TOD Zoning Planning: Floor Area Ratio Attenuation Rate and Center Migration Trajectory

Abstract

A Transit-Oriented Development (TOD) strategy aims to reshape the spatial structure of high-density cities by encouraging the development of functional compounding and centralizing development goals. As a primary planning model, TOD station areas are based on zones’ structure. Studies have confirmed, however, that the current land structure between zones displays a high degree of homogeneity. There are several issues shown here, such as blurred station boundaries, spatial confusion, and a deviation of the TOD center. Based on the corridor effect theory, differentiated distribution characteristics of land structural elements are determined between zones. To clarify the difference between station zones, this study uses the floor area ratio attenuation rate as its primary method. As well as measuring their changes, it also measures their trends. The purpose of this study is to investigate the interactive relationship between multiple elements in the station zoning planning process. Also, it aims to explore the endogenous relationship of the station area with its existing spatial characteristics. Accordingly, a zoning planning model of 200–400–700 m is proposed, which lays the foundation for future research on standards for boundary delineation and center migration trajectory rules for station area zones.

1. Introduction

Rail transit construction is currently one of the most crucial methods for achieving spatial intensive renewal within the context of urban stock development [1,2]. With the Transit-Oriented Development (TOD) model, urban spatial layout can be optimized, and the built environment can be enhanced within confined spaces [3]. In recent years, the issue of improving land use efficiency and defining the effective distance between station areas has emerged as a prominent topic in the advancement of TOD given the demand for high-density and multifunctional development in station-area spaces [4,5,6]. However, practical challenges often encountered in TOD planning models, such as insufficient functional complexity and imbalanced land use structures, result in a homogenized functional configuration at the regional level [7]. In turn, this results in a land development dilemma characterized by a lack of spatial heterogeneity. A homogenized development model significantly undermines the recognition of the zoning structure around rail transit stations [8]. Furthermore, the application of gradient development strategies addresses the homogenization of land use structures and densities caused by uniform boundary constraints, thereby supporting the integration of transit stations into multidimensional spatial systems [9].

China’s current TOD zoning planning has two major limitations: First, it lacks a clear understanding of how TOD boundaries should be defined by local conditions. In most urban areas, rail transit systems serve as a supplement to the built environment [10]. Consequently, the government has failed to consider the impact of this project on the existing form and function of the city [11]. For example, in the initial planning phase of Beijing Huilong Station, TOD zoning criteria were rigidly applied by delineating an 800 m radius core zone without accounting for the site’s spatial heterogeneity. By failing to conduct site-specific spatial analyses to establish differentiated regulatory frameworks, this methodological rigidity led to spatial homogenization, resulting in excessive residential clustering, insufficient public service provisions, and significant job-housing imbalances [12]. The second reason is that focusing on the physical station instead of industries will make it more difficult to gather industries and economies in TOD areas. As a result of the absence of a station center in the radiation area around the station, the spatial advantages of each zone cannot be effectively exploited. It restricts functional interaction, optimal resource allocation, and the improvement of land value [13]. Therefore, based on the above problems and goals, this study proposes two development ideas for the subsequent development of TOD station areas: (1) clarify the land difference characteristics and potential improvement opportunities between each zone in the station area, and propose a new paradigm for planning TOD zones; and (2) identify a scientific method for redefining the center point of the TOD circle based on functional aggregation characteristics of the existing station area.

A gradient attenuation model1 is constructed with TOD’s zoning planning theory to reveal the spatial differentiation rules of urban elements [14]. This provides a quantitative basis for the update method for station space. Several layout problems can be solved by post-evaluation in zoning planning theory, including confusion of development priorities, homogeneous land development, and dispersed forms [15]. This method is useful for improving the aggregation and interaction of multiple elements within a station space [16]. In addition, it can contribute to the development of multilayered urban structures [17].

Thus, the Corridor Effect2 can be utilized in zoning planning theory to assist TOD in demarcating boundaries and clarifying regional central structures, and this will allow TOD zoning planning to be differentiated based on spatial centrality and land function. Currently, research on corridor effects in urban transportation focuses only on the attenuation trends of indicator elements [18,19]. The difference in attenuation between zones has not yet been systematically compared, limiting the ability of conventional models to explain variations in development intensity resulting from differing functional orientations within TOD frameworks. A cross-sectional comparative analysis of development intensity enables evaluation of the alignment between planning objectives and actual implementation while establishing differentiated quantitative benchmarks for adaptive regulatory control. Studies have shown that the floor area ratio (FAR) is a key indicator of the intensity of land development [20]. The impact of FAR and other indicators on Shanghai’s carrying capacity has been examined in some studies using multi-scale geographically weighted regression models. A significant improvement in low-volume areas can be achieved by increasing the FAR. It provides a basis for regulating station area development intensity, strengthening corridor effects, and promoting intensive land use [21]. In this article, the Floor Area Ratio attenuation rate (FARa) is employed as a quantitative method to investigate the lateral gradient and functional compatibility by calculating FARa values between adjacent concentric zones across transit stations. This approach precisely delineates spatial boundaries and scope regarding station corridor effects on FAR distributions, forming the basis for dividing central station zones. Further, the center of the area will be shifted by the interaction of various elements within the built environment because of the shifting centrality characteristics of the corridor, and the subsequent evolution of the element composition and spatial agglomeration within the TOD station space. The purpose of this study is to examine the development and intensity agglomeration trend of TOD radiation areas. Also, it proposes a layout strategy for the station space form in accordance with the volume attenuation law and its center offset trajectory.

Overall, this study adopts a dual-dimensional framework comprising “zoning planning + station center migration”. The specific research ideas include: (1) Analyzing the August to September 2024 development characteristics of central TOD station spaces using corridor effect analyses and regional center offsets; (2) Taking the city’s local TOD guidelines as the starting point to redefine TOD station space zoning planning; (3) To explore the regional attenuation rules and changes in the target site based on the TOD station space development model and the aggregation effect, the FARa is used as a dominant factor in circle attenuation; (4) Reflect the FAR under different zone schemes based on Pearson correlation coefficient, analyze the relationship between FARa and other spatial indicators associated with TOD stations. Also, examine the multi-level influences on central station area zoning planning. Meanwhile, applying standard deviation ellipses and ArcGIS, the development trajectory of the zone development center is determined based on the evolution of the FARa in each 100 m zone; (5) Based on the obtained quantitative results, the zoning planning principles and regional center offset rules suitable for the central TOD station space are evaluated, and subsequent construction opinions and references are provided for the development of the surrounding environment of such stations. This is the procedure for the research (Figure 1):

2. Literature Review

TOD zoning planning should first clarify the boundaries and internal structure of the station space [22,23]. Its multi-level planning model can achieve differentiated development of zoning element configurations [24]. Therefore, it is necessary to clarify the basis for dividing zones within the station area. When Peter Calthorpe first proposed the TOD model, he set a 10–15 min walk (with a radius of approximately 400–800 m) as the reachable radius of the radiation zone and defined 1.6 km as the station’s boundary [25]. Currently, most TOD station area studies in China’s first-tier cities set the boundary range at 800 m. For example, the analysis of residential property transaction records for 280 stations in Shanghai found that an 800 m evaluation range for TOD areas is more reasonable [26]. Furthermore, local regulations and TOD planning guidelines in places like Shenzhen and Dongguan indicate that zoning division principles should prioritize four aspects: transportation accessibility, surrounding land characteristics, functional layout, and land development capacity [27,28]. Additionally, due to the variations in city planning and site location, different circle planning standards exist [29]. Studies have shown that multi-mode transportation connections can expand the TOD influence area [30]. An original circle measuring 200–400–600–800 m may be reconstructed into a three-level structure measuring 600–1000–1500 m [28]. This indicates that the method of connecting TOD circles can have a significant impact on the characteristics and changes in spatial elements within station zones. This is particularly important when it comes to the accessibility of the station. There is, however, as a matter of fact, current zoning planning principles are more geared towards the macro-scale of the urban environment, and little interactive research has been conducted on micro-scale changes in the station area, including in-depth discussions of the links between regional factors and land use patterns [31,32].

In order to plan for differentiated zoning, complex and systematic cognition is required, as well as the interpretation of the interactions between multiple indicators in the physical and social dimensions [33]. However, most current studies on TOD station areas take urban travel and financial growth into account when measuring regional sustainability [34,35]. Consequently, zoning planning results are influenced more by non-spatial indicators such as passenger behavior and the economy. As a result, there is a chaotic situation in the spatial arrangement of the station area. The focus on regional economic development is difficult and subsequently loses its influence on sustainability. The light rail project in Addis Ababa, Ethiopia, exemplifies systemic planning deficiencies resulting from the lack of coordination between land use and rail transit corridor planning. Although the project was initially intended to enhance commuter efficiency, it not only failed to achieve this objective but also led to prolonged one-way commute times, exceeding 2.5 h for suburban residents [36]. Thus, zoning planning guidance for station space is reflected both in the allocation of land structure elements at the zone level as well as in the site-centered aggregation effect mechanism [37]. In the current evolution of the TOD model, the focus is always on public transportation stations physically, while the planning model at the zone level is only adjusted based on the type of station (subway, high-speed rail), the location (intercity or suburban), and the policy environment [38].

