Spatiotemporal Evolution of 3D Spatial Compactness in High-Speed Railway Station Areas: A Case Study of Chengdu-Chongqing North–South Line Stations (2015–2025)

Abstract

As a pivotal node in urban spatial restructuring, the evolution of three-dimensional (3D) compactness in high-speed rail station areas is crucial for sustainable development. However, the existing research predominantly focuses on two-dimensional forms and lacks dynamic analysis and models that are adaptable to complex terrains. This study develops an enhanced 3D gravitational model that integrates satellite imagery and Gaode building data to quantify the spatiotemporal heterogeneity and carry out multidimensional classification of the compactness across 16 stations in the Chengdu-Chongqing urban agglomeration (2015–2025), with driving factors being identified through correlation and regression analyses. The key findings reveal the following: (1) The mean compactness increased by 22.41%, exhibiting nonlinear heterogeneity characterized by high initial values with low growth rates versus low initial values with high growth rates. Spatially, the southern line evolved from a dual-core pattern at the terminals to multigradient development, while the northern line maintained stable growth despite gradient discontinuities. These spatial differentiations resulted from synergistic effects of urban sizes (station hierarchy), terrain features, administrative divisions, and the line affiliation. (2) The built-up land area (under equal study conditions) and vertical development emerged as key drivers, with the building height diversity demonstrating dual spatial effects (enhancing both compactness and aesthetic richness). Complex terrain characteristics were found to promote clustered urban land use and compact efficiency during initial development phases. This study proposes a planning framework that integrates morphology-adaptive zoning control, ecology-responsive compactness principles, and urban–rural integrated settlement patterns, providing quantitative tools for mountainous station development. These findings offer theoretical and practical support for achieving urban sustainability goals and meeting the 3D compactness and transit-oriented development requirements in territorial spatial planning.

1. Introduction

1.1. Research Background and Problem Statement

Over recent decades, global urban areas have experienced rapid expansion [1] accompanied by dramatic transformations in three-dimensional urban forms [2]. China, in particular, has undergone the world’s largest and fastest urbanization process [3]. The accelerated development of China’s high-speed rail network has significantly reshaped regional spatial structures, with station areas serving as “urban catalysts” that facilitate population agglomeration, industrial upgrading, external connectivity, and spatial reorganization [4,5,6]. These areas represent the complex interplay of ecological, transportation, economic, and social factors, playing a pivotal role in urban development processes [7].

However, during the rapid urbanization process, urban development patterns often exhibit extensive characteristics that manifesting disordered, low-density, and dispersed urban expansion [8]. Constrained by complex terrain, mountainous cities are particularly prone to fragmented spatial distribution and inefficient land use, which leads to isolated ecological patches where the urban construction land predominantly occupies foothills and valleys, disrupting ecological connectivity and reducing ecological benefits [9]. This issue is especially pronounced in high-speed rail station areas of mountainous cities, where local governments frequently prioritize expanding the urban land scale by capitalizing on high-speed rail construction opportunities while neglecting the station areas’ functional role as pivotal nodes for compact urban spatial restructuring [6]. Consequently, these areas face systemic challenges such as spatial fragmentation, morphological disintegration, and inefficient three-dimensional space utilization [10,11].

The compact city theory, which advocates for intensive urban development patterns, provides a crucial perspective for addressing these challenges [12]. As one of the core concepts of sustainable urban development, compact city theory offers important theoretical foundations for China’s efforts to build resource-efficient and environmentally friendly cities [13]. However, the existing research exhibits four major limitations:

First, regarding measurement dimensions, despite existing discussions on 3D compactness metrics and spatial indices [14,15], the majority of studies still rely on two-dimensional morphological indicators based on urban construction land boundaries, failing to adequately capture the intensive utilization of vertical urban spaces—particularly at key urban nodes.

Second, in terms of research focus, the existing studies on 3D compactness mechanisms primarily concentrate on urban rail transit station areas [16,17], while largely neglecting high-speed rail station zones. High-speed rail stations present unique characteristics including larger spatial scales (1–5 km service radius), stronger terrain constraints (e.g., the mountainous and hilly terrain in Chengdu-Chongqing region), and more complex social functions (often involving rural–urban interfaces). Although some 2D compactness studies related to transportation exist [18,19], 3D morphological compactness mechanisms remain virtually unexplored.

Third, the temporal dimension of compactness measurement has been insufficiently addressed. Most current approaches employ static cross-sectional analysis [20,21], focusing primarily on compactness calculation, empirical analysis, and correlation studies for specific time periods. This approach lacks the examination of evolutionary trajectories and dynamic changes in the contributions of driving factors.

Finally, there is limited investigation into influential factors. Only a few studies have explored compactness measurement in simple mountainous contexts [17], with minimal research examining how terrain indicators and geomorphological characteristics influence compactness values. This represents a significant gap in our understanding of urban form development in topographically complex regions.

1.2. Research Objectives and Innovations

Addressing these research gaps, this study focuses on 16 high-speed rail stations along the Chengdu-Chongqing north–south corridor (2015–2025) to investigate four key scientific questions: (1) Model adaptability—how can traditional gravitational models for dynamic 3D compactness measurement in larger, topographically complex areas be enhanced? (2) Spatial heterogeneity—does compactness growth in stations exhibit a “Matthew Effect”, and how is spatial variation regulated by urban sizes, station hierarchy, geomorphology, and administrative divisions? (3) Driving mechanisms—how do contributions from planning, terrain, land-use, and architectural factors evolve across development stages? (4) Planning strategies—how can compactness be enhanced while implementing territorial spatial planning requirements, protecting ecologically sensitive mountainous areas, and promoting urban–rural integration?

The study makes three primary innovations: First, theoretically, it develops a dynamic 3D compactness model for complex mountainous high-speed rail stations, overcoming limitations of “2D static analysis” and “simplified terrain assumptions”. Second, methodologically, it advances gravitational modeling through standardized grid-based volumetrics and DEM-adjusted terrain distances by employing classification statistics, correlation analysis, and multiple regression to reveal spatiotemporal heterogeneity in driving factors. Third, practically, it proposes a planning framework that integrates “morphologically-adaptive zoning, ecological compactness principles, and urban-rural settlement patterns”, providing decision-support tools for mountainous high-speed rail station area planning.

2. Literature Review

2.1. Research on the Definition of Urban Compactness

Currently, there is no unified standard for defining compact cities. Since the concept was first proposed [22], extensive research has been conducted on key principles including high-density development [12,23,24,25], mixed land use [26], public transit promotion [12], and urban center models [27]. Scholars have emphasized that compact cities should not be simplistically equated with absolute high-density or concentric expansion patterns, and that, rather, the focus should be on achieving efficient spatial organization [28] and conserving urban land resources [29]. This approach aims to minimize encroachment on natural landscapes, farmlands, and water bodies [30,31], reduce environmental pressures, prevent ecological degradation, and ultimately contribute to building an environmentally sustainable and resource-efficient society [32,33].

2.2. Research on Urban Compactness Measurement

Urban compactness is one of the key indicators for evaluating the optimization degree of existing urban spaces, yet there remains no consensus on its definition. Many scholars worldwide have conducted in-depth studies and proposed various evaluation models and methods based on the concept of compact cities. Early approaches included form-based perspectives (Richardson, Cole, Gibbs) [28], scale-oriented views (Hess) [34], and density-focused measures (Galster) [25]. Later, structural perspectives that incorporate five dimensions—continuity, imbalance, clustering, aggregation, and mixed-use—emerged to better reflect the sustainable connotation of compactness measurement and the associated evaluation methods [28]. For instance, Thinh et al. proposed a gravitational model based on the aggregation degree [35]. Building upon these four relatively static computational perspectives, Burton further introduced a process-oriented measurement approach [36]. Most of these methods primarily conduct two-dimensional calculations based on urban planar morphological characteristics and land-use structures.

2.3. Gravitational Model and Research Evolution

The urban compactness model proposed by Thinh et al., rooted in Newton’s law of universal gravitation, stands as one of the most influential methods for quantifying urban spatial morphology. This model utilizes GIS grid technology and land-use databases to overlay standardized grids with urban land-use data, creating fundamental operational data layers [35]. The computational formulas are expressed as follows:

$$\mathrm{A}\left(i,j\right)=S_i{S}_j/c{d}^2\left(i,j\right)$$

(1)

$$\mathrm{T}={\displaystyle \frac{\sum \mathrm{A}\left(i,j\right)}{n(n-1)/2}}$$

(2)

where A(i,j) represents the interaction force between buildings i and j, SiSj denotes the product of land areas (m²), d(i,j) is the Euclidean distance between geometric centers (m), c is a constant, ∑A(i,j) aggregates all interaction forces within the target area, and n indicates the number of land parcels. The T-value quantitatively reflects the urban land-use compactness, with higher values indicating stronger spatial interactions and greater layout compactness.

