The independent super high-rise building weakens and reduces the cooperation of functional subsystems. Implanting aerial courtyards could improve the aerial environment of that corresponding floor and enable the plane courtyards to be stereoscopic. Constructing multiple aerial courtyard-centred functional clusters of higher floors can optimise the overall space structural relationship. The paper uses the space syntax theory to discuss how to construct holistically linked aerial courtyards in a super high-rise building and applies the Grasshopper-based space syntax arithmetic logical unit to analyse and calculate the aerial courtyard of super high-rise building in different space structure modes, and also proposes design optimisation strategies based on these analyses. The paper points out that by setting aerial courtyard between vertical transportation space and functional space, establishing a direct connection between adjacent aerial courtyards, arranging vertical transportation space dispersedly and so on, it is possible to promote vertical cooperative effect, enhance integration and intelligibility of entire space structure, and provide guidelines and foundation for the construction of vertical cities.

#### Keywords

- aerial courtyard
- super high-rise building
- optimisation of space structure
- space syntax

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.

Space syntax is a theoretical method used to explore the language and essence of architectural and urban space mode, and also an organic combination of space and human activities [10]. In space syntax theory, space itself is not important and what’s important is the space itself and mutual geometrical relationship, including topological structure relation. Such relation determines people’s individual and social knowledge about space, confines how people use space, and further affects people’s daily life, social and economic activities [11].

In the study of topological structure under space syntax, by removing the GPS coordinate information of entire space system, an abstractly extracted topological model is established to examine the relations between spaces [12]. In the proposed model, topological structure chart can be redrawn to many states, which is called “Relationship Remapping”. After performing spatial remapping, topological structure relation of space system becomes simple and intuitive, and this is convenient for making a comparative study of different spatial structures.

The aerial courtyards of super high-rise building are in many different forms, with different space relations and topological structures. For the convenience of further study, according to different layout, the aerial courtyards are summarised in five basic forms, namely independent, continuous, integrated, sectional and scattered forms. The paper takes these 5 aerial courtyard forms as research object and adds the traditional super high-rise building without aerial courtyard as research control, to constitute 6 research samples (see Table 1) and carry out follow-up space syntax study.

Research sample.

Common software for space syntax research are DepthmapX, axwoman, and sDNA, et al. But these software require the establishment of complex ‘unit’ and ‘connection’ by manual work at input terminal, which will take a lot of time in repetitive work during early pre-processing when there are several groups of research models, thus affecting research efficiency. Establishing early topological model by virtue of digital programming technique is an effective way to improve research efficiency. The Rhino-based Grasshopper plug-in is used as parametric platform to conduct follow-up investigation.

Topological structure diagram^{1)} is used to handle the selected research samples, create a series of script programs in Grasshopper platform, analyse topological structure variables of sample space and the results by visual figure expression [13]. In the process of design and research, digital programming technique is used to establish the script program of entire connection, to form a real-time interactive logic loop and to realise an architectural design based on optimised space structure.

Because of the diversified space types of super high-rise buildings, the space structures of selected research samples is demonstrated by typified diagrams to adapt to research logic of space syntax,. The study refers to the architectural space classification method proposed by a Chinese scholar named Zhuang Weimin in his works named

Diagrams for space types AB, C and D.

The main space description method used in the paper is topological structure relation, and the corresponding descriptive model is topological structure model. The basic research variables of space syntax include depth, connectivity, control, integration, intelligibility, etc., which describe spatial structure system on basis of above parameters of topological structure operations. This study considers integration^{2)} and intelligibility^{3)} of space syntax operation results as the main basic principle and factors to analyse the space topological structure of selected research samples. Therein, integration examines the accessibility of space unit and describes the potential of a space to gather crowds and attract traffic; while, intelligibility examines how easy it is to understand a spatial structure, a higher intelligibility indicates people are easier to understand the entire spatial structure system through the experience of local space.

The usable space of each floor and the implanted aerial courtyard are taken as the space nodes, and the topological connection relation between spaces is used to construct the interlinkage between elements, so as to form the topological structure of spatial relation. The connectivity of space nodes in topological structure is calculated and further the integration of space nodes is performed and intelligibility of topological structure space, R^{2}, is solved based on the scatter diagrams of integration and connectivity. If R^{2} is above 0.5, it is considered to have a better fitting degree. If R^{2} is above 0.7, it is considered to have a very good correlation and high intelligibility when using linear approximation to simulate scatter distribution [14, 15].

By remapping space relation, the topological structure models of selected samples (Table 3) were built, making its topological relation easy and visual and facilitating further study.

Topological structure model.