Development intensity within TOD station areas demonstrates differentiated patterns shaped by concentric zoning, station typology, and stages of urban development [39]. FAR zoning regulations are formally codified in urban planning guidelines. For example, China’s Urban Rail Transit Corridor Planning Guidelines adopt a dual-zoning structure (“core zone–influence zone”) based on station hierarchy, stipulating FAR lower bound gradients of 6.0–4.0 for central stations and 2.5–2.0 for general stations. Similarly, Arlington Station in the United States enforces a 6.0 FAR cap within its core zone to promote high-density clustered development [40]. Different phases of urban development also influence intensity variation. During urban regeneration, FAR regulations shift from prescriptive standards to adaptive mechanisms, as exemplified by Chengdu’s “transfer of development rights + flexible FAR adjustments” policy, which allows a 20% intensity increase within 100 m of regional stations [41]. Empirical studies confirm a dynamic linear correlation between TOD expansion intensity and development gradients radiating outward from station centers [42]. Although TOD centrality shifts are intrinsically linked to the spatial diffusion of station areas [43], current research methodologies still rely on uncritical assumptions regarding the physical centroid of stations. Therefore, it would be worthwhile to explore what indicators will cause the center point to shift and how to optimize the spatial layout and economic agglomeration by adjusting the development center in the developed station area and implementing TOD zoning planning.

Existing research on TOD zoning delineation and development intensity assessment has established quantitative modeling frameworks that integrate multi-source data. These studies, grounded in transportation accessibility theory, are commonly categorized into two methodological approaches: perceptual behavior quantification through human-environment interactions and structural analysis of land use configurations [44]. For example, Liu developed a human perception–oriented station area model using spatial clustering and inflection point detection algorithms [45]. Tan synthesized transit accessibility and land use mix indices to construct a TOD density threshold stratification system using K-means clustering, thereby enhancing spatiotemporal zoning adaptability [46]. However, current quantitative models lack sufficient explanatory power for capturing nonlinear relationships between FAR and zoning boundaries, thereby limiting the precision of gradient regulation. To address this gap, this study proposes the development of a dynamic gradient response model driven by rail transit corridor effects, establishing parametric linkage mechanisms between concentric zoning boundaries and development intensity, thereby transcending the theoretical limitations of conventional static concentric zoning frameworks.

The study found that a significant amount of literature supports the idea that spatial and temporal evolution characteristics of regional land structures can be analyzed through applied research on the corridor effect [37]. Additionally, it can be used to identify influencing factors. For example, examining the interactive relationship between urban transportation roads and land use in Guangzhou reveals that roads with varying locations, types, and orientations differed in their land use scope and intensity of development, with the corridor effect of roads having the greatest impact on commercial office land in Guangzhou [47]. Moreover, the term “corridor”, given its linear spatial connotation, typically refers to rectangular areas that extend further from the central axis of the road, or to linear corridors that connect TOD stations [48]. Studies that focus on circular areas diffused outward from a central point lack this approach [49,50]. This study aims to clarify the coupling mechanism that affects the land structure and agglomeration form during the outward evolution of the station based on the corridor effect. It also explores the impact of station zoning planning on the assessment and attenuation law of land carrying capacity, improving the efficiency of land use.

3. Materials and Methodology

3.1. Study Area

This study grounds its empirical analysis in Chengdu, China, where TOD serves as a central mechanism driving urbanization. Through proactive TOD planning, Chengdu has become a leading example of the “single-core, multi-ring” spatial strategy, developing high-density, polycentric clusters characterized by mixed-use integration, diverse urban functions, and comprehensive supporting infrastructure, thereby achieving refined TOD spatial development outcomes [51].

Station selection was guided by both national and municipal TOD planning frameworks. Spatially, stations were classified into six categories according to China’s TOD guidelines [27], while functional classification followed Chengdu’s Integrated Urban Design Guidelines for Rail Transit Stations [52]. Priority was given to stations designated as primary or secondary urban centers, with a focus on multi-line interchange hubs, except in cases where strategically significant single-line stations were included. Functionally, the stations were categorized into six typologies: Public Service Central (PSC), Commercial Central (CC), Business Central (BC), Residential Central (RC), Mixed-Use Central (MC), and Transportation Hub Central (THC). These typologies comprehensively represent key regional nodes, including commercial centers and major transit hubs. To ensure data reliability, a temporal filter excluded stations that had been operational for fewer than five years. The final sample includes 30 urban central stations located along Chengdu’s three major development corridors (Figure 2). Their spatial distribution balances the historic urban core with emerging sub-centers, selected under dual constraints of functional complexity and spatial representativeness to support analysis of TOD corridor effects.

Spatial precision control of the concentric study zones is achieved through systematic demarcation of the minimum (Min) threshold, gradient interval, and maximum (Max) threshold. The min threshold (100 m) is derived from empirical studies of Chengdu’s station area morphology: data indicate dominant station footprints (>45% green spaces, squares, and transportation facilities) with limited over-station developments, attributable to rail alignments along existing road corridors. Notably, the gradient interval (100 m) adheres to Chengdu’s planning code specifying “100 m spatial modules”, which aligns with its checkerboard road network and land-parcel divisions, ensuring congruence between analysis zones and urban management grids [53]. The Max threshold (800 m) integrates theoretical and practical considerations: theoretically, it reflects Calthorpe’s pedestrian shed concept, covering >85% of walking catchment areas [25]; locally, Chengdu’s guidelines designate 800 m as the city-level TOD core boundary, accommodating the region’s extensible topography and polycentric development needs. Collectively, these thresholds mitigate micro-scale land use variability while capturing macro-scale spatial gradients of corridor effects [52].

3.2. Data Source

The data for this study primarily consists of vector data formats such as SHP and TIF, covering land use parameters within rail transit station areas of Chengdu from 9 August to 12 September 2024. Specifically including: (1) Multi-temporal building footprint data sourced from OpenStreetMap (https://openmaptiles.org/) (2024) (accessed on 15 August 2024) and the Geospatial Remote Sensing Ecology Network (http://www.gisrs.cn/) (2024) (accessed on 22 August 2024); (2) Land use data obtained from the Resource and Environmental Science Data Center of the Chinese Academy of Sciences (https://www.resdc.cn) (2024) (accessed on 28 August 2024), and the Tsinghua University database (http://data.starcloud.pcl.ac.cn) (2018) (accessed on 5 September 2024); (3) Urban green space data sourced from the Scientific Data Bank (https://www.scidb.cn/en) (2023) (accessed on 10 September 2024); (4) Subway station and road data obtained from OpenStreetMap (https://openmaptiles.org/) (2024) (accessed on 15 August 2024).

A systematic quality control protocol was implemented through preparatory procedures. Building attribute completeness was verified using SQL queries in ArcGIS (v10.8), excluding 2% of incomplete records through threshold-based filtering [54]. Spatial datasets were standardized to the WGS 1984 UTM Zone 48N coordinate system via batch projection in QGIS (v3.28), with positional accuracy assessed using RMSE < 0.5 pixels [55]. Temporal discrepancies between datasets (Tsinghua’s 2018 land use data vs. 2024 ancillary layers) were resolved using time-series dasymetric mapping, incorporating annual building growth rates derived from OpenStreetMap historical snapshots [56]. Raster data underwent bilinear resampling to achieve 30 m resolution alignment, validated through confusion matrix analysis against high-resolution Google Earth imagery (k > 0.85). Anomalous NDVI values in green space data were constrained to the theoretical range [0, 1] using piecewise linear correction. Synthetically integrated outputs employed an ArcGIS Pro topological overlay sequence: administrative boundary masking, station-area zonal statistics extraction, and network service area delineation with topology rules enforcing 0.1 m gap tolerance [57]. Various indicators are presented in

Table 1. The descriptive statistics of the indicators.

