What Kind of Urban Spatial Form Is More Conducive to Disaster Risk Reduction: An Empirical Analysis from 32 Cities in China

Abstract

As urban disasters intensify, the relationship between urban spatial form and disaster risk is increasingly important. Different spatial configurations reflect varying levels of resilience to disasters. However existing research offers limited quantitative evidence linking spatial form indicators and disaster risk indices. This study addresses this gap by developing a quantifiable, city-scale framework to analyze the form–risk relationship across 32 Chinese cities. Urban spatial form is quantified using fractal dimension to measure boundary complexity and compactness to assess internal structure, supplemented by a diagrammatic classification of urban patterns. A comprehensive disaster risk index is developed based on four dimensions: hazards, exposure, vulnerability, and resilience. Regression analysis is then applied to quantify the direction and magnitude of correlations between spatial-form indicators and the comprehensive risk index. The results reveal three major findings: (1) Disaster risk increases with fractal dimension, indicating that cities with more complex and irregular boundaries tend to be more vulnerable. In contrast, compactness has no statistically significant effect on disaster risk. (2) Spatial patterns are strongly associated with risk levels: cluster-type and block-type cities generally experience lower risks than radial-type and constellation-type cities. (3) City size and geography also influence risk, as larger cities typically exhibit lower risks, whereas southern cities face higher risks than those in northern regions. These results highlight the critical role of urban spatial structure in shaping disaster resilience. Managing boundary complexity, fostering polycentric and block-based spatial layouts, and improving road-network redundancy can effectively enhance urban adaptive capacity. These insights provide theoretical foundations and practical guidance for resilience-oriented spatial optimization and disaster-risk reduction in vulnerable cities.

1. Introduction

The 2016 United Nations Conference on Housing and Sustainable Urban Development (Habitat III) in Quito resulted in the New Urban Agenda, drawing unprecedented attention to urban resilience and sustainability. Disasters such as the 2003 SARS virus, the 2008 Sichuan Wenchuan earthquake, and the 2010 Yushu earthquake have highlighted urban vulnerability to disaster. Given the increasing intensity of urban disasters, it is crucial to shift from a traditional event-centered approach to a disaster risk-centered, proactive strategy to enhance urban resilience [1]. Urban space functions as a carrier of disasters and possesses spatial-form characteristics that significantly influence disaster risk and urban resilience [2]. Exploring the correlation between urban disaster risk and spatial form, as well as defining the spatial form of resilient cities, is crucial.

Understanding the correlation between urban spatial morphology and disaster risk is key to urban disaster prevention and safety. Identifying spatial forms that mitigate disaster risk and implementing corresponding strategies are vital for enhancing urban resilience. This study aims to answer the following questions: Is there a quantifiable relationship between urban spatial form and comprehensive disaster risk? What mathematical model best represents this relationship? Do cities with different spatial forms experience varying disaster risks? Is the “spatial form → disaster risk” relationship consistent across cities of various sizes and geographic regions?

This study aims to quantify the relationship between urban spatial form and comprehensive disaster risk at the city scale, focusing on the link between spatial form characteristics and the magnitude of disaster risk. This aim ultimately serves to create a healthy, safe, and sustainable urban environment. The study uses fractal dimension and morphological compactness, supplemented by diagrammatic classification, to quantify spatial form and to construct a comprehensive risk index based on four dimensions: disaster-causing factors, exposure, vulnerability, and resilience. Through correlation, regression analysis, and typological comparisons, it reveals the mathematical relationships and variations between spatial form and disaster risk and tests the robustness of the results across city size and geography. It further maps disaster distribution and high-resilience forms, providing quantitative evidence and actionable strategies for disaster-adaptive spatial optimization, emphasizing boundary-complexity reduction, polycentric-pattern optimization, and road-network redundancy to enhance urban resilience (Figure 1).

2. Literature Review

2.1. Explanation of Basic Concepts

(1)

Urban resilience

The concept of “resilience,” originally from ecology, refers to a system’s ability to maintain function and structure under disturbance. It was later extended to socio-ecological systems, emphasizing adaptation and transformation across scales [3]. Since the 2000s, it has been applied to urban studies, focusing on cities’ robustness and adaptability to climate change and extreme events [4,5]. This paper defines urban resilience as cities’ capacity to absorb, adapt to, and recover from disaster impacts through spatial and functional organization, reflected in changes in disaster risk levels [6]. In this study, the term “urban resilience” is used as a conceptual framework.

Existing literature shows that disaster resilience indicators encompass governance, financial, infrastructural, environmental, institutional, and social capacities, which can be aggregated into a numerical metric using weighted methods [7]. In this study, disaster resilience serves as a key quantitative indicator of comprehensive disaster risk (alongside hazard, exposure, and vulnerability). It serves as a measurable variable that quantifies cities’ capacity for functional recovery from disaster impacts.

(2)

Urban disaster risk

Early research focused on “hazard-induced damage.” With the rise in sustainability science, exposure and vulnerability have become key factors in risk transformation. Disaster risk refers to the potential loss of life and property over a specified period, determined by hazard, exposure, and vulnerability [8]. This paper translates urban disaster risk into a comprehensive index, establishing an evaluation framework based on the four dimensions: hazard, exposure, vulnerability, and capacity, aligned with the IPCC Special Report on Extreme Weather and Climate Events and Disaster Risk (SREX) [8,9].

(3)

Disaster Risk Reduction

Since the late 20th century, the disaster reduction paradigm has shifted from post-event relief to a proactive governance approach focused on eliminating or reducing hazard exposure and risk drivers through spatial governance and land use planning [10]. The Sendai Framework for Disaster Risk Reduction emphasizes integrating DRR into urban planning, development policy, and built-environment decision-making [11]. Accordingly, this study defines urban disaster risk reduction as the ongoing process of preventing, reducing, and managing multi-hazard risks in urban areas through spatial planning, engineering, and governance measures.

(4)

Urban morphology & Urban spatial form & Urban Spatial Patterns

Urban morphology studies the physical form and evolution of cities, focusing on the organization of the “street-block-building” sequence [12]. Urban spatial form emphasizes geometric configurations, such as scale, boundary shape, and compactness [13]. Urban spatial patterns describe macro-structures using landscape pattern indicators [14].

This paper defines its scope as follows: using urban morphology as the theoretical framework; quantifying urban spatial form with two indicators—fractal dimension (representing boundary complexity) and compactness (representing internal aggregation and land use efficiency); and employing the diagrammatic classification of urban spatial patterns as a macro-structural perspective that cross-validates continuous indicators to explore risk variations and mechanisms across different structural organizations [13,15].

(5)

The classification of urban spatial patterns

Chinese urban planning commonly uses the diagrammatic classification method to identify urban morphology prototypes, comparing them with quantitative indicators like fractal dimension and compactness [16]. Zou Deci classified urban spatial patterns into six types: concentrated block, belt, radial, constellation, cluster, and scatter. This typology is widely used in planning materials and education. Designed to identify macro-level patterns, it relies on comprehensive assessments of spatial structure characteristics and lacks strict quantitative thresholds.

“Macro-scale urban spatial form” refers to the spatial layout characteristics at the urban scale, including the city’s structure, functional distribution, and spatial organization. In empirical studies, it serves as a contextual framework, rather than a core independent variable, to explore how different morphologies influence disaster risk.

(6)

Administrative regions

In China’s administrative system, “administrative divisions” refer to the national government’s classification of regions based on criteria to meet management needs. These divisions include provincial, prefectural (i.e., prefecture-level), county-level, and township-level categories [17].

(7)

City scale & City size & Administrative hierarchy

This study distinguishes between “city scale” and “city size.” The former refers to the spatial level of analysis, such as a city, metropolitan area, or region, while the latter denotes the measurement of urban magnitude. In China, city size is defined according to the Notice of the State Council’s on Adjusting the Criteria for City Size Classification [17,18,19]. which uses the urban resident population within built-up areas as the statistical basis and divides cities into “five categories and seven tiers.” Among them, cities with populations of 10 million or more correspond to the United Nations’ definition of “megacities” into “five categories and seven tiers”. This paper treats city size as a variable for exposure and demand, while “administrative hierarchy” proxies governance capacity and its impact on urban resilience and risk [20]. Higher administrative levels typically correlate with more resources and better emergency response, though larger populations increase exposure and complexity, requiring empirical methods to determine the net effects [21,22].

2.2. Quantification Indicators for Urban Spatial Form Characteristics

Early studies of urban spatial morphology relied primarily on qualitative methods, such as textual analysis and visual observation, to describe and explain its structure, characteristics, and evolution. With advancements in remote sensing, GIS, and theories and technologies of urban morphology, researchers have shifted from descriptive analysis to quantitative measurement of urban morphology [23,24]. Standard two-dimensional morphological analysis methods include eigenvalue-based approaches that assess attributes like balance, shape, dispersion, and compactness factors reflecting the geometric characteristics of urban spatial form [25]. Benedikt introduced the concept of “horizon”—the set of all points visible from a specific location—offering tools for geometric and perceptual analysis. Spatial geometric attributes are extracted from remote sensing, aerial photography, and satellite data to calculate indicators such as fractal dimension and edge density, which characterize urban form patterns [24].