After getting the spatial topological structure diagram by early pre-processing, wholly interactive space syntax research script program of research samples is built using programming in Grasshopper, and analytic operation are performed subsequently and the results are obtained. By reference to the formula of depth, connectivity, control, integration and other parameters in space syntax theory algorithm, the digital programming module was used to create program script, so as to implement the translation of analytic operation results of space topological structure. Then, the display module of Grasshopper platform is used to make visual representation of operation results and obtained the analytic result diagram, as shown in Table 4.

Topological structure analysis diagram.

Grasshopper-based digital programming ensures that the data generated in analysis process can be automatically transferred in the computer, and the analytic results can be auto-saved, which reduces the data error caused by link transformation between different software, and thus maximise the accuracy of research data. The operation module interface of Grasshopper platform was used to auto-export data (Table 5) and carry out correlation analysis of integration and connectivity of variables in space syntax calculation. Based on the scatter diagram of Cn and Rn (Table 4), R^{2} was solved, to describe the intelligibility of topological structure space. The accessibility of functional space (space AB) in super high-rise building is largely related to its own function but less affected by topological structure. Therefore, this paper emphasises on the vertical traffic space (space D) and aerial courtyard (space C), and studies how to divert stream of people reasonably, so as to reduce the traffic load pressure of vertical traffic space, and improve the utilisation and accessibility aerial courtyard.

Connectivity and integration of sample space.

Sample I | Sample II | Sample III | Sample IV | Sample V | Sample VI | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Space | Connectivity | Integration | Integration | Connectivity | Integration | Integration | Connectivity | Integration | Integration | Connect ivity | Integration | Integration | Connectivity | Integration | Integration | Connectivity | Integration |