Indicators	Calculation Formula Used	Unit	Std	Mean	Min	Max
Floor area ratio (FAR)	$\mathrm{F}\mathrm{A}\mathrm{R}={\mathrm{S}}_{\mathrm{s}\mathrm{u}\mathrm{m}}/{\mathrm{S}}_{\mathrm{c}}$	/	2.18	4.88	0.26	12.02
Floor area ratio attenuation rate (FARa)	$\mathrm{F}\mathrm{A}\mathrm{R}\mathrm{a}={\displaystyle \frac{\ln {\mathrm{F}\mathrm{A}\mathrm{R}}_{\mathrm{i}}-\ln {\mathrm{F}\mathrm{A}\mathrm{R}}_{\mathrm{j}}}{{\mathrm{d}}_{\mathrm{j}}-{\mathrm{d}}_{\mathrm{i}}}}\ast 100\mathrm{\%}$	%	0.34	−0.08	−3.11	0.55
Building density (D)	$\mathrm{D}={\mathrm{S}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}/{\mathrm{S}}_{\mathrm{c}}\ast 100\mathrm{\%}$	%	11.18	39.51	2.74	97.39
Information entropy (H)	$\mathrm{H}=-{\sum }_{\mathrm{i}}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{i}}\ln {\mathrm{P}}_{\mathrm{i}}$	Nat	0.33	1.28	0.00	1.86
Residential land (R)	/	m2	254,177.47	213,018.80	0.00	1,241,459.30
Administration and public service land (A)	/	m2	114,554.21	84,022.81	0.00	565,102.00
Commercial facility land (B1)	/	m2	72,718.87	38,150.60	0.00	466,710.00
Business facility land (B2)	/	m2	163,437.32	92,178.09	0.00	1,099,104.20
Green space and square land (G)	/	m2	199,416.73	192,467.47	0.00	991,555.50
Road and transportation facilities land (S)	/	m2	170,213.86	151,779.12	0.00	1,132,169.58
Industrial land (M)	/	m2	87,434.69	28,335.38	0.00	700,006.40
Distance between the initial center and the zoning development center (dSDE)	${\mathrm{d}}_{\mathrm{S}\mathrm{D}\mathrm{E}}=2\mathrm{r} {\sin }^{-1}\left(\sqrt{{\mathrm{s}\mathrm{i}\mathrm{n}}^2\left({\displaystyle \frac{{\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}-{\mathrm{y}}_0}{2}}\right)+\cos \left({\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}\right)\cos \left({\mathrm{y}}_0\right){\mathrm{s}\mathrm{i}\mathrm{n}}^2\left({\displaystyle \frac{{\mathrm{x}}_{\mathrm{S}\mathrm{D}\mathrm{E}}-{\mathrm{x}}_0}{2}}\right)}\right)$	m	37.33	56.62	0.00	202.95
Rotation ($\mathsf{\theta }$)	$\tan \mathsf{\theta }={\displaystyle \frac{\mathrm{A}+\mathrm{B}}{\mathrm{C}}}$	°	50.55	96.41	0.00	179.91
Flattening ratio (${\mathrm{d}}_{\mathsf{\sigma }}$)	${{\mathrm{d}}_{\mathsf{\sigma }}=\mathsf{\sigma }}_{\mathrm{x}}-{\mathsf{\sigma }}_{\mathrm{y}}=\sqrt{2}\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\tilde{\mathrm{x}}}_{\mathrm{i}}\cos \mathsf{\theta }-{\tilde{\mathrm{y}}}_{\mathrm{i}}\sin \mathsf{\theta }\right)}^2}{\mathrm{n}}}}-\sqrt{2}\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\tilde{\mathrm{x}}}_{\mathrm{i}}\sin \mathsf{\theta }+{\tilde{\mathrm{y}}}_{\mathrm{i}}\cos \mathsf{\theta }\right)}^2}{\mathrm{n}}}}$	m	39.57	58.41	0.00	248.50
Area of an ellipse (EA)	/	m2	415,592.11	479,880.42	895.18	1,452,692.86

.

3.3. Research Method

3.3.1. Corridor Effect Calculation of Floor Area Ratio and Attenuation Rate

Corridor effect attenuation is typically presented using the logarithmic attenuation function formula [47]. The attenuation function formula illustrates the impact of the site on the surrounding built environment, where e exhibits an attenuation trend as distance $\mathrm{d}$ is increased. In theory, the formula is as follows:

$$\mathrm{d}=\mathrm{f}\left(\mathrm{e}\right)=\mathrm{a} \mathrm{l}\mathrm{n}{\displaystyle \frac{\mathrm{a}\pm \sqrt{{\mathrm{a}}^2-{\mathrm{k}}^2}}{\mathrm{e}}}\mp \sqrt{{\mathrm{a}}^2-{\mathrm{k}}^2}$$

(1)

where $\mathrm{d}$ is the TOD circle radius, increasing outward from the center (unit: m); $\mathrm{a}$ is a constant representing the maximum corridor radiation efficacy at the station center ($\mathrm{d}$ = 0) (dimensionless); $\mathrm{e}$ is the TOD circle gradient field benefit, reflecting the station’s radiation intensity on surrounding built environments, with higher values indicating greater efficacy (dimensionless); $\mathrm{k}$ is the decay rate modulation coefficient controlling the distance-dependent attenuation of radiation efficacy, requiring $\mathrm{k}$ < $\mathrm{a}$ to ensure non-negativity under the radical (unit: m).

Formula (1), however, is only a theoretical attenuation formula, and the specific attenuation value cannot be calculated and quantitatively compared. Consequently, this study introduces the FAR Formula (2) and the logarithmic decay Formula (3), synthesizing them into the FARa Formula (4). Building upon Formula (2), we incorporate percentage calibration and calculate the attenuation rate by dividing the FAR difference between adjacent zones by their inter-zonal distance, thereby evaluating the attenuation characteristics of FAR elements in different circles. The logarithmic decay framework is applied to align with the corridor effect’s logarithmic decay properties and leverage its mathematical capacity to transform exponential decay into linear relationships via natural logarithm (ln), quantifying percentage attenuation per unit distance. This approach visually demonstrates how the corridor effect restructures land use patterns during station-centered outward radiation while enabling comparisons of growth rates and agglomeration status across various zones [58]. In addition, Formula (4) is used to calculate the change rate of other social indicators between different circles, such as building density, residential land, etc., to analyze the correlation between circle change rate and floor area ratio attenuation rate for such elements. In

Table 2. Station floor area ratio zone attenuation rate.

