Architectural design methods for mountainous environments

ABSTRACT As an important part of urban space, mountains play an extremely important role in the overall landscape and ecology of cities. However, with the continuous development of urbanization and building construction, mountains have been occupied and destroyed in unreasonable ways. Therefore, with the aim of reducing the damage to mountains from construction, this paper explores the design methods to deal with the relationship between buildings and mountainous environments. The historic district of Signal Hill in Qingdao is taken as the research area, since buildings here coexist with the mountainous environment harmoniously. Through the combination of modeling and field research, the slope of the mountain can be divided into three grades: “0–5.8°”, “5.8–11.7°” and “11.7–17.3°”. Therefore, the design characteristics and distribution patterns of 20 design methods that dealt with the mountainous environment in different slope grades can be obtained. Furthermore, by analyzing the design characteristics and distribution patterns, the relationship between the design methods and the slope of mountains can be found, providing more suitable design strategies for buildings located on different slopes of mountains. For other mountain cities worldwide, these rational strategies can provide some helpful design suggestions to better use terrain. It can also reduce the amount of construction volume and damage to the mountainous environment, and further better achieve sustainable development goals.


Introduction
Mountainous environments, as an important component of hilly cities, are an indispensable natural resource. Mountains provide spatial diversity for human production, living and leisure. This kind of diversity creates a richness of urban transport networks and landscape interfaces that form the unique landscape of hilly cities (Daniel and Laughlin 2005). However, with urbanization, the role of mountainous environments is gradually changing. Sociologist Kristol argues that urbanization is not only a geographical accumulation of people but also a process of changing cultural values. Applying this concept, Healy examines the impact of urbanization on mountain forestlands in the USA. The result is that mountainous environments are no longer limited in function to timber production but are becoming more responsive to human recreation needs and providing more varied urban spaces (Robert G 1984).
Although the mountainous environment plays an important role in hilly cities, it has been long neglected and misunderstood. In recent years, mountains have been disappearing at an alarming rate. As urbanization has rapidly degenerated large areas of mountainous terrain, some Western biologists and horticulturists are considering recreating inner-city landscapes that mimic mountainous environments (Arendt 1994;K 1976;O W E. Peter Francism 1998). Despite the efforts of some scholars, mountain areas are still disappearing much faster than other urban areas, especially in developing countries. China is a mountainous country, with more than two-thirds of the land area covered by mountains and only 10% covered by plains (Guangyu 2006). Furthermore, as the process of urbanization is continuously accelerating in China, the scale of cities is gradually expanding. Thus, this leads to growing conflict between urban construction and nature conservation. Particularly in hilly cities, the potential buildable areas are fully exploited, leading to serious damage to mountainous environments. Some of the hills and valleys have been isolated, and extreme deterioration has occurred in the quality of the urban environment, such as the urban heat-island effect and landslides. However, with the development of theoretical knowledge and the construction of urban forests, parks and gardens, the important functions and values of mountainous environments are receiving increasing attention. Therefore, this has pushed social organizations, planning experts and urban managers to look for ways to enhance protection and utilization (Chao Yang et al. 2021).
CONTACT Xingtian Wang xt_wang_ismart@163.com 11 Fushun Road Shibei District,Qingdao Shandong Province People's Republic of China ※This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper explores the design methods of architecture located in mountainous areas to identify ways to integrate the architecture effectively and naturally with the mountainous environment. More specifically, it analyses the effect of slope on distribution of building type and design method. The major hypothesis is that various design methods and distribution of building types can be found in areas with different slope, and the higher the slope is in an area, the less the design method and the more complicated the design method could be. The Historic District of Signal Hill in Qingdao is the research area since the buildings here show many methods for dealing with the mountainous environment. During the survey, more than 770 buildings were researched, accounting for 77% of the total number of buildings in the historic district. Through the combination of modeling and field research, the slope of the mountain can be divided into three grades: "0-5.8°", "5.8-11.7°", and "11.7-17.3°". Furthermore, this paper also summarizes the design characteristics and distribution patterns of 20 design methods that dealt with the mountainous environment in different slope grades.
By analyzing the distribution of building types and design methods, this paper explores the interrelationship between architecture and mountainous environment, and the ways in which architecture can live in harmony with the mountainous environment. Moreover, it provides more reasonable design methods for buildings in different mountainous environment around the world. Based on these reasonable design methods, the construction volume and cost can be effectively reduced. Furthermore, it can effectively reduce construction energy consumption and carbon emissions, which will promote sustainable development of buildings located in mountainous environment.