D1 | 21 | 49.322 | D1 | 21 | 18.784 | D1 | 21 | 10.157 | D1 | 16 | 13.086 | D1 | 12 | 4.696 | D1 | 11 | 4.135 |

AB1 | 2 | 2.466 | AB2 | 1 | 2.167 | AB2 | 2 | 2.294 | AB2 | 2 | 2.066 | AB2 | 1 | 1.610 | AB2 | 1 | 1.234 |

AB2 | 2 | 2.466 | AB2 | 1 | 2.167 | AB2 | 2 | 2.294 | AB2 | 2 | 2.066 | AB2 | 1 | 1.127 | AB2 | 1 | 1.234 |

AB3 | 1 | 2.242 | AB3 | 1 | 2.167 | AB3 | 2 | 2.294 | AB3 | 2 | 2.066 | AB3 | 1 | 1.127 | AB3 | 2 | 1.356 |

AB4 | 1 | 2.242 | AB4 | 2 | 2.348 | AB4 | 2 | 2.370 | AB4 | 2 | 2.066 | AB4 | 1 | 1.127 | AB4 | 2 | 1.838 |

AB5 | 1 | 2.242 | AB5 | 2 | 2.348 | AB5 | 2 | 2.370 | AB5 | 2 | 2.066 | AB5 | 1 | 1.127 | AB5 | 2 | 1.426 |

AB6 | 1 | 2.242 | AB6 | 2 | 2.348 | AB6 | 2 | 2.370 | AB6 | 2 | 2.066 | AB6 | 1 | 1.610 | AB6 | 1 | 1.356 |

AB7 | 1 | 2.242 | AB7 | 2 | 2.348 | AB7 | 2 | 2.370 | AB7 | 2 | 2.066 | AB7 | 1 | 1.610 | AB7 | 2 | 1.504 |

AB8 | 1 | 2.242 | AB8 | 1 | 2.167 | AB8 | 2 | 2.370 | AB8 | 2 | 2.066 | AB8 | 1 | 1.610 | AB8 | 2 | 1.880 |

AB9 | 1 | 2.242 | AB9 | 1 | 2.167 | AB9 | 2 | 2.370 | AB9 | 2 | 2.066 | AB9 | 1 | 1.127 | AB9 | 2 | 1.504 |

AB10 | 1 | 2.242 | AB10 | 1 | 2.167 | AB10 | 2 | 2.370 | AB10 | 2 | 2.066 | AB10 | 1 | 1.127 | AB10 | 1 | 1.78 |

AB11 | 1 | 2.242 | AB11 | 2 | 2.348 | AB11 | 2 | 2.370 | AB11 | 2 | 2.066 | AB11 | 1 | 1.127 | AB11 | 2 | 1.532 |

AB12 | 1 | 2.242 | AB12 | 2 | 2.348 | AB12 | 2 | 2.370 | AB12 | 2 | 2.066 | AB12 | 1 | 1.127 | AB12 | 2 | 1.880 |

AB13 | 1 | 2.242 | AB13 | 2 | 2.348 | AB13 | 2 | 2.370 | AB13 | 2 | 2.066 | AB13 | 1 | 1.610 | AB13 | 2 | 1.532 |

AB14 | 1 | 2.242 | AB14 | 2 | 2.348 | AB14 | 2 | 2.370 | AB14 | 2 | 2.066 | AB14 | 1 | 1.610 | AB14 | 1 | 1.378 |

AB15 | 1 | 2.242 | AB15 | 1 | 2.167 | AB15 | 2 | 2.370 | AB15 | 2 | 2.066 | AB15 | 1 | 1.610 | AB15 | 2 | 1.477 |

AB16 | 1 | 2.242 | AB16 | 1 | 2.167 | AB16 | 2 | 2.370 | – | – | – | AB16 | 1 | 1.127 | AB16 | 2 | 1.880 |

AB17 | 1 | 2.242 | AB17 | 1 | 2.167 | AB17 | 2 | 2.370 | – | – | – | AB17 | 1 | 1.127 | AB17 | 2 | 1.402 |

AB18 | 1 | 2.242 | AB18 | 2 | 2.348 | AB18 | 2 | 2.370 | – | – | – | AB18 | 1 | 1.127 | AB18 | 1 | 1.272 |

AB19 | 1 | 2.242 | AB19 | 2 | 2.348 | AB19 | 2 | 2.294 | – | – | – | AB19 | 1 | 1.127 | AB19 | 2 | 1.334 |

AB20 | 1 | 2.242 | AB20 | 2 | 2.348 | AB20 | 2 | 2.294 | – | – | – | AB20 | 1 | 1.610 | AB20 | 2 | 1.798 |

AB21 | 1 | 2.242 | AB21 | 2 | 2.348 | AB21 | 2 | 2.294 | – | – | – | AB21 | 1 | 1.610 | AB21 | 2 | 1.798 |

C1 | 2 | 1.265 | C1 | 4 | 1.374 | C1 | 4 | 1.546 | C1 | 5 | 1.354 | C1 | 5 | 2.087 | C1 | 6 | 2.235 |

– | – | – | C2 | 4 | 1.374 | C2 | 5 | 1.778 | C2 | 5 | 1.354 | C2 | 5 | 2.087 | C2 | 6 | 1.760 |

– | – | – | C3 | 4 | 1.374 | C3 | 5 | 1.871 | C3 | 5 | 1.354 | C3 | 5 | 2.087 | C3 | 8 | 2.668 |

– | – | – | – | – | – | C4 | 5 | 1.922 | C4 | 1 | 1.869 | – | – | – | C4 | 7 | 2.176 |

