Visualization of Construction Sequence and Fuzzy Logic Evaluation of The

Home , 1556 Shaanxi earthquake, Chinese palace, Dougong, Giant Wild Goose Pagoda, Li Hui (Tang Dynasty), Longhua Pagoda

Giant Wild Goose Pagoda (Dayanta) in China

Master Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Masters of Science in the Graduate School of The Ohio State University.

By Fei Yang, B.S. Graduate Program in Civil Engineering

The Ohio State University 2016

Thesis Committee: Dr. Fabian Tan, Advisor Dr. Abdollah Shafieezadeh, Committee Member Dr. Philip Smith, Committee Member Dr. Karen Dannemiller, Committee Member

Fei Yang

2016

Abstract

Dayanta, also called the Great Wild Goose Pagoda, is a square seven-floor pagoda located in Xi’an, Shaanxi Province, China. This thesis provides a visualized investigation of Dayanta in three aspects: (1) redrawing the four different versions of Dayanta in history; (2) providing a 3-D simulation of the structure and construction sequence of today’s Dayanta by using Autodesk 3DS MAX in a step-by-step manner; and (3) evaluating the performance of Dayanta by using Fuzzy Fault Tree Analysis (FFTA) in the form of diagram and fuzzy logic graphics. A graphics pipeline has been proposed as the methodology to accomplish the entire modeling work, and it offers an effective method for the digital reconstruction of ancient buildings and graphical simulation in its structure and construction activities. The significance of the Dayanta modeling work can be reflected in the contributions to preserve ancient architecture, visualize historical data in 3-D graphics, and apply the models in education. The results produced by the two FFTA agree with a real observation of Dayanta, ranging from extremely good to very good, verifying the effectiveness of the use of FFTA to investigate the Dayanta’s performance. In conclusion, the visualized investigation of ancient building can be regarded as an exploration of the application of visualization techniques and the employment of fuzzy methods when investigating the performance of the Dayanta.

KEYWORD: 3-D graphical simulation, angular fuzzy model, construction sequence,

Dayanta, fuzzy fault tree, Giant Wild Goose Pagoda, visualization ii

Dedication

Dedicated to my family

iii

Acknowledgements

First and foremost, I would like to express my gratefulness to my advisor Dr.

Fabian Tan for his encouragement and guidance in my research. With his patient advice and insightful vision, I could finish my research from a small initial idea to this systematic work. This thesis cannot be accomplished without his patient instruction and advising.

Also, I sincerely thank to all my committee members, they are Dr. Abdollah

Shafieezadeh, Dr. Karen Dannemiller and Dr. Philip Smith. With their constructive comments and intellectual suggestions, I could retrospect to my thesis, discover drawbacks and make improvements continuously.

Additionally, I thank all my friends in my program, who provided me with excellent comments and suggestions during my research. Especially, I want to thank Lixin Jia and her son, who helped me take photos onsite. Without their help, I cannot complete such an excellent work. Moreover, I appreciate all my friends in Columbus Chinese Christian

Church (CCCC), and I cannot gain such an achievement without their emotional support.

Lastly and most importantly, I want to thank my parents and my husband for providing me with encouragement and support when I was working on my thesis. Your continuous trust and sincere blessings are inexhaustible motivation for me through my life forever.

Vita

2012 ...... B.S. Civil Engineering, Beijing University of Civil Engineering and Architecture, Beijing, China

2014-2015 ...... Graduate Program of Civil Engineering, Ohio University

2015-Present ...... Graduate Program of Civil Engineering, The Ohio State University

Publications

Yang, Fei, Shilun Hao, Adrian Tan and Fabian Tan. 2016. “Graphic Modeling for Step-By- Step Construction of the Dayan Pagoda In Xi’an.” Proceeding of the 16th International Conference on Geometry and Graphics, ICGG 2016. Beijing, China. Yang, Jin, Adrian Tan, Fabian Tan, Michael Parke and Fei Yang. 2016. “Computer-Aided Construction of The Great Wall of China in Jinshanling.” Proceeding of the 16th International Conference on Geometry and Graphics, ICGG 2016. Beijing, China. Hao, Shilun, Adrian Tan, Fei Yang and Fabian Tan. 2016. “Graphical Simulation of the Construction Process of Chinese Dougong Using Virtual Reality.” Poster Session of the 16th International Conference on Geometry and Graphics, ICGG 2016. Beijing, China. Liang, Man, Fei Yang, Shilun Hao and Fabian Tan. 2016. “Graphical Simulation of Humble Administrator’s Garden and Animations.” Poster Session of the 16th International Conference on Geometry and Graphics, ICGG 2016. Beijing, China.

Fields of Study

Major field: Civil Engineering

Table of Contents

Abstract ...... ii

Dedication ...... iii

Acknowledgements ...... iv

Vita ...... v

Table of Contents ...... vi

List of Figures ...... x

List of Tables ...... xvii

Chapter 1 Introduction ...... 1

1.1 Overview ...... 1

1.2 Goal ...... 4

1.3 Scope ...... 5

1.4 Objective ...... 6

1.5 Limitations ...... 7

1.6 Tasks ...... 9

Chapter 2 Literature Review ...... 12

2.1 Humanity ...... 12

2.1.1 Public culture ...... 12

2.1.2 Buddhist cultural influence ...... 14

2.2 Mechanical ...... 17

2.2.1 Anti-seismic studies ...... 17

2.3 Graphical simulation ...... 20

2.3.1 3-D Modeling ...... 20

2.3.2 VR simulation ...... 23

2.3.3 Digital Reconstruction ...... 25

2.4 Fuzzy Logic ...... 27

Chapter 3 Historical Studies ...... 30

3.1 A Brief History of the Dayanta ...... 30

3.2 First Version of the Dayanta (AD 652–704) ...... 35

3.3 Second Version of the Dayanta (AD 704–930) ...... 39

3.4 Third Version of the Dayanta (AD 933–1604) ...... 42

3.5 Fourth Version of the Dayanta (AD 1604–present) ...... 45

Chapter 4 Substructure ...... 48

4.1 Water Table ...... 48

4.2 Soil Condition ...... 52

4.3 Foundation ...... 56

vii

4.4 Leaning ...... 61

Chapter 5 Superstructure ...... 66

5.1 Introduction of Chinese ancient pagoda ...... 66

5.2 Planning ...... 73

5.3 Materials ...... 76

5.4 Repairing history ...... 79

5.5 Support System ...... 81

Chapter 6 Graphical Simulation ...... 88

6.1 Overview ...... 88

6.2 Software Selection ...... 102

6.3 Model Inaccuracies ...... 112

6.4 Simulation of the Construction sequence ...... 117

6.5 Animation ...... 136

Chapter 7 Fuzzy Fault Tree Analysis...... 141

7.1 Introduction ...... 142

7.2 Angular Fuzzy Model ...... 153

Chapter 8 Summary, Conclusion and Recommendations ...... 176

8.1 Summary and Conclusion ...... 176

8.2 Recommendations ...... 179

viii

References ...... 182

List of Figures

Figure 1.1 Today’s Dayanta in Xi’an ...... 2

Figure 1.2 The Dayanta and the Ji’En Temple in Xi’an ...... 2

Figure 1.3 Graphics pipeline of the graphical simulation ...... 9

Figure 3.1 Four versions of the Dayanta in Autodesk 3DS MAX: Overview ...... 35

Figure 3.2 Four versions of the Dayanta in Autodesk 3DS MAX: Multi-view ...... 35

