Intangible cultural heritage based on finite element analysis: force analysis of Chinese traditional garden rockery construction

Abstract

In traditional Chinese rockery stacking, the peculiarity of the materials and reliance on the personal experience of artisans during the construction process make it challenging to scientifically quantify the structural stress and use scientific methods to ensure the stability of rockery structures and the safety of the construction process. Therefore, the intangible cultural heritage of rockery stacking technology faces the problem of scientific structural inspection and risk estimation during the construction process. This study uses a finite element analysis to evaluate the structural stress of the rockery-stacking site to contribute to the sustainable development and protection of this intangible cultural heritage. After establishing a three-dimensional digital model, mechanical calculations are carried out for the overall structure of the rockery and its different parts. The analysis identifies three types of structural factors in artificial rockeries: contact, structure, and load. It also effectively and intuitively identifies the weak points in the rockery structures and provides an assessment of risks, offering valuable insights for risk prevention and for the construction and maintenance of the structures. These results contribute to the structural safety inspection of traditional Chinese rockery stacking and the structural evaluation of existing rockery heritage.

Introduction

The protection of cultural heritage should include both a site and its intangible cultural heritage. The protection of intangible cultural heritage, such as traditional knowledge, skills, and techniques, closely relates to the protection of a site itself and collectively constitutes the cultural heritage protection methodology [1,2,3]. Classical Chinese gardens, such as the Suzhou gardens, constitute World Cultural Heritage sites. Rockeries are the most distinctive symbols that distinguish traditional Chinese gardens from other gardens worldwide. They are comprised of unique landscape elements in Chinese gardens that showcase classical Chinese garden construction theory [4]. Rockery stacking, an important craft in ancient China, is now listed as an intangible cultural heritage. Therefore, to protect the cultural heritage of rockeries, it is necessary to integrate rockery-stacking techniques and intangible cultural heritage to protect rockery sites.

In recent years, with the acceleration of urbanization, the construction of buildings and gardens has been increasing. The inspection of structural safety and stability during the construction process has become an important part of the construction process. However, the structure of rockeries stacked using traditional methods does have uniqueness. After stacking is completed, it is not possible to accurately calculate the structural stability and analyze and evaluate the structural risks of traditional materials used in architecture and landscape. In addition, the construction of these structures relies on the personal experience and improvisation of artisans working on intangible cultural heritage [5]. Therefore, the particularity of these rockery structures specifically leads to the following two problems:

• i. Conventional landscape and construction materials are mostly modern, processed, and regular materials that can be subjected to objective and scientific structural stress analysis to determine structural stability, risk prediction, and maintenance management. However, since the rocks used for rockery stacking are natural, they are inherently irregular and have unpredictable bumps and irregularities on the surface that prevent us from using conventional standardized constructions in mechanical analysis. Therefore, conventional structural stress tests for standardized constructions cannot be performed.

• ii. The risk assessment of the overall structural stress in traditional rockery construction relies entirely on the experience and subjective judgment of artisans, with no objective and scientific calculation and evaluation methods. Therefore, after the construction of the project, it is not possible to carry out traditional structural stress tests, and subjective estimates can only be made through visual inspections and other methods. The builder cannot provide accurate and objective guarantees of the structural safety of the rockery.

Overall, these points indicate that traditional Chinese rockery construction cannot be subjected to structural safety and stability testing due to the special characteristics of materials, structural combinations, and subjective judgments based on experience during construction, as well as the lack of scientific analysis and judgment on the stability of rockery structures. This limits, to some extent, the persuasiveness of rockery stacking artisans in terms of construction and the structural safety of the project. In addition, the difficulty of learning is high and requires many years of experience to subjectively judge the structure of rockeries, which limits the number of people who can learn and apply this intangible cultural heritage skill. From the perspective of traditional Chinese garden heritage, the inability to scientifically quantify the safety analysis of rockery structures makes it difficult to restore and protect existing rockery heritage, accurately assess the structural stability of existing rockeries, and implement protective measures for this heritage. As a result, the methods used in the restoration of rockery heritage are inappropriate and cause consequential damage or detract from the original appearance of the work [6].

