Access structure

Abstract

Although various hierarchical structures have been investigated with respect to the different elements of urban form, the hierarchical spatial order of access from streets to plots and buildings has not been adequately explicated and objectively assessed. In this article, a new method, access structure, is presented to bridge this knowledge gap. Based on Krop’s generic multilevel diagram of urban form, different types of access structure are developed and symbolically represented. They are then quantitatively measured and compared using three metrics and an associated ternary diagram. Subsequently, the new method is tested first in analysing the internal structure of an individual urban block and then in distinguishing urban blocks with different structural characteristics. Eight urban blocks across the city of Nanjing, China, are selected as case examples. The results show that access structure is capable of accurately describing and evaluating complex spatial relationships between streets, plots and buildings. Access structure is potentially a useful method for studying the complex emerging built form of rapidly changing cities, especially in developing countries such as China.

Keywords

Urban form spatial structure urban block Nanjing

Introduction

The hierarchical order of space is a common pattern that can be recognised across different urban forms (Kropf, 2014). The notion of hierarchy is central to various approaches to urban morphology, especially the historico-geographical and process-typological approaches (for example, Caniggia and Maffei, 2001; Conzen, 1960; Whitehand, 2001), and it also underscores many key concepts that have been widely used for analysing and interpreting the formation and transformation of urban form. To better coordinate the studies of different morphological traditions and address different types of ambiguities in defining urban form, Kropf (2014) developed a generic multilevel diagram of urban form that systematically articulates and explicates the hierarchical relations among buildings, plots, streets and other form elements at different scales. As a registration key, this generic multilevel diagram offers a critical tool that can potentially enable more systematic investigation on the diversity of built forms across different contexts (Kropf, 2014). Nevertheless, Kropf’s approach is predominantly qualitative. This can prevent it from being rigorously applied to studying the contemporary cities, where the built form elements are often not clearly delineated but instead diffused and complex. To address this issue, one possible way forward is to systematically quantify the hierarchical relations between the formal elements.

Quantitative studies on the hierarchical structure of urban form are not new to urban morphology, yet existing studies mostly focused on single form element, especially the street (Gil, 2014; Hillier, 1996; Hillier and Hanson, 1984; Hillier et al., 1993; Karimi, 2012; Marshall, 2005, 2016; Penn et al., 1998; Porta et al., 2010; Serra et al., 2016; Turner, 2007; Wagner, 2008). More recent works, such as place syntax (Ståhle et al., 2005), sDNA (Cooper and Chiaradia, 2015) and the Urban Network Analysis Toolbox (Sevtsuk and Mekonnen, 2012), incorporated other urban form elements like buildings and plots into street network analysis. Nevertheless, these elements are not taken as equal, but largely subordinated, to street, and are primarily used to enhance street network analysis.

Other quantitative research mainly focused on the geometric and/or configurational attributes of urban form, often adopting numerical classification methods to develop new urban typologies, rather than measuring its hierarchical structure. For instance, Berghauser Pont and Haupt (2010) for buildings and Demetriou et al. (2013) for plots. Recently, Berghauser Pont et al. (2019) and Bobkova et al. (2019) also combined quantitative assessments of geometric attributes of plots and configurational attributes of streets, and developed new plot typologies that yield new insights on the composition of urban form across different cities in Europe. These studies suggested a new frontier of urban morphology for ‘integrating multi-variable geometric descriptions with inter-scalar relational descriptions of urban form’ (Berghauser Pont et al., 2019: 2).

So far, however, very few efforts have been devoted to systematically quantifying and analysing the hierarchical relations between urban form elements. Marshall (2014, 2015) developed the Area Structure, a mathematical approach that symbolically articulates the generic relations among streets, blocks, plots and buildings. However, while this new method offers an explicit and accurate description of the morphological structure, it does not quantify built form elements and their relations per se. Therefore, to bridge this gap, in this study we develop a new method, deemed access structure, that aims to symbolically describe and quantitatively analyse the hierarchical relations (i.e. access relations) between the three fundamental urban form elements: streets, plots and buildings.

In the following, we will first explain the concept of access structure and how the different types of access structures can be articulated with simple symbols. Then, we introduce how the access structure can be objectively quantified and assessed and compared using different metrics. Subsequently, we test and evaluate this new method first in analysing and unpacking the complex spatial structure of an urban block, and second in identifying and distinguishing urban blocks dating back to different periods of development.

Defining access structure

Access structure describes the hierarchical spatial order of the access starting from the more public street spaces to the semi-private open areas within plots and the more private rooms within buildings. In particular, this method focuses on the abstract relations (i.e. access relations) between the three form elements (voids), but excludes the specific geometric features such as street width, plot size and building area that may affect the ease, but not necessarily the existence, of access. For this reason, our method for describing and analysing access structure is developed mainly based on, and then to expand, the aforementioned Area Structure (Marshall, 2016) and especially the generic multilevel diagram of urban form (Kropf, 2014).