Fractal dimension and spatial compactness are recognized for capturing the “complexity” and “compactness” of urban spatial patterns [24,26]. Derived from fractal geometry, fractal dimension quantifies the complexity, self-similarity, and nonlinearity of urban patterns, reflecting fragmented boundaries of urban expansion [27]. A high fractal dimension indicates greater compactness in urban centers, while a low value suggests more dispersed, unstable peripheries [28]. Fractal dimension also distinguishes spatial patterns between urban cores and peripheries, highlighting disparities in urban resilience across zones [29].

Urban spatial form compactness measures the degree of agglomeration and land use efficiency within urban built-up areas. A high level of urban compactness indicates more efficient space utilization per unit area, improved infrastructure efficiency, and reflects the rationality and effectiveness of internal development. Chen highlighted that shape indicators, such as compactness, are scale-dependent and should be combined with fractal concepts to normalize these indices, improving their comparability and scientific validity across cities [30]. Compactness can be applied at various scales, including regional, neighborhood, and building group levels, to quantify urban space and compare differences in spatial organization and urban resilience across regions for urban disaster prevention [31].

This study selects the fractal dimension of urban boundaries and the compactness of built-up areas as key indicators balancing urban spatial form’s stability and complexity. These metrics characterize external expansion and internal structure, providing a systematic representation of urban spatial form at the macro scale.

2.3. Urban Disaster Risk Assessment Framework

Recent international disaster risk indicators have advanced urban risk assessment methodologies. The Disaster Risk Indicators (DRI) initiative pioneered socioeconomic vulnerability metrics, emphasizing the role of social factors in disaster risk [32]. The Hotspot Initiative introduced mortality, economic loss, and financial loss/GDP risks, thereby broadening the dimensions of disaster risk assessment [33]. The Americas Initiative established the Disaster Deficit Index (DDI), Local Disaster Index (LDI), Pan-Vulnerability Index (PVI), and Risk Management Index (RMI), providing a multidimensional assessment framework [34]. In China, Shi Peijun proposed that disaster risk is determined by the environment, triggering factors, and disaster-bearing entities, and that it should be measured based on their stability, hazard, and vulnerability. Some scholars argue that disaster risk should also include prevention and mitigation capacity [35], emphasizing that emergency response capabilities reduce risk, while vulnerability and exposure influence risk to disaster-bearing entities [32]. The United Nations’ disaster definition also incorporates disaster resilience and exposure into the urban risk measurement system.

Most studies focus on risk assessment for individual disaster types, such as floods [36,37,38,39,40], earthquakes [41,42,43], typhoons [44,45], fires [46], and geological disasters [47,48,49]. Multi-hazard assessments typically address disaster type identification [50], the relationship between disaster intensity and losses [51], or case studies on disaster reduction [52]. Methodologically, some researchers focus on constructing risk measurement frameworks and evaluating management, planning, policy, and behavioral changes in urban adaptation [53]. Others use random forest algorithms to screen indicators and classify disasters [54] or develop digital prediction models and apply machine learning algorithms. Recent simulation models include artificial neural networks [55], Bayesian networks [56], urban flood predictions using inundation indices [57], and fire simulations [46]. Existing assessment systems are comprehensive in terms of dimensions, with methods aligned with big data simulation. However, most studies focus on single disaster types. While multi-hazard assessment has progressed, a comprehensive analysis of multi-hazard interactions and urban system complexity remains lacking [58].

This study adopts concepts from Chinese and international disaster risk assessment to identify four key factors: hazard level, exposure and vulnerability of disaster-bearing entities, and disaster resilience. These form the basis for constructing an urban disaster risk measurement system [59]. The research views urban disaster risk as a comprehensive reflection of external shocks to the urban system, avoiding a focus on any single disaster type.

2.4. The Correlation Between Urban Spatial Form and Urban Disaster Risk

The relationship between urban spatial form and disaster risk has been extensively explored in academia. Foundational hazard scholarship clarifies how the external urban environment shapes disaster formation and risk management. For example, The Environment as Hazard discusses the relationship between the external urban environment and the formation of urban disasters [60], while Environmental Hazards: Assessing Risk and Reducing Disaster outlines macro- and meso-level response measures across different hazard generators [61]. At Risk: Natural Hazards, People’s Vulnerability, and Disasters systematically synthesizes linkages between regional environments and natural hazards [62]. Building on this risk-centered tradition, a resilience-and-planning perspective has emerged: Resilience-Oriented Urban Planning: Theoretical and Empirical Insights focuses on integrating resilience thinking into urban planning and examines how urban form conditions resilience [63]. Recent empirical work in urban morphology connects form to environmental hazards. For example, Kang analyzed the impact of urban form on the urban heat island effect at both macro and micro scales [64]. Parallel strands of spatial disaster-resilience research move beyond a hazard-centered view to explore how urban space can be organized to enhance resilience, focusing on the ecological characteristics of the regional environment [65], urban disaster carrying capacity [59], disaster prevention functions of urban space [66], resilience-oriented approaches to urban disaster prevention [67], and the construction of regional disaster-prevention spatial systems [68].

Taken together, this literature motivates a clear narrative arc from external environment and vulnerability to urban form and planning, highlighting the need to investigate city-disaster interactions—particularly the joint roles of macro-environmental context and urban spatial form—within a coherent analytical framework. Despite the abundance of studies on disaster risk assessment, no comprehensive framework has been developed from an all-hazards perspective, and few studies integrate risk-hazard measurement with urban spatial form (

Table 1. Summary of the current state of research.

Research Area	Type of Research	Research Scholar
Linkages between urban form and urban disaster risk	Relationship between the external urban environment and urban disasters	Burton [60], Kang Seungwon [64]
	Relationship between the environment in urban areas and urban disasters	Blaikie [62]
	The relationship between urban form and urban resilience	Yamagata & Sharifi [63]
	Urban disaster resilience	Zhang Mingyuan [59]
	Urban disaster preparedness	Zeng Jian [66], Ying Wang [67], Zhitao Wang [68]
Urban disaster risk measurement	Research on different disaster types	Ljubomir Gigovi’c [36], Zhang Yiran [45]
	Risk-disaster-assessment-system construction	Malcolm Araos [53], Zhang [51], Junfei Chen [54]
	Digital model prediction of disaster risk	Ljubomir Gigovi’c [36], Mangkhaseum [55]
	Risk disaster early warning	Yangbo Chen [57], Yuzhen Han [69], Zening Wu [70]

).

2.5. Research Hypotheses

2.5.1. Specific Urban Form Indicators and Urban Disaster Risk

Fractal dimension (FD), a measure of urban spatial form complexity, is widely used in disaster risk research. Studies show that urban spatial form’s fractal characteristics are closely linked to disaster risk, especially in spatial layout, infrastructure resilience, and disaster response capabilities.

First, the fractal dimension affects urban layout. A higher FD typically indicates a more complex and irregular urban structure, which increases emergency response route lengths and complicates resource allocation and evacuation during disasters [71]. Second, FD affects the distribution of infrastructure and the performance of disaster response. Higher FD may lead to more complex water supply systems, impairing performance during disasters [72]. Additionally, uneven distribution of emergency facilities, such as fire stations, can reduce response efficiency [73]. Finally, FD influences ecological vulnerability, with higher values generally corresponding to greater ecological risk exposure and more significant challenges in disaster response [74]. These studies reinforce the connection between urban spatial form complexity and disaster risk. Based on these findings, we propose the following hypothesis:

Hypothesis 1:

Controlling for other factors, fractal dimension positively influences comprehensive disaster risk.

Urban compactness has become a key characteristic of urban form, attracting increasing scholarly attention. Compact cities enhance land use efficiency, reduce transportation emissions, and promote sustainable development through high-density land use, mixed-use layouts, and efficient public transit. However, compactness’s impact on urban disaster risk is multidimensional, influenced by multiple factors.

First, compact cities improve resource utilization and reduce energy consumption through intensive land use and efficient allocation [75]. This consolidation minimizes waste and service disruptions during disasters. Second, compact cities mitigate climate change risks by limiting urban sprawl and protecting ecosystems [76], though dense development may intensify the urban heat island effect, increasing heatwave risks. Third, compact cities enhance land use efficiency and reduce infrastructure costs through high-density, mixed-use development [77]. The concentration of public services improves post-disaster emergency response [78]. Finally, compact cities strengthen community cohesion, improving urban resilience by shortening response times and enhancing resource mobilization [79,80]. Based on these findings, we propose the following hypothesis:

Hypothesis 2:

Controlling for other factors, urban spatial compactness negatively impacts comprehensive disaster risk.