With the development of modern science and technology, the study of cultural and intangible heritage has gradually entered the scientific age [7].

Digital technologies, such as 3D scanning, have been widely applied in the cultural heritage protection field [8,9,10], and much research has emerged in the traditional Chinese garden heritage protection domain in recent years [11, 12]. There has also been much research on intangible cultural heritage using technology such as virtual reality [13,14,15,16]. Modern science and technology can improve the survival of heritage sites and provide additional possibilities for the inheritance and protection of their intangible cultural heritage [17, 18]. However, in the traditional stacking of rockeries in China, the analysis and judgment of the stress on the rockery structure are still based on the first-hand experience of the artisans. In the structural inspection during construction, there is a lack of systematic inspection and research on the structure and detailed stress of the whole rockery by modern scientific technology. Based on the perspective of intangible cultural heritage, this study uses the finite element analysis method to comprehensively evaluate the overall structure and local details of the rockeries stacked by the intangible cultural heritage heirs, analyze their structural stress states, assess the weak points of stress, and thus evaluate the structural and stress risks of the rockeries. This modern technological intervention and support in analyzing the stability of rockery structures is not an attempt to industrialize the stacked intangible cultural heritage of rockeries as a whole. On the contrary, it provides scientific and technological support and assistance for the structural safety and stability of rockery structures and offers modern assistance for this intangible cultural heritage. This approach can not only reproduce old practices but also continue the tradition in a dynamic production, thus preventing traditional crafts from being replaced by industrial practices and gradually disappearing. Therefore, the aim of this study is to use finite element analysis to develop a structural stress analysis method for traditional Chinese garden rockeries, using finite element analysis to assist inheritors of intangible cultural heritage in carrying out structural testing of rockery stacks. This will create a construction process that is more consistent with modern industrialization for the later inheritors of the intangible cultural heritage of rockery stacking and develop more ideas and ways to protect the heritage of rockery stacking. In addition, ideas for the sustainable development of heritage protection are explored from two aspects: intangible cultural heritage techniques and heritage ontology.

Materials and methods

The study site was located in Yangzhou City, China. The site’s overall rockery-stacking design was presided over by the inheritor of intangible cultural heritage who used traditional rockery-stacking techniques. The design and construction area totaled approximately 77.49 m² (Fig. 1). The west side of the site was adjacent to a wall, the south side comprised an internal water body next to a residential area, and the north side was a residential building. The site was flat with no obvious height differences. A water pool totaling 12.28 m² with a depth of about 0.79 m was established on the site. The surveying range was L-shaped.

Fig. 1

Basic status of the site (based on the team’s early scanning of the modeling content)

3D laser scanning and photogrammetry are commonly used digital measurement methods, each with different characteristics and resulting data [19,20,21]. 3D laser scanning can record detailed position and size information [22]; however, the generated data volume is large [23,24,25]. Conversely, photogrammetry can quickly record relative spatial forms [26, 27], even though its dimensional accuracy is inferior to that of 3D laser scanning [28, 29]. This study is based on the team’s preliminary 3D scanning and modeling for site analysis.

To conduct the subsequent structural and stress analyses, it was necessary to first model the site’s base. Because the site itself had no significant undulations and the ground was level, the accuracy requirements could be met by delineating the site’s boundaries from the top view and then modeling through software. Finally, the triangular mesh was reconstructed to obtain a quadrilateral mesh, and the software was used to convert the original surface model into a solid model (Fig. 2) and then build the final model (Fig. 3) based on the on-site situation. Analysis tools can be used to statistically analyze the three-dimensional data of each stone block, including volume (Table 1).