Figure 3.3 First version of the Dayanta (AD 652–704), redrawn by the author from Yang

(2007)...... 38

Figure 3.4 Second version of the Dayanta (AD 740–933), redrawn by the author from

Yang (2007)...... 40

Figure 3.5 Third version of the Dayanta (AD 933–1604), redrawn by the author from

Yang (2007)...... 44

Figure 3.6 Fourth version of the Dayanta from (AD 1604–present), redrawn by the author from Yang (2007)...... 46

Figure 3.7 Tourism at the Dayanta and the Great Ci’en Temple ...... 47

Figure 4.1 Changes of phreatic water levels in the water table of Xi’an from 1986 to 2002

...... 49

Figure 4.2 Changes of confined groundwater levels in the water table of Xi’an from 1982 to 2004 ...... 50

Figure 4.3 Rammed earth foundation of the Dayanta ...... 57

Figure 4.4 Timber pile foundation of the Dayanta ...... 57

Figure 4.5 Strip foundation of the Dayanta ...... 58

Figure 4.6 Mixed foundation of rammed earth and two layers of strip foundation of the

Dayanta ...... 61

Figure 4.7 Change in the lean of the Dayanta in recent years ...... 62

Figure 5.1 Yingxian Wooden Pagoda in Shanxi Province, built using the unique Chinese dougong architectural component ...... 67

Figure 5.2 Composition of a typical Chinese pagoda ...... 68

Figure 5.3. Pavilion-style pagoda: The Dayanta in Xi’an ...... 70

Figure 5.4 Intensive eaves with dougong of Yingxian Wooden Pagoda...... 71

Figure 5.5 Timber pagoda at Hanshan Temple, Suzhou, Jiangsu Province ...... 71

Figure 5.6 Beisi Pagoda of Baoen Temple, Suzhou, Jiangsu Province ...... 72

Figure 5.7 Lamaist pagoda: White Pagoda of Miaoying Temple in Beijing ...... 73

Figure 5.9 Mineral composition of the bricks used in the Dayanta...... 76

Figure 5.10 A metal pagoda in front of Sanqing Hall at the Xuanmiao Temple ...... 78

Figure 5.11 Support system of the fourth floor of the Dayanta in 3-D simulation ...... 83

Figure 5.12 Pillar system of the Dayanta in the 3-D simulation ...... 85

Figure 5.13 Caisson ceiling on the second floor of the Dayanta ...... 86

Figure 5.14 Comparison between the modeled stairs and the real stairs of the Dayanta

...... 87

Figure 6.1 Graphics pipeline of the Dayanta ...... 90

Figure 6.2 Basic modeling of exterior wall of level on of the Dayanta ...... 90

Figure 6.3 Assembled outer structure of level one, including the exterior wall, extended eaves and hanging decorative components...... 92

Figure 6.4 Assembly hierarchy of the Dayanta ...... 93

Figure 6.5 Maps panel and sample textures in the materials editor in Autodesk 3DS Max

...... 94

Figure 6.6 Selecting a bitmap in the diffuse channel in the materials editor and assigning it to the exterior walls ...... 95

Figure 6.7 Adding bump effects to the texture, which can be previewed in the sample ball ...... 96

Figure 6.8 Rendered indoor scene of the Dayanta with adding light effects ...... 99

Figure 6.9 The 172nd frame from the animation of the rendered Dayanta ...... 100

Figure 6.10 Rendering settings panel and the final rendering results in Autodesk 3DS

MAX at an output size of 640 × 480, requiring 00:01:33 for rendering ...... 101

Figure 6.11 Simulation of Roman Colosseum in Google SketchUp ...... 103

xii

(courtesy of Tan 2015) ...... 103

Figure 6.12 Simulation of Roman Colosseum in Cinema 4-D (courtesy of ...... 103

Tan 2015) ...... 103

Figure 6.13 Simulation of Chinese temple with Wudian in Autodesk Inventor (courtesy of

Li 2014) ...... 104

Figure 6.14 Simulation of the Jinshanling section of the Great Wall in

SolidWorks(courtesy of Yang 2016) ...... 104

Figure 6.15 Simulation of the Lalibela Rock Hewn Church in SolidWorks (courtesy of

Ridgill 2016) ...... 105

Figure 6.16 Simulation of Chinese dougong in Autodesk 3DS MAX (courtesy of Hao 2016)

...... 105

Figure 6.17 Simulation of Humble Administrative Garden in Lumion (courtesy of Liang

2016) ...... 106

Figure 6.18 Model inaccuracies of the decorative components on the exterior walls .. 114

Figure 6.19 Model inaccuracies of the masonry guard rails at the base ...... 115

Figure 6.20 Model inaccuracies of the spirally constructed stairs around the pillars .... 116

Figure 6.21 Excavate and build the dual layer strip foundation ...... 118

Figure 6.22 Backfill and compact the rammed earth into the strip foundation ...... 119

Figure 6.23 Build the base of the Dayanta...... 119

Figure 6.24 Build exterior walls for Level 1 in the four directions...... 120

xiii

Figure 6.25 Pillar configuration on the Level 1 in a plane view ...... 121

Figure 6.26 Building the supporting pillars on Level 1 in the 3-D graphical model ...... 122

Figure 6.27 Add the horizontal decorative components on the top of exterior wall on

Level 1 ...... 123

Figure 6.28 Build the eaves extending toward the outside in the middle on Level 1 .... 124

Figure 6.29 Build the stairs, pillars, beams, and caisson ceiling for Level 1 ...... 125

Figure 6.30 Build the exterior walls and eaves for Level 2 ...... 126

Figure 6.31 Build the stairs, pillars and beams for Level 2 ...... 127

Figure 6.32 Build the exterior walls and eaves for Level 3 ...... 127

Figure 6.33 Build the stairs, pillars and beams for Level 3 ...... 128

Figure 6.34 Build the floor slab, interior wall, exterior wall and eaves for Level 4 ...... 129

Figure 6.35 Build the stairs, pillars and beams for Level 4 ...... 129

Figure 6.36 Build the floor slab, interior wall, exterior wall and eaves for Level 5 ...... 130

Figure 6.37 Build the stairs, pillars and beams for Level 5 ...... 130

Figure 6.38 Build the floor slab, interior walls, exterior walls and eaves for Level 6 ..... 131