2.5.2. Urban Spatial Pattern Classification and Urban Disaster Risk

Urban spatial pattern classification (e.g., compact block, belt, radial, constellation, cluster, and scattered patterns) is a key factor influencing urban resilience. Recent studies have examined how different urban spatial patterns affect disaster risk.

Regarding the urban thermal environment, Liu et al. found that building form, ecological infrastructure, and human activities significantly influence the urban heat island effect [81]: high-density, clustered cities with limited green space experience more intense heat islands. Zhu et al. found that building density, green space ratio, and road layout affect urban flooding [82]. Balaian et al. highlighted that urban form shapes flood patterns and their severity [83]. Radial and belt cities, due to their road and drainage designs, tend to concentrate water flow, increasing flood risks. In contrast, clustered and constellation cities, with more uniform drainage systems, reduce localized flooding risks.

Regarding seismic hazards, Del Pinto et al. showed that street network connectivity and building layout influence earthquake vulnerability [84]. An et al. concluded that compact cluster cities, with dense construction, suffer greater casualties during earthquakes, while dispersed cities, with scattered buildings, facilitate evacuation and reduce fatalities [85]. For fires, Zhang et al. found that greenery reduces fire spread by acting as a barrier and inhibiting combustion [86]. At the same time, Zamanialaei et al. noted that building density and layout affect fire spread rates. Cities with wider streets experience slower fire spread, whereas radial cities with narrower streets experience faster fire spread [87].

In summary, urban spatial patterns significantly influence disaster risk. Clustered and block-type layouts promote efficient resource allocation and disaster response. In contrast, radial and constellation cities may face delayed responses and greater damage due to longer travel distances and irregular building patterns. Therefore, we propose the following hypothesis:

Hypothesis 3:

Disaster risk is lower in block/cluster-type cities than in radial/constellation-type cities.

3. Data and Method

3.1. Study Area and Data Sources

To ensure the scientific validity of urban spatial form measurement and the rigor of sample city selection, this study uses the 2018 administrative divisions as the foundational basis. From the 333 prefecture-level and above administrative regions in China, 228 medium-sized and larger cities were selected based on population-based city size classification. The “city size” classification follows the State Council’s “Notice on Adjusting the Classification Standards for City Sizes” (Guo Fa [2014] No. 51), dividing cities into “five categories and seven levels” [17]. City size is defined by urban resident population, while governance capacity, institutional resource allocation, and emergency response performance serve as proxies for institutional capacity. To capture geographic and urban form diversity, we created a region-stratified candidate pool, selecting five cities of varying sizes from each of the seven major regions (Southwest, Northwest, Northeast, East, North, South, and Central China). A diagrammatic classification of built-up area boundaries was performed using a unified base map and fixed scale. A morphology de-duplication rule was applied: within each region, only one representative city with a similar boundary configuration was retained. After this stratified selection, 32 cities were finalized as the research sample (Figure 2).

Administrative boundaries were used as the primary reference in delineating the spatial boundaries of these cities. Global land cover data with 30 m spatial resolution were extracted using ArcGIS. These were refined by cross-referencing each city’s master plan with satellite imagery to confirm and adjust urban boundaries. This methodology ensured the accuracy, feasibility, and comparability of measurements of urban spatial form Landsat 8 remote sensing image data for each municipality were downloaded from the “Geospatial Data Cloud” platform. Using ArcGIS 14.0, the normalized difference built-up index (NDBI) was constructed based on near-infrared and short-wave infrared bands to extract the built-up area index for each city [88,89]. The built-up areas in each city were extracted, identified, cropped, organized, and calculated to construct the urban spatial form vector database. Additional data were obtained from relevant city yearbooks, governmental departments, and other sources.

3.2. Urban Disaster Risk Measurement

3.2.1. Construction of Measurement Index System

From a theoretical perspective, the study clarifies the basic concepts and connotations of disaster risk through a comprehensive literature review, establishes a hierarchical structure for risk measurement, and identifies the factors and mechanisms underlying urban disaster risk. Drawing on established theoretical frameworks in urban risk assessment methodology [90,91], four primary indicators—hazardousness, exposure, vulnerability, and disaster resilience—were formulated. These serve as core components of the proposed indicator system.

The selection of indicators focused on major natural disasters affecting urban areas, including geological disasters, earthquakes, typhoons, and extreme rainfall events (measured by average annual accumulated precipitation). These hazards were chosen based on their historical frequency, spatial extent, and destructive impact in Chinese cities. Parameter values were determined based on widely accepted disaster risk assessment criteria and empirical data from prior studies. The indicators were refined through expert consultation and validation against existing literature to minimize subjectivity. Additionally, representative indicators were identified based on their prevalence in highly cited literature and the feasibility of data acquisition. These were supplemented and adjusted as needed. After expert review and refinement, a final set of 15 program-level indicators was established [92,93]. Due to data limitations and quantification challenges, these indicators are primarily used for preliminary screening and qualitative analysis, rather than comprehensive quantitative assessment. In the Section 5, we clarify the exploratory nature of these indicators and emphasize their role in preliminary screening.

We define comprehensive disaster risk R as a city-level systemic stress proxy that aggregates 15 standardized indicators across hazard, exposure, vulnerability, and resilience. The goal is not to identify hazard-specific mechanisms but to test whether urban spatial morphology correlates with aggregate stress at the city scale. This approach allows cross-city comparability without focusing on a single hazard type and connects to Equation (3), used to compute R. Indicator weights were determined using the Analytic Hierarchy Process (AHP), involving the construction of a judgment matrix and pairwise comparisons by experts in urban planning and disaster risk. The process included assessing the relative importance of each indicator, performing consistency checks, and deriving the final weight values (

Table 2. Index weight of urban disaster risk measurement.

Target Level	Standardized Layer		Weights	Program Level		Weights
Indicators for measuring urban disaster risk	Hazard	A1	0.0983	Geologic hazard	A11	0.0260
				Seismic hazard	A12	0.0412
				Typhoon disaster hazard	A13	0.0137
				Average annual accumulated precipitation from heavy rainfall	A14	0.0174
	Exposure	A2	0.2373	Population density	A21	0.0598
				Construction density	A22	0.1397
				Lifeline system density	A23	0.0378
	Vulnerability	A3	0.2181	Share of the old and young population	A31	0.0703
				Share of the female population	A32	0.0162
				Number of students enrolled	A33	0.0427
				Urban registered unemployment rate	A34	0.0889
	Disaster resilience	A4	0.4464	Number of beds in medical and health institutions	A41	0.0884
				GDP per capita	A42	0.0624
				Green space ratio in built-up areas	A43	0.1729
				Per capita disposable income of urban permanent residents	A44	0.1227

). This methodology led to a scientifically sound, logically structured, and operationally feasible urban disaster risk assessment system.

3.2.2. Measurement Methods

(1)

Standardized Processing of Indicators: To eliminate scale-related discrepancies and ensure uniform measurement across indicators, this study applies min-max normalization to preprocess raw data for the urban disaster risk assessment. This standardization normalizes all indicator values to the interval (0, 1), where values approaching 1 indicate optimal conditions and those approaching 0 reflect the least favorable states, facilitating comprehensive evaluation.

Indicators are categorized into two groups based on their relationship with disaster risk:

Positively correlated indicators, where higher values indicate greater disaster risk (e.g., population density, disaster frequency);

Negatively correlated indicators, where higher values indicate lower disaster risk (e.g., number of hospital beds, GDP per capita, green space ratio in built-up areas, and disposable income per capita of urban residents).

To avoid zero values during normalization—which could lead to instability in subsequent computations—a small constant (+0.001) is added to the denominator. This adjustment enhances numerical stability without affecting the normalization trend or relative ranking of results. The standardization procedures are defined by Equations (1) and (2) below [90].

For positive indicators:

$$y_{ij}=[x_{ij}-min(x_{ij})]/[max(x_{ij})-min(x_{ij})]+0.001$$

(1)

For reverse indicators:

$$y_{ij}=[max(x_{ij})-x_{ij}]/[max(x_{ij})-min(x_{ij})]+0.001$$

(2)

Here, x_ij and y_ij represent the original and standardized values of the indicator, respectively. Max (x_ij) represents the maximum value of the indicator, while min(x_ij) represents the minimum value.

(2)

Disaster risk measurement: urban disaster risk is measured with the following formula [90]:

$$R={\sum }_{i=1}^n{F}_i\times W_i$$

(3)

Here, R denotes the level of urban disaster risk, Fi denotes the standardized value of the ith indicator for a city, and Wi denotes the weight of the ith indicator for that city. R is used here as an all-hazards aggregate; the following normalization and weighting steps produce this comprehensive measure and do not target any single peril mechanism.