Literature review
The persistent effects of human activities have long led to changes in regional environmental patterns and ecological functions, which in turn have had an impact on the quality of human existence and the ability to develop sustainably (Mander 1998). With the rapid development of urban construction, cities continue to extend in all directions. At present, with the progress of human society, the development of science and technology, the proliferation of the human population, the expansion of human living spaces, and the impact of human construction activities on mountainous environments are becoming increasingly significant. Furthermore, this has led to a huge crisis in mountainous environments (Sarmiento 2000). Human activities are the main cause of changes in mountainous environmental structures and functions (Inoue 2001;Ivesjd 1990;Koff and Yli-Halla 1988), receiving worldwide attention academically and socially. Many hills and valleys have been swallowed up and submerged by construction, while they have only partially evolved into urban parks and green spaces. As a result of construction, many hills within mountainous cities are constantly being leveled or eroded. This destroys the mountainous environment and causes mountain cities to lose their inherent environmental character (Zoltán Kovács et al. 2019). Although each city has a different impact on its mountainous environment as it expands, in general, such effects are manifested in two main ways. First, the spatial expansion of a city has integrated mountains into it. Mountains have become part of the city's construction areas and are subject to being damaged by urban construction. Second, the rapid growth of the urban scale and population has led to a demand for the exploitation of mountain resources, resulting in serious environmental problems to the mountainous areas through deforestation and quarrying, land razing, soil erosion, ecological and environmental degradation, mountain fragmentation and destruction of mountain patterns. All of these factors have had a huge impact on mountainous environments and affected the development of mountainous cities (Ai 2015).
However, as an important part of the urban environment, mountains have an inestimable economic, social and ecological value (Alberti et al., 2003). The complex topography of mountainous cities and their unique natural landscape patterns create diverse environments. As a special urban ecosystem, the mountainous environment plays an active role in purifying water systems, regulating water balance, protecting biodiversity, enhancing the urban ecological environment, shaping the urban landscape, and enriching the recreational activities of citizens (Junlu and Ya-Fenggao 2006). In addition, it is also important in biodiversity and urban landscapes (Falcucci, Maiorano, and Boitani 2007;Grimm et al. 2008). On the one hand, as part of urban green space, mountains can provide living space for a variety of organisms (Christopher et al. 2017) On the other hand, mountain and building contours shape a city's skyline. When the location, height, shape and public space of the mountain can be integrated and coordinated with buildings harmoniously, buildings will be able to follow the contours of the mountain and each complements the other. At the same time, mountainous environments can optimize the ecological environment of cities, forming a continuous ecological network around and through cities, which can create composite walking systems and urban ecosystems with mountain characteristics (Hermy 2006). Therefore, it is essential to find ways of harmoniously integrating building construction with mountainous environments when developing areas with mountains.
At present, the research on architecture and mountainous environment mostly focuses on mountain science and ecology. In the famous academic book Site planning and Design Handbook, (Russ 2009) established the basic principles and design basis of site planning with a sustainable site planning model. (Norberg-Schulz 1983), as the author of Thinking on Architecture, established the theories of architectural phenomenology and emphasized the harmony between architecture and place. These two works have certain guiding significance for exploring the relationship between architecture and mountainous environment. In addition, the research of some scholars has also promoted the development of related fields. For example, (Bosia 2004) studied the natural buildings in the Alpine valley from the perspective of building material, type, orientation, and detail, and proposed the maintenance and protection measures as the "dialogue between architecture and environment". (Mutani and Berto 2018) conducted an inductive analysis of the building energy consumption and provided energy-saving design for the buildings located in mountainous areas. (Qing-Shun and Hongyang 2011) studied the buildings in mountain