network system is defined as a complex structural framework composed of interconnected elements, primarily edges (links) and nodes (vertices). Once these elements establish topological connectivity, they delineate one or more potentially traversable routes [7,8]. In emergency management and disaster mitigation practice, network analysis is frequently employed to address complex logistics and evacuation challenges. Standard applications include vehicle navigation systems, the optimization of aviation flight paths, and, critically, the delineation of service areas and catchment networks for emergency medical services (EMSs) and disaster shelters.

However, while these network-based techniques effectively optimize routing and delineate the service boundaries of emergency facilities, they primarily focus on the efficiency of spatial ‘edges.’ To ensure the ultimate efficacy of a disaster mitigation framework, the physical safety and environmental viability of the ‘nodes’—specifically the shelter sites themselves—must be rigorously evaluated. Therefore, network analysis must be conceptually and methodologically complemented by suitability analysis to formulate holistic spatial decisions. Previous studies have demonstrated that utilizing GIS-based spatial models can facilitate scientific site selection and suitability evaluation for post-disaster shelters and open spaces by factoring in topography, population distribution, and environmental constraints [7,9]. Ultimately, a robust spatial disaster management system requires the synergistic integration of network efficiency and site suitability to genuinely enhance community resilience in real-world environments.

To operationalize the network efficiency component of this integrated framework, the fundamental principle underlying service area delineation aligns closely with the computational logic of shortest-path algorithms, most notably Dijkstra’s algorithm [7,8]. To demonstrate this mechanism, Figure 2a illustrates a topological network where multiple potential paths exist between locations, yielding varying cumulative costs or travel distances. For instance, consider the alternative routes connecting node A to node F: a suboptimal route traverses nodes B and C, generating a cumulative distance of nine units (indicated by the red line), whereas the optimal route yields a cumulative distance of only four units (indicated by the green line). Selecting an incorrect or unoptimized path during network modeling would introduce severe computational errors or logical contradictions, rendering subsequent spatial analyses mathematically untenable.

Building upon these shortest-path calculations, Figure 2b demonstrates how a service area boundary (catchment polygon) is generated when an administrative or physical threshold is introduced. Assuming a critical service threshold of four units is applied to node A (e.g., maximum allowable evacuation distance), the reachable network extent is strictly bounded by edge weights and node connectivity. Because the optimal path to node F costs exactly four units, it marks the precise spatial limit of the catchment area. Conversely, locations accessible only via cumulative costs exceeding this threshold (such as node C via the red route) are excluded, thereby establishing the delimited service area polygon shown in the shaded region.

2.3. Dijkstra Algorithm

Dijkstra’s algorithm, initially proposed by Edsger Dijkstra in 1959, remains one of the most foundational pathfinding methods in computational theory. Fundamentally, it operates as a greedy algorithm, which iteratively selects the path with the minimum weight or shortest distance from the current node until the destination is reached, thereby identifying the shortest path based on minimum cumulative cost.

As urban systems become increasingly complex, this algorithm has evolved from simple geometric distance calculations into an integrated assessment tool that incorporates social vulnerability, dynamic disaster conditions, and resource allocation. In the field of urban evacuation and accessibility analysis, the application of Dijkstra’s algorithm is primarily reflected in the following three dimensions:

1.

Precise Delineation of Evacuation Accessibility and Service Areas

Traditional evacuation studies often rely on Euclidean distance (straight-line distance), but research shows that this approach can significantly mislead resource allocation. Anhorn and Khazai [10] utilized Dijkstra’s algorithm combined with network topology and building capacity to assess the suitability and service areas of emergency shelters, highlighting that network analysis can more accurately quantify evacuation deficits. Zhu et al. [7] further employed an improved 3D Dijkstra’s algorithm, taking into account flood risk levels and road slopes, to precisely delineate service areas for urban personnel evacuation. In terms of medical resource allocation, Mirahadi and McCabe [11] developed a real-time evacuation model (EvacuSafe) using this algorithm, confirming that time impedance reflects real spatial burdens more effectively than distance impedance.

2.

Dynamic Disaster Conditions and Multi-Criteria Path Optimization

In the face of large-scale earthquakes or floods causing road network disruptions, the application of evacuation routing algorithms has become increasingly dynamic. Zhu et al. [7] proposed a high-resolution flood numerical model integrated with Dijkstra’s algorithm, using water level changes as dynamic weights to calculate escape routes for disaster victims under evolving flood conditions. Kar et al. [9] further combined mathematical programming and multi-criteria decision analysis within the Dijkstra framework, integrating heat flux, road impedance, and shelter capacity to provide more resilient path choices for post-disaster evacuation. Recent studies emphasize that for vulnerable groups such as the elderly, the shortest path often does not align with the “safest path.” Employing hazard-aware optimization algorithms can significantly reduce their exposure risks during evacuation [12,13].

3.

Network Resilience and Spatial Mismatch of Human Resources

The algorithm is also used to analyze the reliability of urban road networks under extreme events. Dijkstra’s algorithm has been widely applied to examine the impact of network failures on evacuation efficiency, revealing that network redundancy is central to maintaining evacuation functionality [7,8]. Mirahadi and McCabe [11] assessed urban network vulnerabilities by analyzing path reconstruction after link failures. In indoor–outdoor integrated evacuation studies, the relevant literature has explored different dimensions. Bhat et al. [14] compared the application of Bellman–Ford and Dijkstra’s algorithms for evacuation in multi-floor buildings. Meanwhile, to address the connectivity challenges between high-rise buildings and urban road networks, Wang and Niu [15] proposed an integrated indoor–outdoor route planning model. Both studies have significantly improved the accuracy of evacuation simulations.

The implementation of Dijkstra’s algorithm in this research transcends the mere calculation of an 800 m physical proximity. Instead, it provides a high-fidelity analytical framework to precisely quantify the spatial mismatch between the residential distribution of DRVs and localized evacuation demand nodes. By modeling movement across authentic urban road networks, this methodology directly addresses the imperative of operational resilience—the city’s functional capacity to maintain life-sustaining services under extreme pressure. The selection of an 800 m walking threshold—approximately equivalent to a 10 min pedestrian commute—is grounded in several critical considerations: in urban planning standards (the pedestrian shed) and the Transit-Oriented Development literature, 800 m is recognized as the standard “pedestrian shed”, representing the maximum distance individuals are willing to travel on foot to access essential services under normal conditions. In addition, the considerations for setting a walking distance also include “Disaster Psychology and Accessibility” and “Policy Alignment”.

• Disaster Psychology and Accessibility:

In the immediate aftermath of a seismic event, 800 m represents the upper limit of effective accessibility. Factors such as psychological stress, potential debris, and the presence of vulnerable populations (e.g., the elderly or children) significantly reduce effective walking speeds, making this threshold a conservative yet realistic boundary for ‘golden time’ evacuation.