– | – | – | – | – | – | C5 | 5 | 1.871 | – | – | – | – | – | – | C5 | 8 | 2.757 |

– | – | – | – | – | – | C6 | 5 | 1.778 | – | – | – | – | – | – | C6 | 7 | 2.235 |

– | – | – | – | – | – | C7 | 4 | 1.546 | – | – | – | – | – | – | C7 | 8 | 2.757 |

– | – | – | – | – | – | – | – | – | – | – | – | – | – | – | C8 | 7 | 1.969 |

– | – | – | – | – | – | – | – | – | – | – | – | – | – | – | C9 | 7 | 2.363 |

– | – | – | – | – | – | – | – | – | – | – | – | – | – | – | C10 | 5 | 1.532 |

c̅ | – | 1.265 | c̅ | – | 1.374 | c̅ | – | 1.759 | c̅ | – | 1.483 | c̅ | – | 2.087 | c̅ | – | 2.245 |

The calculation results in Table 4 and 5 indicate that Sample I only takes vertical traffic space as vertical connection element to connect the function planes of all floors in the building. The value of integration of Space D reaches up to 49.322, resulting in high utilisation of vertical traffic space and high traffic load pressure. Besides, due to the absence of aerial nodes, longitudinal public space connection only exists between the first and second floors, leading to limited diversion for vertical traffic.

The implanted aerial courtyards, as the spatial backbone to connect each usable space of high-rise building, perform part of vertical transportation function that forms the topological structure of Sample II. The integration of space D is reduced to 18.784, indicating that the overall topological structure is better. For space C, due to more independent spatial relation of its aerial courtyard, its integration is lower at 1.374, indicating that its accessibility is low and it is easy to become an passive place with low use ratio.

Note that by improving the following factors such as increasing the number of aerial courtyards, establishing a spatial relation between adjacent aerial courtyards, and enabling the aerial courtyards in high-rise and the usable space to form an overall topological structure, such as Sample III, the integration of aerial courtyards could be improved to a certain extent, with an average integration reaching up to 1.759. The integration of space D is reduced to 10.157, and its use ratio gap with that of space AB is getting narrower. The overall spatial relation is more reasonable, and topological structure is better.

The topological structure of Sample IV is similar to that of Sample II. The aerial courtyards of space C are more independent, with no connection built between each other. Instead, the top of aerial courtyards is enlarged to form spatial node. The analytic results show that the integration of its aerial courtyards is lower with average value of only 1.483 and this low value indicates low accessibility and low potential of attracting transportation resulting in low use ratio of space.