Fig. 2

Modeling of substrates

Fig. 3

Final model

Table 1 Three-dimensional data of each stone block

Simulated construction

Owing to the natural rock formations during rockery construction, it is difficult to achieve an ideal stacking effect and surface fit of the rocks during the stacking process. Therefore, common methods are to polish and cut the contact positions of the rocks. Because of the previous studies’ difficulty in involving individual stone blocks [5, 11, 12], few studies have assessed surface treatments during stacking, and there is little record of the cutting positions used. The design and construction phases of rockeries rely entirely on the experience of intangible cultural heritage artisans; therefore, there are significant technical barriers pertaining to the inheritance of intangible cultural heritage projects. During this study’s simulation-building process, collision detection was performed using Rhino software after the model was built. After starting the tool, the peak stone was selected as the first group, and the main peak bottom was selected as the second group. The distance between them was set to -5; when the two parts intersected and the intersection range exceeded that of the model error (5 mm), the model considered the parts to intersect. Accordingly, two small collision areas appeared (Fig. 4). The peak stone’s stability was vital and affected the contact areas. Although the peak stone did not tilt or collapse during the on-site construction, the preliminary analysis suggested that it had insufficient stability, requiring reinforcement measures such as brake pads and filling mortar to increase its support. This study used a collision tool to perform collision detection on the remaining stacked parts (Fig. 5b, d). The collision areas were relatively large and evenly distributed, covering the vertical lines of the stones. The collision areas in the remaining parts were small or unevenly distributed, resulting in safety hazards such as toppling and cracking.

Fig. 4

Collision detection of peak stones

Fig. 5

Collision detection of other positions

Structural and force analyses

A scientific stress analysis cannot be performed to determine the structural conditions of rockeries due to the use of natural, irregular stones. All structural and stress judgments rely on the experience and subjective judgment of artisans, unlike other architectural heritage sites. Further, the intangible cultural heritage of rockery stacks cannot undergo a standardized completion inspection, making the construction and inheritance processes difficult. This study used ABAQUS software for the model’s force analysis to determine the structural condition of the rockery. In engineering, ABAQUS can be used to simulate complex physical phenomena and engineering problems [30, 31]. In heritage protection, ABAQUS can be used to evaluate the structural safety performance of ancient buildings and cultural relics [32], as it can analyze the stability, load-bearing capacity, stress performance, and fatigue performance of building structures and predict possible damage situations. Therefore, this study can provide a scientific basis for the construction inspection process of intangible cultural heritage in rockery stacking and also provide a reference for the structural inspection and protection of existing rockery heritage sites.

In the overall rockery-stacking process, the main peak comprises the most scenic part of the rockery stack. Because of its high stack height, its structural stability and uncertainty are stronger. Meanwhile, the caves are the most complex areas during the rockery-stacking construction process. Therefore, this study selected the main peak (first group) and caves (second group) as the research objects (Fig. 6).

Fig. 6

Analysis object

Construction and simplification of analytical models

The first group of main peaks included stone 9, peak stone 1, and the main peak base (Fig. 6). To ensure that all parts, including the site and base, are enclosed, a model is a prerequisite for a finite element analysis. If the model is damaged or only has a surface, it must be repaired. A finite element analysis divides a model into many solid grids for analysis; the more detailed the theoretical grid division, the more accurate the analysis results are. The number of mesh faces in the repaired model often ranges from tens of thousands to hundreds of thousands. After being converted to surfaces, the number of surface meshes ranges from 80,000–10,000 meshes. Similar single cells have a solid mesh of 200,000–300,000 in ABAQUS. Owing to the limited computing power of a general computer, an excessive number of grids will exceed the computing power, resulting in the inability to calculate the results. In a practical application, it is necessary to perform appropriate grid partitioning according to the actual situation to achieve a balance between an accurate analysis and acceptable computational complexity. Therefore, it is necessary to simplify the model appropriately before importing the finite element software.

Accordingly, this study first processed the base part of the site. This stacking combination only made contact with parts within the site. Using the complete site as the base could significantly increase the computational difficulty and have no significant impact on the results. Excess mesh entities could also affect the observation of key contact positions; therefore, it was necessary to extract a certain range of bases for the finite element analysis and exclude the rest (Fig. 7).