3.3. Measurement of Urban Spatial Form

(1)

Urban Fractal Dimension: Building on previous research, the fractal dimensions of urban boundaries are crucial for form identification, providing a quantitative basis for understanding and predicting disaster paths and propagation within urban environments. This approach also explains the evolutionary logic of urban expansion. Typically, the perimeter-area ratio quantifies the complexity and fragmentation of urban patches. The ratio value correlates with the complexity and stability of urban spatial form: as patches become more complex and fragmented, their perimeters increase, thereby raising the fractal dimension [24]. The formula for this calculation is [94]:

$$D = {\displaystyle \frac{2\ln (Pi/4)}{\ln (Ai)}}$$

(4)

Here, D represents the fractal dimension of the urban spatial form, while Pi and Ai denote the sum of the perimeters and areas of each patch in the urban built-up area, respectively. A “patch” refers to individual, discontinuous polygons within the built-up area, not the entire urban area as a single polygon. Thus, the total perimeter and area are the sum of the perimeters and areas of all separate patches. The fractal dimension ranges from 1 to 2, with higher values indicating greater boundary complexity and spatial fragmentation, while lower values correspond to a more regular form and more stable boundaries.

(2)

Urban Spatial Compactness: It describes both the spatial agglomeration and land use intensity of built-up areas, as well as the organizational efficiency and operational logic of the city’s internal structure. This indicator measures the degree of agglomeration and compactness of urban spatial form, estimated by comparing the perimeter of each spatial unit with that of a circle of equivalent area [25]. It is a key indicator for measuring urban spatial form complexity. The calculation formula is: [95]:

$$C ={\displaystyle \frac{2\sqrt{\pi A_i}}{P_i}}$$

(5)

Here, C denotes the compactness of urban spatial form, while P_i and A_i represent the sum of the perimeters and areas of each patch in the urban built-up area. The value of C ranges from 0 to 1, with values closer to 1 indicating a more compact structure and more intensive land use. Smaller values suggest a more dispersed urban space and lower development intensity.

Urban fractal dimension and spatial compactness describe urban spatial form from different perspectives: the former reflects boundary complexity, while the latter measures the intensification of internal structure. Together, these two indicators form an ideal combination for structure-function analysis. The fractal dimension is well-suited for describing the evolution of urban space boundaries, while compactness assesses the spatial efficiency and organizational patterns of built-up areas. These two metrics have a clear spatial division of labor.

Research shows a functional relationship between fractal dimension and compactness; they complement each other in the evolution of urban spatial structure. Based on the geometric derivation of the perimeter-area ratio, Chen suggests that compactness can be expressed as an exponential function of the inverse fractal dimension, supporting a quantitative conversion between the two [26]. Using fractal dimension and compactness as core variables for quantifying urban spatial form captures the consistency of structural and spatial regulatory mechanisms in urban evolution while measuring the expansion and intensification characteristics of urban space.

4. Result

4.1. Urban Disaster Risk

Using the standardized indicators and Equation (3), comprehensive disaster risk across 32 cities ranges from 0.3015 to 0.6141, with a mean of 0.4590, SD of 0.0881, median of 0.4499, and quartiles of 0.3844 and 0.5268 (

Table 3. Summary statistics of comprehensive disaster risk and its components.

Metric	Mean	SD	Min	P25	Median	P75	Max
Comprehensive risk	0.4590	0.0881	0.3015	0.3844	0.4500	0.5268	0.6141
Hazard	0.0329	0.0224	0.0078	0.0196	0.0288	0.0378	0.0984
Exposure	0.0711	0.0365	0.0187	0.0482	0.0687	0.0852	0.2147
Vulnerability	0.0901	0.0310	0.0166	0.0696	0.0900	0.1051	0.1771
Resilience	0.2649	0.0695	0.0418	0.2287	0.2590	0.3145	0.3935

). The extremes are Lanzhou (0.6141) and Lhasa (0.3015) (

Table 4. Comprehensive risk assessment value of urban disaster.

City	Hazard	Exposure	Vulnerability	Disaster Resilience	Disaster Risk Values
Guiyang	0.0281	0.0644	0.1173	0.2958	0.5055
Chongqing	0.0754	0.0631	0.1771	0.2090	0.5245
Chengdu	0.0688	0.1137	0.0748	0.2381	0.4955
Kunming	0.0296	0.0401	0.1150	0.2479	0.4327
Lanzhou	0.0137	0.0921	0.1147	0.3935	0.6141
Xian	0.0204	0.0820	0.0811	0.2210	0.4045
Xining	0.0078	0.0730	0.0413	0.2656	0.3877
Harbin	0.0104	0.1087	0.0928	0.3670	0.5790
Dalian	0.0354	0.0294	0.1019	0.2079	0.3746
Shenyang	0.0178	0.0545	0.0624	0.2351	0.3698
Hefei	0.0236	0.0794	0.0904	0.2446	0.4380
Beijing	0.0356	0.2147	0.0692	0.0418	0.3612
Tianjin	0.0294	0.0491	0.0681	0.2127	0.3593
Nanning	0.0359	0.0605	0.0927	0.3405	0.5295
Zhengzhou	0.0297	0.0821	0.0596	0.2543	0.4257
Changsha	0.0219	0.0515	0.0692	0.1801	0.3226
Jiaxing	0.0984	0.0861	0.0946	0.3099	0.5890
Sanya	0.0906	0.1061	0.0752	0.3326	0.6046
Yichang	0.0523	0.0806	0.1229	0.3170	0.5728
Guangzhou	0.0396	0.0979	0.0697	0.1632	0.3704
Nanchang	0.0251	0.0849	0.0684	0.2398	0.4182
Fuzhou	0.0391	0.0959	0.0895	0.2107	0.4352
Qinhuangdao	0.0322	0.0453	0.0947	0.2994	0.4716
Daqing	0.0107	0.0373	0.0803	0.2622	0.3905
Shizuishan	0.0164	0.0254	0.0980	0.3249	0.4646
Yan’an	0.0374	0.0775	0.1350	0.3317	0.5816
Luoyang	0.0242	0.0530	0.1351	0.3136	0.5259
Heze	0.0204	0.0319	0.1337	0.3541	0.5402
Changchun	0.0134	0.0535	0.0923	0.3027	0.4619
Taiyuan	0.0413	0.0784	0.0791	0.2724	0.4711
Ji’nan	0.0202	0.0187	0.0697	0.2558	0.3644
Lhasa	0.0093	0.0443	0.0166	0.2313	0.3015

). By component, hazard has a mean of 0.0329 (SD 0.0224, extremes Jiaxing 0.0984/Xining 0.0078), exposure 0.0711 (SD 0.0365, Beijing 0.2147/Jinan 0.0187), vulnerability 0.0901 (SD 0.0310, Chongqing 0.1771/Lhasa 0.0166), and resilience 0.2649 (SD 0.0695, Lanzhou 0.3935/Beijing 0.0418) (Table 3). Figure 3 shows the spatial distribution of comprehensive risk and component shares; city-level values are listed in Table 4. These results establish the baseline for the econometric analysis of the form–risk relationship.

After comprehensive calculations, Lanzhou has the highest disaster risk value of 0.6141, due to its high vulnerability and resilience. Located in the upper reaches of the Yellow River, Lanzhou faces significant risks from geological hazards and floods, resulting in the highest combined risk across hazard, exposure, vulnerability, and resilience factors. Conversely, Lhasa has the lowest disaster risk value at 0.3015, due to its plateau location, lower impact from natural hazards, lower population and property density, and correspondingly low vulnerability and exposure. Cities differ significantly in disaster risk due to variations in their economic and social foundations, natural environments, and the types of disasters they face—findings that align with prior literature on urban resilience and disaster risk management [96]. Accordingly, urban resilience must be analyzed within each city’s unique conditions and risk characteristics, rather than assuming a one-size-fits-all model.

4.2. Urban Spatial Form

Using the specified equations, we calculate the fractal dimension (D) and morphological compactness (C) for each city. The sample exhibits a high-D/low-C profile ($\overline{D}$ = 1.7465; ($\overline{C}$ = 0.0879), indicating diffuse spatial layouts. Based on Zou’s diagrammatic classification and integrating remote sensing imagery, built-up maps, spatial axes, and development directions, we classify urban spatial form into agglomeration, belt, radial, constellation, cluster, and scatter (

Table 5. Measured value of the urban pattern.