While traditional gravitational models primarily calculate 2D planar compactness and demonstrate notable sensitivity to area dimensions, subsequent advancements have significantly expanded this framework. Zhao et al. developed a 2D compactness index [36], while Hu et al. established a 3D counterpart [14]. Yuan et al. proposed an area-equivalent 3D measurement model that incorporates building height (both above and below ground) as a third-dimensional factor [16], and Wang et al. introduced terrain-adjusted modifications using average slope values or 3D coordinates (x,y,z) for mountainous cities [17].

3. Materials and Methods

3.1. Study Area and Object Definition

3.1.1. Research Objects

The Chengdu-Chongqing urban agglomeration, as western China’s largest dual-core economic zone, presents an ideal case for analyzing compactness measurements and driving mechanisms in high-speed rail station areas. Its north–south lines feature the following: (1) geomorphological diversity (incorporating mountain terraces and extensive hilly terrain); (2) developmental gradation (connecting megacities, medium-sized cities, and small towns across various station classes); (3) policy demonstration value (designated as a national strategy with explicit “3D compactness and transit-oriented development” objectives in territorial spatial planning). This research not only optimizes intensity control indicators for territorial spatial planning but also provides theoretical references for global mountainous high-speed rail station development, aligning with the Sustainable Development Goals’ call for “inclusive, safe, resilient, and sustainable cities.”

According to the Chengdu-Chongqing Urban Agglomeration Development Plan, the main development axis connecting the dual cores of Chengdu and Chongqing comprises southern, central, and northern corridors. The north–south high-speed rail lines serve as critical rail transport arteries along these corridors (with the central line currently being under construction). The southern line spans approximately 299 km and has 11 operational stations: Chengdudong (CDD), Jianyangnan (JYN), Ziyangbei (ZYB), Zizhongbei (ZZB), Neijiangbei (NJB), Longchangbei (LCB), Rongchangbei (RCB), Dazunan (DZN), Yongchuandong (YCD), Bishan (BS), and Shapingba (SPB). The northern line extends 301 km (via Suining connection) and has six stations: Chongqingbei (CQB), Hechuan (HC), Tongnan (TN), Suining (SN), Dayingdong (DYD), and Chengdudong. The combined network comprises 16 stations, with Chengdu East serving both lines (Figure 1).

3.1.2. Study Scope

The term station areas, alternatively termed station surroundings or influence zones, typically refers to radial regions centered on transit nodes. While lacking strict boundaries, these areas generally exhibit concentric structures, with walking distance being the fundamental criterion for the determination of their scope. The representative “three-zone” model proposed by Schütz E [37] delineates core, influence, and peripheral zones. The existing studies commonly adopt 1000–3000 m radii [38,39,40,41]. Considering the station scale, location, and surrounding ecology, this study establishes a 2000 m radius as the research boundary.

Spatial planning data reveal that concentrated construction zones occupy 64.39% of the study area on average, which indicates that rural construction land, farmland, ecological green spaces, and regional water bodies collectively exceed cover one-third of the area. Field surveys further identify numerous micro-scale mountains and water bodies preserved as parks within the construction zones. Under China’s ecological civilization framework, territorial spatial planning emphasizes both compact development and comprehensive urban–rural coordination through “three zones and three lines” regulation [42].

Consequently, our 2 km radius study scope incorporates not only urban construction zones but also rural settlements that are more significantly constrained by mountainous terrain. GIS analysis of the building land patch density (PD: 16.10/km² in 2015, 16.96/km² in 2025) and mean patch size (MPS: 1.34 ha in 2015, 1.58 ha in 2025) demonstrates strong natural penetration characteristics in the spatial morphology of the area, making it particularly suitable for terrain-integrated 3D compactness research.

3.2. Research Methodology

3.2.1. Enhanced 3D Compactness Measurement Model

(1) Model Adaptation: Grid-based Volume and DEM Surface Distance

The study area encompasses small and medium-sized cities where building footprint data remain incomplete. Satellite imagery serves as the primary data source for building contour extraction, although this approach presents several limitations: inconsistent image quality across the extensive study region, and the frequent misclassification of multiple buildings as single structures in dense urban areas when using historical images. The gravitational model requires precise building contour identification for compactness measurement to be conducted. Previous studies have often selected buildings that exceed 30 m in length/width [43] to enhance the clarity of their results, potentially introducing significant bias by excluding smaller structures. Figure 2 demonstrates that, when applying the gravitational model with building footprint areas, scenario B yields 24.13% higher T-values than scenario A, while scenario C shows 101.05% higher values. These results indicate that the compactness T-index proposed by Thinh et al. exhibits sensitivity to both the area size and the number of spatial units under equal area conditions.

Notably, while conventional approaches that use average slope values or 3D coordinates can effectively calculate distances for objects with a single dominant slope aspect, our study area presents multiple slope aspects across different sites. The topographic analysis reveals significant variations: (1) the 16 stations demonstrate an average slope of 8.46° (14.8%), with a minimum average slope of 5.98° (10.49%) and three stations exceeding 10° (17.63%); (2) built-up areas (including roads, construction sites, plazas, and building lots) comprise 36.59% of the total study area on average; and (3) natural landscapes (mountains, water bodies, farmlands, forests, and grasslands, including parks) account for approximately two-thirds of the area. These distinct mountain–water relationships, prevalent in both urban and rural zones, necessitate methodological refinements in calculating d(i,j) to better account for the complex terrain characteristics.

To enhance the gravitational model’s site adaptability and minimize its limitations, our compactness measurement follows the workflow in Figure 3. Within a 2 km radius around each station, we first standardized the coordinate systems and established equal-area grids [39]. The urban compactness model calculates the gravitational forces between grid pairs, using 200 m × 200 m cells (block width) as horizontal units. Building volumes (replacing footprints) are assigned to corresponding cells to compute the resultant forces, with the cells serving as basic units for comprehensive compactness measurement (Figure 4). This approach mitigates identification errors for adjacent small/medium buildings or parcels.

For vertical dimension analysis, we employed DEM-derived 3D surface distances to better reflect the building interaction distances observed in complex mountainous terrain. The calculation formula is as follows:

$$\mathrm{A}\left(i,j\right)={\displaystyle \frac{V_i{V}_j}{c{d}_1^2\left(i,j\right)}}={\displaystyle \frac{{\sum }_{n=1}^p\left(s_{in}{h}_{in}\right)\times {\sum }_{m=1}^q\left(s_{jm}{h}_{jm}\right)}{c{d}_1^2\left(i,j\right)}}$$

(3)

$$\mathrm{T}={\displaystyle \frac{\sum \mathrm{A}\left(i,j\right)}{N(N-1)/2}}$$

(4)

where A(i,j) represents the interaction force between unit i and unit j, V_iV_j denotes the product of the total building volume of unit i and the total building volume of unit j, s_in and s_jn represent the base area of the nth building in unit i and the mth building in unit j respectively, h_in and h_jn represent the height of the nth building in unit i and the mth building in unit j, respectively, p and q represent the number of buildings in unit i and unit j, respectively (1 ≤ n ≤ p, 1 ≤ m ≤ q), c is a constant, and d₁ is the projection length of the straight line of the Euclidean distance between the geometric centers of unit i and unit j on the DEM surface model. ∑A(i,j) is the collection of all interaction forces A in the target area and N is the total number of units in the target area (i ≤ N, j ≤ N). The T-value quantitatively reflects the 3D compactness measure of the station.

(2) Rate of Change in Compactness Measures

Building upon the enhanced 3D compactness calculations for each station in both 2015 and 2025 by using the improved formulation, we further quantified the temporal dynamics of compactness through change rate analysis. The rate of change (∆T) for each station’s compactness measure was computed as follows:

$$∆\mathrm{T}={\displaystyle \frac{T_{2025}-T_{2015}}{T_{2015}}}\times 100\%$$

(5)

where ∆T represents the percentage change in compactness for individual stations and $T_{2025}$ and $T_{2015}$ denote the compactness measures for the years 2025 and 2015, respectively.

3.2.2. Multidimensional Comparative Analysis

(1) Spatial Classification of high-speed rail Station Areas

To better examine the spatiotemporal variations in compactness across different station types, we classified the stations based on their spatial characteristics. The classification scheme incorporated both quantitative and qualitative attributes, including the initial compactness levels (T_2015 values), station hierarchy, city size, geomorphological features, line affiliation, and administrative divisions. Considering the sample size (n = 16), each classification type was further divided into two subcategories for detailed analysis (see

Table 1. Classification of station areas of Chengdu-Chongqing north–south Line.