city Chongqing and proposed a three-dimensional disaster prevention system by analysing planning regulation and fire protection regulation. It can provide guidance for how to protect the spatial and morphological characteristics of the local buildings. (José, García-Ruiz, and Ruiz-Flano et al. 1996) aim to achieve a stable land structure by proposing the use of abandoned cultivated land and improving shrub coverage to control the land erosion. It explored a new direction in the site selection and mountain structure stabilization in the design process. (Wei 2015) studied the flow rate, pressure, and dynamics of mudslides disaster through data simulation. It found some solutions for mudslide protection and evaluation that can be used in the design process. (Diao and Zhou et al. 2019) found that the slope instability is the main reason that buildings in mountain area get damaged. This study provides certain guidance to improve the slope treatment of the buildings in mountain area. (Zhao and Xu 2019) summarized the residential design methods in Qinba mountain area, and provided a valuable reference for the design of residential buildings in mountainous areas. (Andrew and Sauber 2000) studied the impact of glacial erosion on mountain buildings and illustrated the importance of building design in mountain area in terms of the natural environment protection. Brian (Horton 2018) reconstructed the mountain architecture on the western edge of South America from the perspective of geology. It explored the methods of integrating geology in building design. Michael (Heads 2019) studied the large-scale passive uplift of animal and plant populations under the influence of construction, and emphasized the importance of maintaining the stability of the animal and plant environment. (Fei et al. 2018) proposed an urban morphological method to detect the wind path of mountain cities by analyzing the wind environment of Dalian. It also provided corresponding strategies to alleviate the heat island effect of coastal mountain cities. In addition, the issue of sustainable development of mountainous environments within urban areas is increasingly becoming a focus in various countries since it is of importance to regional and global ecological security and sustainable development (Brown 2000;Jodhans 2001;Jodhins 2000). The idea of sustainable development involving mountainous environment conservation has received much attention, and a number of environmental protection organizations have widely accepted this idea and explored its use to guide practical activities in mountainous environment conservation. As Foreman summarizes the study of environmental ecology as structure, function, and dynamics (Godron 1990), the matrix, corridors and patches are considered to be the three elements that make up the environmental structure (Nancai et al. 2019). Bai proposed the establishment of ecological corridors to link isolated areas of important mountain and species habitats (Bai and Wang et al. 2018). Elsen takes a large mountain range as the object of study and proposes protecting its vertical spatial ecology (Elsen and Merenlender 2018). Moreover, some laws and regulations are gradually being proposed. The French Landscape Protection and Regeneration Act of 1993, the US Environmental Policy Act (SEPA) on landscape impact assessment of development activities, and the landscape regulations of Germany and Japan show a growing concern for the protection of mountainous environments (Solomon Benti and Callo-Concha 2021). As a result, this has led to a number of practical activities, such as San Francisco's post disaster reconstruction. This includes preserving the original green space structure of the city, enhancing the continuity of green space within the city, protecting the natural topographic and mountainous features of the current urban space, and protecting good vantage points and viewpoints. By linking the height of existing buildings and new buildings to the urban skyline and the landscape space of the hills, it can provide protection for the mountainous environment in the course of urban development (Betal 1992).
In summary, as cities grow larger and taller, the desire to live in a city with clean air and a beautiful environment is becoming increasingly pressing. Therefore, it is important to explore how to rationally address the relationship between buildings and the mountainous environment while expanding the building areas of cities. To respect and protect the natural urban environment and to make use of mountain resources rationally, a range of relevant building design methods should be found, which will allow for the rapid and sustainable development of mountain cities and the harmonious integration of buildings into the mountainous environment. Furthermore, it can reduce the damage to the mountainous environment during construction and promote the development of mountain architecture.