Fig. 7

Extraction of the analysis object

Second, this study simplified the stone unit. When simplifying the mesh of the stones, it is necessary to consider the surface complexity and surface area of the stones. A grid surface count of approximately 1200 per m² can minimize the computational complexity while ensuring accuracy. For example, to simplify stone block 9, based on its surface area, this study calculated the appropriate number of grid faces and reduced the original number of grids from 17,500 to 2020 (88%). Similarly, this study reduced the number of grid faces for peak stone 1 to 1215 and the number of grid faces at the main peak bottom to 2104. Figure 8 presents the entities after the triangular reduction, quadrilateral simplification, and final simplification from right to left, respectively. After the reduction was complete, the mesh was converted into quadrilateral faces and solidified. While the accuracy of the simplified model could have decreased, it retained the basic morphological features. By appropriately simplifying the grid, the computational workload could be controlled within a reasonable range while ensuring the accuracy of the analysis. Figure 9 shows the two sets of analysis objects obtained after the mesh simplification and entity reconstruction. The base part comprised a regular entity; therefore, simplification was not required.

Fig. 8

Mesh simplification of analysis object

Fig. 9

Final simplification of analysis objects

Determination of material properties

The main objective of this study was to determine the relationship between the stacked stones, stacked parts, and concrete bases. It focused on studying the common structural problems in rockery stacking while retaining its basic geometric structure. This study did not assess the materials or components involved, such as cement mortar adhesives, gaskets, pins, and steel bars. Instead, it studied two main materials: the lake stone used for the rockery stacking (a calcareous limestone material) and the concrete that formed the base. Lake stone, a type of limestone, contains some impurities and minerals. Limestone generally has good compressive and flexural strengths; however, its tensile strength is relatively low. The compressive strength of the lake stone can reach more than 100 MPa, while its tensile strength is only approximately 1–2 MPa. Its mechanical properties are mainly influenced by its composition and structure rather than by its impurities and minerals. Therefore, this study simplified the lake stone into an isotropic material based on the previous research [33].

Stone experiments usually define an array of physical-property control groups to verify the influence of stone parameters on the experimental results. These physical properties include density, elastic modulus, and Poisson's ratio. Considering the limestone material, this study used universal density measures; these were the elastic modulus, Poisson's ratio, and shear strength to assess the maximum, minimum, and intermediate values within their respective ranges. This study then imported several datasets into ABAQUS to assign simple geometric structures to the materials for analysis and calculation. After the simulation calculation, no significant differences were observed in the numerical simulation results for each group of materials. The lake stone in the rockery stack differed from the metal material. The changes in the stress and strain within its material property range were small, and the difference in the results caused by numerical differences could be virtually ignored. To study the common problems in the rockery stack, this study took the material properties as the average values (i.e., universal density of 2.7 g/cm³, Poisson’s ratio of 0.32, elastic modulus of 75 GPa, and shear strength of 15 MPa). According to the on-site construction conditions, C20 plain concrete was used; thus, the mechanical properties of the C20 concrete were analyzed.

Results and discussion

Force analysis

After importing the model, it was first meshed to satisfy the static analysis requirements (Fig. 10). Subsequently, the material coefficients were assigned to the model. The concrete base had a density of 2.342 × 10⁻⁹ t/mm³, elastic modulus of 30,000 MPa, and Poisson’s ratio of 0.15. The stone material had a density of 2.7 × 10⁻⁹ t/mm³, elastic modulus of 75,000 MPa, and Poisson’s ratio of 0.32. The friction coefficient was 0.12. Regarding the load module, this study performed a force analysis of the rockery stack based on gravity by applying a gravitational acceleration in the Z-axis direction. This study set the amplitude curve as a simple linear relationship and selected the surface at the bottom of the concrete base to establish a fixed constraint.