Guiyang: Cluster Fractal dimension: 1.9027 Compactness: 0.0640	Chongqing: Cluster Fractal dimension: 1.7720 Compactness: 0.0592	Chengdu: Block Fractal dimension: 1.6979 Compactness: 0.0633	Kunming: Radial Fractal dimension: 1.5428 Compactness: 0.1599
Nanning: Cluster Fractal dimension: 1.7123 Compactness: 0.1082	Guangzhou: Belt Fractal dimension: 1.7882 Compactness: 0.0495	Nanchang: Cluster Fractal dimension: 1.6643 Compactness: 0.1111	Fuzhou: Cluster Fractal dimension: 1.7924 Compactness: 0.0894
Changsha: Cluster Fractal dimension: 1.6077 Compactness: 0.1263	Hefei: Cluster Fractal dimension: 1.7180 Compactness: 0.0872	Yichang: Belt Fractal dimension: 1.9326 Compactness: 0.0867	Sanya: Scatter Fractal dimension: 1.9558 Compactness: 0.1165
Jiaxing: Constellation Fractal dimension: 1.8675 Compactness: 0.0672	Lhasa: Belt Fractal dimension: 1.5188 Compactness: 0.1277	Beijing: Block Fractal dimension: 1.7323 Compactness: 0.0527	Tianjin: Cluster Fractal dimension: 1.6821 Compactness: 0.0761
Xi’an: Block Fractal dimension: 1.6134 Compactness: 0.1218	Dalian: Scatter Fractal dimension: 1.7552 Compactness: 0.0747	Zhengzhou: Block Fractal dimension: 1.6121 Compactness: 0.1113	Yan’an: Radial Fractal dimension: 1.9863 Compactness: 0.0676
Luoyang: Radial Fractal dimension: 1.8532 Compactness: 0.0507	Shizuishan: Scatter Fractal dimension: 1.7752 Compactness: 0.0758	Jinan: Belt Fractal dimension: 1.8275 Compactness: 0.0479	Taiyuan: Block Fractal dimension: 1.6196 Compactness: 0.1163
Changchun: Block Fractal dimension: 1.6956 Compactness: 0.0750	Daqing: Scatter Fractal dimension: 1.7829 Compactness: 0.0659	Shenyang: Block Fractal dimension: 1.6916 Compactness: 0.0733	Harbin: Radial Fractal dimension: 1.8386 Compactness: 0.0650
Qinhuangdao: Radial Fractal dimension: 1.6643 Compactness: 0.1221	Lanzhou: Belt Fractal dimension: 1.7363 Compactness: 0.1123	Xining: Radial Fractal dimension: 1.6501 Compactness: 0.1478	Heze: Constellation Fractal dimension: 1.8988 Compactness: 0.0406

) [16]. In subsequent models, D and C serve as continuous predictors, while the six types act as contextual descriptors to enhance interpretation and policy relevance.

Urban form is not a neutral backdrop; its inherent complexity and spatial organization profoundly influence a city’s efficiency and resilience in disaster response [5]. From a physical perspective, the more complex the spatial form and fragmented the boundaries, the greater the likelihood of uncontrollable urban expansion. This expansion results in uneven infrastructure distribution, extended emergency response routes, and delayed organizational actions, creating “blind zones” and “breakpoints” during disasters, thereby exacerbating exposure and vulnerability [97]. In contrast, compact cities with intensive land use tend to have more efficient resource connectivity and response networks, demonstrating stronger adaptive and resilience capabilities during emergencies [98].

4.3. Correlation Between Urban Disaster Risk and Urban Spatial Form

This section examines the relationship between comprehensive urban disaster risk and spatial form in 32 Chinese cities. Spatial form is defined by fractal dimension (boundary complexity), morphological compactness (land use agglomeration), and, using Zou’s diagrammatic approach, six morphology types as contextual strata. Using city-level values in

Table 6. Urban disaster risk and Measured value of the urban form.

City	Disaster Risk Value	Fractal Dimension	Compact-ness	Urban Morphology Type	City Size Classes	Geographical Subdivision
Guiyang	0.5055	1.9027	0.064	Cluster	Type II large cities	South
Chongqing	0.5245	1.772	0.0592	Cluster	Supercity	South
Chengdu	0.4955	1.6979	0.0633	Block	Megacity	South
Kunming	0.4327	1.5428	0.1599	Radial	Type I large cities	South
Nanning	0.5295	1.7123	0.1082	Cluster	Type II large cities	South
Guangzhou	0.3704	1.7882	0.0495	Belt	Megacity	South
Nanchang	0.4182	1.6643	0.1111	Cluster	Type II large cities	South
Fuzhou	0.4352	1.7924	0.0894	Cluster	Type II large cities	South
Changsha	0.3226	1.6077	0.1263	Cluster	Type I large cities	South
Hefei	0.4380	1.718	0.0872	Block	Type II large cities	South
Yichang	0.5728	1.9326	0.0867	Belt	Medium-sized city	South
Sanya	0.6046	1.9558	0.1165	Scatter	Type I small cities	South
Jiaxing	0.5890	1.8675	0.0672	Constellation	Medium-sized city	South
Lhasa	0.3015	1.5188	0.1277	Belt	Type I small cities	South
Beijing	0.3612	1.7323	0.0527	Block	Supercity	North
Tianjin	0.3593	1.6821	0.0761	Cluster	Supercity	North
Xian	0.4045	1.6134	0.1218	Block	Megacity	North
Dalian	0.3746	1.7552	0.0747	Scatter	Type I large cities	North
Zhengzhou	0.4257	1.6121	0.1113	Block	Type I large cities	North
Yan’an	0.5816	1.9863	0.0676	Radial	Type I small cities	North
Luoyang	0.5259	1.8532	0.0507	Radial	Type II large cities	North
Shizuishan	0.4646	1.7752	0.0758	Scatter	Type I small cities	North
Jinan	0.3644	1.8275	0.0479	Belt	Type I large cities	North
Taiyuan	0.4711	1.6196	0.1163	Block	Type I large cities	North
Changchun	0.4619	1.6956	0.075	Block	Type I large cities	North
Daqing	0.3905	1.7829	0.0659	Scatter	Type II large cities	North
Shenyang	0.3698	1.6916	0.0733	Block	Type I large cities	North
Harbin	0.5790	1.8386	0.065	Radial	Type I large cities	North
Qinhuangdao	0.4716	1.6643	0.1221	Radial	Type II large cities	North
Lanzhou	0.6141	1.7363	0.1123	Belt	Type II large cities	North
Xining	0.3877	1.6501	0.1478	Radial	Type II large cities	North
Heze	0.5402	1.8988	0.0406	Constellation	Medium-sized city	North

Note: (1) City size classes follow the State Council (2014) five-category, seven-class scheme, using the resident population of the built-up area (MOHURD, China Urban Construction Statistical Yearbook 2020) as the statistical caliber: ≤0.2 million = Type II small; 0.2–0.5 million = Type I small; 0.5–1.0 million = medium-sized; 1–3 million = Type II large; 3–5 million = Type I large; 5–10 million = very large; ≥10 million = megacity [17]. (2) Urban morphology types are assigned following Zou Deci’s diagrammatic classification method, widely used in Chinese planning practice. (3) “Geographical subdivision” uses the Qinling–Huaihe Line: cities south of the line are classified as South (14 in this sample, e.g., Chongqing, Yichang, Hefei, Changsha, Jiaxing), and those north of the line as North (18 in this sample, e.g., Beijing, Tianjin, Zhengzhou, Xi’an).

, we test the relationship between these metrics and risk and interpret patterns by morphology. Key correlation results are presented in Section 4.3.1 and visualized in Figure 4, Figure 5, Figure 6 and Figure 7, with city size and geographical analyses summarized in Section 4.3.2.

4.3.1. Primary Correlation Analysis

(1)

Lower Risk in Block/Cluster Forms; Higher Risk in Radial/Constellation Forms

Figure 4, Figure 5, Figure 6 and Figure 7 summarize the correlations between urban disaster risk and spatial form across 32 cities. Fractal dimension correlates positively with risk (R² = 0.4138; Figure 4), while compactness shows a weak negative slope and is statistically insignificant (R² = 0.0259; r = −0.161, ns; Figure 5;

Table 7. Pearson correlation coefficient of each factor.

	Disaster Risk Value	Fractal Dimension	Compactness
Disaster risk value	1	0.643 **	−0.161
Fractal dimension	0.643 **	1	−0.637 **
Compactness	−0.161	−0.637 **	1

Note: ** indicate a highly significant correlation at the p < 0.01 level. Pearson correlation coefficients range from −1 to 1, with larger absolute values indicating a stronger correlation between the indicators. Generally, |r| = 1 indicates the complete correlation between the two factors; 0.8 ≤ |r| < 1 indicates a robust correlation; 0.6 ≤ |r| < 0.8 indicates a strong correlation; 0.4 ≤ |r| < 0.6 indicates a moderate correlation; 0.2 ≤ |r| < 0.4 indicates a low correlation; and |r| < 0.2 indicates a weak or no correlation between the factors.