• Policy Alignment:

This threshold is consistent with the benchmarks stipulated in the New Taipei City Regional Disaster Prevention and Protection Plan, ensuring that the analytical results are directly applicable to local administrative decision-making and resource allocation strategies.

By computing path impedances across authentic urban street grids rather than relying on abstract straight-line distances, this methodology directly addresses the “Last Mile” problem in urban evacuation logistics. In sudden-onset seismic events, the last mile represents the final, most volatile leg of civilian transit—the micro-spatial journey from a damaged domestic structure to an operational refuge node amidst localized urban barriers. Reframing the 800 m network catchment as a last-mile accessibility diagnostic allows this framework to cleanly isolate the localized bottlenecks, structural obstructions, and demographic mismatches that structurally impede vulnerable populations during the critical initial phases of self-evacuation.

In summary, this study adopts Dijkstra’s algorithm not merely to obtain an 800 m physical distance, but to precisely quantify the spatial mismatch between “DRV” and “evacuation demand points” on the basis of real urban road networks, thereby addressing the contemporary city’s deep demand for “operational resilience.”

3. Results

3.1. Seismic Scenario Simulation and Sheltering Outcomes

Given that this research utilizes mailing addresses as the geospatial localization points for DRVs, a nocturnal scenario at 5:00 AM was selected to simulate a large-scale earthquake occurring while the population is at home (refer to New Taipei City Regional Disaster Prevention and Protection Plan [5]). The simulation results are illustrated in Figure 3 and Figure 4.

Figure 3 presents the seismic intensity classification, indicating that intensities across the entire study area exceeded Magnitude 5-Lower (JMA scale). Peak intensities reached Magnitude 7—the maximum level—in central Xinzhuang, northern Banqiao, northeastern Yonghe, and western parts of Luzhou. Figure 4 depicts the estimated nighttime evacuation demand, with approximately 460,000 individuals affected. Significant spatial clustering of evacuees was observed in the region spanning Banqiao, Tucheng, and Zhonghe, as well as the Luzhou-Sanchong area. Notably, Xinzhuang District exhibited the highest density of affected persons, where the evacuation demand exceeded 4000 individuals within a single 500 m × 500 m grid cell. The spatial distribution of the nocturnal shelter demand was further delineated (as illustrated in Figure 4). The dataset is categorized into five intervals at 1000-person increments, with a peak density of 4232 individuals per grid cell, primarily located in Longfeng Village on the western side of Xinzhuang District. Overall, the high-impact zones are concentrated in four densely populated clusters: the commercial districts in northern Xinzhuang, transit hubs in western Xinzhuang, eastern Sanchong, and western Luzhou. In most of these regions, the required shelter capacity exceeds 1000 persons, bringing the total estimated shelter demand across the ten studied districts to approximately 300,000 individuals.

3.2. Delineation of Analysis Units and Sheltering Assessment

This study designates evacuation shelters as the focal points and utilizes ArcGIS 3.6 Network Analyst to delineate service areas based on an 800 m walking distance threshold. This distance, approximately equivalent to a 10 min walk, is widely regarded as an acceptable walking range for the general public. The walking distance threshold is also addressed in the New Taipei City Regional Disaster Prevention and Protection Plan.

The selection of an 800 m radius as the primary analysis unit for evacuation service areas is grounded in both urban planning standards and disaster psychology. This study adopts this threshold based on the following academic pillars:

1.

The “Pedestrian Shed” and Urban Service Standards

In urban morphology and Transit-Oriented Development (TOD) literature, 800 m is globally recognized as the standard “pedestrian shed,” representing the maximum distance a typical individual is willing to travel on foot (approximately 10–12 min at a pace of 1.1–1.2 m/s) to access essential services. In hyper-dense urban environments like New Taipei City, this distance serves as a critical policy benchmark for evaluating the accessibility of social infrastructure, including emergency shelters.

2.

The “First 10 Minutes” for Immediate Evacuation

Disaster response research emphasizes the “First 10 Minutes” following a major seismic shock, during which evacuees must reach a safe structural environment to avoid secondary hazards such as fires or aftershocks. An 800 m threshold aligns with this survival window under nominal conditions. By utilizing this distance, the study establishes an idealized operational baseline to identify systemic deficits that occur even under the most favorable mobility assumptions.

3.

Correction of Euclidean Distance Bias

Unlike traditional studies relying on straight-line “as-the-crow-flies” distances, this research employs Dijkstra’s algorithm within a real-world road network. This methodology more accurately quantifies actual spatial impedance, identifying residents who are functionally excluded from shelter services due to urban topography.

4.

Administrative and Regulatory Consistency

The 800 m threshold aligns with the operational standards stipulated in the New Taipei City Regional Disaster Prevention and Protection Plan. Utilizing this distance as an analysis unit ensures that the study’s findings are directly applicable as a policy-making tool for local administrative agencies.

5.

Benchmarking Operational Resilience

Setting a standardized 800 m limit establishes an “idealized baseline”. This allows the study to precisely detect and measure the marginal degradation of urban resilience, highlighting where “spatial mismatch” occurs even under optimal mobility assumptions. While an 800 m radius is derived from the standard “pedestrian shed”, this study adopts it as a conservative operational baseline rather than a fixed physiological limit. This methodology acknowledges that post-disaster variables—including debris, structural failure, and the presence of vulnerable groups—drastically reduce effective walking speeds. By benchmarking against this “idealized” distance, the model provides a rigorous stress test of the urban sheltering network, identifying systemic failure points that exist even before factoring in severe mobility degradation.

Each evacuation shelter is assigned its own distinct service area, which functions as the fundamental unit of analysis and represents the smallest spatial unit within this research, as illustrated in Figure 5. To ensure a comprehensive assessment of urban seismic vulnerability and prevent the underestimation of shelter congestion, this study incorporates a shadow demand redistribution for populations residing beyond the primary 800 m service catchments. While the 800 m threshold defines the primary operational baseline, the analytical processes consider individuals in the gray zones. People in need of shelter under the gray zones gravitate toward the nearest available infrastructure. To account for populations whose mobility is impaired or who reside beyond nominal catchments, a nearest facility assignment protocol was implemented in ArcGIS. This redistributes the resulting “shadow demand” to the nearest geographically available node, thereby integrating the cumulative pressure of underserved residents into the DRV shortfall calculation. To ensure analytical transparency and eliminate population evaporation bias, this study formalizes the redistribution of populations residing beyond the primary thresholds through a rigorous Two-Tier Spatial Demand Allocation Algorithm. The total projected demand accumulating at any discrete evacuation shelter $j$ (denoted by $D_{\mathit{total},j}$) is modeled as a composite function of primary localized demand and peripheral shadow spillover, mathematically formalized as follows:

$$D_{\mathit{total},j}=D_{\mathit{local},j}+D_{\mathit{shadow},j}$$

$$D_{\mathit{shadow},j}=\sum _{i\in S_j}\left({\mathrm{P}}_i\times w_i\right)$$

where $D_{\mathit{local},j}$ represents the primary local demand aggregated from the spatial intersection of populations residing strictly within the ≤800 m network-derived pedestrian catchment of shelter $j$. Conversely, $D_{\mathit{shadow},j}$ represents the accumulated “shadow demand” derived from the unserved peripheral populations residing in spatial gray zones. In this formulation, $P_i$ signifies the total simulated nocturnal evacuation population within an underserved grid cell $i$, and $w_i$ is the area-proportional weight (0 < $w_i$ ≤ 1) representing the percentage of grid $i$ situated outside any primary 800 m catchments.