Station Code	Site	Station Categories	100–200	200–300	300–400	400–500	500–600	600–700	700–800
S1	Chunxi Road	CC	(−) 0.34	(+) 0.03	(−) 0.17	(−) 0.14	(−) 0.07	(−) 0.06	(−) 0.03
S2	Tianfu Square	BC	(−) 2.40	(−) 0.57	(−) 0.19	(+) 0.11	(−) 0.08	(−) 0.04	(+) 0.01
S3	Luomashi	MC	(+) 0.12	(+) 0.05	(+) 0.13	(+) 0.00	(+) 0.02	(−) 0.02	(+) 0.03
S4	3rdTianfu Street	BC	(−) 0.05	(−) 0.36	(+) 0.01	(−) 0.02	(−) 0.07	(+) 0.16	(−) 0.04
S5	North Railway Station	THC	(−) 0.81	(−) 0.23	(−) 0.13	(−) 0.17	(−) 0.05	(+) 0.00	(−) 0.01
S6	5thTianfu Street	BC	(−) 3.11	(+) 0.31	(−) 0.29	(−) 0.21	(+) 0.09	(+) 0.09	(+) 0.07
S7	East Chengdu Railway Station	THC	(+) 0.32	(+) 0.06	(+) 0.09	(+) 0.17	(+) 0.09	(−) 0.07	(−) 0.19
S8	Chengdu West Railway Station	THC	(+) 0.21	(−) 0.09	(+) 0.02	(+) 0.06	(+) 0.14	(+) 0.15	(+) 0.03
S9	South Railway Station	THC	(−) 0.44	(−) 0.22	(−) 0.40	(−) 0.20	(−) 0.17	(+) 0.00	(+) 0.01
S10	Renmin Road North	MC	(−) 0.42	(−) 0.34	(+) 0.10	(+) 0.08	(+) 0.21	(+) 0.11	(+) 0.05
S11	Incubation Park	MC	(−) 0.56	(+) 0.13	(+) 0.06	(−) 0.02	(−) 0.22	(+) 0.11	(+) 0.06
S12	People’s Park	MC	(−) 0.87	(−) 0.01	(−) 0.04	(+) 0.16	(−) 0.01	(−) 0.01	(+) 0.00
S13	Huaxiba	PSC	(+) 0.00	(+) 0.21	(−) 0.39	(−) 0.08	(+) 0.00	(−) 0.05	(−) 0.02
S14	Chengdu Second People’s Hospital	MC	(−) 0.10	(+) 0.00	(+) 0.06	(+) 0.04	(+) 0.03	(−) 0.10	(−) 0.09
S15	Sichuan Gymnasium	MC	(+) 0.29	(+) 0.29	(−) 0.22	(−) 0.16	(−) 0.23	(−) 0.13	(−) 0.13
S16	Nijiaqiao	MC	(+) 0.35	(−) 0.31	(−) 0.11	(−) 0.04	(−) 0.05	(−) 0.15	(−) 0.08
S17	Wuqing South Road	MC	(−) 1.18	(−) 0.41	(−) 0.22	(−) 0.03	(+) 0.14	(+) 0.00	(−) 0.03
S18	Xipu	THC	(−) 0.09	(−) 0.25	(−) 0.03	(+) 0.08	(+) 0.02	(+) 0.00	(−) 0.60
S19	Niuwangmiao	MC	(+) 0.22	(−) 0.19	(+) 0.15	(−) 0.01	(−) 0.05	(+) 0.03	(−) 0.04
S20	Chadianzi	RC	(−) 0.10	(+) 0.05	(+) 0.05	(−) 0.01	(+) 0.12	(+) 0.06	(−) 0.06
S21	Financial City	BC	(−) 0.31	(−) 0.02	(+) 0.20	(+) 0.35	(+) 0.00	(−) 0.02	(−) 0.08
S22	Hongpailou	MC	(−) 0.21	(−) 0.05	(+) 0.14	(+) 0.14	(+) 0.07	(+) 0.01	(−) 0.04
S23	Culture Palace	PSC	(−) 0.36	(+) 0.09	(−) 0.20	(−) 0.20	(−) 0.11	(−) 0.02	(+) 0.03
S24	Simaqiao	RC	(−) 0.23	(+) 0.04	(−) 0.04	(−) 0.14	(+) 0.01	(+) 0.02	(+) 0.03
S25	Yipintianxia	RC	(−) 0.43	(+) 0.04	(+) 0.06	(+) 0.08	(+) 0.03	(+) 0.04	(+) 0.03
S26	Chengdu University of TCM and Sichuan Provincial People’s Hospital	PSC	(+) 0.55	(+) 0.04	(−) 0.18	(+) 0.06	(+) 0.03	(+) 0.00	(-) 0.05
S27	Taipingyuan	CC	(−) 0.27	(+) 0.00	(+) 0.20	(+) 0.06	(−) 0.10	(+) 0.05	(+) 0.04
S28	Yushuang Road	RC	(−) 0.07	(+) 0.15	(+) 0.12	(−) 0.09	(+) 0.03	(+) 0.01	(−) 0.01
S29	Gaoshengqiao	MC	(−) 0.27	(−) 0.17	(−) 0.17	(+) 0.01	(−) 0.03	(−) 0.02	(+) 0.00
S30	Dongguang	BC	(−) 0.71	(−) 0.46	(+) 0.09	(+) 0.08	(+) 0.00	(+) 0.00	(−) 0.01
Sum (−)			(−) 13.32	(−) 3.69	(−) 2.78	(−) 1.51	(−) 1.24	(−) 0.68	(−) 1.5
Sum (+)			(+) 2.08	(+) 1.49	(+) 1.47	(+) 1.47	(+) 1.05	(+) 0.83	(+) 0.39
Sum			15.40	5.19	4.25	2.99	2.28	1.51	1.89

Note: unit %; (−) represents the negative value of the FARa, which represents the growth of the FAR rate. In the circle range, (+) represents a positive value of the FARa, which represents a decrease in the FAR rate; Sum represents the sum of the change rates of the FAR rate in the zone range, without separating positive and negative values.

, the specific results of the FAR of the central site are presented. The formula is as follows:

$$\mathrm{F}AR={\mathrm{S}}_{\mathrm{s}\mathrm{u}\mathrm{m}}/{\mathrm{S}}_{\mathrm{c}}$$

(2)

where the $\mathrm{F}AR$ represents the Floor Area Ratio of the target zone radiation area; ${\mathrm{S}}_{\mathrm{s}\mathrm{u}\mathrm{m}}$ represents the total area of buildings in the target zone radiation area, excluding basement areas (unit: m²); ${\mathrm{S}}_{\mathrm{c}}$ indicates the total land area of the target zone radiation area, excluding green space, park squares, and road area (unit: m²).

$$\mathrm{L}\mathrm{D}={\displaystyle \frac{\ln {\mathrm{k}}_{\mathrm{i}}-\ln {\mathrm{k}}_{\mathrm{j}}}{{\Delta }_{\mathrm{d}}}}$$

(3)

where the $\mathrm{L}\mathrm{D}$ represents the logarithmic decay rate; ${\mathrm{k}}_{\mathrm{i}}$ and ${\mathrm{k}}_{\mathrm{j}}$ represent the metric values at distances i and j, respectively; ${\Delta }_{\mathrm{d}}$ (where ${\Delta }_{\mathrm{d}}=\left|{\mathrm{d}}_{\mathrm{j}}-{\mathrm{d}}_{\mathrm{i}}\right|$) defines the inter-element distance differential, which is typically assigned a positive value.

$$\mathrm{F}ARa={\displaystyle \frac{\ln {\mathrm{F}\mathrm{A}\mathrm{R}}_{\mathrm{i}}-\ln {\mathrm{F}\mathrm{A}\mathrm{R}}_{\mathrm{j}}}{{\mathrm{d}}_{\mathrm{j}}-{\mathrm{d}}_{\mathrm{i}}}}\ast 100\mathrm{\%}$$

(4)

where when zone $\mathrm{i}$ is expanded to circle $\mathrm{j}$, $\mathrm{F}ARa$ is the attenuation percentage of the Floor Area Ratio (unit: %); ${\mathrm{F}\mathrm{A}\mathrm{R}}_{\mathrm{i}}$ and ${\mathrm{F}\mathrm{A}\mathrm{R}}_{\mathrm{j}}$ are the Floor Area Ratios for circle $\mathrm{i}$ and circle $\mathrm{j}$, respectively; ${\mathrm{d}}_{\mathrm{i}}$ and ${\mathrm{d}}_{\mathrm{j}}$ are the distances from circle $\mathrm{i}$ and circle $\mathrm{j}$ to the site (unit: m).

3.3.2. Exploration of the Zone Development Center Migration Trajectory

With ArcGIS standard elliptic difference (SDE), it is possible to visualize the spatial distribution and directional characteristics of physical elements in a target area [59]. In particular, the distribution and aggregation degree and movement change characteristics of regional building development intensity are analyzed by converting single buildings with volume attributes into point elements. In ArcGIS, the area of an ellipse (EA) can be directly drawn, which is the main shape of building elements.

On the basis of the average center, the geographical coordinates of the different circle development centers (${\mathrm{x}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$, ${\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$) within the TOD station domain will be determined. The formula is as follows:

$${\mathrm{x}}_{\mathrm{S}\mathrm{D}\mathrm{E}}=\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{X}}\right)}^2}{\mathrm{n}}}}$$

(5)

$${\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}=\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{Y}}\right)}^2}{\mathrm{n}}}}$$

(6)

where a circle radiation area is defined as its longitude and latitude with ${\mathrm{x}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$ and ${\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$ as the coordinates of the development center, respectively, as well as the average centers of each building element within each target circle ($\overline{\mathrm{X}}$ and $\overline{\mathrm{Y}}$), and the number of building elements (n).

Once the coordinates of the development center of each target zone are determined, the spatial coordinates (${\mathrm{x}}_0$, ${\mathrm{y}}_0$) of the site are calculated in ArcGIS, and then the relative offset between the two in distance and direction is examined. Firstly, the offset distance is the distance between two points relative to each other (Equation (6)). Secondly, the development centers of different zones within the TOD station domain shift in a directional manner. This article utilizes the calculation of the Direction Angle $\mathsf{\theta }$ (Formulas (8)–(11)) to clarify the offset angle and position relationship of the development centers of different zones relative to the site in the direction. The offset direction of the ellipse can be determined by using the N axis as a standard, true north (12 o’clock direction) equals 0 degrees, and rotating clockwise. In this article, the Haversine formula [60] is used to calculate the distance between development centers and sites in various zones $d_{SDE}$.

$${\mathrm{d}}_{\mathrm{S}\mathrm{D}\mathrm{E}}=2\mathrm{r} {\sin }^{-1}\left(\sqrt{{\mathrm{s}\mathrm{i}\mathrm{n}}^2\left({\displaystyle \frac{{\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}-{\mathrm{y}}_0}{2}}\right)+\cos \left({\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}\right)\cos \left({\mathrm{y}}_0\right){\mathrm{s}\mathrm{i}\mathrm{n}}^2\left({\displaystyle \frac{{\mathrm{x}}_{\mathrm{S}\mathrm{D}\mathrm{E}}-{\mathrm{x}}_0}{2}}\right)}\right)$$