). By morphology types, mean risk ranks as follows: Block (0.4285) < Cluster (0.4421) < Belt (0.4446) < Scatter (0.4586) < Radial (0.4964) < Constellation (0.5646) (Figure 6 and Figure 7). This indicates lower risk for block/cluster forms and higher risk for radial/constellation forms. Most cities have fractal dimensions between 1.5 and 1.8, where risk is generally lower. However, this range is descriptive and sample-specific, not a universal threshold. Mechanistically, a higher fractal dimension reflects more fragmented and tortuous edges, lengthening emergency paths and increasing exposure. Compactness alone may not capture response capacity without meso-scale connectivity and redundancy [5,97].

Further analysis reveals that block-type and cluster-type cities not only have lower disaster risk values but also exhibit greater stability in fluctuations in fractal dimension and compactness. Their spatial patterns are more controlled and organized. For instance, cities like Beijing, Xi’an, and Hefei, categorized as cluster-type cities, retain large green spaces, open areas, and ecological buffer zones, creating a comprehensive spatial structure of “structural concentration + ecological infiltration.” This arrangement helps absorb the impacts of disasters and mitigates systemic vulnerability caused by localized overcrowding [5].

(2)

Correlation strength and spatial distributions

Using city-level data that passes the Shapiro–Wilk normality check, Pearson tests (Table 7) show a strong positive correlation between disaster risk and fractal dimension (r = 0.643, p < 0.01), while the correlation with compactness is weak and non-significant (r = −0.161). Fractal dimension and compactness are strongly negatively correlated (r = −0.637, p < 0.01), indicating that cities with more fragmented edges tend to be less compact. Figure 8, Figure 9 and Figure 10 visualize these patterns: areas with higher fractal-dimension classes often align with higher risk classes, while compactness shows a patchy, non-aligned spatial pattern with risk. These findings support using fractal dimension as the primary spatial predictor in subsequent models, with compactness retained as a contextual/control variable to capture agglomeration effects. The map concordance suggests that boundary complexity increases exposure and response distances at the city scale, whereas compactness, lacking meso-scale connectivity and redundancy, does not significantly reduce risk for this sample.

The fractal dimension reflects the geometric complexity of urban boundaries. Studies show that a high fractal dimension often corresponds to disorderly urban edge expansion, fragmentation of development structures, and fragmentation of transportation and infrastructure networks [99]. Such cities are more prone to form “response breakpoints” or “island effects” during natural disasters, hindering the rapid deployment of resources to affected areas and increasing overall disaster exposure and the likelihood of secondary losses [100]. Therefore, fractal dimension is a highly sensitive indicator of risk in urban spatial patterns, with strong predictive and explanatory capabilities [74].

In contrast, morphological compactness represents the degree of agglomeration and land development density within urban areas, improving emergency response efficiency, reducing service radius, and decreasing facility costs. These factors enhance the resilience and connectivity of urban systems [78]. However, in this study, the correlation between compactness and disaster risk is not significant. This may be due to many cities still being in the early stages of low-density, sprawl-oriented development, meaning the disaster-mitigation effects of compact structures at the macro-spatial scale have not yet been fully realized [79].

4.3.2. Contextual Factors: City Size and Geography

(1)

City size

Based on Table 5 and Figure 8, Figure 9 and Figure 10, the sample shows complex boundaries and low compactness. Comprehensive disaster risk is generally higher in small and medium cities, while Type-I large, very large, and megacities report lower values, with few exceptions. This gradient reflects scale effects: larger cities have denser transport and utility networks, specialized emergency preparedness, and more redundant facilities, enhancing urban resilience despite increased exposure. In contrast, small and medium cities often have fragmented spatial forms and sparse networks, increasing the number of response paths and the potential for loss. These findings are descriptive and sample-specific, but they align with the correlations in Section 4.3.1: fractal dimension correlates with higher risk, and compactness shows no stable relationship.

(2)

Geography

Regionally, the mean fractal dimension is slightly higher in the south (1.7481) than in the north (1.7453), with the mean compactness also higher in the south (0.0940 vs. 0.0832). The “high-D–high-C” combination in the south likely reflects hill-constrained, infill-oriented development, forming nested cluster/block structures. In contrast, the northern plains allow outward expansion, leading to looser edges and patchy compactness. Despite these differences, Figure 10 shows no apparent geographic clustering of comprehensive risk: higher-risk cities pair high fractal dimension with patchy compactness, regardless of region. Policy implication at the city scale: prioritize boundary simplification and network redundancy in small and medium cities, and in areas with high boundary complexity, while treating compactness as context-dependent, influenced by meso-scale connectivity and redundancy.

5. Discussion

5.1. Review of Research Findings

This study, based on the empirical analysis of spatial pattern characteristics and disaster risk levels in 32 typical Chinese cities, identifies three key findings:

First, cities with different spatial structures exhibit significant variation in disaster risk. The risk values of cluster-type and group-type cities are notably lower than those of constellation-type and radial-type cities, indicating that spatial organization significantly impacts disaster resistance.

Second, there is a significant positive correlation between fractal dimension and disaster risk, while compactness does not show a statistically significant correlation. This suggests that boundary complexity plays a more critical role in risk prediction, while compactness has limited explanatory power at the city scale.

Finally, urban disaster risk varies by city size and geographic location. Large cities generally exhibit lower disaster risk, whereas southern cities tend to have higher risk than their northern counterparts. This difference reflects the combined effects of administrative resource allocation and natural exposure.

5.2. Interpretation of the Internal Mechanism of the Research Results

5.2.1. Spatial Form and Organizational Pattern Significantly Affect Urban Resilience

Cluster-type and block-type cities exhibit significantly higher disaster resilience than radial-type and constellation-type cities. This is due to the structural redundancy, traffic circuits, and functional autonomy of polycentric spatial patterns, which enhance a city’s resistance to perturbations and recovery capabilities.

At the spatial structure level, cluster and block-type cities exhibit higher spatial connectivity and organizational coordination. Their layouts consist of relatively independent yet functionally complementary modules forming a service and transportation network with low curvature and high redundancy. This structure significantly improves evacuation and rescue efficiency during extreme events. For example, the road system includes multiple redundant channels, enabling bypasses when the main road is blocked, ensuring a continuous flow of people and materials [101,102]. In contrast, radial cities, which rely on radial axes, suffer from structural weaknesses such as district fragmentation and node isolation. These weaknesses are more likely to cause “service blind spots” and “traffic islands” during disasters, hindering network restoration. The transportation function will be compromised for an extended period following the network breakdown [83].

In terms of spatial functions, the modular layout of cluster-type and agglomeration cities minimizes resource waste from overlapping services while enhancing horizontal substitution and regional mutual assistance. Residential, commercial, industrial, and green space units are independent yet closely connected, so when a local area is damaged, other units quickly take over their functions, ensuring urban continuity [103]. Additionally, these cities typically feature multiple connecting roads, facilitating the restoration of spatial order and the efficient transmission of emergency orders [101].

In summary, the spatial organization of cluster and block-type cities creates a synergistic effect in structure, function, and transportation, providing a solid foundation for disaster prevention and control. This is not merely a morphological advantage but a spatial expression of urban resilience in the face of disasters. The dual synergy of “structure-function” in spatial structure allows some cities to exhibit significantly different responses to the same external shocks.

In this study, Beijing’s disaster resilience value (0.0418) is unexpectedly low, given its strong institutional capacity and infrastructure, and warrants further investigation. First, Beijing’s high population density and complex urban spatial structure increase disaster exposure, complicating evacuation and recovery [104]. Second, although Beijing has abundant medical resources, its uneven spatial distribution—especially in suburban districts—impairs response efficiency [105]. Additionally, many older areas in Beijing, with narrow alleys and dense housing, lack modern infrastructure, making them more vulnerable to disasters [106]. Despite robust institutional resources, the complexity of Beijing’s spatial form and social structure may reduce its resilience during extreme events. Thus, urban resilience is shaped by both physical infrastructure, social structure, and spatial layout.

5.2.2. Boundary Complexity Significantly Increases Urban Disaster Risk, While Compactness Patterns Have Limited Predictive Efficacy at City Scale

This study suggests that urban boundary complexity significantly predicts disaster risk, while traditional compactness indicators lack explanatory power at the city scale. Higher fractal dimension values, as a measure of boundary complexity, indicate more fragmented boundaries and correspond to significantly higher disaster risk. In contrast, while compactness can characterize overall urban intensification, it fails to effectively reflect the functional performance and recovery paths of urban systems during the disaster response.

Complex boundaries increase disaster risk by undermining urban spatial coherence and social system synergy, impeding the redundancy of physical pathways, and limiting the efficiency of resource deployment and information transfer, thereby amplifying response and recovery uncertainty.