First, it is important to clearly define the abovementioned three types of voids. To minimise the ambiguities in the definition that may rise from different morphological traditions and disciplinary perspectives, we inherit the generic definitions from Kropf (2014). According to the multilevel diagram (Kropf, 2014: 50), these three types of voids altogether constitute a continuous spatial network that connects different built form elements in a sequence and at the same time, each is coextensive with an upper level element, i.e. streets (simple tissues), plots and buildings, respectively. Following this, a street space refers to the constituent part of a simple tissue that functions at the level of plots/plot series by coextension, and it provides direct access to all plots within the simple tissue. The entire street network of a city or an urban area is then a contiguous space consisted of a number of interconnected street spaces. An area within a plot includes all external spaces that function at the same level of the buildings within a plot and together with the buildings form the single entity of the plot. The room then refers to the internal spaces of a building.

While the definitions of area and room are not ambiguous in describing the internal structure of a plot (i.e. areas and buildings) and they are also flexible enough in accommodating more fully the wide range of specific forms of plot (Kropf, 2014), they are nonetheless largely predicted on clear recognition of plots. On this, we first base our understanding of the plot on the notion that plots are important to generating interface and connections between spaces of occupation (i.e. rooms within buildings) and spaces of movement (i.e. street spaces) (Panerai et al., 2004; Vialard, 2012). Second and more important, instead of solely taking the minimalist definition of the plot as a physical form with measurable geographical location for data points (Scheer, 2018), we also see the plot as socially agreed and spatially defining the limit of control (Kropf, 2018, 2019). This is because the plot and its connections to streets and buildings are not always fully defined and controlled by the physical boundaries. Using this definition, we would be able to more accurately recognise the plots based on analysing their formation and transformation in relation to our behaviours.

A clear recognition of the plot is important also because the access relation between street spaces, areas and rooms can vary dramatically at the plot level. These depend on how a plot as the constituent part of one simple tissue (street) relates to other plots on the one hand; and on the other, how buildings and the external spaces as the components of a plot are connected within the composition. In order to more fully capture these variations, we take plots and plot sub-series (which will be explained later) as the unit of analysis for access structure.

As a point of departure, we define the simplest linear access relation between the three types of void as the basic, or ideal, type of access structure (Figure 1a), that is, accessing directly from a street space to an area (of a plot) and then a room (within a building). As we know, however, the access structure of a plot or a plot sub-series in reality is unlikely to take the ideal form. To accommodate the variations, we further develop the access structure based on two key concepts that Kropf coined to interpret the ambiguities of the built form. The first one is interlock, which refers to the morphological composition that there is access to an individual plot from more than one side of the block (single-plot block is a special case of this interlocked form). We inherit this concept and use it to describe the case, whereby a plot, specifically the area of a plot, is concurrently connected to no less than two street spaces (Figure 1b).

Figure 1.

Access structure types and their representations: (a) basic, (b) interlock, (c) co-inflection of areas, (d) co-inflection of buildings, (e) embeddeding.

The second is co-inflection, which refers to a different morphological composition in which there are at least two plots sharing the same building element (rooms within the building are not necessarily shared) yet their areas are not connected with each other, and each can only be accessed separately from the corresponding street space (Figure 1d). As a result, these two plots constitute what Kropf refers to as plot sub-series. We inherit the concept of co-inflection and use it to describe the same case. Moreover, we also develop this concept further and broaden its scope to accommodate a similar case. That is, the areas of two or more plots are interconnected and even shared with each other, yet each plot is separately connected to the street space (though technically one can be accessed from the street space through another), and their buildings are also independent from each other (Figure 1c). We regard this case as the co-inflection of areas and the former as the co-inflection of buildings.

In addition, to achieve a fuller description, we introduce a new concept, embedding, to describe the morphological composition that a plot is not directly bounded by any street spaces, and as a result, its area is connected to the street space through the area of a neighbouring plot (Figure 1e). It is noteworthy, however, that unlike co-inflection of areas, in this case the two plots are not symmetrical because the area of the embedded plot is not shared with the other that provides it with the access. This case is not derived from Krop’s generic multi-level diagram, nor has it been widely discussed in existing studies of urban morphology. However, it can be frequently observed in many contemporary cities, such as cities in China, that have undergone rapid urbanisation and drastic transformation. Often, it is formed as a result of fragmentation of large plots in the absence of clear planning regulations. We will elaborate this in more detail later based on our work on Chinese urban form.

We regard the above four relations among street spaces, areas and rooms as the four complex types of access structure. Together with the basic type, they form the conceptual foundation for our further investigations. We deem the four complex types respectively interlocking type, co-inflected buildings type, co-inflected areas type, and embedded type. These types are certainly far from being able to cover all kinds of built form, and they are not meant to be inclusive. Capturing the most common built forms, however, these five types of access structure together can be considered the common denominators that allow for more comprehensive description and analysis.

Representing access structure

The various types of access structure described above can be represented using symbols at different levels of depth and links between them. As shown in Figure 1, the basic type of access structure can be represented as ‘■—●—▼’, whereby ‘■’ represents street spaces, ‘●’ areas (of plots), ‘▼’ rooms (within buildings), and ‘—’ the links (connections) between these voids. The horizontal lines at different levels of depth represent the hierarchical spatial order starting from streets spaces all the way to rooms (within buildings). Since ‘street space’ is defined as the starting point of the access, the line on which ‘■’ falls can be referred to as the datum line with a depth value of 0. The value of line ascends by depth. However, it is noteworthy that the depth in this representation is not limited to only three levels. For instance, more horizontal lines are needed to clearly represent the embedded type. The representations of the four complex types of access structures are shown as Figure 1(b) to (e).