Fig. 10

Component grid division

Analysis results of the main peak group

Overall stress analysis

The main peak group consisted of four components: peak stone 1, peak stone 2, main peak bottom, and the concrete base. According to the stress cloud diagram analysis (Fig. 11), the maximum principal stress concentration of the entire block was 3.731 MPa, which occurred at the point where the main peak stone contacted the bottom of the rock block. The stress was relatively concentrated here and could lead to mechanical damage. After cutting, a stress concentration was observed at the contact position between the main peak bottom and the concrete base (Fig. 12a), with a maximum value of 0.177 MPa. There was a large gap between the main peak bottom and the concrete base, resulting in a stress concentration. By advancing the cutting plane along the X-axis (Fig. 12b), there was a stress concentration of 0.105 MPa between peak stone 1 and another contact part at the main peak bottom. The two contact surfaces between the peak stone and the main peak bottom were small, increasing the risk of damage to peak stone 1 and the main peak bottom, which could result in stability issues. The same situation was observed for the contact relationship between peak stone 2 and the main peak bottom (Fig. 12c) due to the sharp contact position. Even if the two parts fit, there was a considerable risk of damage due to the long-term continuous force. A stress concentration of 0.044 MPa was observed in the middle of the main peak bottom due to the two peak stones (Fig. 12d). The impact on the structural stability was relatively small in the short term but could result in problems in other locations after reinforcement, renovation, and addition. Therefore, continuous testing at this location is necessary for its subsequent management.

Fig. 11

Stress cloud diagram of peak formation

Fig. 12

Sections of the stress cloud diagram

Local stress analysis

The maximum principal stress concentration of peak stone 1 was 0.985 MPa, which occurred at the contact position of the main peak bottom (Fig. 13a, b). The stress concentration at the position between the main support function and the weak point of peak stone 1 was approximately 0.65 MPa. There was also a hole in the peak stone structure, and the stress at the bottom of the hole was relatively concentrated, with a maximum value of 0.641 MPa. The maximum principal stress concentration of peak stone 2 was 0.742 MPa, which occurred at the bottom contact position with the main peak bottom (Fig. 13c). The stress was concentrated around the bottom protrusion, and the fracture risk at the bottom increased when the peak stone had long-term contact with the bottom. The maximum principal stress concentration at the main peak bottom was 0.731 MPa, which occurred at the contact position with peak stone 1 (Fig. 13d). Simultaneously, there was a potential risk of structural instability at the contact position with the concrete base (Fig. 13e) due to a stress concentration of 0.165 MPa. The maximum stress concentration of the concrete base was 0.185 MPa (Fig. 13f). A raised edge above the ground was artificially constructed at this location, so the stress concentration could increase the risks of cracking and water seepage in the concrete.

Fig. 13

Stress cloud diagram of components

Deformation analysis

The deformation of the bottom of the entire model, including the concrete and the main peak bottom, was relatively small, and there was a slight downward deformation of peak stone 2 (Fig. 14). The main deformation occurred in peak stone 1, which also underwent significant deformation. The upper part of peak stone 1 underwent X-axis negative direction (backward) deformation, whereas the middle and lower parts underwent Z-axis negative direction (downward) deformation. Thus, peak stone 1 had poor stability and was at risk of tilting backward.

Fig. 14

Deformation analysis

Analysis results of the cave group

Stress analysis

The cave group consisted of three components: the top stone, the bottom of the cave, and the concrete base. The stress concentration occurred at the location in which the three came into contact, with a maximum stress concentration of 0.327 MPa (Fig. 15). At this location, the top stone of the cave was in direct contact with the concrete base, and the edge of the base was relatively sharp. The stacked stones at the bottom of the cave did not provide support for or increase the contact area, resulting in a stress concentration. Considering the possibility of edge stress concentration, this study conducted a separate analysis.

Fig. 15

Stress cloud diagram of cave formation

By establishing a YZ axis cross-section and advancing along the X-axis, the results revealed a stress concentration at the bottom of the cave near the concrete base (Fig. 16a), with a magnitude of 0.875 MPa. This location was located deep in the cave and was influenced by the shapes of the stones. The bottom of the cave did not contact the base, resulting in an arched cavity, and the load was not transmitted evenly to the base. After the construction was completed, the top of the cave was completely closed, and landscape plants were planted. The increased load increased the risk of damage at this location. If a fracture occurred, the integrity of the cave wall and the arched cave body could be damaged, potentially resulting in a local collapse.