Boundary complexity negatively impacts disaster exposure and recovery, primarily by reducing coherence in the physical structure. Cities with high fractal dimension values often have polygonal, stretched boundary contours, leading to disorganized paths and low network redundancy. When transportation nodes or infrastructure are blocked, forming alternative routes becomes difficult, reducing the efficiency of resource transport and evacuation [107]. The failure of critical nodes often triggers a systemic chain reaction, causing widespread disruptions in transportation and services. This structural vulnerability extends to social systems as well. In cities with fragmented boundaries and decentralized blocks, communities are loosely connected, resource allocation and information transfer are limited, and social network reconstruction is slower after disasters [108]. Without an organic spatial structure, physical redundancies may fail to activate effectively due to a lack of community organization, resulting in “governance lag” [109]. These dual structural and social fragmentations magnify post-disaster recovery.

Compactness is ineffective in disaster risk prediction because it fails to reveal spatial heterogeneity and functional ruptures within cities. In the current context of high-density, homogenized urban development, most cities already exhibit high levels of spatial agglomeration, rendering the compactness index insufficiently sensitive and unable to distinguish genuine differences in urban resilience [98,100,110].

The boundary complexity, as measured by fractal dimension, is not merely a static reflection of urban geometry but also a structural manifestation of the potential for recovery from disaster impacts. In contrast, compactness is valuable for urban planning and resource utilization, but its role in risk identification and disaster prediction is limited. Therefore, future research on urban resilience should prioritize microstructural features like boundary complexity and integrate local-scale indicators, such as network connectivity and functional configuration, to build a more explanatory risk identification system at the city scale.

5.2.3. Urban Class and Geographic Location Jointly Influence Disaster Risk Differences

Urban disaster risk shows a clear pattern of spatial differentiation, primarily due to the interaction between geographic location conditions and institutional response capacity. Larger cities tend to have more robust institutional deployment, leading to significantly lower disaster risk levels than smaller cities. Additionally, coastal areas in the south are more exposed to disaster risk than inland northern areas, facing more frequent extreme weather events. This creates systematic differences in the spatial risk structure.

Geographically, location is a crucial factor influencing the types and frequencies of hazards cities face. Research indicates that southern coastal cities (e.g., Shanghai, Guangzhou) experience high-intensity typhoons and torrential rains year-round due to monsoon climates and oceanic air masses. As a result, flooding disasters in these cities exhibit highly normalized characteristics [111]. In contrast, inland northern cities (e.g., Beijing, Zhengzhou) face fewer typhoons but more frequent extreme precipitation events. These events, combined with the high impermeability of urban surfaces, lead to a flood risk mechanism driven by climate extremes and urban sprawl [112].

At the institutional level, city size significantly shapes organizational capacity and the efficiency of resource allocation in disaster response. Larger cities typically have more comprehensive emergency management systems, investments in disaster prevention, and stronger institutional coordination. As a result, these cities can implement more efficient resilience responses during the pre-disaster early warning phase, disaster management, and post-disaster recovery [113]. For example, Shi et al.’s study of the 7–20 Zhengzhou rainstorm found that cities with higher administrative hierarchy (sub-provincial and above) demonstrated superior infrastructure resilience and better cross-system synergies in responding to extreme weather events [114].

In summary, geographic exposure and governance capacity, shaped by city size and shape, shape the basic pattern of urban responses to disaster risk. Small and medium-sized cities in the South form a high-risk cluster due to frequent exposure to natural disasters and weaker institutional capacity. In contrast, large cities in the North benefit from institutional safeguards and spatial expansion, making them more resilient to disasters. Identifying the “external geography-internal governance” composite structure explains the internal and external mechanisms of urban disaster risk and provides theoretical support for urban resilience at different locations and scales.

5.3. Comparison Between This Study and Existing Studies

(1)

Systematically Categorize the Urban Morphological Structure and Expand the Structural Mechanism Perspective of Urban Resilience Modeling

The impact of urban spatial structure on the resilience of urban systems during disasters has attracted significant academic attention. Studies have explored the relationship between urban structure and urban resilience, focusing on two key mechanisms: (1) how spatial structure influences urban system function configuration and synergy; (2) the role of network connectivity and path redundancy in supporting urban resilience.

The first line of research emphasizes how urban structure shapes the collaboration mechanisms between functional units and risk exposure. Sharifi and Yamagata argue that compact, centralized cities typically have shorter response paths and more efficient resource allocation, enhancing recovery efficiency in earthquake and flood scenarios [115]. However, this analysis primarily relies on density and concentration indicators, which do not fully capture structural performance in disaster regulation. This study finds that polycentric cities (e.g., cluster-type and block-type cities) exhibit higher resistance to disturbances due to their modular autonomy and service self-consistency. This extends the empirical explanation of disaster adaptation under the “compactness” index. Additionally, Xu et al. proposed the “functional coupling-horizontal substitution” mechanism to enhance urban resilience but did not address its spatial structure [116]. This study validates the role of horizontal redundancy in the cluster/block structure for post-disaster recovery, enriching the structural support logic.

The second line of research focuses on network connectivity and its ability to sustain urban services during disasters. Wang et al. found that cities with high structural fragmentation and central dependency exhibit lower evacuation efficiency and slower traffic recovery than polycentric network cities, based on simulations of urban flooding in China [100]. We build on this by introducing the classification of spatial morphology types, quantitatively analyzing the structural weaknesses of radial and constellation cities, and highlighting that the “single path + isolated nodes” structure is the core mechanism behind the “congestion in disaster - rupture in disaster” pattern [100]. Boeing and Ha emphasize the importance of redundancy in improving the resilience of global urban networks [117]. This study visualizes these structural advantages, showing that polycentric layouts (e.g., clusters and agglomerations) significantly enhance disaster emergency accessibility and resource deployment efficiency through high-redundancy networks.

Unlike traditional studies based on single variables such as morphological density or centrality, this paper introduces six spatial pattern types—block, belt, radial, constellation, cluster, and scatter—to classify and compare urban macro-scale morphology systematically. This approach fills an empirical gap by identifying structural mechanisms and typological attribution. Additionally, by combining structural type classification with functional organization analysis, a three-dimensional “structure-function-risk” framework is constructed. This framework is both explanatory and operational, emphasizing the importance of understanding the coupling logic between urban form and urban resilience from the overall physical-external and functional-internal system perspective.

(2)

Integration of Geometric Form and Functional Mechanisms to Enhance the Structural Explanatory Power of Urban Disaster Risk Modeling

The impact of urban morphological complexity on risk exposure and responsiveness during disasters is a core topic in urban resilience research. Numerous studies have explored the role of morphological indicators in risk modeling, but disagreement persists over the explanatory power of fractal dimension and compactness.

Regarding boundary complexity, Chen et al. argued that cities with high fractal dimension values often exhibit fragmented boundaries, disordered land use, and poor connectivity. These characteristics increase susceptibility to service disruptions during disasters, affecting emergency response paths and network resilience [118]. Chen analyzed 30 cities in China and found that cities with high fractal dimension values experience significantly reduced post-disaster recovery efficiency, especially in contexts with intensive edge development and weaker spatial organization [99]. Building on this, the statistical relationship between urban boundary form and disaster risk is explored using fractal dimension, revealing that boundary complexity weakens network redundancy and compresses coordination and resource-deployment paths, exacerbating response delays. This mechanism is conceptualized as a “spatial fragmentation-structural blockage-response” pathway, reinforcing Chen et al.’s structural findings.

In terms of spatial compactness, Dehghani et al. noted that while compactness is used as a proxy for intensive urban land use, it has limited predictive ability for post-disaster recovery paths. This limitation arises from its failure to account for functional diversity and the efficiency of service coverage [79]. Sharifi further pointed out that compactness, as a singular morphological indicator, may systematically underestimate urban vulnerability [115]. In contrast, this research empirically demonstrates at the city scale the lack of correlation between compactness and disaster risk. This is due to two factors: first, scale sensitivity challenges the ability to capture spatial heterogeneity between core and peripheral areas; second, spatial homogeneity weakens the indicator’s ability to differentiate cities, reducing its predictive capacity.

(3)

Proposing the “Geography-Size” Coupling Mechanism, Revealing the Two-Dimensional Linkage Effect of Spatial Patterns of Disaster Risk

Existing studies show that the geographic location and size of cities are key factors influencing the distribution and levels of disaster risk. Coastal cities are more exposed to natural disaster risks due to their unique geographic environments. Chen et al. analyzed multi-source remote sensing data and found that typical cities in southern China (e.g., the Yangtze River Delta and the Pearl River Delta) are more exposed to flood risks. They suggested that increased impervious surface coverage and the distribution of typhoon tracks are major contributing factors [57]. Building on this, this study refines geospatial risk differentiation by distinguishing between the north and south and identifying that small and medium-sized southern cities form high-risk clusters due to frequent natural exposures. This highlights the interaction between city size and risk structure.