Operationally, the set $S_j$ encompasses all peripheral grid cells assigned to shelter $j$ via the Nearest Facility Solver in ArcGIS Network Analyst. The algorithm executes a Dijkstra-based routing sequence across the authentic urban road network topology, computing the cumulative network distance ($d_{ij}$) from the geographic centroid of each underserved grid cell $i$ to all 200 concurrent shelter nodes. Grid cell $i$ is dynamically allocated to the set $S_j$ if and only if shelter $j$ minimizes the structural travel impedance, such that

$$S_j=\left\{i|d_{ij}=\min \left(d_{ik}\right),\forall k\in K\right\}$$

where $K$ represents the total set of evaluated evacuation shelters ($\left|K\right|=200$). Through this dual-scale mechanism, the model successfully integrates the cumulative pressure of underserved peripheral residents into the final facility-level stress test, preventing the spatial distortion of shelter saturation metrics.

To ensure absolute methodological transparency, it must be emphasized that the secondary redistribution of shadow demand is strictly predicated on network distance evaluated across the authentic urban road topology, rather than Euclidean metrics. Furthermore, this secondary allocation operates without any maximum distance caps (e.g., uncapped at 2 km or 5 km), and zero shelters or population fractions were excluded from the system stress test. This programmatic constraint guarantees total demographic accountability, ensuring that populations residing in peripheral regions outside nominal catchments are comprehensively absorbed by the nearest available facility, thereby preventing population evaporation bias.

Consequently, this methodological step establishes a Two-Tier Spatial Demand Framework. The final projected pressure on each shelter is composed of two explicit layers: (i) the primary local demand generated strictly within the network-derived ≤800 m pedestrian catchment, and (ii) the macro-level “shadow demand” spilled over from peripheral populations residing in unserved gray zones who migrate to the nearest asset. By coupling micro-accessibility with broader residual redistribution, the final assessment avoids “population evaporation bias” and transitions from a hypothetical proximity map to an integrated operational stress visualization.

Subsequently, the Tabulate Intersection tool within ArcGIS was employed to execute a proportional intersection between each analysis unit and the 500 m × 500 m TERIA grid cells. This area-proportional redistribution operates under the necessary operational assumption of a uniform population distribution within each discrete grid cell. Figure 6 provides a schematic illustration of this geometric allocation: based on the TERIA seismic simulation results, each grid cell represents a distinct localized shelter demand (e.g., Grid A = 500, Grid B = 245, Grid C = 400, and Grid D = 250 individuals).

The network-derived service areas delineate the analysis units for Shelter I (blue) and Shelter II (yellow), which are partitioned by the TERIA grid boundaries. For instance, the service area for Shelter I comprises sub-sectors ①, ②, and ④, while Shelter II consists of ③ and ⑤. The assigned population for each sub-sector is quantified based on its respective intersection area percentage:

●

Sub-sector ①: Covers 60% of Grid A (500 × 60% = 300 individuals);

●

Sub-sector ②: Covers 20% of Grid B (245 × 20% = 49 individuals);

●

Sub-sector ③: Covers 45% of Grid B (245 × 45% = 110.25, rounded up to 111 individuals);

●

Sub-sector ④: Covers 50% of Grid C (400 × 50% = 200 individuals);

●

Sub-sector ⑤: Covers 50% of Grid D (250 × 50% = 125 individuals).

By aggregating the populations of sub-sectors ①, ②, and ④, the total estimated baseline demand for Shelter I is 549 individuals. Similarly, the aggregate demand for Shelter II (③ + ⑤) is 236 individuals. These figures represent the projected spatial shelter requirements under a deterministic seismic scenario involving a magnitude 6.8 Shanjiao Fault rupture at a depth of 15 km. While micro-spatial urban morphologies (e.g., concentrated residential high-rises or commercial voids) inevitably introduce localized sub-grid variations, utilizing this area-weighted split provides a standardized, replicable interpolation baseline when building-specific nocturnal census data remains restricted by administrative privacy policies. More importantly, because the final service area aggregation synthesizes multiple fractional grid intersections, localized micro-scale variations are statistically smoothed out at the broader catchment scale, preserving the diagnostic validity of the aggregate shelter pressure calculations.

Building upon this primary geometric intersection, it is vital to clarify that the secondary nearest facility redistribution protocol for peripheral shadow demand is also deliberately unconstrained by shelter capacity ceilings. While operations research frequently deploys capacity-constrained location-allocation algorithms to optimize systemic efficiency, such prescriptive approaches assume a top-down command capability and perfect information availability that do not exist during sudden-onset nocturnal catastrophes. In accordance with established disaster sociology, evacuated populations instinctively navigate to the closest recognizable refuge node on foot (User-Optimal behavior), regardless of its physical saturation state. Consequently, by allowing shadow demands to naturally accumulate at the nearest nodes, the model functions as an unsmoothed diagnostic stress test, accurately revealing acute localized spatial bottlenecks and systemic vulnerability hotspots that require targeted administrative intervention.

3.3. Shelter Capacity and Overload Analysis

Using the aforementioned Tabulate Intersection method for statistical aggregation, the total projected demand within each service area was summed to determine whether the sheltering requirements within an analysis unit exceed the available shelter capacity.

The spatial distribution of the resulting capacity shortfall is visualized in Figure 7. Figure 8 also further illustrates the status of shelter sufficiency versus overcapacity after accommodating the affected population within each respective analytical unit. Analytical results indicate that 148 shelters within the study area are currently overloaded, representing 74% of the total 200 facilities evaluated. This disparity is primarily driven by high population density and aging building stocks.

The study defines five classification intervals: facilities with a surplus capacity exceeding 1000 persons and those with 1 to 1000 persons are categorized as having sufficient capacity. Conversely, three levels of overload (0–1500, 1501–3000, and >3000 persons) represent insufficient sheltering space. Analytical results indicate that 148 shelters within the study area are currently overloaded, whereas only 52 possess adequate capacity. This disparity is primarily driven by high population density and aging building stocks, which contribute to a significantly high volume of evacuees during a seismic event.