Measuring access structure

In order to quantitatively describe the access relations, different values are assigned to the symbols and their links according to their levels of depth. For instance, the street space ‘■’ only appears at the depth level 0 and accordingly, it obtains the value 0. Similarly, the area ‘●’ at the depth level n gains the corresponding value n. The case of room ‘▼’ is slightly different. Since the shallowest level of depth at which it can appear is the depth level 2, ‘▼’ at the depth level n obtains the value n–1. As for the link ‘—’, it gains the value n if it connects elements between the depth levels n and n + 1. The link connecting two areas at the same depth level n directly obtains the corresponding value n.

On this basis, we introduce three metrics. First, interlocking degree measures the extent to which the areas of a plot or a plot sub-series are connected to street spaces. It is defined as the ratio of the total number street spaces to the total number of areas that are directly connected to them. The second metric is co-inflecting degree, which is defined as the sum of the co-inflecting area degree and the co-inflecting building degree. The former is used to measure the extent to which the areas within a plot sub-series are interconnected and co-inflected. It can be calculated as the ratio of the sum of the value of connections to neighbouring areas per area to the total value of areas at the same depth level for all levels. Similarly, the latter, which can be quantified as the average value of area-building connections in an access structure, is to measure the extent to which buildings are shared by different plots in a plot sub-series. The last metric, embeddedness, is defined as the average depth of an access structure. It is used to evaluate the ease to reach all areas from the street space(s). Because all three metrics are informed by the complex types of access structure, we regard them as the complexity measure of access structure. The definitions and formulas of the three metrics are shown in Table 1.

Table 1.

Three metrics of the complexity of access structure.

Metrics	Definition	Formula
Interlocking degree	The total number of direct connections between areas and street spaces/the count of areas connected to street spaces.	$I = \frac{γ_{1}}{α_{1}}$
Co-inflecting degree (co-inflecting area degree + co-inflecting building degree)	(The sum of the value of the connections to neighbouring areas per area/the total value of areas of the same level) for all levels + the total value of building-area connections for all levels/the total value of buildings for all levels.	$C = \sum_{i = 1}^{n} (i δ_{i} / i a_{i}) +$ $\sum_{i = 1}^{n} (i - 1) ε_{i} / \sum_{i = 1}^{n} (i - 1) β_{i}$
Embeddedness	The toal value of areas/the total number of areas.	$E = \sum_{i = 1}^{n} i a_{i} / \sum_{i = 1}^{n} a_{i}$

a_i: The number of areas at the depth level i; C: co-inflecting degree; E: embeddedness; i: the depth level; I: interlocking degree; n: the total number of depth levels in an access structure; β_i: The number of buildings in the depth level i; γ_i: The total number of direct connections to street spaces per area at the depth level i; δ_i: The number of connections to neighbouring areas per area at the depth level i; ε_i: The number of connections to corresponding areas per building at the depth level i.

Source: Authors.

The capacity of the three metrics to capture and distinguish the level of complexity of different types of access structure is tested using 25 case examples. We start from the basic type to the four complex types and their derivations, and finally the compound types. As shown in Figure 2, the basic type is shown as the origin O and the four complex types as A1, B1, C1 and D1. The complex types are then progressively further derived. For instance, with regard to interlocking type, the number of street spaces connected with the area increases from 2 to 4 in A1, A2 and A3. After that, the derived results of each complex type are combined to produce the even more complex compound types. On this basis, we calculate the interlocking degree (I), co-inflecting degree (C) and embeddedness (E) of each type shown in Figure 2.

Figure 2.

Representation and the complexity measure of 25 types of access structure.

The results of the complexity measure of the above 25 different types of access structure are plotted in a line chart (Figure 3a). Not surprisingly, the overall complexity (i.e. the aggregate value of the three metrics) of the compound types is generally higher than that of the complex types. However, there are also exceptions. The complexity of some mono types, usually attributed to a single dimension, is occasionally higher than that of the compound types, such that the point of A3 is shown higher than that of A2&B2.

Figure 3.

Complexity metrics of the 25 types of access structure (a) line chart and (b) ternary diagram.

While the line chart does describe the complexity of the different types of access structure, it is nonetheless not fully intuitive to identify the dominant dimension of the complexity of an access structure solely based on the absolute values of these metrics. This is because the same value of a metric may not always indicate the same level of the contribution of the corresponding complexity dimension across different types of access structure. It is therefore necessary to introduce the relative value, so that the dominant feature of the access structure can be more intuitively identified and the different types of access structure can be more clearly compared.

The relative value of interlocking degree, co-inflecting degree and embeddedness for an access structure is defined as the ratio of its absolute value to the aggregate. For example, each of the three metrics of type O has an absolute value of 1; hence, each obtains identical relative values of 0.33. The relative values of all three metrics for the above-described 25 types of access structure are shown in Table 2. For each type, the metric gaining the highest relative value indicates the dominant feature (complexity dimension).

Table 2.

Relative values of the three metrics of complexity for the 25 types of access structure.