(7)

where ${\mathrm{d}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$ represents the distance between the target circle development center and the site; ${\mathrm{x}}_0$ and ${\mathrm{y}}_0$ represent the longitude and latitude of the site; and $\mathrm{r}$ represents the Earth’s radius (about 6371 km).

$$\mathrm{A}=\left(\sum _{\mathrm{i}=1}^{\mathrm{n}}{\tilde{\mathrm{x}}}_{\mathrm{i}}^2-\sum _{\mathrm{i}=1}^{\mathrm{n}}{\tilde{\mathrm{y}}}_{\mathrm{i}}^2\right)$$

(8)

$$\mathrm{B}=\sqrt{{\left({\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tilde{\mathrm{x}}}_{\mathrm{i}}^2-{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tilde{\mathrm{y}}}_{\mathrm{i}}^2\right)}^2+4{\left({\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\tilde{\mathrm{x}}}_{\mathrm{i}}{\tilde{\mathrm{y}}}_{\mathrm{i}}\right)}^2}$$

(9)

$$\mathrm{C}=2\sum _{\mathrm{i}=1}^{\mathrm{n}}{\tilde{\mathrm{x}}}_{\mathrm{i}}{\tilde{\mathrm{y}}}_{\mathrm{i}}$$

(10)

$$\tan \mathsf{\theta }={\displaystyle \frac{\mathrm{A}+\mathrm{B}}{\mathrm{C}}}$$

(11)

where $\mathsf{\theta }$ is the degree of clockwise rotation relative to true north; ${\tilde{\mathrm{x}}}_{\mathrm{i}}$ and ${\tilde{\mathrm{y}}}_{\mathrm{i}}$ are the mean center and the difference between ${\mathrm{x}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$ and ${\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$ respectively.

Formula (12) can be used to calculate both the major and minor semi-axes of an ellipse, which indicate the direction in which architectural elements are distributed throughout the circle. This difference between ${\mathsf{\sigma }}_{\mathrm{x}}$ and ${\mathsf{\sigma }}_{\mathrm{y}}$ is known as the oblateness (${\mathrm{d}}_{\mathsf{\sigma }}$). When ${\mathrm{d}}_{\mathsf{\sigma }}$ is large, this indicates that the directions of development of this zone are more apparent, the centripetal agglomeration force is less strong, and the distribution of zones is more distinct. Therefore, we can calculate the oblateness of the ellipse by using the following formula:

$${{\mathrm{d}}_{\mathsf{\sigma }}=\mathsf{\sigma }}_{\mathrm{x}}-{\mathsf{\sigma }}_{\mathrm{y}}=\sqrt{2}\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\tilde{\mathrm{x}}}_{\mathrm{i}}\cos \mathsf{\theta }-{\tilde{\mathrm{y}}}_{\mathrm{i}}\sin \mathsf{\theta }\right)}^2}{\mathrm{n}}}}-\sqrt{2}\sqrt{{\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\tilde{\mathrm{x}}}_{\mathrm{i}}\sin \mathsf{\theta }+{\tilde{\mathrm{y}}}_{\mathrm{i}}\cos \mathsf{\theta }\right)}^2}{\mathrm{n}}}}$$

(12)

where ${\mathrm{d}}_{\mathsf{\sigma }}$ is the oblateness, that is, the difference between the lengths of the X-axis and the Y-axis; ${\mathsf{\sigma }}_{\mathrm{x}}$ and ${\mathsf{\sigma }}_{\mathrm{y}}$ are the lengths of the X-axis and Y-axis, respectively.

Furthermore, the development centers (${\mathrm{x}}_{\mathrm{S}\mathrm{D}\mathrm{E}},{\mathrm{y}}_{\mathrm{S}\mathrm{D}\mathrm{E}}$) of different zones, as determined by the SDE principle, serve as the central gathering points for the architectural elements within each zone. Following clarification of the offset direction, location, and EA range of the zone development center relative to the site, we found that the offset ${\mathsf{\sigma }}_{\mathrm{x}}$ direction, the ${\mathsf{\sigma }}_{\mathrm{y}}$ distribution range, and the specific offset angle conflict with the initial coordinates of the site. Consequently, this area is designated as a priority development zone (PDZ). It is also possible to use this method to determine whether the existing TOD central station area is overdeveloped or underdeveloped. For this reason, ArcGIS is used to visualize the distribution positions between the two. It is established that the coordinate system will be based on the ${\mathsf{\sigma }}_{\mathrm{x}}$ and ${\mathsf{\sigma }}_{\mathrm{y}}$ of the zone development center EA. The PDZ is determined based on the quadrant range of the coordinate system where the site is located minus the EA (Figure 3).

3.3.3. An Analysis of the Corridor Effect in the Land Use Structure Index System

As stated in the previous summary, the applied research on the corridor effect focuses primarily on the exploration of urban land structure in practice. The objective of this study was to investigate the land structure of TOD zoning planning from three perspectives: development intensity, functional mix, and land use classification. Based on statistics on the classification of central sites and Chinese urban construction land [61], the land use classification in this article is classified as residential (R), administration and public service land (A), commercial facility land (B1), business facility land (B2), green space and square land (G), road and transportation facilities (S), and industrial land (M). Open-source data statistics can be used to obtain these six categories of indicators.

A land development intensity index is a measure of the degree of land use and cumulative building density in an area. The building density index D can be used to evaluate the intensity of land development comprehensively. The calculation formula is as follows:

$$\mathrm{D}={\mathrm{S}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}/{\mathrm{S}}_{\mathrm{c}}\ast 100\mathrm{\%}$$

(13)

where in the radiation areas of different circles, $\mathrm{D}$ represents the density of buildings, and ${\mathrm{S}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}$ represents the sum of the base areas of buildings in the radiation areas.

In terms of functional mixing degree, the land mixing information entropy H describes the spatial structure and complexity of land use. The calculation formula is as follows:

$$\mathrm{H}=-\sum _{\mathrm{i}}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{i}}\ln {\mathrm{P}}_{\mathrm{i}}$$

(14)

where $\mathrm{H}$ is the land mixed information entropy of the radiation areas of various circles; ${\mathrm{P}}_{\mathrm{i}}$ is the ratio of the area of different land types in the radiation areas of each circle to the total area of the radiation area, where $\mathrm{i}$ = 1, 2, 3 …n; n is the number of land types contained in the radiation areas of different circles.

3.3.4. Correlation Analysis

There may be an interaction between social indicators and volumetric attenuation rate when station space is expanded across multiple levels. In this article, Pearson Correlation Coefficient is used for conducting correlation analysis research [62]. The Pearson correlation coefficient between the volume attenuation rate of adjacent radius circles, the change rate of each land use structure index, and the development center shift rate is calculated using SPSS 26.0. The formula is as follows:

$$\mathrm{r}={\displaystyle \frac{{\sum }_{i=1}^{\mathrm{n}}({\mathrm{X}}_i-\overline{\mathrm{X}})({\mathrm{Y}}_i-\overline{\mathrm{Y}})}{\sqrt{{\sum }_{i=1}^{\mathrm{n}}{({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}})}^2}\sqrt{{\sum }_{i=1}^{\mathrm{n}}{({\mathrm{Y}}_i-\overline{\mathrm{Y}})}^2}}}$$

(15)

where in this equation, $\mathrm{X}$ is the volume attenuation rate of the adjacent radius radiating area, $\mathrm{Y}$ is the change value of the land use structure index, and the offset of the development center of the adjacent radius radiating area. When $\mathrm{r}$ is closer to 0, the correlation will be weaker.

4. Results

4.1. Analysis of Corridor Effect of Central Stations

4.1.1. Correlation Between Corridor Effect and Floor Area Ratio of Central Stations

According to Table 2 and Figure 4, there is a significant impact of FARa on TOD zoning planning based on the differentiated performance of FARa in different zones. Based on an analysis of corridor attenuation of FAR elements within each station space, the TOD station domain zone includes the following conclusions: (1) As the distance increases, the comprehensive impact of the central station corridor effect on FAR (positive + negative values) gradually decreases. Attenuation continues to decrease from 100–200 m (15.40%) to 600–700 m (1.51%) and then increases to 1.89% at 700–800 m. Accordingly, the corridor effect of the central station on the FAR ceases to be effective at 700 m. (2) A horizontal comparison reveals that the FAR attenuation part (+) continues to decrease as the zone layer increases, and the attenuation situation between 300 and 500 m remains unchanged. As the radius increases, the growth part (−) first decreases and then increases. There is a maximum growth rate (−) in the range of 100–200 m. This shows that the current FAR value of the central site is still a high-growth development zone within 100–200 m, while the growth rate turns zones between 600 and 700 m, displaying an “inverted U” shape. This phenomenon suggests the failure to establish agglomeration effects inherent in station-centered development intensity. Instead, urban development intensity demonstrates progressive enhancement as transit areas expand outward. (3) Vertical comparison indicates that the overall growth rate (−) is generally greater than the attenuation rate (+); however, the opposite is true only at 600–700 m, where the growth rate reaches the lowest level at 0.68%, confirming that the FAR indicator has a strong influence over 700 m. Additionally, FAR showed a general downward trend during this period. As a result, there is still a significant difference between the growth part and the attenuation part between 200 and 400 m. The performance of the same station varies in zones between 400 and 700 m, suggesting that the overall FAR changes in this range are no longer significant.