Figure 6.39 Build the stairs, pillars and beams for Level 6 ...... 131

Figure 6.40 Build the floor slab and exterior walls for Level 7 ...... 132

Figure 6.41 Build the stairs, pillars and beams for Level 7 ...... 132

Figure 6.42 Build the roof on the top level of the Dayanta ...... 133

xiv

Figure 6.43 Build the spire on the top level of the Dayanta ...... 134

Figure 6.44 Build the guard rails around the ground floor ...... 134

Figure 6.45 Build the access stairs from the lower base to the upper base of the Dayanta

...... 135

Figure 6.46 Finished structure of the Dayanta ...... 135

Figure 6.49 Step-by-step animation of the construction sequence of the Dayanta: Level 1

...... 138

Figure 6.50 Step-by-step animation of the construction sequence of the Dayanta: Level 3

...... 138

Figure 6.51 Step-by-step animation of the construction sequence of the Dayanta: Level 6

...... 139

Figure 6.52 Visual walk-through of the Dayanta: Overview ...... 139

Figure 6.53 Visual walk-through of the Dayanta: Guard rails and access stairs ...... 140

Figure 6.54 Visual walk-through of the Dayanta: Inside the Dayanta ...... 140

...... 149

Figure 7.2 Angular fuzzy model ...... 153

Figure 7.3 Welcome page of the Windows-based application ...... 158

Figure 7.4 Basic events of FFTA in the Windows-based application ...... 159

Figure 7.5 Results of the intermediate events of FFTA in the Windows-based application

...... 162

Figure 7.6 Result of top events of FFTA in the Windows-based application ...... 163

Figure 7.7 Customized basis events of FFTA in the Windows-based application...... 165

Figure 7.8 Less positive evaluation of the top events of FFTA in the Windows-based application ...... 166

Figure 7.9 Graphics model of interior wall in the pop-up window...... 168

Figure 7.10 Graphics model of strip foundation in the pop-up window ...... 169

Figure 7.11 Tree-diagram of the structure of Dayanta ...... 170

Figure 7.12 Graphical simulation of the construction sequence of the Dayanta ...... 172

Figure 7.13 A zoomed out view of construction sequence ...... 173

Figure 7.14 Graphical simulation of foundation assumptions of the Dayanta ...... 174

xvi

List of Tables

Table 4.1 Soil conditions of the Great Wild Goose Pagoda ...... 52

Table 4.2 Physical properties of the loess in the Loess Plateau in northwestern China .. 53

Table 4.3 Granular composition of the loess in the Loess Plateau in northwestern China

...... 53

Table 5.1 General dimensions of the Dayanta...... 75

Table 5.2 Detailed dimensions of the Dayanta ...... 75

Table 5.3 Destruction history of the Dayanta ...... 79

Table 5.4 Repair history of the Dayanta ...... 80

Table 6.1 Software selection evaluation ...... 112

Table 7.1 Comparison using the inductive and deductive methods ...... 145

Table 7.2 The components of FTA ...... 146

Table 7.3 The calculation procedures of FTA using probability theory ...... 150

Table 7.4 Definitions of membership functions in angular model ...... 154

Table 7.5 Evaluations of basic events in the angular FFTA ...... 155

Table 7.6 Weights assigned for the intermediate events in the angular FFTA ...... 160

xvii

Chapter 1 Introduction

1.1 Overview

The Dayanta, also called the Dayan Pagoda or the Great Wild Goose Pagoda, is a square, seven-floor pagoda located in Xi’an, Shaanxi Province, China. Originally built in

AD 652, the Tang Dynasty in Chinese history, the Dayanta has been the symbolic building of Xi’an as well as ancient Chinese culture. The initial function of the Dayanta was to preserve Buddhist scriptures. It was reconstructed three times from the Tang

Dynasty to the Ming Dynasty due to earthquake and war damage and deteriorating structural components, finally reaching the way it appears today (Figure 1). The Dayanta began to tilt during the Qing Dynasty, and by 1996, its inclination was measured at approximately one meter. The Dayanta has been under official protection since the

People’s Republic China was founded, and in 1963, the Dayanta was listed as one of the most important national treasures by the National Culture Preservation Commission. In

2013, it became one of the stations on the Silk Road, which runs from Chang’an to

Tianshan and is a well-known historical bridge connect Eastern and Western cultures. To preserve the Buddhist scriptures, Xuanzang, a famous Chinese monk, brought them from India in AD 652 and translated them to Chinese (Yang, 2007). The architectural style of the Dayanta was intended to mimic ancient Indian style. Its original name, "Ci’En

Si Ta," means "this building is a part of the temple named 'Ci’En Si'—the “Ci’En” or

“Ji’En” Temple, as shown in Figure 2. The pagoda located in front of the temple changed its name to the “Dayanta” or the “Dayan Pagoda," meaning the "Giant Wild Goose

Pagoda,” as opposed to the “Small Wild Goose Pagoda” located in the same city.

Regarding the origin of the name of these “Wild Goose” pagodas, legend has it that they were built on locations where wild geese were buried.

Figure 1.1 Today’s Dayanta in Xi’an

Figure 1.2 The Dayanta and the Ji’En Temple in Xi’an

Initially, the Dayanta, whose exterior was made of bricks and its interior of adobe, had only five floors. During the Wu Zhou Dynasty (AD 690–705), plant grew among the bricks, causing the pagoda to deteriorate. The empress Wu Zetian renovated the pagoda and also added two more floors. By the late Tang Dynasty (AD 828–907), the pagoda had been extended to ten floors. Unfortunately, the pagoda was destroyed during the frequent wars in the Late Tang Dynasty. It was later reconstructed, but with only seven floors. From AD 930 to AD 933, local officials in Xi’an reinforced and renovated the walls and stairs of the pagoda, which are still in use today. In the North Song Dynasty (AD

960–1127), the buildings in the Ci’en Si compound were ruined and totally ignored by the government: only the Dayanta was preserved. During the Ming Dynasty in AD 1466, the pagoda and the Ci’en Si were both reconstructed; stairs were installed and exterior walls were built by adding an extra layer of bricks as reinforcement, which can be seen to this day. The evolution and variations of the Dayanta over time, including its appearance, style and the architectural culture behind it, are discussed in Chapter 3.

Owing to the ongoing development of computer science and graphics technology, digital modeling has been widely used in civil engineering, archaeology and architecture, especially for ancient buildings, such as the reconstruction of Roman Colosseum modeled by Tan (2013 and 2015), the digital simulation of a unique structure called dougong used in ancient Chinese architecture (Hao 2014) and the author’s own research concerning the simulation of the Dayanta (Yang 2016). In an era where information expands and becomes more intensive daily, using graphics as a form of interaction and communication has undoubtedly been considered as one of the most efficient and

effective ways to convey messages and educate students. When faced with ancient

(original but often fragmented) descriptions of ancient buildings, sometimes the best way to interpret or reinterpret them is to model the building by applying 3-D graphics data to build a 3-D model in software, reconstruct the buildings digitally, and present the models to the public. Due to the subjective information and scarcity of this data, the most effective way to present the results is likely be through the use of fuzzy fault tree analysis methods. In short, the process, method, design and realization of visualization is the central point of this paper, which focuses, as the title implies, on both a graphical simulation of the construction sequence used for the Dayanta and employing graphics- based fuzzy logic analysis methods to create the simulation.