	Relative interlocking degree	Relative co-inflecting degree	Relative embeddedness
O	0.33	0.33	0.33
A1	0.50	0.25	0.25
A2	0.60	0.20	0.20
A3	0.67	0.17	0.17
B1	0.25	0.50	0.25
B2	0.23	0.54	0.23
B3	0.22	0.56	0.22
C1	0.30	0.40	0.30
C2	0.29	0.43	0.29
C3	0.28	0.44	0.28
D1	0.29	0.29	0.43
D2	0.25	0.25	0.50
D3	0.22	0.22	0.56
A1&B1	0.33	0.44	0.22
A2&B2	0.29	0.50	0.21
A1&C1	0.39	0.35	0.26
A2&C2	0.35	0.39	0.26
A1&D1	0.44	0.22	0.33
A2&D2	0.50	0.17	0.33
B1&C1	0.23	0.54	0.23
B2&C2	0.21	0.58	0.21
B1&D1	0.25	0.42	0.33
B2&D2	0.23	0.46	0.31
C1&D1	0.20	0.47	0.32
C2&D2	0.28	0.34	0.38

Source: Authors.

To intuitively compare and analyse the different types of access structures, we plot them in a ternary diagram according to the relative value of the three metrics. As Figure 3(b) shows, the X axis of the ternary diagram represents the relative interlocking degree, the Y axis the relative co-inflecting degree and the Z axis the relative embeddedness. The basic type O falls right at the centre because its all three metrics have identical relative values. The closer a point falls towards the centre, the more balanced complexity dimensions the represented type of access structure has. In contrast, if a point falls towards one endpoint (a corner), the represented type of access structure tends to exhibit more evidently the corresponding feature. For instance, the points of A1, A2 and A3 extend away from the centre O along the X axis in a sequence. This means that A3 is strongly dominated by interlocking type, followed by A2 and A1. The points of the other complex types and their derivations exhibit similar patterns.

The points of the compound types are shown falling into the three zones demarcated by the three axes. Taking the compound types A1&C1, A2&C2, A1&B1 and A2&B2 as examples, all their points are found in the upper left zone defined by the X and Y axes. Both A1&C1 and A2&C2 combine the interlocking type and the co-inflected buildings type at different derivation levels. It is evident from the ternary diagram that the former is located relatively closer to corner X, suggesting a stronger feature of interlock, whereas the latter, in contrast, has a stronger feature of co-inflection of buildings. In the case of the compound types combining interlocking type and the co-inflected areas type, namely A1&B1 and A2&B2, the co-inflected areas type is shown clearly standing out as the dominant complexity dimension of both. This feature becomes more evident when the derivation level of the constituent types increases (the point of A2&B2 is shown closer to corner Y than that of A1&B1).

An interesting pattern revealed by the ternary diagram is that the points of those compound types that include either co-inflected areas type or co-inflected buildings type are exclusively gravitated towards corner Y, whereas those comprising embedded type are nonetheless mostly dominated by the other complex types and located far away from corner Z. This seems to indicate that of all the compound types, the two co-inflected types generally tend to be dominant in the complexity of access structure, whereas the influence of embedded type is relatively weaker.

Based on the above analysis, we can tentatively conclude that using the three metrics of complexity, especially their relative values and the ternary diagram, we can accurately and more intuitively identify and compare different types of access structure, i.e. the basic type, the complex types and their derivations, and the compound types. In the following, we place the metrics into a real urban environment for further test and evaluation.

Applying access structure

So far, access structure and its representations and measurements have been discussed based on the plot and plot sub-series as the unit of analysis. Access structure can also be applied to the urban block, which is the resultant urban form of co-inflected streets (Simple tissues) (Kropf, 2014). In the following, using real case examples, we will test the access structure first in untangling the complex spatial structure of urban blocks and second in distinguishing urban blocks dating back to different periods of development.

Morphological analysis of urban blocks

The Gaoloumen block in Nanjing, China, is selected as the case example to examine how the access structure, especially its three metrics of complexity, can be used to analyse and untangle the complex spatial structure of urban blocks. This case example provides an ideal test ground because it encompasses not only a rich variety of formal elements but also diverse types of plot and plot sub-series (Figure 4). For clarity, we give every single plot a unique numerical ID from 1 to 27 and then use English letters to refer to the 11 plots/plot sub-series constituted by them. As explained before, each plot/plot sub-series has its own access structure. The 11 plots/plot sub-series are each connected to the corresponding street spaces S1, S2, S3 and S4 that bound the block. For clarity of presentation and discussion, we will also use the 11 English letters to directly refer to the access structures.

Figure 4.

Case example of the Gaoloumen block: (a) figure-ground mapping showing the access paths to individual buildings, (b) plots and plot sub-series and (c) access structures.

Figure 5(a) shows the representation of the access structures of the Gaoloumen block. Each edge of the outermost square represents one of the four street spaces mentioned above and is regarded as the datum level (depth level 0). As the square offsets equidistantly towards the centre, the depth level increases from 1 to 4. The symbol ‘■’ is placed at the midpoint of each edge of the outermost square, representing the street spaces from which the access structure of the 11 plots/plot sub-series begin. Each access structure is shown as a dotted line box (for clarity of presentation, street spaces are not included in the boxes). The symbols ‘●’ and ‘▼’, denoting areas (of plots) and rooms (within buildings) respectively, are located on the edges of the squares at different levels of depth. The access connections between street spaces, areas and rooms are represented using the links in bold.