Fig. 16

Stress cloud diagram of components

By establishing the XZ axis cutting plane and advancing along the Y axis (Fig. 16b), a stress concentration was observed at the contact point between the top stone and the bottom of the cave, with a maximum value of 19 MPa. Compared to the other side of the cave, the contact relationship between the top stone and the bottom of the cave was better at this position; however, the contact surface size was insufficient and could damage the supporting structure. The maximum stress concentration was 0.038 MPa, and the supporting “cave pillar” was an arc-shaped stone (Fig. 16c). This study did not consider the anisotropy of the material; therefore, no significant anomalies were observed. However, in similar situations, when a “cave pillar” is constructed from multiple stones, special attention should be paid to the stacking condition, as it can affect the stability of the entire opening.

The stress concentration was on the left side of the concrete base and cave (Fig. 16d). A stress concentration of 0.047 MPa was observed in the middle of the cave’s roof stone. The was a characteristic edge extended along the X-axis at this location. Although there was no significant decrease in thickness, the cave roof stone was at risk of cracking, which could first occur at this location.

After separately assessing the concrete base, a maximum stress concentration of 0.026 MPa was observed (Fig. 16e–f). There was a stress concentration in the lower part of the concrete base rather than in the upper part, potentially due to the characteristics of the large upper and small lower parts after stacking in the cave. The cave formed an arched structure, and the load was transmitted to the lower part of the concrete base; thus, the stress at the bottom part of the cave was more concentrated than that at the upper part. Blue patches appeared on the point cloud map of the bottom of the cave, indicating that technical means could be used to improve the contact relationship and further reduce the risk of damage to the bottom of the cave. This could also be verified by observing the stress symbol map.

Deformation analysis

The maximum deformation occurred in the middle right side of the cave’s roof stone (Fig. 17a), which was consistent with this study’s expectation. However, its deformation direction along the negative X-axis (forward) exceeded this study’s expectations. Owing to the complex shape of the cave’s roof stone, it was difficult to accurately predict its deformation based on the visual analysis. The finite element analysis showed that the cave’s roof stone could tilt forward. Moreover, the stone at the top of the cave could undergo a tangential deformation with that at the bottom of the cave (Fig. 17b). Therefore, it is necessary to pay special attention to the stability of the rockery stacking at this location to avoid tangential displacement along the contact surface.

Fig. 17

Deformation analysis

A discussion of the analysis results with inheritors of this intangible cultural heritage revealed that the overall and local stress conditions analyzed in the experiment were basically consistent with the inheritor’s judgment during the process of rockery-stacking and could assist the inheritor in conducting a more comprehensive inspection of the stress weaknesses of each component after design, enabling them to use small sheet stones (Fig. 18) for reinforcement. Regarding the deformation results, the inheritors stated that continuous monitoring can be carried out in the subsequent process, which can avoid the influence of other factors that may arise during the subsequent construction process. The results are mostly consistent with empirical judgments; however, there are some issues that are easily overlooked, which are listed below.

• i.i.i. The main peak group

Fig. 18

Sheet stones for reinforcement

Contact problems: When standing on a peak, the main peak is a focal point in design and construction. Sharp contact problems on the surface of the peak stones can be detected by empirical evaluation. However, even in cases of good contact conditions, the structural properties of the stones themselves can lead to stress concentrations that are difficult to detect and require the use of scientific analysis tools.

Stability problem of the multi-block structure: The volume of the main peak is larger than that of other positions, and the stability evaluation of the multi-block structure exceeds the general empirical evaluation, so potential hazards are difficult to detect.

Potential gaps: It is difficult to avoid potential gaps during the stacking process of the main peak. If the gaps are close to the foundation, unsatisfactory ground contact can easily occur, which can affect the overall stability. This problem is easily overlooked during the stacking process.

The issue of foundation stability: whether the foundation load is within a reasonable range and whether the stress concentration leads to foundation damage, which is easily beyond the scope of empirical evaluation.