1.2 Goal

As the use of computers in classrooms expands, it becomes worthwhile to apply visualization tools to improve education. In architectural classes, adopting graphical modeling to explain specific construction-related topics and using it as a visual evaluation method both makes such visualization possible and also serves to make these techniques accessible to greater numbers of students. From an educational point of view, this thesis provides its audience, which ranges from the large group of students interested in an ancient Chinese building—the Dayan Pagoda—to a narrower group who are eager to learn about the historical variations the pagoda has undergone, its structural details, and its current performance, with research outcomes that introduce a

Chinese treasure, the Dayan Pagoda, with pride and confidence. With this goal in mind, I believe my thesis, which combines computer graphics with digital modeling and the evaluation method, fuzzy fault tree analysis (FFTA), will be an invaluable resource for future educational purposes.

1.3 Scope

This paper has two objectives: to document the construction sequence of the

Dayanta visually using advanced 3-D graphics techniques and to investigate the performance of the Dayanta by adopting fuzzy fault tree approaches. In more detail, the first objective involves graphically simulating the structure and the construction sequence of the Dayanta by using 3-D modeling software; specifically, by simulating the steps that show how this pagoda was built from its foundation to its spire, along with its structural components and decorative features, internal facilities such as stairs and the building façade. However, not only will the main body of the building itself be graphically modeled but also its underground foundation, soil conditions and the water table beneath the Dayanta. Combined, these will present the Dayanta's composition in layers, in 3-D graphical form.

The other objective involves visualizing the process of assessment of the pagoda's performance. Unlike some common evaluation reports, in which statistical models have been widely applied and the results shown mostly in the form of numbers, this paper performs an evaluation of the performance of the Dayanta using fuzzy fault tree

analysis. Specifically, the angular fuzzy fault tree analysis method are presented in graphical forms. Considering the fact that the true and exact conditions of the Dayanta have barely been measured—especially the soil condition, inconsistencies within the historical documents, and incomplete records about the construction and repair of this building, the adoption of fuzzy logic approaches can provide relatively satisfactory results with respect to evergreening and maintaining the structural reliability of the

Dayanta. These techniques are discussed in detail in Chapter 7.

1.4 Objective

As defined in the scope, the overall objective is to visualize the investigation of the

Dayanta with respect to its construction and as an evaluation of its structural safety and reliability. Specifically, for the first aspect, the structure of the Dayanta is graphically modeled in a step-by-step manner in 3-D graphics. In this graphical simulation, the structure of the entire main body of this pagoda, including its foundation, substructure, superstructure, floors, pillars, support systems, etc., are modeled using several different

3-D modeling software tools. The normally invisible soil conditions and the water table beneath the pagoda as well as access facilities such as stairs are then simulated using 3-

D models. By adopting advanced 3-D graphics techniques, the entire construction sequence of the Dayanta is simulated.

Second, to assess the performance of Dayanta, a visualization of the assessment process is realized by using fuzzy logic methods; however, the results are presented

graphically rather than through numerical or descriptive textual results as in traditional research. By adopting one of the fuzzy logic models (i.e., the angular fuzzy fault tree analysis), the Dayanta’s performance will be investigated, including a review of the substructure and the superstructure. Readers will be provided with choices about the assessment for each of the Dayanta’s components. After assessing the performance, the evaluation of the performance will be illustrated using an angular model. Moreover, the models generated in previous chapters can be imported to the Visual Studio as well.

Thus, the readers will be provided with graphics of detailed models if they wish to have a look of them. This study recognizes, analyzes, and calculates the results using graphics as the result medium, which are produced by using the two aforementioned fuzzy logic approaches.

1.5 Limitations

In this thesis, due to the limitations of the historical documents that describe the

Dayanta, incomplete data about its structural configuration and dimensions, missing records about how its features have varied over time, and so on, the graphical simulation fuzzy-based evaluation of evergreening and maintaining the reliability of the

Dayanta are conducted based on the following limitations:

 As introduced in Section 1.1, at least four major versions of the Dayanta are documented historically and each version is quite different in architectural style and number of levels from the next. In this paper, the construction

sequence is graphically modeled for only the latest version—the one that still stands in Xi’an (previously Chang’an) today, which was built in the Ming Dynasty. For the earlier versions of the Dayanta, which were built (or rebuilt) during previous dynasties, only the exterior structure will be graphically modeled, without showcasing their construction sequences in a step-by-step manner.  Due to incomplete data about the dimensions of the components of the Dayanta, particularly the dimensions of its decorative components and interior features, the graphical model of the Dayanta is not sufficiently precise in comparison with the real building.  In this project, all the facts about Dayanta from historical documents are assumed to be true and valid. However, in the real world, some of those facts are still under investigation, and there are disagreements among

scholars concerning their accuracy.  Information about the water table, climate and soil condition is assumed to have remained constant over the nearly 1,300 years of the Dayanta's existence; however, all the measurements obtained in this report were obtained in recent years.  In Chapter 7, some of the grades are rated subjectively by the author based on the author’s own engineering experience and deductions based on other studies about the performance of the Dayanta. Although this subjective rating is surely inaccurate at times, thanks to the definitions and properties of the fuzzy logic methods employed, the validity and effectiveness of such an evaluation can be guaranteed by adopting those approaches. The results can be verified by the studies about the true condition and how the repair project is proceeding.  Although the author discusses the leaning of the Dayanta in Chapter 5, the reasons behind this issue are complicated and involved; it is beyond the scope of this research.

1.6 Tasks

As defined in the scope and objective, there are two main tasks in this research: the graphical simulation and the fuzzy logic analysis. For the first part, the exterior of the four versions of the Dayanta will be graphically modeled using Autodesk 3DS Max

2014, the student version. In this paper, the entire modeling process, or graphics pipeline, can be described as shown in Figure 1.3.

Figure 1.3 Graphics pipeline of the graphical simulation

For the first task, there are three stages of modeling work in the graphics pipeline defined above. The first stage involves modeling work, in which the basic components of the Dayanta, including its foundation, pillars, beams, support systems, exterior and interior walls, decorative features, access facilities and spire are modeled using

Autodesk 3DS MAX. Next, based on the references and general engineering knowledge, those components will be assembled to construct the entire main body of the Dayanta.

