A study of aerial courtyard of super high-rise building based on optimisation of space structure

In traditional architectures, courtyard space is not only the core for organising transportation and function, but also the place for group interaction [1], which affects the design and usage of architectural space in various aspects. The purpose of space in modern super high-rise buildings is often very clear, but such space always exists as a highly independent functional module, rather than integrating with public space, which is an inhumane aspect of design. The design of aerial courtyard helps to reproduce courtyard space in super high-rise buildings, create a shared space integrating transportation organising, recreation and sightseeing, naturally constructed scene and other elements [2], and provide quality interaction place on higher floors that are too far from the ground. These may improve the environment of higher floors, help people there to relax and recover physically and mentally, and become important means and factors to be considered when constructing vertical city [3].

Aerial courtyard implanted in super high-rise building increases a space type different from traditional ones, optimises architectural space structure, modifies a building’s own functional system and can operate stably for a long term. In the aspect of architectural function, aerial courtyard, as an interaction space, can effectively promote people’s spontaneous activities, and stimulate the vitality inside a building; from space structure, aerial courtyard functions as a multi-function adaptive space and its connecting area is distributed in different functional module which can not only adapt to capacity expansion of different functional modules, but also promotes interaction between functional modules, so as to optimise architectural space structure. Functional interaction refers to that different types of functions of super high-rise buildings promote and influence each other initiatively in the process of interactions and cooperation [4]. Functional interaction may cause communication, motivate potential activity and behaviour of various crowds, and give play to and even improve the functional efficiency of architectural space.

The paper uses the space syntax theory and method, integrates relevant software to predict the space use modes objectively and scientifically, and quantitatively analyses the optimisation of spatial topological relations and space structure by implanting aerial courtyards [5]. By this way, the decision-makers can be provided with theoretical basis and data support for the design of aerial courtyard, and the research can have better design guidance significance. In existing studies, space syntax is mostly applied in the analysis of plane space structure of commercial buildings, but few topic research focus on longitudinal space structure, and the study on space syntax for super high-rise building is rarely seen. Li Yan et al. [6] use space syntax to accurately forecast the commercial foot passenger distribution of shopping centre under different space organisation modes, which verifies the quantitative analysis ability of space structure; Kong Weitan et al. [7] implemented real-time syntax analysis of block-type commercial architectural complex and established the space structure optimisation method; Zhuang Yu et al. [8] applied space syntax theory in three-dimensional level to analyse the relation between the flow of people in multi-storey commercial space and its space organisation and structure, and thus make space syntax to expand longitudinally.

This paper studies and summaries the planning and organising mode of aerial courtyard, and further, the paper consider it as a research sample before establishing a corresponding topological structure model. By using Grasshopper-based space syntax arithmetic, the spatial topological structure of super high-rise building under different space organising modes is analysed and worked out [9], and the influence of aerial courtyard on space structure of super high-rise building and its acting mechanism are discussed.

Based on the analytic results of topological structure of selected research samples, the Samples III, V and VI with better topological structures were selected for further design optimisation research. According to the analytic results and data in Tables 4 and 5 and the comparison of simulation results of Samples II and V, it can be inferred that setting aerial courtyards between vertical transportation space and functional space can effectively promote the integration of aerial courtyards and motivate the generation of public activities. Comparing the simulation results of Samples III and IV, it can be inferred that constructing the topological relation between adjacent aerial courtyards can effectively improve the integration of aerial courtyards and optimise overall topological structure. Comparing the simulation results of aerial courtyards with different positions in Sample VI, it can be inferred that the aerial courtyards connected directly with vertical transportation space have higher integration and better accessibility than those with no connection. Depending on the above inferences, topological structural optimisation schemes were proposed for Samples III, V and VI, respectively, and subsequently the optimisation schemes were substituted into the completed topological structural analysis program to obtain new analytic results. Then, it was compared with the scheme before optimisation to verify whether above inferences were correct or not, and then, a design strategy for aerial courtyards of super high-rise building based on topological structural optimisation objective was proposed at the end.

Optimisation scheme for Sample III: adjust the position of aerial courtyards in overall topological structure to form a topological structural pattern of Spaces D-C-AB, as shown in Table 6: Sample III-Optimised. The local and overall variables of topological structural nodes were figured out as shown in Table 7. From the perspective of local variables, the integration of implanting aerial courtyards has been significantly promoted from 1.759 before optimisation to 2.028. Aerial courtyards, as space backbone to connect all usable space of high-rise, are located more centrally in overall topological structure. The integration of vertical transportation space falls from 10.157 to 3.386, indicating that vertically connected aerial courtyards could undertake the function of diverting vertical transportation and greatly reduce transportation load pressure of vertical transportation space. From the perspective of overall variables, the value of R² is 0.7669 based on the scatter diagrams of integration and connectivity of topological structure for Sample III-before optimisation as shown in Table 6, and this value is increased to 0.873 after optimisation, which indicates that spatial structural intelligibility is greatly improved. Based on the calculation results of overall and local variables, it is known that setting aerial courtyards between core walls and functional rooms can not only promote the intelligibility of overall spatial structure but also activate aerial courtyards, so it is considered as a better overall topological structure.