3.4. DRV Distribution and the Manpower Gap

In this study, 800 m service areas were delineated as primary analysis units, within which the total number of DRVs was quantified (as illustrated in Figure 8). Within the study area, 42 analysis units were found to contain no resident DRVs, while only five units exceeded a count of 13. The service area corresponding to the Zhonghe District Office exhibited the highest concentration, with a maximum of 18 DRVs. Following the recommendations of the Mass Care and Shelter Guidance for Emergency Planners [2] and the FEMA (2011) [16], an operational staff-to-occupant ratio of approximately 100:6 is required for effective shelter management [1]. It is critical to note that the 100:6 staffing ratio is treated as a deterministic operational constraint rather than a stochastic variable. In tactical emergency planning, utilizing a standardized regulatory benchmark provides a rigorous administrative baseline for system-level “stress testing”. Rather than predicting fluctuating human behavior, the DRV shortfall metric functions as a diagnostic compliance tool. Consequently, the transferability of this framework resides not in the rigidity of the 100:6 parameter, but in the replicability of the spatially explicit network topology, which can seamlessly accommodate varying international statutory standards to identify localized urban vulnerabilities.

It should be noted that applying a standardized linear ratio (R = 0.06 N) across all facilities represents a macro-level analytical baseline rather than a tactical shift-scheduling protocol. In real-world shelter operations, resource allocation is stepped; even micro-shelters accommodating minimal populations (e.g., the Taishan Gymnasium with nine evacuees or the Guanyin Community Activity Center with 16 evacuees) require a non-zero baseline skeleton crew to structurally activate the five essential operational sections (Manager, Operations, Logistics, Care, and Security). By omitting these fixed operational labor thresholds, the “DRV shortfall” calculated in this spatial coupling model functions as an ultra-conservative lower-bound estimation of human resource demand. This mathematical assumption ensures that the identified 74% shelter saturation rate and localized manpower deficits remain highly robust, as any operational step-functions or shift-rotation realities would only further widen the quantitative volunteer deficits across the hyper-dense urban landscape.

Consequently, this 100:6 service ratio was applied to the projected shelter populations to estimate the required manpower for successful facility activation and actual events in Taiwan [1]. Figure 9 demonstrates that the simultaneous operation of multiple evacuation shelters generates a massive demand for human resources. Notably, Yongping High School in Yonghe District requires 319 DRVs due to its high estimated occupancy, while the Siwei Community Activity Center in Xinzhuang District necessitates 365 DRVs.

Under a large-scale seismic scenario, numerous evacuation shelters reach saturation. This overwhelming demand results in a severe supply–demand imbalance, where the number of available DRVs is insufficient. Nearly all 200 shelters within the study area operate under extreme manpower and spatial strain, underscoring a significant deficiency in sheltering capacity across hyper-dense urban environments.

4. Discussion

The minimum manpower required for the successful activation and operation of evacuation shelters is determined by subtracting the projected DRV requirement (derived from simulated occupancy) from the existing DRV population. This study evaluates human resource adequacy by computing the “DRV Balance” for each analysis unit, defined as follows: DRV Balance = Existing DRVs − Required DRVs. Under this formalized mathematical convention, a negative value (DRV Balance < 0) consistently signifies a localized manpower shortfall, implying that the evacuation shelter will encounter severe obstacles during initial activation due to insufficient human capital. Conversely, a positive value (DRV Balance > 0) indicates a resource surplus, identifying highly resilient nodes capable of deploying auxiliary support to neighboring units.

Strategic policy framework for multi-shelter activation and operational resilience could be figured out according to the results of the research. Beyond identifying spatial deficiencies, this study contributes a comprehensive policy framework for multi-shelter activation under extreme seismic uncertainty. By transitioning from a static capacity-based assessment to a dynamic, resource-synchronized management paradigm, the following framework pillars are proposed:

1.

DRV shortfall Informed Prioritization and Activation Sequencing

Under large-scale seismic scenarios where simultaneous activation of all 200 shelters is operationally infeasible due to extreme manpower strain, the DRV shortfall should serve as the primary diagnostic tool for activation sequencing.

• High-Deficit Nodes (Critical value < 0): Shelters such as the Siwei Community Activity Center, exhibiting extreme deficits, must be flagged as “High-Risk Convergence Nodes.” Policy should prioritize the pre-deployment of external professional responders to these sites to prevent immediate operational collapse.
• Resource Surplus Nodes (Positive value > 0): Facilities with resident manpower surpluses should be designated as “Support Hubs,” integrated into a dynamic dispatch system to provide auxiliary aid to neighboring high-deficit units.

2.

Spatio-Temporal Synchronization of Hardware and Human Capital

The framework advocates for a shift from “Shelter-Centric” to “Resource-Synchronization” planning. This study demonstrates that urban resilience is often compromised by the spatial mismatch between certified autonomous personnel and peak demand points.

• Manpower Spatial Coupling: Policy must require that shelter capacity updates (hardware) be systematically coupled with DRV recruitment and training data (software) within the same 800 m analytical units.
• Vulnerability-Targeted Recruitment: In districts like Banqiao where the volunteer-to-evacuee ratio is grossly diluted, government interventions should shift from broad regional training to targeted neighborhood-level recruitment within identified service gaps to ensure the baseline “Self-help” and “Mutual-help” capacities.
• Targeted Recruitment and Strategic Training: Local authorities should implement “precision recruitment” programs focusing on the 42 analysis units identified as having zero resident DRVs. Prioritizing training in these “manpower vacuums” ensures that every evacuation node possesses the baseline capacity for initial facility activation.

3.

Dual-Track Resource Synchronization Framework

The empirical identification of 42 analysis units completely lacking resident certified volunteers offers a critical spatial diagnostic for municipal emergency management, though its resolution suggests a flexible, multi-tiered administrative approach rather than a rigid recruitment mandate. To optimize resource allocation, municipal authorities could adopt a Dual-Track Resource Synchronization Framework that balances immediate hyper-local containment with regional mutual aid:

• Track 1: Dynamic Cross-District Dispatching Networks. Rather than treating each analysis unit as an isolated island reliant solely on its resident demographic pool, the identified volunteer-vacuum nodes could be integrated into a horizontal mutual aid network. Under this framework, neighboring analysis units exhibiting a positive DRV Balance could serve as priority reinforcement reserves. Establishing formalized inter-district governance protocols would allow municipal managers to dynamically dispatch auxiliary volunteer management teams across border lines, mitigating localized deficits through surrounding spatial surpluses.
• Track 2: Conditional Precision Recruitment as Local Anchors. Concurrently, the viability of cross-district dispatching remains conditional upon post-disaster road accessibility and mobilization time-lags during the immediate “golden window” of shelter activation. Because the initial 30 min of emergency staging typically require immediate on-site key holders and core section managers, a highly localized precision recruitment initiative could be selectively implemented in high-deficit commercial zones. This localized approach should be deployed not as an exclusive requirement, but as a targeted method to establish a minimal on-site “skeleton crew” capable of initiating shelter registration protocols prior to the arrival of neighboring cross-dispatched teams.