After the first stage of the initial modeling work has been completed, in the second stage, materials and texture will be assigned to the surfaces of the geometric objects created in the first stage, making the graphical model more realistic. In this stage, the textures must be assigned to the modelled geometric surfaces carefully by specifying the exact UVW coordinates (a basic coordinate system used in the xyz coordinate system in 3-D space) to position the bitmap on the appropriate surface of the geometric object. When this stage is complete, the parts of the model can be displayed with the correct textures. In the final rendering stage, effects such as light and shadow are added in the rendering environment. Then, after choosing an appropriate renderer and setting the related parameters, the entire model of the Dayanta can be rendered. The graphical simulation of the construction sequence of this ancient building, inner structure, components and the walk-through animation can then be conducted based on this model.

The graphical simulation can help learners comprehend and assess the construction sequence used for the pagoda. After the graphical simulation to understand the basic structure of the pagoda, the focus moves to the performance of the building. From a construction perspective, Fuzzy Fault Tree Analysis (FFTA) can serve as an important tool to evaluate the pagoda’s performance from every possible cause: both those based on the literature and on expert assessment of each aspect. Using common linguistic expression evaluations, it is important to be able to transform the linguistic descriptions into valid data used to model the evaluation results. Accordingly, after using FFTA to stabilize the basic foundation for analysis, one model—Angular

FFTA—are generated by employing a grading system to present the evaluation outcomes for the performance of the Dayanta.

Finally, the generated graphics can not only be used to show the structural details of the pagoda but can also be exported in bitmap form using the C# programming language, which is helpful in augmenting students’ understanding of the performance the

Dayanta.

The second major task of this paper is to construct an intelligent system which is designed to evaluate the performance of the Dayanta by asking the users several questions through a user-friendly interface. The users' answers will be processed based on the fuzzy logic algorithms and a defined membership function. Then, the results will be shown graphically, as fuzzy diagrams, indicating the current performance of the

Dayanta based on the currently available data or on expert deductions. One fuzzy logic models are used in this paper, the angular fuzzy fault tree analysis. Using the C# programming language and Microsoft Visual Studio 2015, two standalone windows form an application utilized to display the expected results of the evaluation described above

(see Figure 1.4), in which the graphical user interface (GUI) is designed to ask users some questions. Users select their evaluation, such as “Very Positive” “Positive,” “Fairly

Positive,” “Negative,” “Fairly Negative” or “Very Negative,” from a prompted pull-down list. Then, the system analyzes the users’ options and presents the final results. The principles, working procedure and a demonstration of the system based on fuzzy fault tree analysis and the angular fuzzy method are discussed in Chapter 7.

Chapter 2 Literature Review

This chapter presents a comprehensive literature review concerning the Dayanta, including the previous studies that cover the following major aspects: human aspects, mechanical performance, graphical simulation and fuzzy logic. As a well-known Chinese ancient pagoda, the Dayanta is not merely a building that represents fantastic ancient

Chinese architectural design and outstanding engineering techniques but also a culture carrier that embodies the development and evolution of Chinese philosophy.

Specifically, this chapter reviews the research on Chinese culture, the Buddhist cultural influence, anti-seismic studies, 3-D modeling, VR simulation, digital reconstruction and the applications of fuzzy logic in civil engineering.

2.1 Humanity

2.1.1 Public culture

Using Habermas’ theory, Li (2012) examined how the public space around the

Dayanta currently functions as a historical and cultural tourism site. Li (2012) proposed that the role the Dayanta now plays as a public space originates from the decreasing influence of religion and the resurrection of royal sovereignty in Chinese history. By analyzing the appearance, design, color, configuration, and the impact of the

development of commercial tourism on the Dayanta, this paper showed how the

Dayanta's role as a public space is changing even in present day.

Cui (2008), using the Post Occupancy Evaluation (POE) method, which has been widely applied in western countries to investigate feedback on the design of public facilities, assessed four city public recreational sites around the Dayanta: the North

Square, South Square, West Park and East Park, concentrating on the development of tourism and its corresponding influence on the Dayanta as a tourist attraction in the urban area of the city of Xi’an.

Gao (2004) reviewed the adoration of the Dayanta by analyzing poems written by

Lian Yang and Dong Han, two young modern Chinese poets who use the Dayanta as a rebellious metaphor to present their anxieties about the exponentially increasing impact of scientific and technological development on ancient relics, and noted that the

Dayanta has functioned as a representative prototype ever since it was built in AD 652.

From the perspective of cultural differences between northern and southern

China, Bai (2015) compared the disparate architectural styles of northern and southern

Chinese pagodas, using the Dayanta in Xi’an as a typical example of a northern Chinese pagoda and Longhuata in Shanghai as a typical example of the southern Chinese pagoda. The former symbolizes strength and power while the latter symbolizes decency and agility. Bai (2015) proposed that such exterior differences in architecture stem from local culture differences between northern and southern China, in which the former emphasize practicability, while the latter focus more on visual beauty, arguing that

these reasons are why the Dayanta looks “stable and solid,” while the Longhuata appears “slender and elegant.”

Rong (2014) analyzed the symbolization of the Dayanta in Chinese history and noted it had four distinct meanings as follows:

 In Buddhism: The original function of the Dayanta is to preserve Buddhist

texts and figures brought from India by Xuanzeng.

 In art: The architectural design of the Dayanta has great aesthetic value

that originally stemmed from Indian pagodas (AD 652–704) but was later

adapted to Chinese local conventions (AD 704–present).

 In culture: The Dayanta was the location to which Xuanzeng led a team of

monks to translate the Buddhist scriptures. It was also the building where

the names of the winners of imperial examinations were recorded during

the Tang Dynasty

 In empire. The construction and re-construction of the Dayanta was a

direct reflection of the religious faith of the emperors who built and

renovated it through several dynasties.

2.1.2 Buddhist cultural influence

Dou and Zou (2005) used the phenomenological method to interpret the function and cultural status of Buddhist pagodas in China, which are regarded as multi-fold artificial structures. They noted that in India, before Buddhism was introduced in China,

Buddhist pagodas have dual initial purposes, serving both religion and politics. However, as Buddhism gradually disseminated through China, the function and appearance of

Buddhist pagodas has been localized, secularized and humanized. This is clearly reflected in the development of the Dayanta; it has been verified that its initial design imitated a typical Indian Buddhist pagoda in the 7th century.

To investigate the original appearance of the Dayanta, Yang (2007) made a comprehensive study about the different four versions of the Dayanta over different historical periods. This aspect of the Dayanta will be discussed and illustrated in Chapter

3. Yang (2007) precisely identified that the source model for the first Dayanta (from AD

652–710) originates from the famous Bodh Gaya pagoda in the Gupta Dynasty (AD 320–

500) as it appeared in the 5th century. According to the available historical documents in

China and India, the founder and designer of the Dayanta is the famous Buddhist monk

Xuanzeng, who travelled to India and brought back a number of Buddhist sculptures.