Optimisation scheme for Sample V: There will be no change in the original topological structural pattern, but only i topological connection between adjacent aerial courtyards is increased to form a new spatial topological structure, as shown in Table 6: Sample V-optimised. Local and overall variables of topological structural nodes were worked out according to space syntax, as shown in Table 7. From the perspective of local variables, it is known based on calculation results that the integration of aerial courtyards with increased topological connections has significantly improved, with a higher increase than other usable space. Therein, due to the addition of two direct topological connections (see red lines in the figure), the integration of space C2 rises to 3.315, local spatial connection has been improved, and the integration of overall spatial structure nodes has been optimised to some extent. From the perspective of overall variables, it is observed that the value of R² is 0.8721 in the scatter diagram of connectivity and integration of topological structure for Sample V-before optimisation as in Table 6, and the value is improved to 0.9492 after optimisation, which indicates that the spatial structural intelligibility is greatly improved. Based on the comprehensive consideration of overall and local variables, it is observed that increasing the topological connection between adjacent aerial courtyards can greatly improve integration and accessibility of aerial courtyards without changing its architectural spatial structure.

Optimisation scheme for Sample VI: The topological structural relation of spaces AB and C is not changed, space D is divided into two sub-spaces D1 and D2, that is, vertical transportation space dispersedly arranged and the topological connection between them and aerial courtyards (see red lines in the figure) is increased, as shown in Table 6: Sample VI-optimised. The local and overall variables of topological structure nodes were figured out, as shown in Table 7. From a perspective of local variables, it is known from the calculated results that the integration of implanting aerial courtyards has been significantly improved compared to that before optimisation, with average integration improved from 2.245 to 2.597, especially for the aerial courtyards originally located far from vertical transportation space. From the perspective of overall variables, in the scatter diagram of connectivity and integration of topological structure for Sample VI-before optimisation in Table 6, the value of R² is 0.7768, and it is increased to 0.8947 after optimisation, which indicates the spatial structural intelligibility is largely improved. From the calculated results of overall and local variables, it is known that arranging vertical transportation space dispersedly is conducive to increasing the direct topological connection between aerial courtyards and vertical transportation space and forming a topological structure with higher integration and accessibility. This not only helps users to understand overall structure and easily perceive space and orientation, but also effectively activates aerial courtyards and facilitates the generation of pubic activities in the higher floors.

Implanting connected aerial courtyards in high-rise space could enable the spaces to form an overall spatial topological structure, and thus can achieve the purpose of increasing spatial integration and intelligibility by increasing connections between different spaces. For the usable spaces with lower integration, the increase in connections has limited effect on the improvement of overall structure. For aerial courtyards with higher integration, the construction of connections between them has a significant effect on the improvement of overall structure. Based on the above analysis, the summary of aerial courtyard design method may provide guidance on the spatial structural optimisation design of super high-rise buildings.

In the cases of existing super high-rise building, many of them can be improved in internal space accessibility by the design of aerial courtyards, so as to optimise overall spatial structure. For example, in Sentafei Tower (Fig. 1) designed by Yang Jingwen, several aerial courtyards with different sizes and functions are distributed at different heights and locations of the building, which use up-and-down connected vertical atrium to promote their connections and become a scenic courtyard system extending from underground space to the top of building. By this way, adjacent aerial courtyards may have visual connection. Some aerial courtyards even have direct transportation connection and they are connected by escalator to form a well-integrated aerial courtyard system, which effectively promotes space accessibility inside the building and activates the vitality of building.

Fig. 1

In Shenzhen Vertical City project designed by WOHA (Fig. 2), the high-rise public spaces are expanded as aerial courtyards and arranged between functional rooms and vertical transportation spaces, which turn out to be important places for human’s public activities in higher floors and motivate the generation of interpersonal communication. The core walls are divided into four parts and arranged to form connected aerial courtyards, and adjacent aerial courtyards are linked by escalator, which construct a direct traffic connection and form a street system that provides green scenery and public domain. This design can effectively improve the potential of each spaces to attract traffic, facilitate the generation of public interaction activities in higher floors, help building users to keep a healthy state, and implement an ecological and long-acting design of super high-rise building.

Fig. 2

Based on the space syntax theory system and its analytic method, the paper uses digital programming technique to establish a wholly connected script program to form a real-time interactive logic loop and forecast the use mode of super high-rise building space. It contributes to realising the combination of spatial structure analysis and optimisation in the process of design and research, and achieves the purpose of promoting design through research. From the analytic results, the following conclusions can be drawn:

Aerial courtyards are set between vertical transportation space and functional space as a transition of public space and private space, which not only forms a spatial sequence with rich layers but also promotes the use efficiency of aerial courtyards.