Risk assessment of the main deformation peak and displacement: Due to the irregularity of the rock, it is difficult to empirically assess the deformation and displacement trends, and the understanding of the tilting problems can only remain at the level of right and wrong. The direction and extent of tilting require the use of analytical tools.

• ii.ii.ii. The cave group

The problem of the integrity of the arch structure at the entrance: due to the different shapes and properties of the stones, the stacked entrance may not conform to the integrity of the vault structure, which greatly increases the risk of collapse. By using 3D digitization and finite element analysis, problems can be detected in time.

The problem of large-scale cracking in the stones of the cave roof: a stone with a large span is at risk of cracking in the central part. A finite element analysis can quantify the risk and facilitate subsequent management.

Stress problem on the tunnel wall: If the stress on the tunnel wall structure is uneven, there will be a concentration of stress, leading to an increased risk of localized damage, which in turn affects the overall structure. As visual observation is limited, there is insufficient experience to understand this problem. With the help of analysis tools and stress cloud maps, the problem can be visualized.

The results clearly and intuitively show that finite element analysis can reveal the weak points in the process of rockery stacking. Moreover, this has been confirmed by the heirs of this intangible cultural heritage. It can also help the heirs of the intangible cultural heritage to identify stress risks that cannot be clearly determined based on experience alone. This result proves that finite element analysis can play a supporting role in the process of rockery stacking by enabling scientific force detection and analysis during the construction process. This provides a scientific basis for traditional rockery stacking that strengthens the rockery stacking process based on the experience of the artisans. The analysis clearly shows that through the application of finite element analysis, this study has successfully deciphered the structural loading problems inherent in the traditional rockery stacking process. Compared to previous methods that used models to analyze and derive the internal structures of existing rockery [4, 33], this study proposes a quantifiable modern technology that helps in determining the stability and safety of rockery structures. According to the simulation method used in this study, the main parts of the rockery model must first be divided into four parts: Summit, Cave, Individual Stones, and Revetment. After the construction is completed, the stresses and deformations of the model should be analyzed with finite element software (e.g., whether there is a large area of uneven stresses) to determine whether the model structure is safe. If the model structure is found to be unsafe, it should be rebuilt. However, if the structure is safe, risk prevention and identification of key monitoring areas for rockery structures are carried out based on the force analysis to facilitate the continuous monitoring of rockery structures in the later stage and appropriately strengthen weak points under stress. This study serves as a reference for later safe and standardized construction (Fig. 19). It not only supports the structural safety and scientific risk assessment of this intangible cultural heritage but also serves as a reference for subsequent structural reviews of the existing rockery heritage.

Fig. 19

Flowchart of finite element analysis for rockery structure stress

Conclusion

This study used a finite element analysis to explore the application of modern technology to evaluate the safety and stability of traditional rockery-stacking structures. It also analyzed various structural stress problems that might occur after the completion of stone stacking. Moreover, the use of the finite element analysis to evaluate the potential structural hazards enabled this study to propose targeted rockery-stacking improvement and maintenance suggestions. This approach addresses the limitations of previous methods, in which the determination of the stress and stability of rockery structures solely relied on the subjective judgment of inheritors of intangible cultural heritage through personal experience. It also solves the problem of rockeries’ unpredictable structural safety risks after construction is completed. The results are of great significance for the sustainable development of this intangible cultural heritage and can provide a reference for the structural risk assessment of existing rockery heritage in other traditional Chinese gardens.

The results of the stress analysis conducted on the entire rockery revealed the main structural stress problems that may be faced during the stacking process of rockeries. In particular, in standing peaks, both sharp and non-sharp contact can cause excessive stress and lead to fracture or detachment. The stability problem of multi-block structures can determine the instability of the entire structure. Potential void problems may also cause the collapse of the entire structure. Basic stability issues can lead to structural detachment or instability, whereas main peak deformation and displacement issues can cause structural tilting or displacement and even fracture. Both potential and indirect contact in the revetment may lead to excessive stress and cause detachment or displacement. Additional load issues may also cause structural detachment or instability, fracture, or displacement. The structural stability issues of the standing stone itself may lead to its detachment, instability, and even fracture. The risk of tipping over is also an important issue. If the standing stone tilts or deviates, it may cause displacement or collapse of the entire structure. The integrity issues of the cave arch structure may lead to detachment or instability. The problem of large-span cracking of the roof stone may also determine fracture. The stress problem on the cave wall may lead to structural tilting or displacement and even collapse (Table 2).