Xuanzeng's travels to India have been verified, as have his visits to the Bodh Gaya pagoda—considered the only Buddhist pagoda where Xuanzeng could have undergone his training. He built a similar pagoda (the Dayanta) when he returned to Xi’an in AD

648. Additionally, from Yang's studies, the assumption that the Dayanta is the product of the introduction of Indian Buddhist culture is reinforced by additional archaeological evidence: some round embossment slates were discovered in the area near the Patna

District in India, on which there a Buddhist pagoda is engraved that is surprisingly similar to the descriptions of the original Dayanta, which, according to Chinese historical documents, was built in AD 652.

Ge (2010) regarded the Buddhist style of the Dayanta as an example of an invasive heterogeneous culture whose influence that can be clearly seen from features of the

Dayanta such as its odd number of levels and its underground chamber. On the other hand, the Dayanta can also be considered as a combination of Indian and Chinese architectural styles, which Ge called a heterogeneous culture product in her research because it is typical of a pavilion-style architecture in ancient Chinese pagodas that is totally different from that of Indian pagodas; therefore, it can be considered as a localization of the Indian Stupa pagoda.

Wang (1998) reviewed the official historical records and concluded that both the

Dayanta, which can also be literally translated as the “Big Wild Goose Pagoda” and the

Xiaoyanta, the “Small Wild Goose Pagoda,” belong to the buildings of two different

Buddhist temples. The Dayanta is part of the Great Ci’en Temple built in AD 648, while the Xiaoyanta is part of the Great Jifu Temple built in AD 684. From Wang's research, from the typical configuration of ancient temple buildings, the pagodas in the two temples mentioned above are not central buildings but only memorial and secondary ones; in such temples, the temple hall is always located in the center, indicating its primary status in architecture design.

On the macro level, Yang (2009) made a comprehensive study focusing on the development of Buddhist pagodas in China, discussing the introduction, localization and evolution of Buddhism in China in detail. In particular, Yang (2009) painstakingly recorded the changes in Chinese Buddhist pagodas over time, including their function, design, classification, appearance, configuration and decorative properties. In Yang's 16

work, the Dayanta (built in AD 652) is used as example that exemplifies the impact of

Buddhist culture on Chinese local architectural styles during the early Tang Dynasty.

2.2 Mechanical

Much research has been conducted concerning the mechanical aspects of the

Dayanta, especially its earthquake resistance, which is closely related to the various renovations and reconstructions of the Dayanta that have occurred over its history.

2.2.1 Anti-seismic studies

Li et al. (1994) pointed that the materials used to construct the Dayanta are primarily clay brick and mortar, which is a typical rigid and brittle masonry material whose ability to resist earthquakes is far worse than that of reinforced concrete.

Additionally, considering the instability masonry structures and the randomness with which earthquakes occur, Li et al. (1994) used probability theory to investigate the structural stability of the Dayanta. Based on historical earthquake records and reasonable assumptions of the structure of the Dayanta, the probability of damage can be obtained by simulating the maximum deformation and cumulative energy consumption of certain components of the building. Their research yielded the following results: the part of the Dayanta most vulnerable to earthquakes is its top level. The simulation results indicated that over a 500-year span, the probability that the top level would be damaged is 1.78%, over a 1000-year span, it is 2.54%, and over 2000 years it is

3.0%. From these results, it can be seen that even over long periods the probability of damage is small, and under conditions in which no significant changes occur to its immediate environment, the Dayanta is safe and can be perfectly preserved. This study is an attempt to introduce the methods of probability to investigate the Dayanta's vulnerability to earthquakes, and it can—at least statistically—provide some guidance and reference for repair and renovation work on the Dayanta.

Xi’an was the capital of the Tang Dynasty (AD 618–907) and is geographically located at the center of Shaanxi province, which part of the northwestern seismic zone of China. On May 12th, 2008, the Wenchuan earthquake, which reached 8.0 on the

Richter scale, caused considerable damage to the Dayanta's structure, causing a relatively large displacement between levels and, accordingly, putting the entire building at risk of collapse. However, this is not the most intensive destructive impact that earthquakes have had on the Dayanta. In AD 1563, during the Ming Dynasty (AD

1368–1644), a more powerful earthquake occurred (8.3 on the Richter scale) in the Xi’an area. This event caused the entire spire of the Dayanta to fall and huge fissures were subsequently found in the Dayanta's main tower. Afterward, although it was renovated several times in the following periods, the structural damage caused by the earthquake in 1563 has never been fully repaired—and that is the reason why anti-seismic studies about Dayanta are so important for protecting this historical heritage. Based on the potential risk of the Dayanta being destroyed by an earthquake as discussed above,

Chen et al. (2010) used the finite element method to perform a comprehensive examination of the structure of the Dayanta and simulate its structural behavior in an

earthquake by creating 3-D models using the finite element analysis software ANSYS.

Based on the calculation and simulation results obtained in ANSYS, they created a diagram of the displacement at the various levels of the Dayanta and a cloud diagram of shear force and concluded that the fifth and sixth level of the Dayanta are weakest under earthquake dynamic loads. The entire pagoda may fall due to a structural failure between these two levels. In addition, the observations of the older existing damage to the Dayanta validate this conclusion. The study concludes that based on field inspections and theoretical calculations, the location where the largest displacement between levels is most likely to occur is at the fifth and sixth levels, and it proposes the following corresponding remedies and precautions:

 Based on the experience of the successful reinforcing project for the

Xiaoyanta, adding grouting in fissures and soft steel-stirrup rebar above

the domed doors on the exterior walls have been shown to be effective

way to increase the building's bearing capacity and overall stability.

 By comparing the value of the first natural period of vibration (0.80s as

obtained from the computer simulation and 0.67s as surveyed on site), the

relative error of these two values is 18.3%, which shows that when real-

time surveys of masonry pagodas are infeasible, the finite element method

can be used as a valid approach to simulate its structural behavior under

earthquake dynamic loads.

 This study revealed three destructive patterns of the Dayanta: the fall of

the spire, the failure of the fifth and sixth levels and the vertical fissures

along the axis line of the four sides of the Dayanta. Such conclusions are

basically in accord with the observations of damage commonly seen on

other ancient pagodas in the Shaanxi area.

Jiang (2013) proposed similar suggestions for reinforcement as Chen et al. In his master's thesis, he used another finite element analysis tool, ETBAS, to simulate the failure pattern of the Zhengjue Temple pagoda, another ancient masonry pagoda in the northeastern seismic zone. By using the index method, he identified that the Zhengjue

Temple pagoda is in a mid-degree injury condition and proposed the following procedures to reinforce the building: filling the cracks, rebuilding the peeled walls and adding hoop rebar on the beams.

In addition to the traditional methods to increase the earthquake resistance of ancient pagodas mentioned above, which can be described as enhancing the structure’s bearing capacity and stiffness, Zhao et al. (2011) developed the Shape Memory Alloy

(SMA) damper to absorb energy released during an earthquake, thereby enhancing the anti-seismic performance of ancient masonry pagodas.