Category	Subclass	Quantity	Station Area Name	Classification Criteria
Initial compact measure	Medium-low and Low Measurement	12	DZN, BS, DYD, JYN, LCB, NJB, RCB, SN, TN, YCD, ZYB, ZZB	Based on the T_2015 distribution characteristics described in Chapter 4.1, with 40,000 as the critical value, values less than 40,000 are classified as medium-low and low; values equal to or greater than 40,000 are classified as medium-high and high.
	Medium-high and High Measurement	4	CDD, CQB, HC, SPB
Urban Sizes (Station Hierarchy) 1	Small Cities (Stations)	8	BS, DYD, DZN, JYN, LCB, RCB, TN, ZZB	The size of the city is determined according to the “Notice on Adjusting the Classification Standards for Urban Sizes” (Guo Fa [2014] No. 51) [44]; in this study, stations of the third grade and below are classified as small, while the rest are classified as medium or large.
	Large and Medium Cities (Stations)	8	CDD, CQB, HC, NJB, SN, SPB, YCD, ZYB
Geomorphic features	Global Hills	7	CDD, CQB, DZN, HC, SPB, YCD, ZYB	Based on the 3D elevation model and field investigation: flat areas with relatively concentrated, regular, and certain scale features (surrounded by mountains) are called terraces.
	Mountain Terrace	9	BS, DYD, JYN, LCB, NJB, RCB, SN, TN, ZZB
Admin Divisions	Sichuan Province	8	BS, CQB, DZN, HC, RCB, SPB, TN, YCD	Administrative divisions of Chongqing City and Chengdu, Suining, Ziyang, and Neijiang cities in Sichuan Province.
	Chongqing City	8	CDD, DYD, JYN, LCB, NJB, SN, ZYB, ZZB
Line ownership	North Line	11	BS, CDD, DZN JYN, LCB, NJB, RCB, SPB, YCD, ZYB, ZZB	Chengdu-Chongqing High-Speed Railway (South Line), Chengdu-Suining-Chongqing Railway (North Line)—Baidu Encyclopedia.
	South Line	6	CDD, CQB, DYD, HC, SN, TN

¹ The classification results are consistent with the urban sizes and station hierarchy.

for complete classification details). This typological approach enabled the systematic comparison of compactness measures and their rates of change across distinct station categories.

(2) Calculation of Average Compactness Measures

Given the influence of the varying 3D built-up volumes across stations, conventional averaging methods would distort the compactness measurements. Therefore, we employed weighted calculation methods:

$$\text{T\_ave}={\displaystyle \frac{{\sum }_{m=1}^n\left[\sum {\mathrm{A}}_m\left(i,j\right)\right]}{{\sum }_{m=1}^n\left[N_m(N_m-1)/2\right]}}$$

(6)

$$∆\text{T\_ave}={\displaystyle \frac{{\text{T\_ave}}_{2025}-{\text{T\_ave}}_{2015}}{{\text{T\_ave}}_{2015}}}\times 100\%$$

(7)

where T_ave represents the category-specific mean compactness; ∆T_ave denotes the mean rate of change; ΣAm(i,j) is the sum of the interaction forces for station m; $N_m(N_m-1)/2$ indicates the number of force pairs for station m; n is the number of stations in each category (1 ≤ m ≤ n); ${\text{T\_ave}}_{2025}$ and ${\text{T\_ave}}_{2015}$ are category means for the respective years of 2025 and 2015.

Based on the computational results derived from the aforementioned formulas, we obtained systematic categorical statistics for both T_ave and ∆T_ave across 2015 and 2025. This analytical process involved calculating category-specific compactness averages using the weighted formulation, determining the mean rates of change between temporal intervals, and integrating multidimensional quantitative attributes to examine station-specific ∆T values. The comprehensive statistical analysis enabled the identification of both general distribution patterns and exceptional spatial variations in the evolution of compactness, providing crucial insights into the heterogeneous development trajectories across different station types while accounting for scale effects that are inherent in 3D urban morphological analysis.

3.2.3. Driving Mechanism Analysis

(1) Variable Indicator System

This study established a comprehensive analytical framework with compactness measurements (Y_2015, Y_2025) and their rates of change (∆Y) as dependent variables. Independent variables were selected from four categories (planning, terrain, land-use, and architectural characteristics) and comprised 14 spatial form indicators (

Table 2. Model variable description.

Variable	Index	Code
Dependent Variable	3D Compactness Index	Y
	Compactness Change Rate	∆Y
Independent Variable	Centralized Construction Zone Planning Proportion	X1	Planning
	Relative Distance from the Station to the City Center	X2
	Planned Floor Area Ratio	X3/∆X3
	Elevation Standard Deviation	X4	Terrain
	Terrain Undulation Range	X5
	Mean Slope Gradient	X6
	Built-up Land Area	X7/∆X7	Land use
	Land Patch Density	X8/∆X8
	Largest Patch Index	X9/∆X9
	Aggregation Index of Land Patches	X10/∆X10
	Building Footprint Area	X11/∆X11	Building
	Building Density	X12/∆X12
	Mean Building Height	X13/∆X13
	Standard Deviation of Building Heights	X14/∆X14

). The variable relationships were structured as follows: dependent variable Y corresponds to independent variables X1–X14; X3 and X7–X14 were extracted from vector spatial characteristics for 2015 and 2025, respectively; X1–X2 and X4–X6 were time-invariant variables; dependent variable ∆Y corresponds to ∆X3 and ∆X7–∆X14 (change rates of respective variables). Within this indicator system, planning factors primarily guide the development of 3D spatial configurations; terrain factors predominantly constrain 3D spatial formations; construction land serves as the primary carrier of 3D spatial structures; architectural elements represent the concrete manifestations of 3D spatial characteristics. This systematic framework enables comprehensive analysis of the driving forces behind the spatial compactness evolution in high-speed rail station areas, capturing both the directional influences and physical constraints that shape their three-dimensional development patterns.

① Three planning indicators

Centralized construction zone planning proportion (X1): The ratio of planned centralized construction area to the total station area (2 km radius). This indicator primarily regulates the scale of construction land development, with higher values indicating greater development potential.

Relative distance from the station to the city center (X2): The ratio of the geometric distance between the station and the urban center to the diameter of the minimum circumscribed circle of the built-up area. Smaller values indicate closer proximity to the urban core and stronger functional linkages.

Planned floor area ratio (X3): The ratio of the total building floor area to the plot area. This metric serves as the primary determinant of the plot-level development intensity. Higher floor-area ratio values better support three-dimensional development. Field surveys in the Chengdu-Chongqing region revealed that, while the building height and density exhibit diverse patterns within regulatory limits, the actual floor-area ratio values consistently approximate planned indicators. For measurement consistency, we standardized our calculations by assuming a uniform floor height of 3 m, deriving current floor area ratio values from actual built volumes, and using these values to replace original planning indicators.

② Three terrain indicators

Elevation standard deviation (X4): The standard deviation of the elevation values within the study area, which were derived from DEM data. Higher values typically impose greater constraints on horizontal expansion.

Terrain undulation range (X5): The maximum elevation difference within local 7 × 7 grids (≈210 × 210 m, aligned with study cell size). This metric reflects the neighborhood-level leveling difficulty. Larger values indicate stronger development constraints.

Mean slope gradient (X6): The average slope across the study area, calculated as the mean value of DEM slope raster cells. Steeper slopes correlate with higher development costs.

③ Four land use sndicators

Built-up land area (X7): The area of parcels containing substantial 3D built structures (residential, public facility, commercial, industrial/mining, transportation hub, and rural settlement lands), excluding non-built or minimally-built areas like roads, squares, and parks. Generally, land expansion forms the foundation for compactness.

Land patch density (X8): The number of built parcels per unit area. Higher densities suggest greater spatial fragmentation.

Largest patch index (X9): The proportion of the largest built patch relative to the total construction land area. Larger dominant patches generally enhance the spatial continuity.

Aggregation index of land patches (X10): A measure of the spatial adjacency among land parcels, where higher values indicate reduced spatial barriers.

④ Four architectural indicators

Building footprint area (X11): The total horizontal projection area of building outlines. This metric reflects the extent of ground coverage and jointly drives compactness with the built-up land area.

Building density (X12): The ratio of the total footprint area to construction land area. While moderate densities improve spatial efficiency, excessive values may yield diminishing returns.

Mean building height (X13): The volume-weighted average height. This metric serves as the core metric of vertical expansion.

Building height standard deviation (X14): The volume-weighted dispersion of building heights. Diversified height profiles contribute to the three-dimensional urban form.

(2) Data Processing and Analytical Methods

Data Normalization: To eliminate dimensional effects and ensure comparability across variables, we standardized all data using the min-max normalization method, scaling all values to a fixed range of [0, 1]. This approach offers four key advantages: enabling accurate correlation measurement; enhancing the comparability of correlation analyses; improving regression model convergence and stability; and increasing the interpretability of regression coefficients while mitigating sensitivity to outliers.

SPSS Statistics 26 correlation analysis was conducted to examine the linear relationships between the processed independent variables and the compactness measurements (Y_2015, Y_2025), as well as the compactness change rate (∆Y) obtained using Pearson’s method, with a significance level set at α = 0.01 (two-tailed test). For variables that demonstrated significant correlations in at least one study year, we compared the magnitudes of their correlation coefficients to analyze temporal variations in their effects. The mean correlation coefficients of statistically significant variables were calculated to assess the relative influence of different indicator categories between the two periods. Additionally, Pearson correlation analysis was employed to evaluate the impact strength of independent variable change rates (∆X) on the compactness change rate (∆Y).