Figure 5.

Access structures within the Gaoloumen block: (a) representation and (b) ternary diagram.

All four complex types of access structure can be clearly identified in the representation of the Gaoloumen block. Area ‘● 6’, for example, is connected with both street spaces ‘■ S1’ and ‘■ S2’, and this gives rise to the interlocking type. We can also see that while some pairs of areas, namely, ‘● 2’ and ‘● 3’, ‘● 4’ and ‘● 5’, and ‘●12’ and ‘● 13’, are connected respectively to buildings ‘▼ 2&3’, ‘▼ 4&5’ and ‘▼ 12&13’, producing the co-inflected buildings type, the other pairs of areas, such as ‘● 1’ and ‘● 3’, and ‘● 21’ and ‘● 22’, are interconnected and produce the co-inflected areas type. The embedded type can be identified straightforwardly by looking at the squares at the different levels of depth. It is evident that access structure j is the deepest one in which three progressively embedded plots span across four levels of depth.

Based on the representation, we calculate the three metrics for all 11 access structures. Both their absolute and their relative values are listed in Table 3. They are also plotted in the ternary diagram shown in Figure 5(b). The 11 access structures exhibit 9 different types. Specifically, access structures g, h and k are the basic type, and the corresponding points overlap with each other, falling right at the geometric centre of the ternary diagram. Access structures d and j are of, or derived from, the embedded type. Both have identical absolute values of interlocking degree and co-inflecting degree, both being 1, and higher value of embeddedness. Therefore, in the ternary diagram, their points are distributed, depending on their relative values of embeddedness, along axis Z from the centre to corner Z. Another complex type, co-inflected buildings type, can be seen in access structure a, of which the point falls on the Y axis. Access structure b is the compound type that combines interlocking type and co-inflected buildings type, and its point is found in the upper left zone of the ternary diagram. Similarly, access structures c and e are both of the combination of co-inflected buildings type and embedded type, with the former type more evident. Access structures f and i are both of the compound types comprising interlocking type and embedded type. The former feature of access structure f is more conspicuous since it is clear from the ternary diagram that its point more closely approaches corner X. In contrast, the point i is closer to corner Z, so the more conspicuous feature of access structure i is the latter feature.

Table 3.

Access structures of the Gaoloumen block and their complexity measure.

Access structure (Plot sub-series)	Plot	Interlocking degree	Co-inflecting degree	Embeddedness	Relative Interlocking degree	Relative co-inflecting degree	Relative embeddedness
a	1, 2, 3	1	2	1	0.25	0.50	0.25
b	4, 5, 6	1.33	1.67	1	0.33	0.42	0.25
c	7, 8, 9	1	1.8	1.67	0.23	0.38	0.38
d	10, 11	1	1	1.5	0.29	0.29	0.43
e	12, 13, 14, 15, 16	1	1.29	1.4	0.26	0.37	0.37
f	17, 18	2	1	1.5	0.44	0.22	0.33
g	19	1	1	1	0.33	0.33	0.33
h	20	1	1	1	0.33	0.33	0.33
i	21, 22	1.5	2	1	0.33	0.44	0.22
j	23, 24, 25, 26	1	1	2	0.25	0.25	0.50
k	27	1	1	1	0.33	0.33	0.33

Source: Authors.

As the case example reveals, the access structure can clearly describe and effectively capture the intricate spatial structure of the Gaoloumen block and the tangled relationships among street spaces, plots (areas) and buildings (rooms). In particular, the three metrics of complexity together with the ternary diagram are shown to be useful in accurately analysing different types of access structure and distinctively comparing and contrasting their nuanced complexity.

Comparing urban blocks of different periods of development

There has been a consensus in the field of urban morphology that because of the different social and economic processes of the city, built forms of different periods of development usually exhibit distinct characteristics (Kropf, 2009; Moudon, 1986; Scheer, 2016). The distinctions lie not only in the specific configuration of formal elements but also in the ways in which these elements are connected and organised to constitute a larger entity. Therefore, it is not unreasonable to hypothesise that the access structure is also capable of capturing and differentiating built forms that date back to different periods of development. In the following, we will test this hypothesis using urban blocks in the city of Nanjing, China, that originates from different periods of development.

In the course of urban development in modern China, the land use system largely shaped the social and economic practices in the different periods of development and exerted significant influences on the formation and transformation of urban form (Liang and Sun, 2007; Sun and Xi, 2003). Therefore, according to the changes in the land use system, the urban development process of Nanjing can be divided into four stages (Supplementary Table 1). Eight representative blocks (two for each stage) are selected for the test (Supplementary Figure 1). The details of the land use system and the corresponding characteristic urban form of each development stage can be found in the supplementary materials. In the following, we will focus on analysing and comparing the access structure of all eight case examples.