Method
This paper mainly focuses on the research of building design methods dealing with mountainous environments of various slopes. The historic district of Signal Hill in Qingdao is taken as the research area since it has a many buildings and complex terrain. Through the combination of terrain modeling and field research, the number and distribution of design methods are counted, obtaining a series of regional design methods for mountainous environments. The process structure is shown in Figure 1.

Introduction to research area
Qingdao is located in a hilly seaside area, and the mountains account for approximately 15.5% of the city area. The unique mountainous terrain of Qingdao can be characterized by a high northeast, a low southwest coast, and an undulating central hillside. The Signal Hill Historic District is built around Signal Hill, which is 98 meters above sea level and covers an area of 63,936 m2. Due to its mountainous environment, the Historic District forms a complex slope and a typical residential space where the buildings are loosely arranged. Its landscape also has the characteristics of mountainous space. The buildings in different slope areas have their own special methods of dealing with the mountainous environment; thus, buildings with different slopes in the whole Historic District are investigated and the distribution of the different design methods used is analyzed. The scenarios of the research areas are shown in Figure 2.

Modeling the research area
A 3D model is built to analyze the design methods and slopes used by buildings on different slopes. The process can be summarized in three main steps as follows: First, the topographic data of the Historic District is obtained from an open-source data site named the "Geospatial Data Cloud". On this site, the contour vector data files of the Historic District are obtained, which are imported into the Global Mapper software. As a result, elevation dwg files (a kind of file format type with elevation data) are obtained through analysis of the contour data.
Second, a topographic model of the Historic District is formed by importing the dwg file with elevation data into Rhino software (software for making 3D models).
Finally, the model is divided into several quadrangles in the Grasshopper interface by cutting in the Xaxis and Y-axis directions. Projecting the highest point of quadrangles onto the lowest plane forms a series of spatial triangles that are used to analyze the range of slopes in the Historic District. Through the analysis, the range is divided into three slope levels so that field research and distribution statistics aimed at building design methods on different slopes can be conducted. The modeling process can be seen in Figure 3.

Field research and statistics
Based on the model, the GH (the abbreviation of Grasshopper, which is software for parametric design) analyzes the slopes of the Historic District. It divides the overall slope into three grades: 0°-5.8°, 5.8°-11.7°, and 11.7°-17.3°. By counting the total number of buildings in different slope grades and conducting field research on them, this paper summarizes the building design methods for the mountainous environment. The statistical data can be seen in Table 1.
Furthermore, the Historic District was divided into three research areas based on the division of the slope grades. Field research work was carried out in these three research areas. The overall field research routes included 8 streets, and it took 6 days to complete the research. The total walking distance of the research is 7.1 kilometers. The total number of buildings researched is 669. The firstgrade research area is approximately 376,039 m2, mainly surrounded by 9 primary roads. In this area, 361 buildings, which account for 60% of the total number of buildings, were analyzed. The secondgrade research area is approximately 352,857 m2, and 253 buildings were analyzed, which account for 72% of the total number of buildings. The third-grade research area is approximately 35,601 m2. In this area, 55 buildings accounting for 100% of the total number of buildings were analyzed. The overall research mapping and classification of slope grade can be seen in Figure 4. The distribution of each design method and building type in different slope areas area were recorded. Further, the proportion of different design methods and building types in different slope areas were also obtained. Analyzing the collected data can testify if the proposed hypothesis was valid.

Results
Through the field research work, the numbers and distribution of various building design methods dealing with the mountainous environment are counted and summarized. Nine design methods are used to deal with the variation of ground levels inside and outside the building site, 4 design methods to deal with the variation of ground levels inside the building site, 4 design methods to deal with the site fence, and 4 design methods to deal with the interrelationship between architecture and the mountainous landscape. Meanwhile, some distribution patterns for building types are shown. Finally, by comparing the distribution of design methods and building types in different research areas, the distribution pattern is analyzed and obtained.