Multiple linear regression analysis was performed in SPSS to comprehensively identify factors driving compactness changes. Independent variables (∆X) that showed significant correlations (α ≤ 0.05) with the compactness change rate (∆Y) were incorporated into regression models using stepwise selection, with only predictors that met the significance threshold (p ≤ 0.05) being retained in the final equation construction. The model diagnostics included the variance inflation factor (VIF < 5) for multicollinearity assessment and the Durbin–Watson statistic (DW ≈ 2) for residual independence testing, with adjusted R² values evaluating the explanatory power. We first developed a global regression model that incorporated all 16 stations, followed by category-specific models stratified by their initial compactness levels, urban sizes (station hierarchy), geomorphic features, administrative divisions, and line ownership. Regression results were visualized using GraphPad Prism10.4.2 to elucidate driving mechanisms at both the aggregate and categorical levels.

3.3. Research Procedure

This study follows a systematic three-phase methodology that comprises nine key steps (Figure 5). Phase 1: compactness measurement: (1) acquisition of building and land-use vector data; (2) optimization of gravitational model parameters to address spatial constraints; (3) calculation of 3D compactness indices and their temporal rates of change for each station area. Phase 2: spatial classification and statistical analysis: (4) categorical classification of station areas based on spatial characteristics; (5) computation and analysis of type-specific average compactness measures and their change rates. Phase 3: driving factor analysis: (6) construction of a comprehensive variable indicator system; (7) data collection and standardization of independent variables; (8) correlation analysis to identify key influencing factors; (9) regression analysis to determine drivers of compactness change.

3.4. Data Sources and Preprocessing

The research incorporated four principal data categories (

Table 3. Data sources.

Data Types	Sources	Time	Type	Purpose
3D Building Data	Amap API, ArcGIS Online, Field surveys	2015, 2025	Vector &1 m grid	Construction of 3D models
Built-up Land Data	ArcGIS Online, Field surveys	2015, 2025	1 m grid	Calculation of building land indicators
DEM	Geospatial Data Cloud (GDC)	——	30 m grid	Calculation of elevation, slope, and undulation
Spatial Planning	Websites of district (county) people’s governments in various places	2021	picture	Definition of centralized construction areas
Ancillary Data	Tianditu and s-FARM, Amap Street View panoramic	2015, 2025	Grid & picture	Auxiliary identification of construction land, building outlines and heights

), each of which was processed through systematic protocols to ensure methodological rigor.

The three-dimensional building data were acquired as follows. For the 2025 dataset, building footprints were initially extracted via the AMap API and subsequently refined through the integration of satellite imagery, AMap Street View panoramas, and field surveys, with height information being calibrated through façade feature comparison to establish the baseline dataset. The 2015 historical 3D vector data were reconstructed through comprehensive the temporal pattern analysis of archival imagery—buildings present in 2025 but lacking corresponding patches in 2015 imagery were systematically removed, while structures showing no morphological changes between periods (comprising > 90% of buildings, as determined through texture characteristics and construction era analysis) retained their 2025 footprints and heights after validation via shadow-length inversion was applied to a random sample of 100 buildings (demonstrating 95.3% consistency with ≤1 floor height variation). For the <10% of buildings that underwent morphological changes (primarily rural–urban conversions), the heights were derived from shadow-length calculations combined with texture-based visual interpretation, with the rural structures being constrained by Chengdu-Chongqing regional building height regulations (maximum 12 m or three stories). This integrated approach ensured both temporal accuracy and compliance with local planning standards while maintaining methodological consistency with the gravitational model’s volumetric parameters.

The land-use data were acquired as follows. Historical imagery from ArcGIS Online (“2017-2” and “2024-11” datasets) was acquired via Bigemap GIS Office 30.0.31.6, with temporal referencing being established through landmark building inventories and high-speed rail operational timelines to confirm the image capture dates as 2015 and 2023, respectively. We manually delineated the construction parcel boundaries for both years by integrating the 2015 and 2025 3D building datasets, which was followed by morphological metric extraction using ArcGIS 10.7 and FRAGSTATS 4.2.

The terrain data were acquired as follows. A hydrologically corrected 30 m resolution digital elevation model (DEM) was processed to generate slope and relief amplitude parameters, with station-specific statistics being computed through zonal analysis.

The planning data were acquired as follows. Centralized construction zone boundaries were vectorized in AutoCAD2008 based on regional territorial spatial planning drafts.

4. Results

4.1. Spatiotemporal Characteristics of 3D Compactness Evolution

4.1.1. General Growth Trends and Heterogeneity

The comprehensive analysis reveals distinct spatiotemporal patterns in the compactness evolution across the studied high-speed rail stations. The mean compactness index demonstrated significant growth from 34,712 to 42,491 during the study period, which represents an average increase of 22.41%. However, substantial heterogeneity was observed, as evidenced by the high standard deviation in the growth rates (131.49%), indicating pronounced inter-station variability (Table 4). The station performance of each station was categorized based on its initial compactness levels and growth patterns:

(1)

High-compactness stations (SPB, CQB) exhibited initial values exceeding 60,000, with SPB increasing from 150,211 to 171,955 (14.48% growth) and CQB from 70,908 to 77,971 (9.96% growth). Both demonstrated below-average growth rates, which suggests potential saturation effects in these mature urban nodes;

(2)

Medium-high compactness stations (HC, CDD) displayed initial values above 40,000 but showed more dynamic growth trajectories. The compactness of HC increased by 36.74% (43,092→58,925) while that of CDD grew by 46.74% (42,519→62,392), substantially outpacing the mean growth rate. This pattern indicates accelerated development in secondary urban centers during the study period;

(3)

The medium-low compactness cohort (YCD, NJB, SN) exhibited initial values between 10,000 and 40,000 but divergent growth patterns. YCD and NJB achieved remarkable expansions that exceeded 100%, whereas SN showed a more modest 15.16% growth. These variations likely reflect differential investment priorities and urban development stages across intermediate stations;

(4)

Low-compactness stations (BS, DYD, JYN et al.) demonstrated the most pronounced growth dynamics from sub-10,000 baselines. Most exceeded the average growth rates, with JYN (405.76%), TN (241.40%), and ZYB (225.35%) representing exceptional cases of rapid intensification. Notably, DYD constituted the sole low-compactness station with below-average growth (9.13%), which potentially indicates unique local constraints.

(5)

An anomalous case emerged with DZN station, which uniquely exhibited a 5.00% compactness decline (4981→4733). This deviation may reflect either data anomalies or specific redevelopment patterns that require further investigation through case-specific analysis.

Table 4. 3D compactness metrics and change rates of Chengdu-Chongqing high-speed rail station areas (2015–2025).

Station Name	T_2015	T_2025	∆T
SPB	150211	171955	14.48%
BS	6992	11631	66.35%
YCD	29358	63988	117.96%
DZN	4981	4733	−5.00%
RCB	2491	3846	54.41%
LCB	932	1455	56.06%
NJB	17262	48534	181.15%
ZZB	671	894	33.12%
ZYB	6102	19853	225.35%
JYN	382	1934	405.76%
CDD	42519	62392	46.74%
DYD	4953	5406	9.13%
SN	15623	17992	15.16%
TN	970	3311	241.40%
HC	43092	58925	36.74%
CQB	70908	77971	9.96%
Average	34712	42491	22.41%

Table 4. 3D compactness metrics and change rates of Chengdu-Chongqing high-speed rail station areas (2015–2025).

Station Name	T_2015	T_2025	∆T
SPB	150211	171955	14.48%
BS	6992	11631	66.35%
YCD	29358	63988	117.96%
DZN	4981	4733	−5.00%
RCB	2491	3846	54.41%
LCB	932	1455	56.06%
NJB	17262	48534	181.15%
ZZB	671	894	33.12%
ZYB	6102	19853	225.35%
JYN	382	1934	405.76%
CDD	42519	62392	46.74%
DYD	4953	5406	9.13%
SN	15623	17992	15.16%
TN	970	3311	241.40%
HC	43092	58925	36.74%
CQB	70908	77971	9.96%
Average	34712	42491	22.41%

4.1.2. Spatial Pattern Evolution

The spatial-temporal analysis revealed distinct evolutionary patterns between the north and south high-speed rail corridors. The southern line transitioned from a “dual-core concentration at terminals” pattern in 2015 to a more complex “dual-core + dual-fulcrum + dual-node” configuration by 2025. In contrast, the northern line maintained relatively stable spatial characteristics, preserving its “dual-core + single-fulcrum” structure while demonstrating consistent compactness growth across all stations (Figure 6).

In 2015, the southern line exhibited high (SPB) and medium-high (CDD) compactness stations at both terminals (Chongqing and Chengdu metropolitan areas, respectively), with intermediate stations showing lower values. The northern line similarly featured terminal cores (CQB, CDD), with HC serving as a medium-high compactness fulcrum station in Chongqing’s non-central area. By 2025, significant restructuring had occurred along the southern corridor: CDD and YCD joined SPB as high-compactness stations; NJB upgraded from medium-low to medium-high status; multiple stations (e.g., BS, ZYB) achieved categorical upgrades.