Regarding city size, it reflects the institutional capacity and resource allocation in disaster response. Shi et al. noted that larger cities, as seen in the 2021 Zhengzhou rainstorm, typically have more robust emergency response systems and better resource allocation, enabling stronger recovery [114]. This study incorporates city size into the analysis framework and compares risk distribution across cities of different sizes. It finds that large cities exhibit institutional resilience during recovery and lower disaster risk levels during exposure due to efficient resource allocation. This expands the understanding of administrative variables throughout the disaster process.

Both UNDRR (2023) and ICLEI East Asia (2024) emphasize integrating natural exposure and institutional capacity into urban disaster governance [119,120]. While these international organizations propose a dual concept of geography and governance, their reports mainly remain at the policy or macro-level of awareness. This study provides a more operational spatial framework by integrating multi-source city-scale data and constructing a two-dimensional model of geographic location and city size hierarchy. This model strengthens empirical support for policy direction in regional governance.

Unlike existing studies that emphasize univariate analysis of “geographic exposure” or “institutional capacity,” this study couples “external geography” and “internal governance.” By integrating both geographic and city-size dimensions, this study reveals the linkage between geographic location and city size in shaping the spatial pattern of disaster risk. It offers explanatory theoretical support and methodological tools for managing risk zones and optimizing resource allocation for disaster prevention.

In conclusion, this study contributes to the literature on fractal and compactness studies by: first, integrating fractal dimension into the urban resilience framework, clarifying the negative impact of boundary complexity on disaster response through the path mechanisms and system structure analysis; second, attributing the failure of compactness to structural reasons and demonstrating the applicability of morphological intensity indicators at the city scale, prompting reflection on the effectiveness of urban spatial form indicators. Therefore, unlike traditional approaches that treat morphological variables in isolation, this paper links “geometric indicators-functional mechanisms-risk performance” and expands the system of structural variables used in disaster risk modeling.

5.4. Research Limitations

Although this study develops a framework integrating “spatial structure-disaster risk-institutional capacity” and identifies the coupling relationship between urban form and disaster response, some theoretical and methodological limitations remain.

First, the study measures spatial form at the city scale, missing potential spatial heterogeneity between core and peripheral areas. This scale aggregation effect may obscure structural vulnerabilities in high-risk areas, limiting the precision of risk identification for policy and resource allocation. Future research should downscale to the neighborhood or micro-functional unit level to better identify internal structural diversity.

Second, this study relies on static remote sensing images and GIS data, limiting the incorporation of dynamic changes in real-time traffic flow, crowd migration, and shifts in rescue routes. This limits the modeling of post-disaster recovery processes. Future research should integrate multi-source spatio-temporal dynamic data, multi-agent modeling, and system dynamics to simulate feedback mechanisms between disaster evolution and urban response, creating a process-oriented urban resilience model.

Third, all-hazards positioning and limitations. This study defines comprehensive risk (R) as an all-hazards city-level proxy for systemic stress, aggregating 15 standardized indicators across hazard, exposure, vulnerability, and resilience. It identifies city-scale links between urban spatial morphology and aggregate risk: boundary complexity (fractal dimension) affects routing, coverage, and fragmentation regardless of hazard type, whereas compactness is context-dependent. However, two limitations remain. First, aggregation may obscure peril-specific signals (e.g., stronger correlation with flood risk than seismic risk). Second, the model does not simulate compound or cascading events, missing triggering paths, cross-system dependencies, and critical nodes. Therefore, the findings should be considered baseline aggregate associations. Future research should disaggregate R by hazard, report dimension-level results, and develop multi-hazard models to assess hazard-specific sensitivity and improve predictions in complex scenarios.

Fourth, the sample cities were selected using a region-stratified approach based on city size classification. Despite efforts to standardize the process, subjectivity may influence the final sample. The visual classification of urban built-up area boundaries, using a fixed base map and scale, was shaped by the researchers’ interpretations of spatial diversity. This subjectivity could affect the representativeness of the selected cities and the generalizability of the findings. While morphological de-duplication reduced redundancy, selecting one representative city per region may not fully capture spatial heterogeneity. Future research could use more objective, data-driven methods, such as automated classification or multi-researcher validation, to reduce subjectivity in the selection process.

6. Conclusions and Policy Recommendations

6.1. Conclusions

This study develops a comprehensive risk indicator system covering “hazards-exposure-vulnerability-resilience” through urban systems and spatial form. It quantifies urban spatial form using fractal dimension (boundary complexity) and compactness (internal agglomeration and land use efficiency), supplemented by typological analysis. An empirical “form-risk” assessment was conducted across 32 cities.

At the indicator level, fractal dimension is positively correlated with disaster risk, while compactness shows weaker relevance. Higher fractal dimensions indicate fragmented urban boundaries, longer emergency response distances, reduced coverage, and greater spatial fragmentation, thereby increasing overall risk. Compactness alone cannot capture response capacity, as its impact depends on meso-level connectivity and redundancy [97,121].

At the typological level, cluster-type and block-type cities have lower risks, while radial-type and constellation-type cities have higher risks. Belt-type and scattered-type cities fall in between. These differences suggest that a “moderately complex + orderly clustered” pattern promotes accessibility, functional coupling, and emergency recovery. Meanwhile, fragmented boundaries and dispersed units create “island effects” and “response discontinuities,” increasing exposure and losses [5,122].

At the contextual level, scale and location affect the “form-risk” relationship: small and medium cities exhibit higher risk, while megacities and super-megacities exhibit lower risk. Southern cities have slightly higher fractal dimensions and compactness than northern cities, but no significant geographic clustering is observed. Overall, boundary complexity is the most stable risk factor, while compactness is a contextual variable that depends on mesoscale conditions such as road network connectivity, node redundancy, and ecological permeability [123].

This study innovates by: first, exploring the relationship between specific quantitative indicators of urban spatial forms and disaster risks using a comprehensive, all-hazard approach. Second, it integrates a quantitative framework with a diagrammatic classification method for both qualitative and quantitative analysis of urban spatial patterns and disaster risk. Third, it uses a diverse sample of Chinese cities of varying sizes, geographic locations, and urban forms, thereby enhancing the reliability of the findings.

In summary, the “external geography-internal governance” framework explains the findings: external hazard environments and spatial exposure shape baseline stress whereas internal governance and infrastructure resilience determine the efficiency of absorption and recovery. Thus, compactness alone does not automatically reduce risk; it must align with connectivity, redundancy, and ecological permeability. Based on these insights, Section 6.2 provides policy recommendations for planning and risk governance.

6.2. Policy Recommendations

Based on the empirical findings of the “form-risk” relationship, we propose a tiered, actionable strategy ordered by cost and time to effect.

(1)

Prioritize boundary complexity reduction (low cost, rapid effect): Establish “boundary smoothing” indicators and fractal limits in spatial plans and regulations. Strictly control jagged expansions and leapfrog development in ecologically sensitive areas. The goal is to reduce boundary lengths, shorten emergency routes, and minimize service gaps [13,15]. Simultaneously, implement risk-sensitive land use controls: reduce development intensity or convert high-risk areas into buffers. Avoid the “safety development paradox” by integrating risk into planning and investment [11,96].

(2)

Promote orderly clustering through “clustering/blocking” (medium cost, structural benefits): Prioritize “structural clustering + ecological permeation” to create multi-centered, ordered cluster/block patterns. This layout curbs sprawl, enhances transport accessibility, and preserves green spaces to separate risks and absorb impacts [5]. In a “one city, multiple nodes” framework, aim for a “moderate fractal, compact” range. Avoid excessive compactness, which exacerbates heat-island effects or inefficient dispersion [122].

(3)

Enhance road network connectivity and redundancy (medium-high cost, critical bottleneck management): Prioritize road network improvements to enhance urban resilience. Measures include reinforcing the grid framework, increasing road density and intersection connectivity, and establishing cross-cluster linkages. Implement “redundancy + decoupling” for critical infrastructure to prevent cascading failures [124,125]. Where budgets are constrained, focus on upgrading vulnerable infrastructure to maximize resilience with minimal investment.

Although this study provides valuable insights into the relationship between urban form and disaster risk, several limitations remain. First, spatial form was measured at the city scale, neglecting spatial heterogeneity within different urban areas. Future research should shift the analysis scale to neighborhoods or micro-functional units to better identify internal structural diversity. Second, relying on static remote sensing imagery and GIS data overlooks dynamic factors such as post-disaster traffic flows, population movements, and shifts in emergency response routes. Future studies should incorporate dynamic spatiotemporal data, multi-agent modeling, and system dynamics to improve recovery simulations. Finally, although the all-hazards approach provides a comprehensive framework for urban risk management, it does not reveal the specific impacts of individual hazards. Future research should focus on modeling single-hazard risks and exploring the effects of compound and cascading events on urban resilience.