Analysis of building type distribution
From Figure 5, we can see that different building types show different distribution characteristics on different slopes. Slope Grade I includes all building types, including single housing, group housing, religious buildings, educational buildings, commercial buildings and other public buildings. Group housing accounts for 50%, which is the largest proportion. Single housing accounts for 39%, while the smallest proportion is for commercial buildings, which is 1%. Slope Grade II includes five types of buildings, including all types except religious buildings. The largest proportion is still group housing, which accounts for 50%. Single housing accounted for 45%. The smallest proportion is educational buildings, which account for 1%. In slope grade III, there are only three building types. The largest proportion is single housing, which accounts for 85%. Group housing accounts for 13%, while the lowest proportion is found for other public buildings, which account for only 2%.
In summary, educational buildings, commercial buildings, religious buildings and public buildings that have large volumes tend to be located in Grade II or lower slope areas. Because of the small change in slope, the complexity of the structure can be reduced for building types with large volumes, reducing the difficulties of construction and capital investment. Conversely, in terms of structure, buildings with small volumes are better able to accommodate the complex changes in slope than buildings with large volumes. Therefore, it is found that there are large numbers of residential buildings located in all three slope areas. Among them, group housing is mostly located in the grade II or lower slope areas, while single housing tends to exist in the Grade III area.

Design methods to deal with the height difference
Due to the complexity and variability of mountainous terrain, there are a variety of height differences. There are two main approaches for the design methods to deal with this: one is how to handle height differences inside building sites; and the other is how to deal with height differences between building sites and external roads. The type of design methods can be divided into three categories: "flatten", "steps" and "ramps". The "flatten" design method refers to flattening the different ground levels to the same level.
Through field research, this kind of design method is mainly used in Grade I. When this design method is used inside a building site, the variation in the height differences always needs to be simple, which makes it easy to find a base ground level. More details of the design methods can be seen in Figure 6(a). When dealing with the height differences between building sites and external roads, height differences are generally less than 0.5 m. Based on these qualifications, the difficulty and cost of construction are minimized. More details of the design methods can be seen in Figure 6(b).  For the "steps" design method, as the difference in height increases, the number of steps increases. Meanwhile, the type and position of steps will change depending on the size of the space available to address the height difference. To deal with the height difference between building sites and external roads, based on different height differences and available space sizes, four design methods are used: the "few steps", "single-run staircases", "folded stairs" and "long single-run staircases". When the height difference is below 1 m, the "few steps", which have no more than 3 steps, are generally used. Because it requires less space, the "few steps" are always set inside the site. As the height difference reaches 2-3 m, the "single-run staircase" and "folded stairs", which have 10-20 steps, are more commonly used. As the height difference between the building site and external road becomes even greater, reaching 3-9 m, a "long single-run staircase" is used to solve the problem. Because more space is needed, this kind of staircase, which always uses more than 30 steps, is always set outside the site. This will not only solve the traffic problem of the height differences between sites and external roads but also connect streets with different ground levels. More details of the design methods can be seen in Figure  7. When dealing with height differences within a site, the design methods of "steps" are always used where the building site is divided into several sections with different ground levels. When the height difference between each section is below 1.5 m, "multistep" with 3 to 10 steps is always used to solve the problem. With the increase in height difference, the number of steps increases. When there is enough space inside the building site, the steps are integrated to form an "internal long single-run staircase". As a result, this design method simplifies construction and reduces the use of space. More details on the design methods can be seen in Figure 8.
For the "ramps" design method, the slope is generally less than 10°, which is more suitable for human walking. In dealing with the height differences between building sites and external roads, the type of design method can be divided into three categories: "external ramps", "internal ramps" and "fan ramps". The "external ramp" is always used in situations where the building site is small and does not have enough space to deal with the height differences inside and outside the site. In this situation, the ramp encroaches on a certain space on the external road. In contrast, the "internal ramp" is used in situations where the site has enough space. It can maintain the integrity of the external road rather than encroaching it. A "fan ramp" is always used in situations where the external road has a certain tilt angle. Therefore, there is a fan-shaped area between the flat building site and the external road, which can be handled by a "fan ramp". When dealing with height differences inside a site, a "long ramp" is generally used where the building site has sufficient space. For the use of occupants, the slope will normally not exceed 10°. More details on the design methods can be seen in Figure 9.