Briefly, case examples A and B (first stage) were both formed at the period of time before 1949 when land was privately owned and could be freely traded. The access structures of most plots are of the basic type, despite that case example B clearly exhibits irregular layout of streets and plots (Figure 6a and b). The second stage of development was under the planned economy between 1949 and early 1980s. Case example C is the Gaoloumen block that was discussed in detail in the previous section. In contrast, case example D is a typical compound (Danwei) with a small number of plots along streets transformed to accommodate some public amenities. While the access structures of the plots along the streets are mostly of the basic type, the embedded type can usually be identified inside the block (Figure 6d). The third stage of development was primarily driven by the immature market economy right after the 1980s and lacking of regulations. As a result, the access structures of plots for both case examples E and F are generally complex, including different complex types and compound types (Figure 6e and f). Case examples G and H of the last stage of development were built after 2000 following more systematic land use planning. In particular, the former is single plot for business use, and its access structure is an extreme case of the interlocking type, in which the plot is directly connected to all four surrounding street spaces (Figure 6g).

Figure 6.

Figure-ground map with access paths, plot and plot sub-series, and the representation of the access structure of eight case examples.

The complexity metrics of the aggregate access structures for the eight case examples are calculated (Table 4), and the eight aggregate access structures are plotted onto the ternary diagram (Figure 7). On this basis, the characteristic built forms pertaining to the four periods of development can be clearly distinguished. As shown in Figure 7, the points of the two blocks of the first stage are located around the centre of the diagram. Block A obtains identical relative values for all three metrics and its point falls exactly at the geometric centre. Slightly different, the point of block B is located right next to block A on the Z axis, suggesting that the access structures of its plot and plot sub-series primarily consist of the basic type and the embedded type.

Table 4.

Complexity measures of the aggregate access structures of eight case examples.

	Interlocking degree	Co-inflecting degree	Embeddedness	Relative interlocking degree	Relative co-inflecting degree	Relative embeddedness
A	1	1	1	0.33	0.33	0.33
B	1	1	1.09	0.32	0.32	0.35
C	1.17	1.40	1.37	0.30	0.36	0.35
D	1.04	1.12	1.32	0.30	0.32	0.38
E	1.36	1.72	1.07	0.33	0.41	0.26
F	1.33	2.66	1	0.27	0.53	0.20
G	4	1	1	0.67	0.17	0.17
H	2.25	1.5	1	0.47	0.32	0.21

Source: Authors.

Figure 7.

Ternary diagram of the aggregate access structures of eight case examples.

For the second stage, both blocks C and D contain many plot sub-series, of which the access structures are of the compound type that combines the co-inflected buildings/areas types and embedded type. Their points therefore fall in the lower part of the ternary diagram. While block C has almost the same relative value of co-inflecting degree end embeddedness with the corresponding point located at an equal distance to both corners X and Z, the point of block D is slightly inclined to the Z axis, suggesting that its plot sub-series in general exhibit a stronger feature of embedding. The difference between C and D shown in the diagram accurately reflects the aforementioned different metamorphosis of these two blocks. It is noteworthy that compared with the locations of the four points representing the case examples of the third and fourth stages, those of blocks C and D are much closer to the centre of the diagram. This means that the plot sub-series of these two blocks have relatively balanced features of interlock, co-inflection and embedding.

For the third stage, it is evident that the points of blocks E and F fall in the upper left zone and close to the Y axis. This suggests that the access structures of both blocks are dominated by the co-inflected buildings/areas types followed by interlocking type. The point of block F is located relatively close to corner Y, which means that its access structures in general exhibit a stronger feature of co-inflection.

For the last stage, the access structures of both blocks G and H show an obvious feature of interlock. In particular, the access structures of block G are largely dominated by the interlocking type, as its point is clearly approaching corner X. In contrast, the access structures of block H are generally more balanced, combining both the co-inflected buildings/areas type and the interlocking type. Its point is located farther away from corner X in the upper left zone.

Regarding the production of different complex types of access structure, at the first stage when the land ownership was private, all buildings were built strictly following the property/physical boundaries of plots, and the access relations between street spaces, areas and rooms (buildings) were explicitly defined. As a result, the access structures of plots and plot sub-series are mostly of the basic type. Block A was systematically planned and built, and the relationships of its formal elements are more easily recognisable than those of block B, which were formed through a more spontaneous process. Along with the continuous growth of super plots, which were formed either as a result of the accretion of small-scale plots or the wholesale construction of compounds (Danwei), and the growing demand of modern buildings and transportation facilities, an increasing number of plots became connected with two or more street spaces, making the interlocking type very common. From the variation in the three complexity metrics of the aggregate access structure of all eight blocks, we can see that interlocking type increasingly becomes an evident type of access structure for plots through the transformation from traditional cities to modernist cities.

The co-inflected buildings/areas types were formed in two different approaches. One is the result of the mix and integration of different land uses in urban planning and development such as that block H integrates residential buildings and commercial buildings following the master plan. The other approach is through continuous changes introduced to urban blocks by users in their everyday practice. In blocks C, D, E and F, the co-inflected buildings type was produced because that many users, in response to the insufficient supply of everyday life amenities, tore down some building walls and converted their residential units into commercial facilities. As the ternary diagram shows, blocks E and F are mroe dominated by this feature than blocks C and D. These two approaches contribute considerably to the pervasiveness of the co-inflected buildings type. As seen from the distribution of the eight points in the ternary diagram, the blocks of the second, third and fourth stages are all characterised by the feature of co-inflection.