4.

Multi-District Governance and Mutual Aid Protocols

Addressing the “shadow demand”—the population residing beyond nominal walking catchments —requires a multi-district governance protocol.

• Dynamic Demand Migration: Policy frameworks must account for inter-district demand migration where evacuees from unserved zones gravitate toward existing shelters.
• Adaptive Shelter Networks: Rather than operating shelters as isolated units, the framework employs an integrated network where facility activation is coordinated across administrative boundaries to balance the localized saturation of both spatial and human resources.
• Integration into Strategic Human Resource Management: DRVs should be formally integrated into the local governmental disaster frameworks of Human Resource Management rather than being treated as auxiliary volunteer pools. This integration facilitates the development of a “Mutual Aid Protocol,” allowing analysis units with a positive DRV Balance to dynamically support adjacent high-deficit facilities during multi-site activations.

5.

Cultivating Community-Based “Self-Help” Resilience

Mirroring the Japanese “Bousaisi” principles of self-help and mutual cooperation, DRVs should serve as the primary liaison between the public sector and residents. By identifying localized vulnerabilities during non-disaster periods, they enhance the risk awareness and autonomous response capacity of hyper-dense neighborhoods.

6.

Theoretical Contribution: Enhancing Operational Resilience

The primary academic contribution of this framework is the formalization of “operational resilience”—the ability of a system to not only provide physical space but also to maintain functional stability through synchronized human resource allocation. By quantifying the DRV shortfall and mapping the spatial mismatch, this study provides a replicable methodology for international urban centers to diagnose and mitigate systemic vulnerabilities in their emergency sheltering networks.

7.

Methodological Boundaries: Attrition, Network Degradation, and Spontaneous Compensation

While this spatially explicit coupling utilizes the total registered DRV roster as an idealized upper-bound capacity baseline, operational reality dictates a certain rate of localized manpower attrition due to personal injury, residential displacement, or structural road damage. However, disaster response literature demonstrates that such post-disaster structural gaps are dynamically compensated for by the rapid convergence of unaffiliated, spontaneous volunteers within the affected neighborhood [17]. Therefore, the certified DRVs modeled in this research function primarily as an organizational nexus rather than isolated physical laborers. Even a fractional survival rate of certified DRVs within an 800 m catchment can effectively absorb, structure, and direct the chaotic influx of emergent community groups, turning localized convergence into functional order. Nonetheless, this inherent vulnerability reinforces the necessity of moving beyond single-site reliance toward the dual-layered redundancy and inter-district governance frameworks detailed herein.

To transition the framework’s “upper-bound best-case” framing from a conceptual assumption into a rigorously quantified predictive boundary, a Macro-Analytical Volunteer Attrition Array was integrated into the validation suite. Real-world emergency deployments indicate that post-disaster participation levels are heavily constrained by localized mobility barriers, physical injuries, and immediate familial obligations. To estimate these unmodeled dynamics, we introduce a systemic availability coefficient τ (where 0 < τ ≤ 1) applied directly to the existing registered DRVs pool, such that the effective supply is modeled as Effectively Mobilized DRVs = τ × Existing registered DRVs. Based on empirical attrition ranges documented in contemporary disaster sociology (e.g., Twigg and Mosel [17]), three plausible post-disaster participation regimes were evaluated (see

Table 1. Macro-analytical sensitivity array of post-disaster DRV participation levels (τ).

Post-Disaster Participation Scenario	Availability Coefficient (τ)	Effectively Mobilized DRVs	Total Required DRVs (Metropolitan)	Net Metropolitan Shortfall Range	Systemic Risk Assessment and Implications
Idealized Baseline	τ = 1 (0% Attrition)	612	18,000 DRVs	−17,388	Perfect readiness baseline; unmasks structural system-level deficiencies under optimal conditions.
Moderate Mobility Blockage	τ = 0.75 (25% Attrition)	459		−17,541	Localized containment via road debris; shortfalls deepen across 83% of metropolitan shelters
Severe Catastrophic Attrition	τ = 0.5 (50% Attrition)	306		−17,694	Acute personal and network disruption; widespread functional paralysis of initial shelter staging.

).

The execution of this analytical sensitivity array establishes an a fortiori mathematical proof regarding the robustness of the study’s conclusions. Sliding the participation coefficient from a perfect baseline (τ = 1) down to a severe post-disaster disruption state (τ = 0.50) systematically expands the net metropolitan human resource shortfall from −17,388 to −17,694 personnel. Because the system faces an overwhelming and highly concentrated resource deficit under every plausible availability rate, the exclusion of dynamic attrition parameters in the primary GIS routing engine does not weaken the validity of the findings. Instead, it confirms that the main text’s spatial mismatch metrics function as an ultra-conservative, diagnostic lower-bound baseline of system failure, mathematically guaranteeing that real-world operational frictions will only further accelerate and deepen the localized facility crises unmasked by this stress test.

A recognized methodological boundary of this framework is the modeling of pedestrian accessibility across an optimal, undegraded physical road topology, omitting post-earthquake bridge collapses, soil liquefaction, and structural debris blockages. In a real-world magnitude 6.8 Shanjiao Fault rupture, network degradation will inevitably compress the effective pedestrian service areas and restrict volunteer mobility. To address the realism of our estimates under these degraded conditions, the model relies on a spatially explicit Two-Tier Demand Allocation logic. Mathematically, if structural road blockages were introduced, the nominal 800 m pedestrian catchments would contract to a smaller effective functional radius. While this accessibility constraint reduces the primary local demand immediately surrounding a facility, the affected urban population is structurally conserved. These excluded residents are dynamically shifted into the peripheral shadow demand layer, migrating via surviving local micro-topologies to the nearest geographically accessible node. Because shelter infrastructures represent fixed, discrete assets within the hyper-dense metropolitan core, this restriction of traversable paths generates an acute “Inward Funneling Effect”. Displaced survivors and certified DRVs, constrained by localized link failures, are forced to converge onto the same remaining visible refuge hubs. Consequently, this spatial contraction acts as an accelerating vector: since 74% of shelters already exhibit severe overcapacity and acute volunteer shortfalls under perfect mobility assumptions, real-world network degradation will not stabilize the network; rather, it will exponentially intensify localized overcrowding and deepen volunteer isolation at critical hotspots. Benchmarking the system against an intact topology thus establishes a rigorous operational floor—a best-case capacity ceiling—mathematically guaranteeing that real-world operational crises will be significantly more severe than our reported figures, thereby validating the diagnostic necessity of our resource-synchronization frameworks. As observed by Twigg and Mosel [17], post-disaster population displacement triggers both immediate hyper-local neighborhood gathering and broader geographic convergence toward major surviving municipal hubs. Modeling the final shelter saturation as a combination of local walking access and shadow spillover migration reflects this empirical behavioral continuum.