Fence design methods
In situations where the external roads around building sites have different ground levels, there are variations in the height differences between the building sites and external roads. Although the problem can be solved by the design methods introduced, they only deal with one kind of height difference rather than multiple height differences. Therefore, fences are always used to hide the variations in height differences to maintain harmony. The fencing design methods analyze two types: "fence height" and "fence style".
The height of the fence increases as the height difference of the external road becomes greater. In Grade I or Grade II areas, the height of the fence is generally below 3 m, since the inclination angle of the external road is small and the height difference is only up to 3 m. In the area of Grade III, the height of the fence is generally above 3 m. As the length of the external road becomes longer, resulting in a greater height difference, the height can reach 4 m. More details of the design methods can be seen in Figures  10(a-b). The style of the fence shows different forms with the change in height difference. In the area of Grade I, because of less variation in the height difference, the height is low. As a result, the construction of the fence is less difficult, which makes the form of the fence more flexible. Therefore, a fence that shows a stepped shape followed by an external road is always used. In the area of Grade II, because of the large change in height difference, the height is above 3 m. To reduce the difficulty of construction, the height of the fence generally maintains a consistent rather than a stepped shape. In the area of Grade III, with greater variation in height difference, the height of the fence can reach up to 4 m. Therefore, the fence is always used in combination with the garage. More details of the design methods can be seen in Figures 10(c-d)

Design methods for interrelationship between architecture and landscape
The design methods introduced above mainly deal with variations in ground level, while the next method  focuses on the interrelationship between buildings and landscapes. Since this design method is most evident in residential buildings, the paper focuses on the design methods aimed at two types of buildings: "single buildings" and "group buildings".
The design methods that address the interrelationship between single buildings and landscapes show different forms due to the variation in height difference. In the area of Grade I, the building site has enough space to be utilized since there is no need to deal with complex height differences. Therefore, most of the landscape is artificially planted inside the site. In Grade II and Grade III areas, because there is more space to handle complicated variations in the ground level inside the building site, it is not suitable for creating artificial landscapes inside the site. Therefore, buildings mostly use the plants planted outside the building site as the main landscape. More details of the design methods can be seen in Figures 11(a-b) For the design methods that deal with the interrelationship between group buildings and landscape, because more buildings are built inside the site, there is less available open space. Therefore, buildings all tend to take advantage of the landscapes outside the site. Nevertheless, the type of landscape varies with the height difference. In areas with low slopes, buildings mostly use streetscapes as the main landscape. In areas with a high slope, buildings mostly use mountainous plants as the main landscape. More details of the design methods can be seen in Figures 11(c-d) Through the research work on the entire Historic District, a total of 20 design methods are obtained with four styles: "Design Methods to Deal with Height Differences Inside and Outside the Building Site", "Design Methods to Deal with Height Differences Inside the Building Site", "Fence Design Methods", and "Design Methods for the Interrelationship between Architecture and Landscape". Furthermore, according to the data counted, the distribution of different design methods in different research areas can be obtained. More data can be seen in Figure 12. At the same time, by counting the number of different design methods, the percentage of distribution in different research areas was obtained. Additional data can be seen in Figure 13.