The northern line maintained its three core stations without exhibiting categorical changes, although all intermediate stations showed measurable compactness increases. This differential evolution suggests stronger developmental dynamics and spatial restructuring along the southern corridor, which potentially reflect variations in terrain constraints, development policies, or regional economic factors between the two lines. The findings highlight the importance of considering corridor-specific characteristics in high-speed rail station area planning and development strategies.

4.2. Evolution Patterns of Compactness Based on Multidimensional Classification

Through the systematic classification and statistical analysis of compactness measures, we obtained category-specific average compactness values (T_ave) for 2015 and 2025 (

Table 5. Classification statistics of average compactness and average change rate.

Major Categories	Subcategory	T_2015_ave	T_2025_ave	∆T_ave
Initial Compact Measure	Medium Low and Low Measurement	7263	15310	110.81%
	Medium High and High Measurement	83635	99545	19.02%
Physical geography	Small Cities or Stations	2531	3472	37.18%
	Large and Medium-sized Cities or Stations	59863	75010	25.30%
Admin Divisions	Global Hills	6257	11816	88.84%
	Mountain Terrace	68136	78458	15.15%
Line ownership	Sichuan Province	13178	21530	63.38%
	Chongqing City	60018	68917	14.83%
City size (Site level)	North Line	32675	42552	30.23%
	South Line	37116	45013	21.28%

), along with a comprehensive visualization of station-level change rates (∆T) overlaid with multidimensional attributes (Figure 7).

4.2.1. Initial Compactness Perspective

The analysis reveals significant disparities in urban development patterns based on initial compactness levels, demonstrating a clear “first-mover advantage” phenomenon among station areas. Notably, only four stations (Shapingba, Chongqingbei, Hechuan, Chengdudong) achieved high/medium-high compactness status, which reflects the Chengdu-Chongqing region’s late-starting high-speed rail development and relatively low overall urbanization rate. These stations had undergone prolonged development since the conventional rail era, accumulating substantial spatial advantages. The high and medium-high compactness stations exhibited substantially greater absolute T_ave values (83,635 in 2015, increasing to 99,545 in 2025), measuring 6.1–15.1 times higher than their medium-low and low compactness counterparts (7263 to 15,310 during the same period).

However, this initial advantage translated into markedly different growth trajectories, with the more compact stations showing only modest, average growth rates of 19.02%—merely 17.16% of the remarkable 110.81% expansion observed in less compact stations. This inverse relationship suggests a potential convergence mechanism where stations with initially high compactness maintain spatial advantages but experience growth deceleration (“early high-compactness with later slowdown”), while their less compact counterparts demonstrate strong catch-up effects through rapid growth despite lower baseline values.

4.2.2. Urban Sizes (Station Hierarchy) Perspective

The analysis of compactness evolution from an urban hierarchy perspective reveals systematic variations in development patterns between different city sizes (station hierarchy). The large and medium-sized city stations (classified as medium-high tier stations) maintained significantly higher absolute compactness values (increasing from 59,863 to 75,010) compared to the small city stations (low-tier stations: 2531 to 3472), exhibiting a 23.7–37.2-fold difference and demonstrating the characteristic of “early high compactness with later growth deceleration” in larger urban areas. However, this advantage in magnitude of the larger stations was accompanied by more modest growth rates (25.30%) relative to their smaller counterparts (37.18%), which illustrated a clear inverse relationship between the initial urban scale and subsequent compactness growth.

Notably, while core metropolitan nodes like Shapingba (second-tier station) and Chongqingbei (special-tier station)—which were relatively saturated in development by 2015—demonstrated stable but slower growth trajectories (≤15%), other major stations exhibited more dynamic expansion. This included both large and medium-sized cities like Ziyangbei (first-tier station), Neijiangbei (first-tier station), and Yongchuandong (first-tier station) showing >100% growth, as well as Chengdudong (special-tier station) and Hechuan (second-tier station) exceeding average growth rates.

Small city stations (third-tier stations), typically located in peripheral urban areas or county-level towns with constrained construction scales and limited vertical development (characteristic “low baseline” condition), presented a more complex bifurcated pattern. While demonstrating greater growth potential overall, the outcomes ranged dramatically from accelerated growth (>200% in Jianyangnan and Tongnan) to stagnation (below-average in Dayingdong) and even decline (negative growth in Dazunan). This variability highlights how the initial urban context and station hierarchy mediate development trajectories, with the peripheral location and administrative level being key determining factors.

4.2.3. Geomorphic Features Perspective

The analysis of terrain influences reveals distinct patterns in the compactness evolution between different geomorphological settings. The mountain-terrace stations demonstrated relatively high baseline compactness values (68,136 in 2015, increasing to 78,458 in 2025), with most stations exceeding 30,000 in 2015 and surpassing 40,000 by 2025, except for Dazunan and Ziyangbei. However, these areas exhibited slower growth rates (15.15% average), with only Ziyangbei and Yongchuandong exceeding 100% growth, while the others remained below 50%, including some cases of negative growth. This pattern of high initial compactness but moderated growth appears to be closely tied to the geomorphological advantages of terraces, which provide naturally flattened areas that facilitate early spatial accumulation but become constrained as the available terrace land is exhausted, which causes subsequent development to encounter more challenging mountainous terrain; this is particularly evident in prominently terraced stations like Hechuan and Shapingba.

In contrast, the hilly terrain stations showed markedly different developmental characteristics, beginning with much lower initial compactness (6257 in 2015, rising to 11,816 in 2025). Only Neijiangbei and Suining exceeded 15,000 in 2015, with just Neijiangbei surpassing 40,000 by 2025. Nevertheless, these areas demonstrated vigorous growth dynamics (88.84% average), featuring three stations with >180% increases, a predominant growth range of 30–60%, and a minimum growth rate that still exceeded 9%. This transition from initially constrained development to accelerated growth suggests that technological advancements in hillside construction and intensifying land resource pressures have progressively overcome the early limitations imposed by the hilly topography, as notably exemplified by the rapid development of Neijiangbei station area.

4.2.4. Administrative Division Perspective

From an administrative division standpoint, the average compactness values of Chongqing’s stations (60,018 in 2015; 68,917 in 2025) were significantly higher than those of Sichuan (13,178 in 2015; 21,530 in 2025), while the mean growth rate of compactness in Chongqing (14.83%) was notably lower than Sichuan’s (63.38%). Regarding the threshold of ≥40,000 for medium-high compactness, Chongqing had three stations that met this criterion in 2015, whereas Sichuan only had Chengdu East Station. By 2025, Chongqing added Yongchuandong to this category, while Sichuan included Neijiangbei.

In terms of growth rates, Sichuan exhibited a broader range (9–406%) compared to Chongqing (−5–242%), with higher variability. Although all 16 stations experienced fluctuations, Chongqing’s more pronounced mountainous terrain influenced its station planning. Unlike Sichuan, where stations such as Longchangbei, Jianyangnan, and Zizhongbei were developed as new independent high-speed rail towns that were far from urban cores, Chongqing’s stations—including Hechuan, Yongchuandong, and Rongchangbei—were predominantly integrated into existing urban fringes. This integration contributed to Chongqing’s initially higher compactness values.

Additionally, Chongqing’s stricter topographical constraints and land-use challenges led to more lenient urban planning regulations, such as reduced building setback requirements. Consequently, higher-density high-rise developments were more common, which resulted in greater built volume per unit area and further elevated initial compactness levels.

4.2.5. Line Ownership Perspective

From the perspective of north–south line distribution, the average compactness values of the southern line stations (37,116 in 2015; 45,013 in 2025) were slightly higher than those of the northern line (32,675 in 2015; 42,552 in 2025). However, the compactness growth rate of the southern line (21.28%) was marginally lower than those of the northern line (30.23%). The southern line exhibited higher variability in its growth rates, with two stations exceeding 200%, five between 50% and 200%, and four below 50% (including one negative growth case). In contrast, the northern line demonstrated more stable growth, with most stations clustered between 9% and 47%, except for Tongnan, which showed a notably higher rate.

The southern line commenced operation in December 2015, while the northern line opened in September 2009 (with conventional rail service since 2005). Excluding SPB (operational since 1979) to account for historical development, the southern line’s average compactness (12,976 in 2015; 23,779 in 2025) was substantially lower than that of the northern line, yet its growth rate (83.26%) far surpassed the latter. This divergence highlights the southern line’s recent development as primarily expansion-driven, with this line being characterized by low initial compactness but rapid growth. Conversely, the northern line’s higher baseline compactness and slower growth reflect its longer urban development history. During the study period, most southern line stations (e.g., Yongchuandong, Neijiangbei) underwent large-scale expansion, except Shapingba, which followed infill redevelopment. The northern line, while including some expansion cases (e.g., Tongnan), also featured infill development (e.g., Hechuan, Suining, Dayingdong), which reflects its mixed growth patterns.