The embedded type seems to germinate from the second stage, the transition period. This type of access structure is directly associated with the hierarchy level of the plot sub-series. That is why blocks B, C and D all exhibit an obvious feature of embedding, while the blocks of the following two periods, which lack hierarchical plot sub-series, show the opposite. This is also to say that the embedded type is more likely to come into existence in the case where super blocks contain a large number of small plots. In the modernist city where small blocks usually consist of a limited number of large plots, this type of access structure is less likely.

Conclusions

In this study, we have developed a new method, access structure, that can symbolically describe and quantitatively analyse and compare the hierarchical relations between three key urban form elements, namely streets, plots and buildings. Specifically, the method unpacks the spatial order encapsulated in the continuous access that usually starts from the more public street spaces to the semi-private areas within plots and the more private rooms within buildings. We have described how the access structure can be represented using symbols and links, and on this basis, how it can be objectively measured and assessed using three metrics. These then enabled accurate description and comparison of different types of access structure. Finally, using eight urban blocks in Nanjing, China, we tested and proved the usefulness of this new method in untangling the complex spatial structure of urban blocks as well as in distinguishing urban blocks dating back to different periods of development.

This method is developed based on, and also to expand, Marshall’s (2014, 2015) Area Structure and especially Kropf’s (2014) generic multilevel diagram of urban form. In particular, the three types of voids, namely street spaces, areas and rooms, that each individually is coextensive with streets (simple tissues), plots and buildings and altogether constitute a continuous spatial network of access are adopted as the basis for defining access structure. Two key concepts, interlock and co-inflection, that were used to address the ambiguities in defining urban form in contemporary cities are adapted and expanded to develop the basic type and four complex types of access structure as well as the three metrics of access structure. From this perspective, this study potentially suggests a possibility for objectively quantifying the hierarchical relations between different form elements in Kropf’s generic multilevel diagram, and rigorously applying this useful tool, which is qualitative in nature, to studying and comparing various urban forms.

More importantly, this study contributes to the quantitative description and analysis of urban form by starting to bridge a methodological gap. Existing studies investigating on the hierarchical structure of urban form mostly focus on a single form element, i.e. street, whereas other quantitative studies mainly examine the specific geometric and configurational properties of urban form, but not its hierarchical structure. Quantifying the basic relations (i.e. access relations) between streets, plots and buildings, this study is an initial attempt to address the lack of research on the hierarchical relations between urban form elements. It is also hoped that this study can serve as the starting point of a series of endeavours to connect and integrate different quantitative methods for studying urban form.

Last, despite that the theoretical basis of the access structure is rooted in the urban form discourse based on the development of Western cities, we deliberately selected the urban blocks in a Chinese city as case examples for testing and evaluating the method. The main reason is that, compared to cities in the West, the urban form of cities in East and Southeast Asia in general lacks continuity due to drastic changes in their urban development, hence producing diffused urban form and complex spatial relationships between built form elements. It is presumed that if the access structure can survive the tests based on the case examples of a Chinese city, it should be a fairly useful tool to study and even compare urban form of various cities. Moreover, provided the increasingly rapid transformation of cities in many developing countries in East and Southeast Asia, these tests also provide direct evidences and references for using access structure to investigate the growing complexity of urban form of these cities. However, at the same time, this strategy also poses limitations to this study by constraining it to a single context. More empirical studies are definitely needed to test, verify and refine this new method in different social and cultural contexts. Equal attentions in future research should also be paid to issues such as how this method can be incorporated into urban planning and design and how it may inform urban policy making.

Supplemental Material

sj-pdf-1-epb-10.1177_2399808320988560 - Supplemental material for Access structure

Supplemental material, sj-pdf-1-epb-10.1177_2399808320988560 for Access structure by Yacheng Song, Ye Zhang and Dongqing Han in Environment and Planning B: Urban Analytics and City Science

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Research for this paper was supported in part by the National Natural Science Foundation of China, for project “Analysis and optimization of superblock morphology based on the measurement of ‘scaling hierarchy and access structure’” (Program No. 52008082), January 2021–December 2023.

ORCID iD

Ye Zhang

Supplemental material

Supplemental material for this article is available online.

Biographical notes

Yacheng Song, PhD, is a Lecturer at Department of Architecture, School of Architecture, Southeast University. He is engaged in the teaching, research and practice of urban design. He focuses on the improvement and optimisation of urban morphological methods to analyse China’s urban form, and apply them to the urban design practice. He recently studies on the quantitative description method of the complexity of urban block form.

Ye Zhang is an Assistant Professor at the Department of Architecture, School of Design and Environment, National University of Singapore. His principal research interest resides in synergising different methods for understanding and analysing the built form. Ye has published widely in the field of urban morphology and urban design. He is now the programme director of Master of Arts in Urban Design (MAUD) at NUS and also serving as the director general of the International Forum on Urbanism (IFoU).

Dongqing Han, PhD, is a professor at Department of Architecture, School of Architecture, Southeast University. As the discipline leader in SEU, he teaches courses of urban design and architectural design. He is now the executive director of Architectural Society of China, which is the most important academic organization in China. He emphasizes the combination of theory and practice, and has widely published papers in the field of urban design and won many national practical awards

References

Berghauser Pont

Haupt

(2010) Spacematrix. Rotterdam: NAi Publishers.