Figure 5 illustrates the FAR distribution of different stations in different zones. Furthermore, it shows that the FAR continues to increase as the scale of the station domain expands to the 700 m circle. It is evident that the FAR value of the same site changes significantly between 100 and 700 m, which is indicative of the fact that FAR is an important guiding factor to TOD zoning planning.

4.1.2. Different Results of Land Structure Indicators on Floor Area Ratio Attenuation Under Different Zone Conditions

To mitigate the risk of multicollinearity among predictor variables, a Variance Inflation Factor (VIF) analysis was performed on the built-environment indicators. The results indicated that all variables had VIF values below the commonly accepted threshold of 5, thereby confirming the absence of significant multicollinearity. Accordingly, the land structure indicators were retained in the final analytical model to examine their influence on the FARa.

Table 3. A statistical analysis of the correlation between changes in land structure indicators and changes in floor area ratio attenuation rate.

Indicators	Floor Area Ratio Attenuation Rate (di−dj)
	100−200	200−300	300−400	400−500	500−600	600−700	700−800
Rate of Change in Building Density (Dr)	0.867 (0.000 ***)	0.622 (0.000 ***)	0.755 (0.000 ***)	0.81 (0.000 ***)	0.645 (0.000 ***)	0.662 (0.000 ***)	0.853 (0.000 ***)
Rate of Change in Information Entropy (Hr)	0.24 (0.201)	0.068 (0.721)	0.036 (0.849)	−0.078 (0.682)	−0.037 (0.847)	0.168 (0.375)	0.06 (0.753)
Rate of Change in Residential Land (Rr)	−0.64 (0.000 ***)	−0.107 (0.572)	0.255 (0.173)	−0.45 (0.013 **)	0.19 (0.314)	−0.185 (0.329)	−0.151 (0.425)
Rate of Change in Public Service Land (Ar)	−0.045 (0.812)	−0.075 (0.692)	−0.012 (0.950)	0.085 (0.654)	0.055 (0.775)	−0.02 (0.916)	−0.19 (0.314)
Rate of Change in Commercial Service Land (B1r)	0.393 (0.032 **)	−0.013 (0.944)	−0.084 (0.660)	−0.188 (0.319)	0.158 (0.404)	0.24 (0.202)	0.038 (0.843)
Rate of Change in Business Office Land (B2r)	0.529 (0.003 ***)	0.303 (0.104)	−0.16 (0.398)	−0.121 (0.524)	−0.067 (0.724)	−0.013 (0.945)	−0.123 (0.519)
Rate of Change in Green Space and Plaza Land (Gr)	−0.172 (0.364)	−0.21 (0.265)	0.154 (0.417)	0.275 (0.141)	0.199 (0.291)	0.431 (0.018 **)	0.354 (0.055 *)
Rate of Change in Road and Transportation Facilities Land (Sr)	0.002 (0.992)	0.004 (0.985)	−0.111 (0.561)	−0.03 (0.875)	−0.04 (0.834)	0.395 (0.031 **)	0.12 (0.528)
Rate of Change in Industrial Land (Mr)	0.071 (0.711)	−0.135 (0.477)	−0.103 (0.587)	−0.254 (0.176)	−0.026 (0.890)	0.03 (0.875)	0.122 (0.521)

Note: *, **, *** mean significant correlation at p < 0.05, p < 0.01 and p < 0.001, respectively.

shows that the correlations between FARa and the change rate of land use structure indicators vary by zone, with the greatest impact at 100–200 m, 400–600 m, and 600–800 m. A positive correlation exists between FARa and Dr in all zones, with the strongest correlation occurring between 100 and 200 m, 400–500 m, and 700–800 m (0.867%, 0.817%, 0.853%). FARa also exhibits a negative correlation with Rr in 100–200 m, as well as a positive correlation with B1r and B2r (0.393**, 0.529***). It has been observed that the FAR can be increased by increasing the Commercial Service Land (B1r) and 2 Rate of Change in Business Office Land (B2r), thus adjusting the development rhythm to achieve central agglomeration. In contrast, increasing R will result in a decrease in FAR. Consequently, this result is in line with the current strategy of developing commercial office land in TOD core areas. A positive correlation exists between FARa and Green Space and Plaza Land (Gr) and Rate of Change in Road and Transportation Facilities Land (Sr) between 600 and 700 m (0.431**, 0.395**). FARa and Rr are significantly correlated in the range of 400–500 m (−0.45), while FARa and Gr are significantly correlated in the range of 700–800 m (0.431). Also, it was confirmed that FARa is not affected by changes in the Public Service Land (Ar) or Rate of Change in Industrial Land (Mr).

4.2. The Impact of Floor Area Ratio Changes on the Offset of the Development Center Under Zoning Variations

4.2.1. The Offset of the Development Center and Its Directionality Leading to a Decrease in Floor Area Ratio

The correlation analysis of the distance between the development centers and the sites in different zones and the FAR indicates that as the station domain gradually expands, the changes in the FAR are directly related to the shift in the development center into the radiation area (

Table 4. Correlation between floor area ratio and the offset of the development center.

FAR	Distance Between the Initial Center and the Zoning Development Center (dSDE)
	100	200	300	400	500	600	700	800
100	−0.21 (0.266)	−0.545 (0.002 ***)	−0.004 (0.982)	−0.04 (0.835)	−0.179 (0.344)	−0.097 (0.611)	−0.054 (0.777)	−0.056 (0.768)
200	−0.232 (0.217)	−0.317 (0.088 *)	−0.038 (0.842)	−0.147 (0.437)	−0.167 (0.377)	−0.185 (0.328)	−0.218 (0.247)	−0.208 (0.271)
300	−0.224 (0.235)	−0.278 (0.136)	0.17 (0.368)	0.004 (0.982)	−0.039 (0.836)	−0.016 (0.933)	−0.037 (0.844)	−0.098 (0.607)
400	−0.2 (0.289)	−0.277 (0.138)	0.137 (0.471)	0.044 (0.816)	−0.05 (0.793)	−0.056 (0.770)	−0.098 (0.606)	−0.186 (0.324)
500	−0.218 (0.248)	−0.207 (0.273)	0.14 (0.461)	0.033 (0.864)	−0.038 (0.840)	−0.033 (0.861)	−0.09 (0.637)	−0.186 (0.324)
600	−0.168 (0.375)	−0.252 (0.180)	0.03 (0.877)	−0.037 (0.845)	−0.122 (0.519)	−0.04 (0.833)	−0.057 (0.767)	−0.158 (0.403)
700	−0.185 (0.327)	−0.313 (0.092 *)	−0.019 (0.921)	−0.065 (0.734)	−0.195 (0.301)	−0.143 (0.450)	−0.155 (0.414)	−0.255 (0.174)
800	−0.189 (0.316)	−0.331 (0.074 *)	−0.045 (0.814)	−0.112 (0.556)	−0.255 (0.173)	−0.168 (0.376)	−0.128 (0.499)	−0.225 (0.232)

Note: *, **, *** mean significant correlation at p < 0.05, p < 0.01 and p < 0.001, respectively.

). With the expansion of the station area, the development center shifts outward but is primarily located within the 0–100 m core zone (Figure 6). A negative correlation has been observed between d_SDE and FAR only within the 200 m zone, and the center offset of this circle also exhibits a negative correlation with FAR at 100 m, 700 m, and 800 m (Table 4). Based on the linear fitting of d_SDE and FAR for the 200 m zone layer (Figure 7), the FAR gradually decreases with shifts in the development center of the zone.

A comparison of the correlation results with the development center of each circle reveals the degree to which the development center’s directional shift influences FAR (

Table 5. The correlation between floor area ratio and the directionality of the development center and centripetal agglomeration.