2.3 Graphical simulation

2.3.1 3-D Modeling

Another aspect of ancient building study is graphical simulation, in which advanced computer graphics techniques are employed to simulate, reconstruct and model ancient buildings according to the related references, most of which are data and

documents from ancient books. In this area, some colleagues of the author have done some excellent work. In his master's thesis and doctoral dissertation, Tan (2013 and

2015) performed a comprehensive 3-D simulation of the famous Roman Colosseum, including its entire structure, the components at each level, its construction sequence and its decorative items. By reviewing a number of literary sources and records about the Roman Colosseum throughout history and using several modeling software packages (Autodesk Inventor, Google SketchUp, Cinema 4-D and Unity 3D) to complete the work, Tan (2015) proposed a general methodology, which he termed as a "graphics pipeline," to conduct 3-D graphical simulations of ancient building. Following Tan’s approach, Hao (2014) graphically simulated a unique component of ancient Chinese architecture, namely, dougong, to present its complex structure and construction sequence. On the basis of data from an ancient books on construction techniques

(Yingzao Fashi, which was published in AD 1105 and written by Jie Li), Hao (2014) compiled a 3-D graphics database of the structure, engineering drawings, and the construction sequence at various levels and dimensions for all the types of Song-style dougong. For the Dayanta, Yang (2016) used Autodesk 3DS MAX to create basic 3-D models used to present its construction sequence, which will be presented in more detail in Chapter 6.

Yang (2013) shared the experiences gained in building a 3-D graphical model of an ancient building using Autodesk Maya, another very popular 3-D modeling software application. He created the 3-D modeling of the Dayanta by following these tasks:

1. Importing a photograph of the Dayanta into Autodesk Maya to build a

model of its first level. The key during this step is to maintain the proper

proportions of the model.

2. Duplicate levels 2–7 using the completed model of level 1 and then scale

each level with reference to the photograph and to the structure's true

dimensions to ensure the entire 3-D model is precisely proportional to the

real building.

3. Adjust the details of the 3-D models, including adding components such as

doors and windows and deleting redundant geometric elements.

4. Build a 3-D model of the spire at the very top of the pagoda

5. Assembly the levels and modify their relative positions, making sure the

connected parts are assembled properly.

Although the software employed in this thesis is Autodesk 3DS MAX while Yang

(2013) used Autodesk Maya, the procedures proposed by Yang (2013) were followed as a reference and are similar to the modeling graphical sequence used here, which will be discussed in Chapter 6.

One difficulty in modeling ancient buildings is that, often, there is no data available for use. Even when official records or literature about ancient buildings exist, most are simply descriptions from the perspectives of politics, culture and art, and few provide information useful for modeling, such as the building's dimensions, configuration or construction techniques. Therefore, to some extent, to create 3-D models of ancient buildings, the completeness and the accuracy of the 3-D graphical 22

model largely depends on the accessibility to preserved valid data. Additionally, during the renovation work, sometimes the damaged parts need to be measured and detected without increasing existing damage to the ancient building itself. To solve this problem,

Jo and Lee (2014) proposed a non-destructive method to obtain accurate data (mostly concerning building dimensions) using scanning equipment. Taking the Magoksa Temple in Korea as an example, they used temperature analysis to detect and map the blistering zones of this ancient temple. After inputting the data to modeling software, they were able to obtain a complete and accurate graphic representation of the blistering zones in the form of a 3-D graphical model, which can also be used as a reference during renovation tasks for this ancient temple.

2.3.2 VR simulation

The term "Virtual Reality" (VR) was first coined in the 1960s but has become increasingly popular in recent years, mostly due to hardware advances in CPU and graphics technology, which are now powerful enough that a fully immersive, interactive and fluent VR user experience can be realized today on a personal computer. Unlike traditional modeling, in which 3-D graphics could be presented only on a plane surface

(such as a display monitor, which—strictly speaking—is still a two-dimensional space),

VR can provide an authentic 3-D virtual world by wearing a head-mounted display

(HMD) such as VR glasses. Furthermore, man-machine interactivity can be realized such as manipulating virtual objects by using VR gloves. Applications of VR in civil

engineering, archaeology and architecture have been proposed by several scholars. Tan

(2015) proposed a graphics pipeline to create a VR environment in which the construction sequence, the entire building and a virtual exploration of the Roman

Colosseum were conducted by using VR glasses—the Oculus Rift DK2. Based on the graphical models he completed for his master's thesis (Tan, 2013), in his dissertation,

Tan (2015) discussed methods for modeling, software selection, software and hardware compatibility, and optimizing the VR experience. Yang (2016) created a graphical simulation of Jinshanling, a part of the Great Wall in China and used virtual reality to show its construction sequence and architectural design.

Bai (2008) used the Virtual Reality Modeling Language (VRML) to develop a virtual exploration system of the buildings in the Dayanta complex. Aiming at solving the complexity and reality problems of 3-D models, he adopted texture mapping techniques and modularized the geometry models to reduce the computing load and bandwidth requirements during online rendering and data transfers, respectively. Additionally, to make this VR system more immersive and interactive, Bai (2008) used JavaScript to program some controls and functions, including a first-person walk-through, collision detection, viewpoint alteration and navigation.

Another requirement of VR applications is that they need to be accessible through the Internet in real-time. Zhang et al. (2010) discussed modeling ancient architecture using VRML, which is considered as the standard language for constructing online VR scenes at present. They used Autodesk 3DS MAX to complete the initial modeling work of an ancient Chinese palace and then rewrote the modeling code in VRML to launch 24

their 3-D models online. It has been shown that these models run quite well in a web browser environment: users can view and interact with them perfectly. The methodology, or graphics pipeline, they followed to establish this VR system includes the following: selecting development tools, establishing the overall model, adding collision detection, designing special effects, file optimization, combining scenes and system release.

2.3.3 Digital Reconstruction

Another direction taken by graphical simulation studies concerns 3-D digital reconstruction, which can be roughly categorized into reconstructions of buildings that still exist and those that no longer exist. For the former, as Tan (2013 and 2015) did in the 3-D simulation of the Roman Colosseum and Jing (2016) did with a part of the Great

Wall, the references for digital reconstruction depend largely on photographs from field trips and satellite images obtained by Google Earth. However, for the latter, as Hao

(2014) showed in simulating Song-style dougong, nearly all the original works were destroyed many years ago; thus, reconstruction work must rely on preserved data and descriptions from ancient documents. Therefore, the feasibility, quality and accuracy of digital reconstruction of ancient buildings is highly dependent on access to the data that is indispensable for modeling work and, consequently, data collection, interpretation and processing techniques also require thorough consideration during the modeling process.