The choice of an unconstrained nearest-facility assignment over a capacity-optimized location-allocation model delineates a clear methodological boundary between prescriptive geometry and descriptive behavioral realism. Rerouting displaced residents to farther, lower-density shelters within the model would introduce a systemic bias of perfect communication networks and compliance. As argued by Twigg and Mosel [17], informal urban disaster responses are fundamentally decentralized and hyper-local. Panic, visibility degradation, and cognitive strain compel survivors to cluster at the nearest physical facility. Factoring this behavioral trajectory into our spatial coupling engine confirms that the 74% shelter saturation rate is a highly accurate reflection of aggregate public pressure. This structural bottleneck further justifies the urgency of shifting municipal policies from static, shelter-centric capacity expansions toward the dynamic resource-synchronization and Support Hub networks advocated by this research.

A recognized boundary of this spatial explicit coupling framework is the reliance on area-weighted interpolation for population disaggregation from 500 m × 500 m TERIA grid. In hyper-dense metropolitan areas, non-uniform residential density can potentially introduce localized allocation noise at specific grid boundaries. However, within a macro-level systems stress test encompassing 200 shelters across ten hyper-dense districts, these spatial errors act as balanced vectors that cancel out upon catchment-scale aggregation. Future extensions of this model could incorporate multi-spectral dasymetric mapping or real-time mobile network big data to refine sub-grid spatial precision. Nevertheless, the current standardized framework provides a highly conservative, actionable diagnostic tool for immediate municipal activation sequencing and resource synchronization.

In a catastrophic Shanjiao Fault rupture scenario, real-world accessibility will inevitably be impaired by complex secondary hazards, including soil liquefaction, structural debris accumulation, and bridge failures. However, by modeling pedestrian sheds under optimal infrastructure conditions, this research intentionally establishes an idealized operational baseline. The empirical outcome that 74% of metropolitan shelters face concurrent spatial and manpower saturation under perfect mobility assumptions represents an a fortiori proof of urban vulnerability. It mathematically guarantees that if the urban sheltering network fails to maintain functional stability under optimal conditions, its operational degradation under physical network degradation will be exponentially more severe, confirming that our findings represent a highly conservative lower-bound metric of system failure. At the micro-pedestrian scale, this baseline layout appropriately captures the immediate, hyper-local “Self-help” phase documented by Twigg and Mosel [17], where survivors instinctively traverse immediate local blocks to reach nearby recognizable assets, reinforcing the diagnostic necessity of our resource-synchronization and targeted recruitment frameworks.

As illustrated in Figure 9, even the facilities with the least critical shortages exhibit a deficit of at least one DRV. Notable examples include the Taishan Gymnasium in Taishan District and the Guanyin Community Activity Center in Wugu District; these sites face simulated demands of 9 and 16 evacuees, respectively, yet both currently possess zero resident DRVs. The most severe supply–demand imbalance is observed at the Siwei Community Activity Center in Xinzhuang District, which faces a critical DRV Balance of existing (4) − required (365). This mathematical deficit represents far more than a numerical shortage; it indicates a systemic failure point. In this specific analysis unit, only four resident DRVs are available to manage an overwhelming simulated demand of 6083 evacuees, completely missing the statutory 100:6 staffing target. In hyper-dense urban environments, such a gap suggests that critical life-sustaining services—including medical care for vulnerable groups and registration of mass evacuees—cannot be maintained during the “golden window” of disaster response. Conversely, our analysis identifies nodes with a positive DRV value. These should be designated as “Support Hubs” within a multi-district governance protocol, enabling a dynamic redistribution of human capital to stabilize high-risk facilities. Furthermore, the simulated occupancy far exceeds the facility’s planned capacity of 300, highlighting an extreme localized saturation of both spatial and human resources.

The selection of a 5:00 AM nocturnal scenario delineates a necessary temporal boundary regarding the modeling of transient versus permanent populations. While the introduction highlights the systemic vulnerabilities associated with daytime transient populations—such as commuters, students, and tourists stranded around transit hubs—the simulated earthquake purposefully isolates a nighttime setting when these transient fluidities are at a minimum. This temporal constraint should be interpreted as a deliberate administrative baseline for system-level stress testing. In hyper-dense Asian metropolises characterized by Transit-Oriented Development (TOD) and intensive mixed-use zoning, commercial corridors and mass transit nodes are integrated with vertical residential high-rises. Consequently, the acute shelter overcapacity and localized volunteer deficits observed in these zones at 5:00 AM are driven entirely by sleeping permanent residents. By capturing a severe DRV Balance deficiency under zero transient load, the model establishes an ultra-conservative macro-level lower bound. It mathematically guarantees that if these transit and commercial clusters are already operationally paralyzed by their resident populations alone, their real-world functional collapse under daytime transient influxes will be exponentially more catastrophic, validating the strategic necessity of our proposed multi-district Support Hub deployment networks.

While the current spatial explicit coupling framework functions as a post-event strategic baseline, its operational utility can be dynamically expanded by interfacing with advanced geophysical telemetry infrastructures. Future iterations of this model could be integrated with Taiwan’s state-of-the-art Earthquake Early Warning (EEW) networks. By utilizing automated algorithms designed for the rapid assessment of damage potential derived within the very beginning seconds of seismic P-waves [18], the localized DRV Balance calculations and multi-shelter activation sequences derived in this study can be pre-triggered automatically. Coupling early-warning telemetry with our 800 m pedestrian network engine will allow municipal authorities to initiate targeted volunteer dispatch alerts and hardware synchronization protocols during the critical “golden seconds” prior to the arrival of destructive S-waves, moving the metropolitan sheltering network closer to absolute real-time operational resilience.

Additionally, the deterministic selection of the 800 m walking threshold, the 100:6 staff-to-occupant ratio, and the magnitude 6.8 Shanjiao Fault parameters defines a deliberate operational boundary between speculative probabilistic risk forecasting and prescriptive administrative compliance auditing. To verify the structural robustness of the framework’s principal findings against alternative modeling inputs, a formal mathematical invariance deduction was executed across a plausible range of alternative staffing assumptions (from 100:4 to 100:8), as presented in Table 1,

Table 2. Macro-analytical sensitivity matrix of staffing ratios and aggregate DRV shortfalls.