FAR	Flattening Ratio (dσ)
	100	200	300	400	500	600	700	800
100	−0.048 (0.803)	−0.556 (0.001 ***)	−0.299 (0.108)	−0.19 (0.315)	−0.204 (0.280)	−0.148 (0.436)	−0.216 (0.252)	−0.192 (0.308)
200	−0.034 (0.859)	−0.168 (0.376)	−0.127 (0.503)	0.116 (0.542)	0.169 (0.372)	0.101 (0.594)	−0.061 (0.751)	−0.101 (0.595)
300	0.182 (0.335)	0.002 (0.993)	−0.081 (0.672)	0.022 (0.908)	0.084 (0.660)	−0.015 (0.938)	−0.117 (0.538)	−0.232 (0.217)
400	0.167 (0.378)	0.076 (0.688)	−0.01 (0.959)	0.191 (0.312)	0.181 (0.338)	−0.017 (0.928)	−0.164 (0.387)	−0.33 (0.075 *)
500	0.112 (0.556)	0.019 (0.920)	0.056 (0.771)	0.278 (0.137)	0.279 (0.136)	0.034 (0.857)	−0.147 (0.439)	−0.375 (0.041 **)
600	0.167 (0.376)	0.051 (0.790)	0.088 (0.644)	0.283 (0.129)	0.214 (0.256)	0.021 (0.912)	−0.141 (0.456)	−0.357 (0.053 *)
700	0.089 (0.639)	0.004 (0.982)	0.108 (0.569)	0.248 (0.186)	0.135 (0.478)	−0.038 (0.841)	−0.2 (0.290)	−0.403 (0.027 **)
800	0.091 (0.634)	−0.041 (0.831)	0.07 (0.713)	0.147 (0.437)	0.072 (0.707)	−0.059 (0.758)	−0.205 (0.278)	−0.418 (0.022 **)

Note: *, **, *** mean significant correlation at p < 0.05, p < 0.01 and p < 0.001, respectively.

). They are negatively correlated only in the 200 m and 800 m circles. FAR within the 100 m circle and ${\mathrm{d}}_{\mathsf{\sigma }}$ at 200 m show a significant negative correlation (−0.556***). There is a negative correlation among many circles at 800 m, ranging from 400–800 m. A further finding was that FAR decreased gradually with the strengthening of the development direction and a weakening of the central concentration. The data shows that the ${\mathrm{d}}_{\mathsf{\sigma }}$ of the central station reaches the maximum value (76.22 m) at 800 m, demonstrating the strongest directionality and weakest central aggregation force. As a result, this circle has the greatest impact on FAR.

4.2.2. The Floor Area Ratio Attenuation Rate and Development Center Offset Rate Influenced by Multiple Zoning Layers

A correlation analysis of the development center deviation rate ${\mathrm{d}}_{\mathrm{S}\mathrm{D}\mathrm{E}\mathrm{r}}$ of adjacent zones and FAR (

Table 6. Correlation between floor area ratio attenuation rate and development center offset rate.

FARa	Distance Between the Initial Center and the Zoning Development Center Attenuation Rate (dSDEr)
	100−200	200−300	300−400	400−500	500−600	600−700	700−800
100–200	−0.337 (0.069 *)	0.387 (0.035 **)	−0.061 (0.749)	−0.239 (0.203)	0.23 (0.221)	0.222 (0.239)	0.148 (0.434)
200–300	−0.043 (0.823)	−0.14 (0.460)	−0.004 (0.985)	−0.049 (0.799)	−0.145 (0.444)	−0.052 (0.785)	0.262 (0.162)
300–400	0.022 (0.906)	0.214 (0.257)	−0.409 (0.025 **)	0.212 (0.261)	0.252 (0.179)	0.25 (0.182)	0.343 (0.064 *)
400–500	−0.212 (0.260)	0.186 (0.325)	0.002 (0.992)	−0.125 (0.509)	0.017 (0.931)	0.215 (0.254)	0.286 (0.126)
500–600	0.256 (0.171)	0.303 (0.103)	−0.133 (0.483)	0.095 (0.618)	−0.386 (0.035 **)	−0.175 (0.354)	0.216 (0.251)
600–700	0.112 (0.556)	0.1 (0.600)	−0.048 (0.803)	0.421 (0.020 **)	0.198 (0.293)	−0.029 (0.881)	−0.009 (0.964)
700–800	−0.065 (0.733)	0.192 (0.309)	0.154 (0.417)	0.034 (0.860)	−0.186 (0.326)	−0.464 (0.010 ***)	−0.255 (0.174)

Note: *, **, *** mean significant correlation at p < 0.05, p < 0.01 and p < 0.001, respectively.

) indicates that FARa will be affected by both $d_{SDEr}$ from its circle and other circles. The results of ${\mathrm{d}}_{\mathrm{S}\mathrm{D}\mathrm{E}\mathrm{r}}$ in the three zones of 100–200 m, 300–400 m, and 500–600 m, respectively, indicate zero correlation with FARa. With an increase in ${\mathrm{d}}_{\mathrm{S}\mathrm{D}\mathrm{E}\mathrm{r}}$ between adjacent circle layers in this range, FARa will decrease.

5. Discussions

5.1. Differentiation of Floor Area Ratios on the Boundaries of TOD Stations

Developing TOD station spaces under differentiated zoning has a significant positive impact on the agglomeration effect. As of right now, zoning delineation is generally based on two main classification methods: “zoning boundaries” and “internal layers.” In comparison to the existing “1373” and “3584” tiered planning principles, the “137” principle primarily focuses on functional layout and spatial experience at the internal level, whereas the “358” principle incorporates development intensity and land price differentials as additional considerations [63]. Some studies suggest that zoning boundaries are defined based on walking distances [64]. The purpose of this study is to propose a more rational spatial follow-up improvement strategy for existing station areas, as well as enhance the understanding of surrounding urban land use patterns and the multi-factor driving mechanism for TOD.

According to our analysis in Section 4.1.1, the comprehensive radiating effect of central stations on the FAR diminishes with the expansion of the zoning scale. However, it increases again at the range of 700–800 m. As a result of this phenomenon, the development benefits of the station area are no longer limited to the station’s immediate area. As a result of the less than 1.6 km distance between adjacent stations, their catchment areas exhibit spatial superposition within a 700–800 m radius (Figure 2). Such overlay zones are subjected to interactive influences from multiple stations, compromising the independence of spatial units required for single-station zoning studies. Significantly, this research delineates the concentric boundary at 700 m. Coincidentally, this demarcation aligns with Chengdu’s current TOD “137” tiered planning principles, where 700 m is designated as the development boundary within its tertiary planning ring.

Furthermore, in order to achieve the ideal center-type station corridor effect with high density in the center, it must follow the principle that the greater the distance from the station, the smaller the floor area ratio, that is, the FARa has three attenuation processes: large, medium, and low (Figure 1), which serves as a guiding principle for internal hierarchical divisions within the zone. There are significant changes in the FARa inside the zone mainly occurring at 200 m and 400 m (Table 3). This proves that the following: (1) 100–200 m is the circle area with the most significant increase in floor area ratio, mainly due to commercial office land within 100–200 m, indicating that this range belongs to the core high-density development of the central site area, and this is the first zone; (2) in the range of 200–400 m, the increase in floor area ratio is still greater than the attenuation, but it is significantly lower than the range of 100–200 m, indicating that the land structure has changed, and this is the second zone; (3) the attenuation trend at 400–700 m is the same as the growth trend. Many residential properties occupy land within the range of 400–500 m, resulting in a decrease in the floor area ratio. In accordance with the general rules of TOD construction in China, the proportion of residential land gradually increases as the zone expands. According to this article, it is a characteristic of the third zone. There is also still a small amount of high-intensity development in the 200–400 m range, confirming the existence of differentiated land use properties near the 400 m zone.

Our research has led to the development of a zoning planning layout that is consistent with Chengdu’s central city sites, specifically the “200–400–700” zone plan (also known as the “247” zone plan). In comparison with traditional zoning planning, “247” not only clarifies the principles of TOD zone division but also conforms to the spatial aggregation law of interactive evolution of multiple elements within a station area.

5.2. Changing Development Centers Guide Differentiated TOD Zones

Although the development centers of each zone are primarily located within the 0–100 m radius of the station, their offset trajectory (OT) and distribution orientation vary significantly. Figure 8 illustrates a coordinate system with the station at its center. Currently, central stations are primarily located in the southwest and northeast areas of various zones. According to Figure 6, the nearest development center located within a 100 m circle is the center of the ellipse, and the furthest is 700 m away. Zones do not, however, affect the position of development centers and stations within a single station. For instance, in the S22 station domain, the distance from the center of the 800 m ellipse to the station is 10.2 m, while the average distance from other zones is 38.31 m. Several development centers and stations in different zones may have different development directions, even though their distances are the same. Similarly, in the S11 station domain, the development centers between the 400 m and 500 m zones are approximately 25 m away from the station, but are in the southwest and northwest, respectively. Nearest to the 200 m circle are the four stations’ space like S4, S9, S27, and S30, which are the development centers of the 600–700 m zone. Additionally, the offset trajectories of the elliptical centers of the four stations are a single line, and there is no intersection or overlap between them.