4.3. Driving Mechanism Analysis

4.3.1. Identification of Compactness Measurement Drivers

At a significance level of 0.01, higher correlation coefficients indicate stronger influences of selected indicators (X) on the 3D compactness measurements (Y) of the station areas, which we term as “driver intensity”. Analysis across two periods (Figure 8) revealed distinct patterns: In 2015, the mean slope gradient (X6) failed significance testing, while the centralized construction zone planning proportion (X1), relative distance from the station to the city center (X2), land patch density (X8), and building density (X12) were only significant at p < 0.05. The remaining factors demonstrated significance at the stricter 0.01 threshold. Ranking these significant drivers (p < 0.01) by their correlation coefficient magnitude yielded the following order of influence: built-up land area (X7) > building footprint area (X11) > largest patch index (X9) > planned floor area ratio (X3) > mean building height (X13) > elevation standard deviation (X4) > building height standard deviation (X14) > terrain undulation range (X5) > patch aggregation index (X10).

By 2025, significant changes emerged: the mean slope gradient (X6), land patch density (X8), and building density (X12) became non-significant, while the patch aggregation index (X10) only reached p < 0.05. The 0.01-level significant drivers were ranked as follows: built-up land area (X7) > building footprint area (X11) > planned floor area ratio (X3) > mean building height (X13) > largest patch index (X9) > building height standard deviation (X14) > centralized construction zone planning proportion (X1) > relative distance from the station to the city center (X2) > terrain undulation range (X5) > elevation standard deviation (X4).

Among the 13 independent variables, 11 maintained significance (p < 0.01 in at least one period) when we applied the dual criteria of two-tailed testing at the 0.01 level. Longitudinal comparison showed that seven drivers had an increased influence magnitude while that of four was decreased. Particularly notable changes were that the effects of three factors substantially strengthened and those of another three significantly weakened over the study period (Figure 9).

Among the five indicators with influence values ranging from 0.76 to 0.95, built-up land area (X7) and building footprint area (X11) consistently demonstrated the strongest correlations (>0.9 in both periods), which indicates their dominant role in determining compactness at the horizontal level. The planned floor area ratio (X3) and mean building height (X13) also exhibited substantial influence (>0.85), which confirms the significant contribution of vertical development parameters to compactness measurements. These four cornerstone indicators showed minimal temporal variation (<5% change), which validated their fundamental role in the modified gravitational model, which calculates compactness based on building volume (footprint area × height). Notably, the largest patch index (X9), while maintaining statistical significance across both periods with relatively high values, experienced the most substantial decline in its influence magnitude (15.61%), suggesting that, while large contiguous land parcels initially enhance compactness during early development phases, this advantage gradually diminishes as the plot numbers and area increase through urban expansion.

The secondary influential factors (0.57–0.76 range) displayed more dynamic temporal patterns. The centralized construction zone planning proportion (X1) increased by 15.17% and the relative distance from the station to the city center (X2) rose by 11.29%, which reflects the growing importance of planning interventions (including concentrated development zones and strategic location selection) in promoting compact development. The building height standard deviation (X14) increased by 9.58%, which demonstrated that diversified vertical skylines contribute not only to urban aesthetics but also to functional compactness. While the elevation standard deviation (X4) decreased by 8.36%, the terrain undulation range (X5) within 210 m grids remained relatively stable. This pattern suggests that, during urban expansion, neighborhood-scale terrain features were strategically utilized with only moderate leveling modifications, while the macro-scale elevation differences were largely preserved. The patch aggregation index (X10) showed a 12.56% reduction, suggesting that horizontal land clustering becomes less influential as vertical development indicators (building scale, height, and height diversity) intensify.

The relative importance of driver categories underwent significant reorganization between 2015 and 2025 (Figure 10). The initial hierarchy (land use > building > terrain > planning) transitioned to building > land use > planning > terrain, which revealed several evolutionary trends: (1) the building-related parameters superseded land-use metrics as primary determinants, which reflects the progression from initial land consumption to three-dimensional built environment optimization; (2) planning factors gained prominence through accumulated station area development, which demonstrates the increasing effectiveness of regulatory tools; (3) terrain constraints almost maintained their position as the weakest influence, serving primarily as passive limitations rather than active shaping forces. This evolution underscores the dynamic nature of urban development processes and their differential impacts on spatial compactness over time.

4.3.2. Identification of Driving Factors for Compactness Change Rates

The correlation analysis of ∆X and ∆Y revealed a hierarchical structure of the influencing factors, where only the patch aggregation index change rate (∆X10), mean building height change rate (∆X13), and building height standard deviation change rate (∆X14) demonstrated strong statistical significance (p < 0.01). The built-up land area change rate (∆X7), largest patch index change rate (∆X9), and building density change rate (∆X12) showed marginal significance (p < 0.05), while the floor area ratio change rate (∆X3), land patch density change rate (∆X8), and building footprint area change rate (∆X11) failed to pass significance testing.

The global regression model encompassing all 16 station areas exhibited robust performance metrics, including an adjusted R² of 0.831, a Durbin–Watson U index of 1.755, and VIF values that were consistently at 1.592, confirming the model’s reliability, independent sample characteristics, and minimal multicollinearity. The model demonstrated significant explanatory power for variability in the dependent variable (Figure 11a). Notably, the building height standard deviation change rate (∆X14, p = 0.000) and patch aggregation index change rate (∆X10, p = 0.010) emerged as primary determinants of compactness variation. However, the absence of ∆X13, ∆X7, ∆X9, and ∆X12 in the global model—despite their significance in the correlation analysis—suggested that these variables might exert localized effects on station-specific compactness changes. To verify this hypothesis, we conducted stratified regression analyses across five classification systems (10 subgroups total) under rigorous diagnostic criteria (Durbin–Watson U index, VIF multicollinearity tests, and variable significance tests). These analyses yielded category-specific regression equations, visualizations, and adjusted R² values (Figure 11b–k).

Subgroup analyses across five classification systems (10 subgroups total) revealed distinct spatial patterns in driver importance, with the frequency statistics (Figure 11i) showing the building height standard deviation change rate (∆X14) to be the most influential factor (appearing in 6 subgroups), followed by the built-up land area change rate (∆X7, 3 occurrences), patch aggregation index change rate (∆X10, 2 occurrences), and building density change rate (∆X12, 2 occurrences), while the largest patch index change rate (∆X9) and mean building height change rate (∆X13) each appeared only once. While the initial compactness classification and urban size (station hierarchy) categories consistently depended on ∆X10 and ∆X14, significant variations emerged across geomorphological, administrative, and line ownership classifications: (1) globally hilly stations showed particular sensitivity to ∆X7, the building density change rate (∆X12), and the mean building height change rate (∆X13) due to terrain constraints limiting high-density development; (2) Chongqing area stations exhibited strong responsiveness to the largest patch index change rate (∆X9), as mountainous conditions restrict large contiguous land parcels; (3) the north line, with 23.04% greater elevation variability, 40.07% steeper slopes, and 18.23% more pronounced relief than its southern counterpart, demonstrated heightened sensitivity to land aggregation improvements (∆X10), where even modest gains could markedly enhance ∆Y. Collectively, these results demonstrate how geomorphological characteristics fundamentally shape urban land-use patterns and govern compactness evolution dynamics through both direct and indirect pathways.

4.3.3. Key Driving Factors: Land-Use Scale and Vertical Development

Through systematic analysis of the 10 factors that influence compactness measurements, we classified them into three distinct categories based on their impact strength and mechanistic roles: critical factors, important factors, and auxiliary factors. The critical factors, identified by their direct influence on building volume calculations (the core component of compactness computation) and mean effect values exceeding 0.85, represent indispensable elements that fundamentally determine system outcomes. Important factors, characterized by mean values above 0.70, exert significant but more generalized influences through either direct or indirect pathways in compactness calculations. Auxiliary factors, with mean values surpassing 0.60, primarily function in supportive or synergistic roles. Applying this same classification framework to the six factors that affected compactness change rates, we established modified threshold values of 0.85, 0.65, and 0.55, respectively, to account for observed effect size differences.

The constructed influence mechanism diagram (Figure 12) reveals the built-up land area (X7), building footprint area (X11), mean building height (X13), and floor area ratio (X3) as critical determinants of compactness measurements. This finding underscores that both the horizontal scale of construction land (which inherently influences building footprint dimensions) and vertical development intensity constitute the dominant drivers of spatial compactness. Notably, in the context of compactness change rates, the variation in building height diversity (∆X14) assumes particular importance as a key indicator. These results collectively demonstrate that the interplay between land-use patterns and three-dimensional built form characteristics fundamentally governs the evolution of station area compactness, with vertical development parameters gaining increasing prominence during urban maturation processes.

5. Discussion

5.1. Re-Examination of Driving Mechanisms

This study reveals unique characteristics in the evolution of the three-dimensional compactness around high-speed rail stations, aligning with certain existing research findings while challenging others. Consistent with previous studies, our results confirm that land-use diversity (correlated with land-use scale) [45] and vertical development indicators (including underground space utilization [16], floor area ratio, and building height [17]) significantly enhance compactness. Specifically, we identified the land-use scale (within equivalent study areas) and vertical development as critical determinants of compactness measurements, which supports key conclusions from prior research.