Discussion
Tables 2 and 3 show that the distribution trend of building types and the tendency to choose particular architectural design methods have some patterns that are influenced by different slopes.
First, compared with other complex building types, the number of residential buildings is the largest in the three research areas. As the slope increases, the number of mid-rise residential buildings gradually decreases, and the number of low-rise residential buildings increases significantly, especially in the "11.7-17.3°" research area. Low-rise residential buildings are mainly distributed in the "11.7-17.3°" research area, while there is a small number of mid-rise residential buildings. This distribution characteristic shows that residential buildings can better adapt to the undulating terrain in the mountainous environment because of their wide choice of structures. The larger the slope, the simpler the structure of the building form and the greater its adaptive ability. Therefore, the choice of building type in a mountainous environment should be based on a simple structure, which reduces the difficulties in construction. Meanwhile, simple structures also make the building more flexible in the mountainous environment and weaken the damage caused by construction to the natural environment of the mountain.
Second, there are also some tendencies regarding building design methods to cope with the mountainous environment. In areas with gentle slopes, because the variation in ground level is slight, there is no need to use many areas to address the problem of height difference, leading to more available land resources. As a result, there are a variety of design methods that mainly include steps and ramps. Even the methods involve flattening without destroying the original mountain environment. With the gradual increase in the slope, the variation in ground level becomes more complicated, and the available land resources are reduced. Therefore, the design methods of "folding stairs" and "long single-run staircases", which take up fewer land resources, will be more suitable. For the choice of building fences, as the slope becomes greater, the height of the fences will also increase, and some can even be used for the function of garages. For the interrelationship between the buildings and the surrounding landscape, in areas of gentle slopes, sufficient space inside the site can be used for artificial landscaping. However, when the slope increases, to reduce the excavation and filling of the mountain, which will destroy the mountain environment, the space inside the building site is generally small. As a result, buildings usually adopt the stepped arrangement and the method of elevating buildings following the mountain topography to take advantage of the external landscape. In summary, it can be seen that under different environmental conditions, buildings will also have different design methods. Therefore, exploring the harmonious relationship between architecture and the environment and finding the most suitable design methods for different environments is of great significance for the sustainable development of architecture.
At present, some scholars have made meaningful research on the harmonious coexistence between architecture and environment. For example, (Hermawan and Švajlenka 2022) analyzed the thermal performance of buildings in terms of temperature and humidity to determine the proper types of cladding, materials, shapes, and load-bearing elements that can provide a comfortable and energy-efficient building. (Lin, He, and Zhao et al. 2021) analyzed the ecological sensitivity and site suitability of the buildings in mountain area, and proposed an optimal development and construction plan. Jozef (Švajlenka and Kozlovská 2020) evaluated the efficiency and sustainability of buildings in the mountain region, and proposed a method to determine the material efficiency. Taking Akedala Station as the study case, (Zhao, Lu, and He et al. 2022) explored the characteristics of the development and growth of greenhouse gas emissions in the building construction. Compared with these studies, this paper explores the harmonious coexistence of architecture and mountainous environment and focuses specific design methods and further explores the distribution patterns of various design methods and building types in different slope areas. For Qingdao and other mountain cities around the world, this research can provide more ideas for mountain building design, which will effectively improve the utilization of the mountain terrain for the building. As a result, this will effectively reduce the volume of building construction, and further reduce the energy consumption of building construction, reduce carbon emissions, and promote the sustainable development of buildings located in mountainous environment.
Finally, through the field research of more than 600 buildings in the Signal Hill historic district, it is found that single housing and group housing are fully integrated into the mountainous environment. They also have many different design methods to deal with height differences. However, these design methods are mostly applied to single residential buildings of 1-2 stories and group residential buildings with fewer than 6 stories. All of this shows that there are no reasonable design methods for high-rise residential buildings. With the continuous development of modern society in China, urban populations continue to increase. Therefore, people have more requirements for housing. In view of the lack of land in cities, the relevant departments have been considering the feasibility of high-rise residential buildings in mountainous areas. Therefore, it is of significance to consider how to translate and modify the various design methods to apply to high-rise residential buildings to cope with mountainous environments. Thus, high-rise residential buildings in different slope areas can fit into the mountainous environment. Moreover, it can reduce the destruction of the original mountainous environment, make the buildings suitable for this particular environment and reflect the real local conditions.

Conclusion
In conclusion, this study discusses the relationship between building and mountain environment by taking Qingdao as an example. This paper analyzes the design methods of buildings located in mountainous areas and summarizes the characteristics and distribution rules of 20 design methods. It also explores the relationship between various building types and slope angles. The research hypothesis is valid according to the data analysis: the distribution of building types was affected by the slope. Small and mediumsized buildings with strong structural tolerance can be found in areas with higher slope angles, whereas large and structurally complicated buildings are more often to be found in flat terrain. Moreover, the number of design methods and building types decreased as the slope increased. The findings provide more reasonable strategies for the construction of buildings in mountain areas, which will effectively reduce the volume of construction, reduce energy consumption and carbon emissions, and promote the sustainable development of buildings in mountain areas. The limitation of this research is that the study mainly focuses on the investigation of low-rise buildings rather than high-rise buildings, and the various analysis number of the design method is insufficient due to the number of buildings being large. Future studies can explore the relationship between high-rise buildings and slopes, and how the two can co-exist with nature.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Notes on contributors
Guangzhao Zeng is a postgraduate of Qingdao University of Technology. His research interest lies in regional design methods of architecture.