Staffing Ratio Scenario	Required Personnel per 100 Evacuees	Total Metropolitan DRV Demand	Net Systemic Shortfall Range	Systemic Vulnerability Status
Minimum Skeleton (100:4)	Four Regular Staff/DRVs	12,000 DRVs Required	Rounding −11,400	Severe Shortfall/Non-Compliant
Baseline Audit (100:6)	Six Regular Staff/DRVs	18,000 DRVs Required	Rounding −17,400	Baseline Crisis
Enhanced Care (100:8)	Eight Regular Staff/DRVs	24,000 DRVs Required	Rounding −23,400	Catastrophic Deficit/Systemic Collapse

and

Table 3. Qualitative Validation and Benchmarking Matrix.

Validation Benchmark	Core Parameters/Empirical Characteristics	Alignment with This Study’s Model	Methodological and Replicability Justification
New Taipei City Regional Disaster Prevention Plan	Mandates emergency readiness for a maximum credible accident along the Shanjiao Fault (M6.8, 15 km depth), estimating about 300,000 displaced shelter-seekers.	Perfect Macro-Alignment: Our model’s hazard engine generates an identical total demand baseline.	Confirms our model operates as a high-fidelity “Administrative Audit” perfectly calibrated against official statutory planning expectations.
Historical Baseline: 1999 Chi-Chi Earthquake (Taiwan)	Magnitude 7.3 rupture along the rural/suburban Chelungpu Fault; horizontal rural displacements; single-story or low-rise building damage dominant.	Morphological Contrast: Our model targets a hyper-dense metropolitan core characterized by Transit-Oriented Development (TOD) and vertical high-rise vulnerability	Explains why direct quantitative back-testing against 1999 data introduces severe geographic bias, validating our use of a descriptive modern behavioral model instead.
Empirical Human Resource Data	Real-world, government-certified list containing exact registration addresses of active disaster volunteers.	The supply layer uses point-at-address verified locations rather than loose statistical aggregates.	Replaces randomized spatial assumptions with verified ground-truth human resource assets, achieving the highest empirical precision available for predictive planning.

. Crucially, sliding the parameter to a laxer 100:4 ratio or an escalated 100:8 ratio alters the quantitative depth of the shortfall but is mathematically incapable of altering the core findings. For the 42 analysis units characterized by a complete absence of resident certified volunteers, the supply layer is exactly zero. Because the required staffing always evaluates to a positive integer under any plausible ratio, the resulting DRV Balance remains consistently negative across all scenarios. Furthermore, because required staffing is a strictly linear derivative of simulated shelter occupancy, varying the ratio functions as a uniform scalar that alters the absolute volume of shortages while perfectly preserving the spatial topology, geographical hot-spot clustering, and relative rank-ordering of the 200 shelter nodes. Because these specific values represent the official statutory baselines mandated by NCDR and the New Taipei City Regional Disaster Prevention and Protection Plan, treating them as deterministic parameters ensures that the analytical outputs function as a focused system-level “stress test”. Altering these constraints via sliding sensitivity arrays would misrepresent the fixed legal mandates that local emergency planning authorities are structurally required to satisfy.

To evaluate the parametric stability and numerical sensitivity of our deterministic framework without misrepresenting its regulatory auditing function, a Macro-Analytical Sensitivity Analysis was executed for the core operational thresholds. First, because the required human resource supply layer is mathematically linear relative to simulated shelter occupancy, sliding the statutory 100:6 staffing ratio across international variations (from a minimal 100:4 skeleton configurations to an intensive 100:8 care configuration) reveals a predictable, shifting range of the aggregate metropolitan deficit (see Table 2). Under a fixed total simulated demand of approximately 300,000 shelter-seekers, the system-level DRV shortfall expands rounding from −11,400 to −24,000 personnel. Crucially, even under the most conservative staffing constraint (100:4), the system remains profoundly in deficit, validating that our diagnostic conclusion of systemic human resource insufficiency is robust and invariant to minor adjustments in administrative ratios.

Second, regarding the 800 m walking threshold, the model exhibits high topological stability due to the operational mechanics of the Two-Tier Spatial Demand Allocation Algorithm. If the walking threshold were varied to 600 m or 1000 m, it would merely alter the internal boundary partitioning primary local demand and peripheral shadow demand. Because the secondary assignment rule utilizes an uncapped nearest-facility network path solver via Dijkstra’s algorithm, displaced residents excluded from a shrunken 600 m service area are automatically captured as shadow demand and routed to the exact same geographically closest shelter node. Given that shelter infrastructures represent fixed, discrete destination points in the urban fabric, the aggregate public pressure accumulating at any given facility remains stable and spatially convergent, neutralizing the necessity for micro-routing variations.

To verify the structural robustness of the framework’s principal findings against alternative modeling inputs, a formal spatial and mathematical invariance deduction was executed across a plausible range of staffing assumptions (from 100:4 to 100:8). The analytical stability of our core conclusions is anchored upon two structural dimensions. Regarding the spatial mismatch diagnostics, this study identified 42 analysis units characterized by a complete absence of resident certified volunteers (Existing DRVs = 0). Because the human resource demand function yields a positive integer for all populated catchments under any non-zero staffing ratio, the resulting DRV Balance remains consistently and invariably negative across all evaluated variations. Sliding the parameter to a laxer 100:4 ratio or an escalated 100:8 ratio alters the quantitative depth of the shortfall but is mathematically incapable of flipping these 42 units into a resource surplus. Because the required staffing is a strictly linear derivative of simulated shelter occupancy, varying the ratio functions as a uniform scalar that alters the absolute volume of shortages while perfectly preserving the spatial topology, geographical hot-spot clustering, and relative rank-ordering of the 200 shelter nodes. High-vulnerability nodes, most notably the Siwei Community Activity Center, consistently emerge as primary failure points under all alternative staffing assumptions. Consequently, the principal findings of this research—namely, the acute regional spatial mismatch, the systemic vulnerability of the sheltering network, and the strategic necessity of a Dual-Track Resource Synchronization framework—are highly robust and structurally invariant to variations in operational staffing thresholds.

Furthermore, to establish institutional credibility and provide a rigorous proxy validation, Table 3 establishes a Qualitative Validation and Benchmarking Matrix, explicitly cross-referencing our simulated spatial outcomes against both official government planning targets and empirical historical earthquake evacuations in Taiwan.