However, our findings present nuanced insights regarding building density’s role. While some studies emphasize its importance [25,46] and others suggest minimal correlation with compactness [47,48], our analysis reveals an intermediate relationship. Although X12/∆X12 (building density) showed limited overall influence on the compactness (Y) and its rate of change (∆Y), their exhibited significant negative effects in medium-high and high measurement and global hills station types. This counterintuitive result stems from the prevalence of point-type high-rise buildings in these areas, where special spacing regulations (typically 28–30 m for point-type vs. 1:1 for row-type buildings) constrain the height potential when density increases, ultimately reducing compactness.

Further, our study uncovered several novel findings that challenge conventional understanding.

5.1.1. Spatial Effects of Building Height Diversity

The building height diversity index (X14) demonstrates a consistently positive influence on compactness measurements, with its effect strengthening progressively during urban development. Equation (3) demonstrates that, when the total building volume remains constant between two units, the interaction force A(i,j) reaches its theoretical maximum when the volumes are equally distributed (∑(S_in × h_in) = ∑(S_jn × h_jn)). If the total footprint areas of both units were equal (∑S_in = ∑S_jn), this maximum interaction would require identical average building heights (h_in = h_jn), suggesting that lower height diversity (smaller X14 values) should enhance compactness. Under these idealized conditions, X14 would indeed show a negative correlation with compactness measurements. This mathematical expectation creates an apparent paradox with our empirical findings, where greater height diversity (higher X14) actually improves compactness.

This apparent contradiction resolves when considering three key urban development dynamics: First, heterogeneous land-use patterns naturally emerge during urbanization, creating variations in the floor area ratio across different locations and site conditions. Even with identical floor area ratio allowances, divergent development approaches (e.g., high-density low-rise vs. low-density high-rise configurations) generate inevitable height variations. Our data reveal strong positive correlations (0.652–0.852, all p < 0.01) between height diversity and three growth indicators: built-up land area, aggregation index of land patches, and mean building height. Second, the intrinsic trajectory of urban maturation favors height diversification. As cities develop, the coexistence of historic low-rise structures, modern mid-rise buildings, and contemporary high-rises creates organic vertical heterogeneity—a phenomenon documented in urban morphology studies [49]. Third, deliberate planning interventions actively promote varied skyline profiles for both functional and aesthetic purposes [50]. Many municipalities implement zoning tools like height bonuses, setbacks, and view corridor protections that institutionalize height diversity.

Thus, the positive compactness effects of building height diversity represent a composite outcome of the following: natural urban growth processes that generate height variations; technical regulations that shape vertical cityscapes; the spatial economics of land development under constraints. This explains why height diversity’s compactness benefits intensify over time—as cities accumulate more development cycles, these three mechanisms compound to create richer vertical profiles that enhance spatial integration. This metric therefore captures not just physical dimensions but the complex interplay between urban form, planning systems, and development economics.

5.1.2. The Dual Effects of Topographic Constraints

Conventional planning theory suggests that complex terrain typically leads to dispersed spatial patterns to accommodate topographic features and preserve natural landscapes [51], which would negatively impact compactness. However, our results reveal a counterintuitive positive correlation between terrain complexity (elevation standard deviation X4 and terrain undulation range X4) and compactness measurements. This apparent paradox stems from the dual constraints imposed by natural geographic conditions: while topographic complexity limits overall land-use options, it simultaneously forces concentrated, high-intensity development in the most suitable or potentially developable areas to maximize land value [52], thereby enhancing local compactness. This phenomenon aligns with our finding that built-up land parcels occupy only 36.59% of the study areas on average, which indicates a relatively low overall development intensity.

First, topographic limitations create natural land-use filters, concentrating development in the most suitable areas. The development pattern of the mountain-terrace station areas analyzed in this study demonstrates this mechanism clearly. When development ratios are low, terrace areas facilitate the rapid accumulation of built-up areas and three-dimensional growth, as seen in the 117.96% decade-long growth of Yongchuandong Station, which is a key expansion zone near the urban core. However, as suitable terrace lands become exhausted (e.g., Hechuan Station’s 36.74% growth), development constraints emerge. Second, the economics of terrain modification create threshold effects in globally hilly station areas, and limited flat terrain leads to high-density, high-intensity land-use configurations once leveling is completed (e.g., Neijianbei Station’s rapid compactness increase), although growth rates gradually slow as development ratios increase (e.g., Dayingdong Station’s below-average growth). Notably, Dazunan exhibited negative compactness growth due to dispersed development patterns that were constrained by topography, negative changes in the total built-up area, aggregation index, and largest patch index during rural–urban transition, and new industrial buildings with low, uniform heights. Third, regulatory adaptations in mountainous areas often relax certain planning standards (e.g., reduced building setbacks) to compensate for terrain challenges, enabling more efficient use of the limited flat areas. These adjustments permit greater building volumes per unit area than would be allowed in flatter terrains (Figure 13).

In contrast, plain cities demonstrate more stable growth patterns with weaker terrain constraints. Stations like Zhengzhoudong and LuoyangLongmen maintained steady growth over five years even at medium-high development ratios (≥50%), with Zhengzhoudong showing continued expansion potential until it neared saturation [40]. This comparative analysis confirms terrain complexity as a double-edged sword that simultaneously constrains overall development potential while actively promoting compact spatial patterns through three mechanisms: physical concentration in optimal areas, economic justification for high-intensity development, and regulatory adaptations to terrain realities. These findings necessitate adjustments to conventional anti-sprawl measures in mountainous cities to account for these inherent terrain-mediated compacting effects.

5.1.3. Indicator Influence Disparities from an Urban–Rural Integration Perspective

The analysis reveals unexpected findings regarding indicator influences when applying an urban–rural integration lens. The mean slope gradient (X6) and land patch density (X8) demonstrated significantly weaker effects than anticipated, which highlighted unique characteristics of mountainous urban development.

The limited influence of X6 emerges from distinct spatial development patterns in transitional urban–rural areas. Our field investigations identified three characteristic approaches to terrain adaptation: the concentrated development on naturally occurring terraces, the preservation of steep slopes as ecological buffers, and selective land modification through engineering interventions. This tripartite adaptation strategy effectively decouples micro-scale slope variations from macro-scale development patterns, explaining X6’s attenuated statistical influence despite its apparent terrain relevance.

The urban–rural dynamics underlying X8’s muted impact are particularly revealing. Conventional urban theory suggests that a higher patch density typically increases landscape fragmentation, reduces aggregation, and consequently diminishes compactness. However, our longitudinal data (2015–2025) showed stable patch density values despite significant urban expansion. This apparent paradox stems from two simultaneous processes: while urban areas gained numerous new patches (19.28% area increase vs mere 5.31% quantity growth), rural patches disappeared through consolidation. Furthermore, the “small block, dense road network” urban policy [53] led to smaller individual patch sizes in newly developed urban areas. These combined effects resulted in decreased largest patch index values, which correspondingly explains the reduced influence of X9 that was observed in our models.

Key implications emerge from these findings: mountainous terrain induces unique development selectivity that buffers slope effects; urban–rural land dynamics create compensatory patch patterns; conventional indicator–compactness relationships require contextual adaptation in mountainous regions. These results fundamentally challenge standard assumptions about terrain and density impacts, highlighting the need for context-sensitive analytical frameworks in mountainous urban environments. The urban–rural interplay and policy interventions create complex, non-linear relationships that conventional models may fail to capture.

5.2. Planning Strategies for Mountainous High-Speed Rail Station Areas

5.2.1. Morphological Adaptation: Quadruple-Category Management Based on Dual Metrics Integration

The National Development and Reform Commission and three other ministries jointly issued the “Guidelines on Promoting Rational Development of Areas Surrounding High-Speed Rail Stations,” which explicitly requires station areas to pursue distinctive and differentiated development pathways. The document emphasizes that cities should leverage their unique resource endowments and competitive advantages to prevent disorderly competition among adjacent stations along the same line [54]. While “three-dimensional compactness” has been established as a key objective for station area development in the new round of territorial spatial planning, the pursuit of compactness should not blindly focus on scale or rapid expansion. Instead, it requires comprehensive consideration of multiple indicators across planning, terrain, land-use, and architectural dimensions, as well as the balancing of current conditions with territorial spatial planning requirements.

Based on the 2025 compactness measurements and land development intensity, calculated as the ratio of built-up area (including construction land parcels, roads, and plazas, but excluding public green spaces, which account for approximately 10–15%) to planned centralized construction zones, stations can be classified into four categories (Figure 14) by comparing their values against the obtained mean and high-intensity development thresholds (exceeding 70%). This classification enables differentiated management strategies (

Table 6. Morphologically differentiated management strategies in four station types.