Berghauser Pont

Marcus

Stavroulaki

, et al. (2019) The spatial distribution and frequency of street, plot and building types, across five cities identifying common as well as unique traits. Environment and Planning B 46(7): 1226–1242.

Bobkova

Berghauser Pont

Marcus

(2019) Towards analytical typologies of plot systems: Quantitative profile of five European cities. Environment and Planning B: Urban Analytics and City Science. Epub ahead of print 14 October 2019. DOI: 10.1177/2399808319880902.

Caniggia

Maffei

(2001) Architectural Composition and Building Typology: Interpreting, Basic Building. Firenze: Alinea.

Conzen

MRG

(1960) Alnwick, Northumberland: A Study in Town-Plan Analysis. Institute of British Geographers Publication 27. London: George Philip.

Cooper

CHV

Chiaradia

(2015) sDNA: How and why we reinvented spatial network analysis for health, economics and active modes of transport. In: GISRUK 2015 proceedings (ed. N Malleson), Leeds, UK, 15–17 April 2015, pp.122–127. Leeds: University of Leeds Publishing.

Demetriou

Stillwell

See

(2013) A GIS-based shape index for land parcels. In: First international conference on remote sensing and geoinformation of the environment, Paphos, Cyprus, 8–10 April 2013.

Gil

(2014) Analyzing the configuration of multimodal urban networks. Geographical Analysis 46: 368–391.

Hillier

(1996) Space is the Machine. Cambridge: Cambridge University Press, electronic edition.

10.

Hillier

Hanson

(1984) The Social Logic of Space. Cambridge: Cambridge University Press.

11.

Hillier

Penn

Hanson

, et al. (1993) Natural movement: Or, configuration and attraction in urban pedestrian movement. Environment and Planning B: Planning and Design 20(1): 29–66.

12.

Karimi

(2012) A configurational approach to analytical urban design: ‘Space syntax’ methodology. Urban Design International 17(4): 297–318.

13.

Kropf

(2009) Aspects of urban form. Urban Morphology 13(2): 105–120.

14.

Kropf

(2014) Ambiguity in the definition of built form. Urban Morphology 18: 41–57.

15.

Kropf

(2018) Plots, property and behaviour. Urban Morphology 22(1): 1–10.

16.

Kropf

(2019) Plots, formalism and the limits of the minimal. Urban Morphology 23(1): 84–86.

17.

Liang

Sun

(2007) Pattern and Mechanism-the Urban Transformation of City Centers in China. Beijing: China Architecture & Building Press.

18.

Marshall

(2005) Streets and Patterns. London and New York: Spon Press.

19.

Marshall

(2014) A symbolic articulation of morphological structure. Urban Morphology 18: 73–75.

20.

Marshall

(2015) An area structure approach to morphological representation and analysis. Urban Morphology 19: 117–134.

21.

Marshall

(2016) Line structure representation for road network analysis. Journal of Transport and Land Use 9(1): 29–64.

22.

Moudon

(1986) Built for Change: Neighborhood Architecture in San Francisco. Cambridge: MIT Press.

23.

Panerai P, Castex J, Depaule J, et al. (2004) Urban Forms: Death and Life of the Urban Block. Oxford: Architectural Press

24.

Penn

Hillier

Banister

, et al. (1998) Configurational modeling of urban movement networks. Environment and Planning B: Planning and Design 25: 59–84.

25.

Porta

Latora

Strano

(2010) Networks in Urban Design. Six Years of Research in Multiple Centrality Assessment, Network Science: Complexity in Nature and Technology. London: Springer, pp.107–130.

26.

Scheer

(2016) The epistemology of urban morphology. Urban Morphology 20(1): 5–17.

27.

Scheer

(2018) Towards a minimalist definition of the plot. Urban Morphology 22(2): 162–163.

28.

Sevtsuk

Mekonnen

(2012) Urban network analysis toolbox. International Journal of Geomatics and Spatial Analysis 22(2): 287–305.

29.

Ståhle

Marcus

Karlström

(2005) Place syntax: Geographic accessibility with axial lines in GIS//Space Syntax Steering Committee. In: 5th International space syntax symposium, Delft, the Netherlands, 13–17 June 2005, pp.131–144. Amsterdam: Techne Press.

30.

Sun

(2003) Thinking on the land use right and urban planning development. City Planning Review 27: 12–16.

31.

Turner

(2007) From axial to road-centre lines: A new representation for space syntax and a new model of route choice for transport network analysis. Environment and Planning B: Planning and Design 34(3): 539–555.

32.

Vialard

(2012) Measures of the fit between street network, urban blocks and building footprints. In: Eighth international space syntax symposium, pp.8101:1–8101:16.

33.

Wagner

(2008) On the metric, topological and functional structures of urban networks. Physica A: Statistical Mechanics and Its Applications 387(8–9): 2120–2132.

34.

Wang

(2010) A study on situations and prospects of China’s regulatory planning. Urban Planning Forum 87–97: 188.

35.

Zhou

(2011) Legislation and formulation logic of regulatory detailed planning. City Planning Review 35: 60–65.

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