The position of aerial courtyards is adjusted or changed and taken as a transition of core walls and functional spaces, to form a pattern of space D-space C-space AB, such as Sample V. From the perspective of local variables, the integration of aerial courtyard is significantly improved, with an average of 2.087, while the integration of space D decreases to 4.696 and the use ratio gap with that of space AB becomes narrower. All of these values indicate a more reasonable overall spatial relation and a better topological structure. From the perspective of overall variables, connectivity and integration of topological structure of Sample V in the scatter diagrams (the value of R^{2)} is 0.8721, whose value is improved a lot compared to Sample IV, and its spatial structural intelligibility is increased. From a comprehensive consideration of overall and local variables, setting aerial courtyards between spaces D and AB can facilitate users to understand the overall structure.

Further, a large aerial courtyard is divided into multiple small courtyards and they are scattered up and down the section with mutual connection, to form a multiple connections among vertical transportation space, functional space and aerial courtyards, and a new spatial topological structure, such as Sample VI, is generated. In order to work out the local and overall variables of topological structure, local variables are analysed at first. The integration of aerial courtyards increases significantly, with an average reaching up to 2.245, which becomes the highest integration node of topological structure. From the perspective of overall variables, in the correlative analysis of connectivity and integration of topological structure of Sample VI, R^{2} is 0.7768, indicating its space intelligibility is at a higher level.

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 R^{2} 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.

Comparative analysis of topological structures before and after optimisation.

Connectivity and integration of optimised scheme.