Table 2 Structural stress problems

To tackle the above issues, adjustments can be made based on three types of factors: contact, structure, and load.

• i.i.i. Contact

Sharp Contact: Increase the contact area and reduce the stress concentration by changing the contact angle or increasing the contact area.

Non-Sharp Contact: Implement regular controls of the status of contact points to promptly identify and address problems.

Potential Contact: Adjust the layout or structure, move the contact points away from fragile areas, or use other materials to replace the contact points.

Indirect Contact: Strengthen monitoring and management, promptly identify loose or damaged connections, and carry out repairs.

Integrity of the Arch Structure: Increase the contact area, reduce stress concentration, and improve the support structure of the arch.

• ii.ii.ii. Structure

Stability of the Multi-body Block Structure: Adjust the layout or structure, adjust the position of stones, or add support to enhance structural stability.

Potential Gaps: Strengthen monitoring and management, check the impact of gaps between stones, and promptly fill or fix them.

Main Peak Deformation and Displacement: Add support or replace stones with more stable support materials.

Self-Structural Stability: Rearrange the position of the stones or add support, and cancel the placement if necessary.

Risk of Tipping Over: Increase support, increase the number of support points, or replace stones with more stable support materials.

Large Span Cracking of Cave Roof Stone: Strengthen monitoring and management and regularly inspect the condition of the roof stones.

Stress on the Cave Wall: Adjust the layout or structure to reduce the occurrence of uneven stress on the tunnel wall.

• iii.iii.iii. Load

Foundation Stability: Strengthen monitoring and management, regularly check the status of the foundation, promptly identify problems and implement reparations.

Additional Load: Adjust the layout or structure, rearrange the position of the stones, or add support to enhance the load-bearing capacity of the structure.

At the same time, in response to the above issues, the stress risk of the rockery can be labeled and a risk monitoring map (Fig. 20) can be drawn. The foundation, main body, accessories, and other parts of the rockery must be regularly inspected and any problems must be promptly addressed. In addition, the surface of the rockery must be regularly cleaned from water stains, dirt, and so on, repaired, and reinforced. Different maintenance and management methods must be adopted for different materials and parts according to their characteristics.

Fig. 20

Schematic diagram of key monitoring areas

Although this study combined modern technology with traditional rockery-stacking techniques, the research remained in the exploratory stage and had the following limitations. First, owing to the size of the research object, this study lacked coverage of the various elements and techniques related to rockery stacking despite summarizing some general issues. Future studies should use more complex rockery-stacking projects as their research objects to enrich this study’s analysis results. Second, owing to the limited ability of the analysis equipment’s computational power, the model accuracy of the finite element analysis process was reduced; meanwhile, the selected analysis materials were common materials. Future studies should use higher-precision analysis models to better comply with standardized construction materials. Despite these limitations, this study demonstrates the advantages and necessities of using finite element technology in the inheritance and protection of intangible cultural heritage in rockery stacking:

The rockery-stacking model was imported into ABAQUS software for the finite element analysis. By analyzing the stress and deformation concentrations, problems in the stacking structure could be identified. Accordingly, on-site targeted improvements were proposed and implemented. In the future, the results of the analysis can also assist in engineering stacked structures. Potential hazards identified through the analysis can be recorded in the database, allowing for targeted monitoring and management work to be conducted in the future that implements precise maintenance strategies to make maintenance management more scientific. Simultaneously, such scientific analysis can advance the understanding of the ancient rockery-stacking technique, which can further facilitate the structural understanding of the extant rockery heritage sites and provide more scientific methods for heritage detection and monitoring. It can also provide a reference for the protection of the extant heritage rockery sites and future research on rockery structures.