Finally, a recognized boundary of this predictive spatial allocation is the absence of direct empirical ground-truthing against past historical earthquake evacuations, such as the landmark 1999 Chi-Chi earthquake. However, direct historical behavioral back-testing is structurally constrained by severe geographic and morphological non-comparability. The 1999 Chi-Chi event primarily disrupted low-to-medium-density rural and suburban typologies along the Chelungpu fault system in central Taiwan. In contrast, the Shanjiao Fault rupture simulated herein targets the hyper-dense, high-rise, mixed-use metropolitan core of modern New Taipei City. The distinct structural vulnerabilities of aging vertical building stocks and massive population concentrations in modern transit corridors generate entirely different spatial evacuation pressures that cannot be accurately benchmarked against historical rural data without introducing significant spatial biases. To mitigate this empirical validation constraint, the demand metrics in this study are systematically anchored within official municipal planning parameters. The deterministic magnitude 6.8 seismic scenario is directly derived from the official statutory hazard baselines established in the New Taipei City Regional Disaster Prevention and Protection Plan. Consequently, the resulting macro-demand estimation of approximately 300,000 potential shelter-seekers functions not as an isolated theoretical speculation, but as a high-fidelity, spatially explicit manifestation of the municipal government’s own official emergency preparedness targets. By matching these authoritative government baselines with localized volunteer rosters, this study provides an empirical, policy-aligned audit of the urban sheltering network’s real-world operational thresholds under the maximum legally anticipated stress state.

5. Limitations and Future Research Directions

While this study formalizes a novel, spatially explicit coupling framework for disaster risk management, several inherent methodological boundaries and parameter constraints must be transparently acknowledged.

First, the hazard input is restricted to a deterministic seismic scenario predicated on a single structural event—a magnitude 6.8 rupture along the Shanjiao Fault at a 5:00 AM nocturnal baseline. Although this temporal and spatial configuration captures maximum residential saturation, it does not account for complex daytime fluidities, variable fault-plane dynamics, or localized cascading hazards. Rather than functioning as a speculative probabilistic forecast, this rigid baseline serves as an official administrative stress test calibrated against the New Taipei City Regional Disaster Prevention and Protection Plan to evaluate institutional compliance under maximum legal pressure.

Second, the network routing models accessibility across an optimal, undegraded physical road topology, deliberately omitting post-earthquake bridge collapses, soil liquefaction, and structural debris blockages. Calculating pedestrian catchments under perfect infrastructure conditions intentionally constructs an idealized operational baseline. This methodological choice operates on a fortiori logic: since 74% of metropolitan shelters already exhibit severe capacity overloads and 42 units suffer complete volunteer vacuums under flawless mobility assumptions, the actual degradation of system performance under real-world physical road blockages will be exponentially more catastrophic. This simplification isolates the structural supply demand mismatch without introducing confounding stochastic routing noise.

Third, the model assumes 100% immediate availability and willingness among the registered DRV roster, omitting localized personal attrition, physical injuries, or familial obligations during the initial post-event window. By treating human capital as fully mobilizable, the model establishes a theoretical best-case capacity ceiling. Consequently, the reported localized manpower deficits represent an ultra-conservative lower bound of real-world resource scarcity.

Finally, this study strictly models certified, trained DRVs as the sole human resource supply layer, drawing no operational distinction between varying individual training proficiencies while entirely excluding untrained spontaneous volunteers. In practical municipal emergencies, certified DRVs undergo standardized civil defense training to serve as an organizational skeleton capable of activating core functional shelter sections (Management, Logistics, and Care). Excluding uncertified public populations is a deliberate parameter constraint designed to prevent the artificial inflation of administrative and management capacities. Nonetheless, this framework does not mathematically capture the micro-level operational friction or coordination bottlenecks that arise when a small group of trained DRVs is overwhelmed by a massive influx of spontaneous, untrained volunteers. Moreover, while this model utilizes a standardized 100:6 staffing ratio as a deterministic administrative benchmark, it does not dynamically account for the critical sociological frictions inherent to volunteer-based disaster management, including operational burnout, uneven training quality, and systemic liability issues. In a prolonged real-world catastrophic response, certified DRVs face rapid cognitive and physical exhaustion (burnout) across multi-day operational shifts, while variable depths of local training can trigger internal coordination friction. Additionally, ambiguities regarding legal liability for civilian volunteers executing emergency care or structural staging present major administrative barriers to autonomous activation. Acknowledging these constraints reinforces the utility of our baseline DRV Balance model: since the urban system already exhibits such profound deficits under the assumption of perfect, unexhausted, and fully uniform volunteer readiness, the overlay of real-world burnout and training disparities will exponentially exacerbate shelter vulnerability. This structural fragility underscores the urgency of shifting from static single-site reliance toward the dynamic, multi-tiered regional human resource synchronization networks advocated by this research.

Future extensions of this spatial coupling model should incorporate multi-scenario probabilistic seismic variations, dynamic edge-weight decay functions for road debris accumulation, and empirical behavioral attrition coefficients derived from disaster sociology. Additionally, integrating agent-based simulations could help model the micro-interaction and leadership delegation structures between certified DRVs and emergent, spontaneous civilian groups, further refining the spatial precision of urban operational resilience metrics.

6. Conclusions

Under a large-scale seismic scenario, the projected shelter demand is double the current sheltering capacity and is distributed extremely unevenly. These analytical results highlight the intense urban density and the critical shortage of evacuation shelter space. Such a massive requirement for sheltering is driven by the prevalence of aging building stocks in certain areas and excessive population concentration, both of which contribute to high seismic vulnerability. Beyond the issues of structural collapse and damage associated with older buildings, the inability of shelter service areas to achieve comprehensive regional coverage remains a significant concern. Simulations conducted on the TERIA platform for a magnitude 6.8 Shanjiao Fault earthquake scenario reveal that approximately 460,000 individuals in the core population centers of New Taipei City would be affected at night, with shelter demand reaching as high as 300,000. ArcGIS Network Analyst (Dijkstra’s algorithm) was used to delineate an 800 m walking service radius, and the results indicate that a staggering 74% of evacuation shelters are currently operating in an overcapacity (overloaded) state, particularly those situated around mass transit hubs and primary commercial districts.

DRVs play a pivotal role in reducing vulnerability through self-help and mutual aid during disasters. Training programs for DRVs enhance individual disaster awareness; when a larger segment of the population possesses and applies foundational disaster prevention and protection knowledge, the burden on institutional human resources can be slightly mitigated. However, in hyper-dense areas, a numerical increase in DRVs does not necessarily equate to sufficient local disaster prevention capacity; it may instead indicate a dilution of the service-to-evacuee ratio, rendering it inadequate for the demands of a large-scale earthquake response. Beyond individual competency, the mobilization of manpower for shelter operations remains a critical issue. Based on the observed service ratio (approximately 100 evacuees to 6 service personnel), establishing a large-scale shelter accommodating over 2000 people would require more than a hundred DRVs. For instance, Banqiao District, which has the highest DRV count in New Taipei City, possesses only 131 volunteers to manage 28 shelters. With a projected demand of 90,000 evacuees, the supply of manpower is grossly insufficient. Furthermore, 42 analysis units within the study area lack any resident DRVs. This reflects a significant spatial mismatch between certified autonomous disaster prevention personnel and shelter demand points in dense urban areas, leading to a profound deficiency in disaster resilience.