D1 | 21 | 10.157 | D1 | 7 | 3.386 | D1 | 12 | 4.696 | D1 | 12 | 4.696 | D1 | 11 | 4.135 | D1 | 11 | 3.939 |

AB1 | 2 | 2.294 | AB1 | 1 | 1.094 | AB1 | 1 | 1.610 | AB1 | 1 | 1.610 | AB1 | 1 | 1.234 | D2 | 11 | 3.939 |

AB2 | 2 | 2.294 | AB2 | 1 | 1.094 | AB2 | 1 | 1.127 | AB2 | 1 | 1.252 | AB2 | 1 | 1.234 | AB1 | 2 | 1.844 |

AB3 | 2 | 2.294 | AB3 | 1 | 1.094 | AB3 | 1 | 1.127 | AB3 | 1 | 1.252 | AB3 | 2 | 1.356 | AB2 | 2 | 1.844 |

AB4 | 2 | 2.370 | AB4 | 1 | 1.166 | AB4 | 1 | 1.127 | AB4 | 1 | 1.252 | AB4 | 2 | 1.838 | AB3 | 2 | 1.520 |

AB5 | 2 | 2.370 | AB5 | 1 | 1.166 | AB5 | 1 | 1.127 | AB5 | 1 | 1.252 | AB5 | 2 | 1.426 | AB4 | 2 | 1.884 |

AB6 | 2 | 2.370 | AB6 | 1 | 1.166 | AB6 | 1 | 1.610 | AB6 | 1 | 1.610 | AB6 | 1 | 1.356 | AB5 | 2 | 1.576 |

AB7 | 2 | 2.370 | AB7 | 1 | 1.166 | AB7 | 1 | 1.610 | AB7 | 1 | 1.610 | AB7 | 2 | 1.504 | AB6 | 2 | 1.926 |

AB8 | 2 | 2.370 | AB8 | 1 | 1.166 | AB8 | 1 | 1.610 | AB8 | 1 | 1.610 | AB8 | 2 | 1.880 | AB7 | 2 | 1.635 |

AB9 | 2 | 2.370 | AB9 | 1 | 1.166 | AB9 | 1 | 1.127 | AB9 | 1 | 1.409 | AB9 | 2 | 1.504 | AB8 | 2 | 1.926 |

AB10 | 2 | 2.370 | AB10 | 1 | 1.166 | AB10 | 1 | 1.127 | AB10 | 1 | 1.409 | AB10 | 1 | 1.78 | AB9 | 2 | 1.667 |

AB11 | 2 | 2.370 | AB11 | 1 | 1.166 | AB11 | 1 | 1.127 | AB11 | 1 | 1.409 | AB11 | 2 | 1.532 | AB10 | 2 | 1.926 |

AB12 | 2 | 2.370 | AB12 | 1 | 1.166 | AB12 | 1 | 1.127 | AB12 | 1 | 1.409 | AB12 | 2 | 1.880 | AB11 | 2 | 1.667 |

AB13 | 2 | 2.370 | AB13 | 1 | 1.166 | AB13 | 1 | 1.610 | AB13 | 1 | 1.610 | AB13 | 2 | 1.532 | AB12 | 2 | 1.926 |

AB14 | 2 | 2.370 | AB14 | 1 | 1.166 | AB14 | 1 | 1.610 | AB14 | 1 | 1.610 | AB14 | 1 | 1.378 | AB13 | 2 | 1.667 |

AB15 | 2 | 2.370 | AB15 | 1 | 1.166 | AB15 | 1 | 1.610 | AB15 | 1 | 1.610 | AB15 | 2 | 1.477 | AB14 | 2 | 1.926 |

AB16 | 2 | 2.370 | AB16 | 1 | 1.166 | AB16 | 1 | 1.127 | AB16 | 1 | 1.409 | AB16 | 2 | 1.880 | AB15 | 2 | 1.635 |

AB17 | 2 | 2.370 | AB17 | 1 | 1.166 | AB17 | 1 | 1.127 | AB17 | 1 | 1.409 | AB17 | 2 | 1.402 | AB16 | 2 | 1.926 |

AB18 | 2 | 2.370 | AB18 | 1 | 1.166 | AB18 | 1 | 1.127 | AB18 | 1 | 1.409 | AB18 | 1 | 1.272 | AB17 | 2 | 1.576 |

AB19 | 2 | 2.294 | AB19 | 1 | 1.094 | AB19 | 1 | 1.127 | AB19 | 1 | 1.409 | AB19 | 2 | 1.334 | AB18 | 2 | 1.884 |

AB20 | 2 | 2.294 | AB20 | 1 | 1.094 | AB20 | 1 | 1.610 | AB20 | 1 | 1.610 | AB20 | 2 | 1.798 | AB19 | 2 | 1.520 |

AB21 | 2 | 2.294 | AB21 | 1 | 1.094 | AB21 | 1 | 1.610 | AB21 | 1 | 1.610 | AB21 | 2 | 1.798 | AB20 | 2 | 1.844 |

- | - | - | - | - | - | - | - | - | - | - | - | - | - | - | AB21 | 2 | 1.844 |

C1 | 4 | 1.546 | C1 | 5 | 1.871 | C1 | 5 | 2.087 | C1 | 6 | 2.562 | C1 | 6 | 2.235 | C1 | 6 | 2.281 |

C2 | 5 | 1.778 | C2 | 6 | 2.091 | C2 | 5 | 2.087 | C2 | 7 | 3.315 | C2 | 6 | 1.760 | C2 | 7 | 2.407 |

C3 | 5 | 1.871 | C3 | 6 | 2.091 | C3 | 5 | 2.087 | C3 | 6 | 2.562 | C3 | 8 | 2.668 | C3 | 8 | 2.708 |

C4 | 5 | 1.922 | C4 | 6 | 2.091 | - | - | - | - | - | - | C4 | 7 | 2.176 | C4 | 8 | 2.796 |

C5 | 5 | 1.871 | C5 | 6 | 2.091 | - | - | - | - | - | - | C5 | 8 | 2.757 | C5 | 8 | 2.796 |

C6 | 5 | 1.778 | C6 | 6 | 2.091 | - | - | - | - | - | - | C6 | 7 | 2.235 | C6 | 8 | 2.796 |

C7 | 4 | 1.546 | C7 | 5 | 1.871 - | - | - | - | - | - | C7 | 8 | 2.757 | C7 | 8 | 2.796 | |

- | - | - | - | - | - | - | - | - | - | - | - | C8 | 7 | 1.969 | C8 | 8 | 2.708 |

- | - | - | - | - | - | - | - | - | - | - | - | C9 | 7 | 2.363 | C9 | 7 | 2.407 |

- | - | - | - | - | - | - | - | - | - | - | － | C10 | 5 | 1.532 | C10 | 6 | 2.281 |

C̅ | 1.759 | C̅ | 2.028 | C̅ | 2.087 | C̅ | 2.813 | C̅ | 2.245 | C̅ | 2.597 |

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 R^{2} 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 R^{2} 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.

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.

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.

Constructing direct spatial connection between adjacent aerial courtyards improves the accessibility between them, the cooperation between each module of space system, and the integration and intelligibility of overall spatial structure.

Arranging vertical transportation spaces dispersedly can evacuate vertical transportation pressure of high-rise building, help to establish multiple topological connections between aerial courtyards and vertical transportation space, and form a topological structure with higher integration and accessibility.

Understand the relationship between aerial courtyards and functional rooms of super high-rise buildings from topological perspective, figure out and feedback the local and overall variables of topological structure nodes of architectural space, and achieve the purpose of scientifically quantifying the spatial structural optimisation effect. This can help architects to shift from subjective design to subjective-objective combined design, and make more scientific schemes.

In space syntax research, the human residential spatial structure is quantitatively described by abstractly extracting the form, dimension and relation of spaces. And after analysis, the integration, intelligibility and other parameters are obtained. However, considering the complexity of architecture discipline, the influential factors of architectural design are not limited to space itself and spatial connection and further discussion is needed in follow-up research.