Currently, the development centers of the different zones of central sites are located 56 m southwest or northeast of the site, which represents a significant offset. As the direction of rotation of the development center is mainly between (90, 180] (Figure 9), the main deflection direction of the zone development center is the “northwest-southeast” direction of the station, and this phenomenon is most apparent near 400 m. There is insufficient development intensity in the “northeast-southwest” direction 400 m away from the station. Near 700 m, the development direction converges. As a result of this, it has once again been demonstrated that the critical point and directionality of the development area of the 700 m radiation zone to the site have clearly been defined. In Figure 10, only S2, S9, and S28 can meet the all-directional extension of the area because the station’s overall directionality is weak, but the central aggregation force is strong. There is a strong central aggregation force between 500 and 800 m, and the development directions of each zone are different. As a result, the problem of development center offset or direction instability in high-density land can be solved by intermittently developing high-density plots in adjacent zones or by increasing the development intensity in reverse zones.

It is necessary to control the offset distance and direction of the development center of different circles. As shown in 4.2, firstly, the offset distance of the development center will be affected by the floor area ratio of multiple zones. Therefore, for the floor area ratio of different zones, it is necessary to continuously correct the offset of the development center. This ensures the ideal state in which the overall development center of the station area is mainly centered on the site, and the floor area ratio gradually decreases.

Taking the South Railway Station—characterized by the maximum average development center offset of 122 m—as a case study, this section investigates strategies to mitigate development center displacement across concentric zones ranging from 100 to 700 m. Two complementary approaches are employed as follows: (1) Mitigation boundaries for each zone are delineated using the PDZ determination framework established in Section 3.3.2. As shown in Figure 11, the aggregation of PDZs across all zones enables the identification of High-Impact Development Zones (HDZs), with HDZ1 representing the primary intervention area. (2) Correlation analysis presented in Table 4 demonstrates that increasing the Floor Area Ratio (FAR) within the 100 m, 200 m, and 700 m radii is associated with a reduced development center offset at the 200 m radius. The spatial extent for FAR enhancement corresponds with the boundaries derived from PDZs, as illustrated by HDZ100/200/700 in Figure 11, with HDZ2 denoting the core area for targeted intervention. In subsequent urban renewal phases, PDZs identified as low-intensity development zones within the South Railway Station’s concentric catchment should be prioritized for intensification. This spatially targeted approach ensures more effective realignment of development centers by TOD planning principles.

6. Conclusions and Suggestions

6.1. Research Conclusions

A summary of the main results can be provided by focusing on the station as the center and exploring the changes in the FARa and regional center migration trajectories across different zoning layers:

As distance increases, the influence of central stations on the FAR gradually decreases, up to a boundary of 700 m. With the expansion of radius, the FAR exhibits an increasing trend within the 0–400 m range. Empirical data demonstrate that this indicates the current central stations in Chengdu have not fully implemented TOD principles, and a consolidation effect has not yet been created from the outside in. There is a clear inconsistency between the development of stations and their planning and implementation, which is largely dependent upon market factors such as economic conditions, passenger traffic, and land prices.

Generally, the influence of different land structure indicators on the FARa adheres to existing TOD planning principles, which involve planning commercial, office, residential, and green space gradually from the inside out, validating the rationality of current land use planning through this study. However, in contrast to the existing development principles of Chengdu central sites around the station center, the current development centers are located mainly within a 50 m radius of the site, reflecting the stations’ decision-making role as the center which drives the development of the zoning planning. Due to the lack of clear definition of the industrial and functional agglomeration center, the production efficiency of TOD is not optimal.

With the expansion of the zone radius, the main development direction of the central site is “northwest-southeast”, whereas in subsequent phases, development efforts in the “northeast-southwest” sectors of the station areas to achieve omnidirectional spatial development.

6.2. The Suggestions of Improving Circle Planning

According to actual research, the “247” proposed in this article optimizes existing station area circle delineation principles and redefines the land distribution and land structure as compared to the traditional circle planning structure (Figure 12). By doing so, it solves the problem of homogeneous layouts of TOD sites and discrete development centers. Using the findings of this study, the following optimization suggestions are provided for circle planning of TOD station areas in Chengdu:

(1)

According to the optimization of land structure elements, high-density commercial service facilities will be concentrated within a radius of 0–200 m; medium-density development will occupy a radius of 200–400 m, and an appropriate amount of public management and public service land, green space and squares, roads, and transportation facilities will be developed. Within this range, improvements in accessibility, functional mix, and ecological construction of station space are essential optimization methods. In general, 400–700 m should be developed in a low-density mode, primarily for residential use, in accordance with current TOD zoning planning principles, as well as reducing the attenuation rate of the floor area ratio in a direct manner. In addition, green space and road land should be added to the station area within 500–700 m to mitigate the negative impact of changes in spatial density inside and outside the station.

(2)

In terms of the Development Center: To achieve TOD centered on the station, it is imperative that the offset distance and direction of the development centers be controlled across different zones. To begin with, the offset distances of development centers are influenced by the cumulative FAR of multiple zones, as described in Section 4.2. Therefore, a gradual decrease in the FAR is crucial. Continually adjusting the offset of development centers between zones will result in the overall development center remaining centered around the station. With an initial goal of achieving a high FAR within the 200 m zone, when FAR = 200 m and d_SDE = 200, the correlation r = −0.317* indicates that the offset distance of the development center within this zone should be minimized, which can be achieved through symmetrical distribution of FAR. The offset rate of the development center from 100 to 200 m will decrease as the distance to the center within the 200 m zone decreases. Consequently, when FARa = 100–200 d_SDEr = 100–200, the correlation r = −0.337* suggests that the Floor Area Ratio attenuation rate within the 100–200 m range will increase. Also, in the 200–300 m range, the offset rate of the development center will increase (as shown in Table 6, when d_SDEr = 200–300 and FARa = 100–200, r = −0.337*). In the end, the development center will be moved within a radius of 200–300 m. The FARa rate and the offset rate of the development center in the adjacent 300–400 m zone show a negative correlation (−0.409°), allowing the development center to return by lowering the FAR. In order to maintain a continuous reduction in FAR and form a central agglomeration, the FARa in the 500–600 m zone must continue to decrease. However, this attenuation rate shows a negative correlation with the offset rate of the development center (−0.386**), leading to an increase in the offset rate of the 500–600 m development center. To achieve the goal of returning the development center, the FARa rate in the 600–700 m zone should be reduced to decrease the offset rate of the 400–500 m center (as shown in Table 6, when d_SDEr = 400–500 and FARa = 600–700, r = 0.421**). Secondly, regarding the overall control of development directionality, the zoning layers should increase the regional FAR within 100 m to mitigate drastic changes in central agglomeration in the 200 m zone (as shown in Table 5, when d_σ = 200 and FAR = 100, r = −0.556**). Moreover, as mentioned in Section 5.2, it is essential to alleviate issues related to the directionality of FAR development by discontinuing development in adjacent zones and intensifying development in reverse zones.

This study is grounded in the core principles of TOD and compact urban growth, with its methodological framework exhibiting strong cross-regional applicability and offering replicable strategies for precision-guided station area development. The proposed “247” zoning model is empirically derived from prototype analyses of Chengdu’s central stations and is inherently shaped by hierarchical station classifications and regional urbanization contexts. The findings provide transferable insights for cities at similar developmental stages that aim to intensify land use through TOD strategies, such as Kunming and Guiyang in China, as well as emerging Southeast Asian metropolises, including Bangkok and Ho Chi Minh City.

Furthermore, the proposed methodology proves particularly valuable in urban regeneration contexts. It facilitates the identification and enhancement of development compensation mechanisms in underperforming zones and allows for empirical validation of agglomeration effects in established station-centered areas. The framework’s extensibility supports the spatial mapping of green space ratios and other built-environment indicators across TOD and non-TOD zones, thereby revealing spatial coupling relationships between ecologically underdeveloped areas and low-carbon efficiency gradients within station areas.

Nevertheless, there are still some limitations in the study. (1) Data limitations: Corridor effects in overlapping station areas were not examined, leaving compound spatial influences underexplored. The dataset also suffers from constraints in temporal validity and completeness, lacking essential indicators such as underground development intensity and detailed land use structure. Moreover, relying solely on FAR as a proxy for development intensity may introduce measurement bias. (2) Methodological constraints: Although the “247” zoning model demonstrates general applicability, its adaptability to individual stations remains uncertain due to Chengdu’s unique urban morphology and the functional heterogeneity of selected stations. Future research should address these limitations by integrating multi-source spatiotemporal data, establishing multidimensional evaluation metrics, and conducting cross-regional comparative analyses using analogous station typologies across various cities to enhance the model’s generalizability.