Type	Characteristics	Measures
Type I: SPB CDD	High Compactness—High Development Intensity: (1) Development is relatively saturated, with commercial and business functions in the core station area being well-developed. (2) Few or no vacant plots remain in areas distant. (3) Some low-efficiency spaces exist, such as urban villages, wholesale markets, and aging residential areas.	Functional replacement and three-dimensional renewal: Enhancing urban land-use efficiency through functional replacement optimizes the urban form of aging, low-efficiency areas and facilitates industrial upgrading [55]. (1) Strengthen coordination with major urban transportation corridors to amplify the catalytic effect of transit on precinct regeneration; (2) Holistically regulate building plot ratios and height controls to optimize three-dimensional urban morphology through functional replacement; (3) Prioritize spatial efficiency by employing vertical development to enhance urban compactness; (4) Preserve landmark structures while strategically shaping skylines to reinforce spatial identity.
Type II: CQB NJB CYD HC	High Compactness—Medium Development Intensity: (1) A certain amount of vacant land remains undeveloped. (2) The overall building quality within the station area is relatively new. (3) The spatial layout has been largely established. (4) Building density is low, but the average building height is notably high.	Gradient regulation and functional mix: Implementing building height gradients balances development intensity with livability, fostering integrated industrial, social, and innovation ecosystems [56]. Future infill development should adopt context-sensitive strategies: (1) Maintain high-density development near station cores through transit-oriented design, intensifying commercial functions with varied building heights to create urban landmarks; (2) Implement transitional intensity and height reductions in peripheral zones, optimizing residential functions with lower density, moderated heights, and enhanced greening for improved environmental quality; (3) For vacant parcels, create three-dimensional streetscapes integrating terrain features with lifestyle needs, developing integrated high-speed rail-living-industry communities.
Type III: DYD DZN	Low Compactness—Medium Development Intensity: (1) A certain amount of vacant land remains undeveloped. (2) The station area is predominantly occupied by industrial buildings, exhibiting homogeneous land-use types. (3) Building heights are uniform, and the overall floor area ratio is low.	Land-Use Transition and Base floor-area-ratio Control: Urban ecological resilience necessitates diversified land uses beyond monofunctional development [57], adopting job-housing balance and transit-integrated concepts: (1) Coordinate interregional construction land quotas and total building volumes during territorial spatial planning; (2) Direct infill development toward residential and supporting functions to intensify land use; (3) Convert inefficient industrial land to commercial uses [58], enriching street facades and architectural height diversity; (4) Enforce minimum industrial plot ratios while avoiding uniform height restrictions.
Type IV: JYN TN BS RCB LCB SN ZYB ZZB	Low Compactness—Low Development Intensity: (1) Ample vacant land is available for future construction. (2) Abundant natural landscapes and distinct topographic features are present. (3) Some existing construction provides a foundational development base.	Ecological Conservation and Patch Agglomeration: Dual emphasis on ecological protection and compact development safeguards natural resources while optimizing built environments: (1) Conduct micro-scale analysis of terrain variation to identify critical ecological features, extending macro-level ecological networks [59]; (2) Integrate new development parcels with existing built patches for clustered, compact layouts; (3) Explore the characteristic resources of the city and Leverage high-speed rail passenger flows to develop distinctive station area identities;Harvesting the unique resources of the city; (4) Promote intensive land use through diversified building heights and development intensities in new projects.

).

5.2.2. Ecological Adaptation: Compactness Ethics Based on “Three-Zone” Coordination

The spatial regulation of compactness metrics must adhere to an adaptive governance framework [60] and dynamically balance socioeconomic demands and ecosystem service values [61] rather than pursuing the singular quantitative [62,63] maximization of density, intensity, or compactness—approaches that may exacerbate ecological degradation and human–land conflicts [62,63]. Comparative case studies reveal critical trade-offs: stations such as Neijiangbei, Jianyangnan, and Tongnan achieved rapid compactness growth through large-scale terrain modification, but triggered increased landscape fragmentation and degraded ecological resilience. Conversely, Suining, Dayingdong, and Zizhongbei adopted low-impact development models, preserving approximately two-thirds of the original landforms (particularly mountain resources) and achieving gradual compactness improvement while maintaining ecological integrity—an approach that aligns with the “nature-led development” paradigm of ecological urbanism (Figure 15).

Building on urban ecology principles and ecological security pattern theory [64], we propose a three-tiered spatial management system grounded in the “patch-corridor-matrix” model [65]. First, prohibited zones must safeguard critical ecological elements—including key hydrological features and slopes exceeding 25°—as non-negotiable constraints on development. Second, intensive development zones should concentrate high-density, mixed-use construction to maximize vertical compactness and land-use efficiency [26,66]. Third, restricted zones require morphological adaptive design that features gradient floor area ratio controls and clustered height variations to harmonize development with ecological preservation. This integrated framework achieves a Pareto-optimal balance between spatial efficiency and ecosystem services, offering a replicable model for ecologically responsive compact urban development in territorial spatial planning contexts.

5.2.3. Urban–Rural Integration: Settlement Patterns Based on Core-Periphery Synergy

Under the “glocalization” paradigm, high-speed rail station areas are emerging as pivotal nodes for reconciling urban efficiency with rural vitality, serving as crucial catalysts for urbanization and integrated urban–rural development. In adopting a core-periphery collaborative framework [61], urban cores should prioritize the development of TOD-driven compact hubs through integrated transit networks and mixed-use industrial communities [67], focusing on high-speed rail-derived industries such as transportation operations and commercial services to curb sprawl while enhancing spatial efficiency.

Beyond the urban concentrated development zones, the locational advantages conferred by high-speed rail stations should be strategically leveraged across a broader radius (extending beyond the traditional 2 km influence zone). This presents an opportunity to transform the conventional unidirectional rural–urban labor migration pattern. Through rural revitalization policy support, urban technical talent can be encouraged to reverse-migrate into emerging rural sectors like cultural tourism and e-commerce. This facilitates the formation of specialized industrial clusters centered on eco-tourism and smart agriculture, enabling comprehensive rural industrial restructuring. Simultaneously, these clusters can provide urban areas with ecosystem services including leisure tourism, nature experiences, organic food supply, and cultural heritage homestays, and can thereby establish a mutually beneficial eco-industrial chain that serves both urban and rural development needs.

The model integrates spatial justice and landscape ecology principles with careful consideration of rural residents’ place attachment and employment service radii. By strategically aggregating rural settlements along key transportation corridors and around essential public service facilities, it promotes the formation of clustered, specialized living and service communities [68]. Ultimately, this creates a symbiotic settlement pattern that pairs “urban high-speed rail communities (core, high-skilled service clusters)” with “rural specialty settlements (periphery, cultural-ecological vocational networks)”—a compact, efficient spatial model that transforms high-speed rail station areas into demonstrative interfaces for new urban–rural relationships.

The framework establishes reciprocal metabolic loops between urban and rural systems: core zones act as economic accelerators that absorb capital and labor flows, while peripheral rural clusters reciprocate with ecosystem services and cultural capital. Gradient land-use policies ensure balanced employment radii and infrastructure equity, while clustered rural settlements minimize landscape fragmentation to enhance regional resilience. This “high-speed rail urban communities + specialized rural clusters” approach redefines urban–rural relationships through spatially embedded reciprocity, offering a scalable prototype for sustainable regional development that harmonizes compactness, equity, and ecological integrity.

6. Conclusions

As a sustainable urban development paradigm, the compact city concept provides crucial insights for addressing spatial fragmentation and inefficient land use in mountainous high-speed railway station areas. This study employs a grid-based volumetric calculation method and a modified gravitational model that incorporates DEM terrain distance correction and is integrated with GIS technology and satellite imagery data to quantify the three-dimensional compactness metrics and their rate of change across 16 stations along the Chengdu-Chongqing north–south high-speed railway corridor during 2015–2025. Through in-depth analysis of key influencing factors, the research enriches the application of compact city theory in high-speed railway station areas while offering empirical support for spatial form optimization, demonstrating both theoretical and practical significance.

The principal findings reveal the following: (1) Spatial heterogeneity: Mountainous high-speed rail station areas exhibit unbalanced compactness evolution, with a mean increase of 22.41% but a standard deviation surge of 131.49%, which confirms the nonlinear trajectories of “high-value/low-growth vs. low-value/high-growth” patterns. The southern line demonstrates a shift from dual-core driven polycentric diffusion, whereas the northern line shows gradient fault-locking with steady growth. These disparities stem from the station area development duration. (2) Land-use expansion and vertical intensification emerge as primary compactness accelerators. Building height diversity enhances compactness through floor area ratio dispersion effects while enriching urban skylines and street aesthetics. Notably, terrace clustering effects induced by mountainous topography drive efficient spatial agglomeration.

This study establishes a collaborative analytical framework that encompasses “constraint diagnosis—methodological optimization—spatial compactness evaluation—driving mechanism analysis—planning response”, providing researchers in architecture, environmental science, and management with novel approaches for studying spatial optimization in specialized contexts. Furthermore, the proposed trinity planning strategy system of “morphological adaptation—ecological responsiveness—urban–rural integration” offers practical solutions for achieving ecologically friendly, intensive-efficient, and coordinated urban–rural development in mountainous HSR station areas. Limitations exist, as this study primarily considers urban morphological characteristics among 14 selected factors while omitting socioeconomic dimensions. The preliminary correlation analysis indicated that the station area population size (with coefficients of 0.951 and 0.972 for 2015 and 2025, respectively) significantly influences compactness metrics, which suggests the need for future research incorporating broader socioeconomic variables to better explain spatiotemporal variations in mountainous HSR station compactness.