Illustration is a discipline that takes graphics as research object. It uses graphics to express and analyse design thinking and describe the rules of spatial structure.

Integration is divided into overall integration and local integration. Overall integration represents how closely the node is related to all nodes in the system. Local integration represents how closely the node is related to neighbouring nodes. The research variables in the paper are overall integration.

Intelligibility describes the correlation between overall space and local space information, and is a key link in the interaction between human and spatial environment.

#### Connectivity and integration of optimised scheme.

D1 | 21 | 10.157 | D1 | 7 | 3.386 | D1 | 12 | 4.696 | D1 | 12 | 4.696 | D1 | 11 | 4.135 | D1 | 11 | 3.939 |

AB1 | 2 | 2.294 | AB1 | 1 | 1.094 | AB1 | 1 | 1.610 | AB1 | 1 | 1.610 | AB1 | 1 | 1.234 | D2 | 11 | 3.939 |

AB2 | 2 | 2.294 | AB2 | 1 | 1.094 | AB2 | 1 | 1.127 | AB2 | 1 | 1.252 | AB2 | 1 | 1.234 | AB1 | 2 | 1.844 |

AB3 | 2 | 2.294 | AB3 | 1 | 1.094 | AB3 | 1 | 1.127 | AB3 | 1 | 1.252 | AB3 | 2 | 1.356 | AB2 | 2 | 1.844 |

AB4 | 2 | 2.370 | AB4 | 1 | 1.166 | AB4 | 1 | 1.127 | AB4 | 1 | 1.252 | AB4 | 2 | 1.838 | AB3 | 2 | 1.520 |

AB5 | 2 | 2.370 | AB5 | 1 | 1.166 | AB5 | 1 | 1.127 | AB5 | 1 | 1.252 | AB5 | 2 | 1.426 | AB4 | 2 | 1.884 |

AB6 | 2 | 2.370 | AB6 | 1 | 1.166 | AB6 | 1 | 1.610 | AB6 | 1 | 1.610 | AB6 | 1 | 1.356 | AB5 | 2 | 1.576 |

AB7 | 2 | 2.370 | AB7 | 1 | 1.166 | AB7 | 1 | 1.610 | AB7 | 1 | 1.610 | AB7 | 2 | 1.504 | AB6 | 2 | 1.926 |

AB8 | 2 | 2.370 | AB8 | 1 | 1.166 | AB8 | 1 | 1.610 | AB8 | 1 | 1.610 | AB8 | 2 | 1.880 | AB7 | 2 | 1.635 |

AB9 | 2 | 2.370 | AB9 | 1 | 1.166 | AB9 | 1 | 1.127 | AB9 | 1 | 1.409 | AB9 | 2 | 1.504 | AB8 | 2 | 1.926 |

AB10 | 2 | 2.370 | AB10 | 1 | 1.166 | AB10 | 1 | 1.127 | AB10 | 1 | 1.409 | AB10 | 1 | 1.78 | AB9 | 2 | 1.667 |

AB11 | 2 | 2.370 | AB11 | 1 | 1.166 | AB11 | 1 | 1.127 | AB11 | 1 | 1.409 | AB11 | 2 | 1.532 | AB10 | 2 | 1.926 |

AB12 | 2 | 2.370 | AB12 | 1 | 1.166 | AB12 | 1 | 1.127 | AB12 | 1 | 1.409 | AB12 | 2 | 1.880 | AB11 | 2 | 1.667 |

AB13 | 2 | 2.370 | AB13 | 1 | 1.166 | AB13 | 1 | 1.610 | AB13 | 1 | 1.610 | AB13 | 2 | 1.532 | AB12 | 2 | 1.926 |

AB14 | 2 | 2.370 | AB14 | 1 | 1.166 | AB14 | 1 | 1.610 | AB14 | 1 | 1.610 | AB14 | 1 | 1.378 | AB13 | 2 | 1.667 |

AB15 | 2 | 2.370 | AB15 | 1 | 1.166 | AB15 | 1 | 1.610 | AB15 | 1 | 1.610 | AB15 | 2 | 1.477 | AB14 | 2 | 1.926 |

AB16 | 2 | 2.370 | AB16 | 1 | 1.166 | AB16 | 1 | 1.127 | AB16 | 1 | 1.409 | AB16 | 2 | 1.880 | AB15 | 2 | 1.635 |

AB17 | 2 | 2.370 | AB17 | 1 | 1.166 | AB17 | 1 | 1.127 | AB17 | 1 | 1.409 | AB17 | 2 | 1.402 | AB16 | 2 | 1.926 |

AB18 | 2 | 2.370 | AB18 | 1 | 1.166 | AB18 | 1 | 1.127 | AB18 | 1 | 1.409 | AB18 | 1 | 1.272 | AB17 | 2 | 1.576 |

AB19 | 2 | 2.294 | AB19 | 1 | 1.094 | AB19 | 1 | 1.127 | AB19 | 1 | 1.409 | AB19 | 2 | 1.334 | AB18 | 2 | 1.884 |

AB20 | 2 | 2.294 | AB20 | 1 | 1.094 | AB20 | 1 | 1.610 | AB20 | 1 | 1.610 | AB20 | 2 | 1.798 | AB19 | 2 | 1.520 |

AB21 | 2 | 2.294 | AB21 | 1 | 1.094 | AB21 | 1 | 1.610 | AB21 | 1 | 1.610 | AB21 | 2 | 1.798 | AB20 | 2 | 1.844 |

- | - | - | - | - | - | - | - | - | - | - | - | - | - | - | AB21 | 2 | 1.844 |

C1 | 4 | 1.546 | C1 | 5 | 1.871 | C1 | 5 | 2.087 | C1 | 6 | 2.562 | C1 | 6 | 2.235 | C1 | 6 | 2.281 |

C2 | 5 | 1.778 | C2 | 6 | 2.091 | C2 | 5 | 2.087 | C2 | 7 | 3.315 | C2 | 6 | 1.760 | C2 | 7 | 2.407 |

C3 | 5 | 1.871 | C3 | 6 | 2.091 | C3 | 5 | 2.087 | C3 | 6 | 2.562 | C3 | 8 | 2.668 | C3 | 8 | 2.708 |

C4 | 5 | 1.922 | C4 | 6 | 2.091 | - | - | - | - | - | - | C4 | 7 | 2.176 | C4 | 8 | 2.796 |

C5 | 5 | 1.871 | C5 | 6 | 2.091 | - | - | - | - | - | - | C5 | 8 | 2.757 | C5 | 8 | 2.796 |

C6 | 5 | 1.778 | C6 | 6 | 2.091 | - | - | - | - | - | - | C6 | 7 | 2.235 | C6 | 8 | 2.796 |

C7 | 4 | 1.546 | C7 | 5 | 1.871 - | - | - | - | - | - | C7 | 8 | 2.757 | C7 | 8 | 2.796 | |

- | - | - | - | - | - | - | - | - | - | - | - | C8 | 7 | 1.969 | C8 | 8 | 2.708 |

- | - | - | - | - | - | - | - | - | - | - | - | C9 | 7 | 2.363 | C9 | 7 | 2.407 |

- | - | - | - | - | - | - | - | - | - | - | － | C10 | 5 | 1.532 | C10 | 6 | 2.281 |

C̅ | 1.759 | C̅ | 2.028 | C̅ | 2.087 | C̅ | 2.813 | C̅ | 2.245 | C̅ | 2.597 |

#### Connectivity and integration of sample space.

Sample I | Sample II | Sample III | Sample IV | Sample V | Sample VI | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Space | Connectivity | Integration | Integration | Connectivity | Integration | Integration | Connectivity | Integration | Integration | Connect ivity | Integration | Integration | Connectivity | Integration | Integration | Connectivity | Integration |

D1 | 21 | 49.322 | D1 | 21 | 18.784 | D1 | 21 | 10.157 | D1 | 16 | 13.086 | D1 | 12 | 4.696 | D1 | 11 | 4.135 |

AB1 | 2 | 2.466 | AB2 | 1 | 2.167 | AB2 | 2 | 2.294 | AB2 | 2 | 2.066 | AB2 | 1 | 1.610 | AB2 | 1 | 1.234 |

AB2 | 2 | 2.466 | AB2 | 1 | 2.167 | AB2 | 2 | 2.294 | AB2 | 2 | 2.066 | AB2 | 1 | 1.127 | AB2 | 1 | 1.234 |

AB3 | 1 | 2.242 | AB3 | 1 | 2.167 | AB3 | 2 | 2.294 | AB3 | 2 | 2.066 | AB3 | 1 | 1.127 | AB3 | 2 | 1.356 |

AB4 | 1 | 2.242 | AB4 | 2 | 2.348 | AB4 | 2 | 2.370 | AB4 | 2 | 2.066 | AB4 | 1 | 1.127 | AB4 | 2 | 1.838 |

AB5 | 1 | 2.242 | AB5 | 2 | 2.348 | AB5 | 2 | 2.370 | AB5 | 2 | 2.066 | AB5 | 1 | 1.127 | AB5 | 2 | 1.426 |

AB6 | 1 | 2.242 | AB6 | 2 | 2.348 | AB6 | 2 | 2.370 | AB6 | 2 | 2.066 | AB6 | 1 | 1.610 | AB6 | 1 | 1.356 |

AB7 | 1 | 2.242 | AB7 | 2 | 2.348 | AB7 | 2 | 2.370 | AB7 | 2 | 2.066 | AB7 | 1 | 1.610 | AB7 | 2 | 1.504 |

AB8 | 1 | 2.242 | AB8 | 1 | 2.167 | AB8 | 2 | 2.370 | AB8 | 2 | 2.066 | AB8 | 1 | 1.610 | AB8 | 2 | 1.880 |

AB9 | 1 | 2.242 | AB9 | 1 | 2.167 | AB9 | 2 | 2.370 | AB9 | 2 | 2.066 | AB9 | 1 | 1.127 | AB9 | 2 | 1.504 |

AB10 | 1 | 2.242 | AB10 | 1 | 2.167 | AB10 | 2 | 2.370 | AB10 | 2 | 2.066 | AB10 | 1 | 1.127 | AB10 | 1 | 1.78 |

AB11 | 1 | 2.242 | AB11 | 2 | 2.348 | AB11 | 2 | 2.370 | AB11 | 2 | 2.066 | AB11 | 1 | 1.127 | AB11 | 2 | 1.532 |

AB12 | 1 | 2.242 | AB12 | 2 | 2.348 | AB12 | 2 | 2.370 | AB12 | 2 | 2.066 | AB12 | 1 | 1.127 | AB12 | 2 | 1.880 |

AB13 | 1 | 2.242 | AB13 | 2 | 2.348 | AB13 | 2 | 2.370 | AB13 | 2 | 2.066 | AB13 | 1 | 1.610 | AB13 | 2 | 1.532 |

AB14 | 1 | 2.242 | AB14 | 2 | 2.348 | AB14 | 2 | 2.370 | AB14 | 2 | 2.066 | AB14 | 1 | 1.610 | AB14 | 1 | 1.378 |

AB15 | 1 | 2.242 | AB15 | 1 | 2.167 | AB15 | 2 | 2.370 | AB15 | 2 | 2.066 | AB15 | 1 | 1.610 | AB15 | 2 | 1.477 |

AB16 | 1 | 2.242 | AB16 | 1 | 2.167 | AB16 | 2 | 2.370 | – | – | – | AB16 | 1 | 1.127 | AB16 | 2 | 1.880 |

AB17 | 1 | 2.242 | AB17 | 1 | 2.167 | AB17 | 2 | 2.370 | – | – | – | AB17 | 1 | 1.127 | AB17 | 2 | 1.402 |

AB18 | 1 | 2.242 | AB18 | 2 | 2.348 | AB18 | 2 | 2.370 | – | – | – | AB18 | 1 | 1.127 | AB18 | 1 | 1.272 |

AB19 | 1 | 2.242 | AB19 | 2 | 2.348 | AB19 | 2 | 2.294 | – | – | – | AB19 | 1 | 1.127 | AB19 | 2 | 1.334 |

AB20 | 1 | 2.242 | AB20 | 2 | 2.348 | AB20 | 2 | 2.294 | – | – | – | AB20 | 1 | 1.610 | AB20 | 2 | 1.798 |

AB21 | 1 | 2.242 | AB21 | 2 | 2.348 | AB21 | 2 | 2.294 | – | – | – | AB21 | 1 | 1.610 | AB21 | 2 | 1.798 |

C1 | 2 | 1.265 | C1 | 4 | 1.374 | C1 | 4 | 1.546 | C1 | 5 | 1.354 | C1 | 5 | 2.087 | C1 | 6 | 2.235 |

– | – | – | C2 | 4 | 1.374 | C2 | 5 | 1.778 | C2 | 5 | 1.354 | C2 | 5 | 2.087 | C2 | 6 | 1.760 |

– | – | – | C3 | 4 | 1.374 | C3 | 5 | 1.871 | C3 | 5 | 1.354 | C3 | 5 | 2.087 | C3 | 8 | 2.668 |

– | – | – | – | – | – | C4 | 5 | 1.922 | C4 | 1 | 1.869 | – | – | – | C4 | 7 | 2.176 |

– | – | – | – | – | – | C5 | 5 | 1.871 | – | – | – | – | – | – | C5 | 8 | 2.757 |

– | – | – | – | – | – | C6 | 5 | 1.778 | – | – | – | – | – | – | C6 | 7 | 2.235 |

– | – | – | – | – | – | C7 | 4 | 1.546 | – | – | – | – | – | – | C7 | 8 | 2.757 |

– | – | – | – | – | – | – | – | – | – | – | – | – | – | – | C8 | 7 | 1.969 |

– | – | – | – | – | – | – | – | – | – | – | – | – | – | – | C9 | 7 | 2.363 |

– | – | – | – | – | – | – | – | – | – | – | – | – | – | – | C10 | 5 | 1.532 |

c̅ | – | 1.265 | c̅ | – | 1.374 | c̅ | – | 1.759 | c̅ | – | 1.483 | c̅ | – | 2.087 | c̅ | – | 2.245 |

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