Li et al. (2005) simulated a currently-preserved early Tang Dynasty timber- structure building in Hong Kong. They created a database of the dimensions of this building by scanning the building's surface using laser measurements, a technique that has been verified as an effective tool for collecting data for 3-D reconstructions of ancient buildings without damaging them. Such techniques can be used to protect, research, repair, restore and record information about ancient buildings using 3-D graphics. In addition, Hu et al. (2016) led a research team in digitally reconstructing the

Liangyi Temple, a Wudang tourist destination, using a multiple terrestrial laser scanner

(TLS) approach, which they relied on to obtain the fine-grained surveying data used for modeling. To ensure data accuracy and overcome missing data problems, they adopted a three-level TLS with a scalable distance and controlled measurement errors to within 3 millimeters. A review of the resulting 3-D reconstruction model, with its high accuracy and attention to detail, shows that the applying the terrestrial laser scanner (TLS) technique is very promising for gathering data for 3-D models.

Tang and Wang (2015) proposed a new approach to obtain the geometric shape of an ancient pagoda and the axial shape along its vertical direction. Specifically, they measured and monitored at least three points on each façade of the pagoda using an electronic total station. After collecting the data from the electronic total station, they used the least squares method to calculate the coordinates of each component of the pagoda in 3-D space. Tang and Wang (2015) emphasized that this method is especially practical in digitally reconstructing high-rise buildings (such as ancient pagodas in China) for which traditional laser scanning techniques are often not feasible.

Airas and Caamano (2007) applied the low-cost Close Range Digital

Photogrammetry technique to circumvent the difficulties involved in collecting modeling data from buildings with irregular structures. Photogrammetry is a nondestructive approach for quickly and safely acquiring precise 3-D information that can be used for digital modeling, such as the shape and dimensions of ancient buildings and structural injury detection and renovation—all of which are significant in efforts toward ancient heritage protection.

2.4 Fuzzy Logic

As coined by Dr. Zadeh in 1965, fuzzy logic and its related algorithms and methods have been increasingly applied in civil engineering—especially in the construction field— because there are many descriptive, qualitative and non-numerical measurements for specifying the details and standards of construction activities that fuzzy logic is well- suited to handle. For example, when evaluating the safety performance of ancient buildings, it is uncommon to find a number used to describe their condition; instead it is common to find ratings such as “fairly good” or “very poor.” The definition, concept and mathematical operations of fuzzy logic will be introduced in Chapter 7; the following includes a literature review of the applications of fuzzy logic in civil engineering.

Al-Labadi et al. (2009) employed the alpha-cut method and angular fuzzy logic model to assess the safety of grouting operations in sewage tunnel projects, in which inspection results and construction evaluations are often provided in the form of

subjective linguistic expressions. By developing the alpha-cut method and the angular fuzzy logic model to solve the problems of incomplete and imprecise judgment concerning safety assessments of grouting operations, and by verifying the results produced by the fuzzy model through a comparison with experts’ opinions obtained via questionnaires, this study showed how the alpha-cut method and angular fuzzy logic model can be applied to predict potential risks in grouting operations in sewage tunnel construction projects.

By combing fuzzy logic with Fault Tree Analysis (FTA), Al-Humaidi and Tan (2010) applied Fuzzy Fault Tree Analysis (FFTA) to analyze delays in a construction project. They used two types of fuzzy models, the Baldwin alpha-cut method and angular FFTA, to perform a comparison with the true performance using these two models to predict delays. They concluded that, although both models can produce satisfactory results, in practice, the angular FFTA model is more functional than Baldwin's rotational model, largely because the definition of the membership function of the former is closer to the true delay conditions in construction projects than is the latter and, therefore, can provide some constructive suggestions to avoid losses of time and money due to delays.

In addition, Tan (1988) used the trapezoid or triangular fuzzy model to evaluate the performance of construction facilities. Subjective judgements given by testers or technicians as linguistic values are quite common in the assessment of complex procedures in the facilities construction in civil engineering, and they often cause misunderstandings and misinterpretations in communications among general contractors, engineering contractors, owners and other involved parties. The application 28

of trapezoid fuzzy logic can be used to provide a relatively accurate overall performance assessment of the building, and—more importantly—the mechanics of this method and its final results can easily be understood by technicians, managers and laborers on the construction site.

Chapter 3 Historical Studies

This chapter presents a historical study of the Dayanta, including the developmental history of this ancient Chinese pagoda covering four different versions of the Dayanta through various dynasties or periods in Chinese history along with reflections on the cultural, political and religious conditions behind them. To provide illustrated full views of the four versions of the Dayanta (from AD 652, AD 710, AD 933 and the present, respectively) and based on Yang’s study of the changing appearance of the Dayanta in history (Yang, 2007), the author has redrawn the reconstructed pictures of these different Dayanta versions by hand and modeled them in Autodesk 3DS MAX.

3.1 A Brief History of the Dayanta

Pagodas, or tower-like buildings, were not originally created in China as an architectural form. Instead, the Chinese pagoda originated from India, modeled after

Buddhist buildings that were built since the 1st century. These first appeared in the

Eastern Dynasty in China (AD 25–220); subsequently, pagoda construction was gradually localized by blending in Chinese local culture, conventions and styles to meet the needs of politics, religion and memorials.

According to studies of the Chinese pagoda of Cai (2015), pagoda development in

China can be roughly divided into the following three major periods: the Eastern

Dynasty in China (AD 25–220), the Tang Dynasty (AD 618–907), during which the blending and combining of the traditional Indian Buddhist Stupa and Chinese traditional buildings occurred. The style of Chinese pagodas during this period was quite similar to their counterparts in India. According to Cai’s investigation (Cai, 2015), many of these early pagodas were replicas of contemporaneous Indian pagodas. The first version of the Dayanta—the one built in AD 652—is regarded as a replica of the highly imitated

Bodh Gaya building style used for Indian pagodas. This style will be discussed further in

Section 3.2.

The second stage is from the Tang Dynasty (AD 618–907) to the Song Dynasty (AD

960–1279). This period is considered the peak of the development of Chinese pagodas.

In addition to the number of pagodas built during this period, far exceeding the number built in previous dynasties, the construction materials used in pagodas became much more diverse during this period, expanding to include masonry, timber, stone, bronze, iron and colored glazes. Accordingly, the architectural styles and construction methods of pagodas also evolved along with the variety of materials. One of the most obvious changes was that the geometric form of each pagoda level gradually changed from square to hexagonal and then octagonal.

The last stage stretches from the Yuan Dynasty (AD 1271–1368) to the Qing

Dynasty (AD 1644–1912). During this stage there were no significant breakthroughs in the development of local Chinese pagodas—neither in construction materials nor in 31

structural design. Due to the continuously diminishing practice of Buddhism in China over several centuries, pagoda development stagnated as well. However, one type of exotic pagoda from Tibetan Buddhism, called the Lama pagoda, thrived during this period. The most obvious feature of a Lama pagoda is that its body forms a semi-circular covering structure with a tall spire on top standing on a giant footing. These pagodas convey concepts such as “strong,” “solemn” and “respect” to worshipers.

The first version of the Dayanta was built in AD 652 in the early Tang Dynasty, in the second or peak period of Chinese pagoda development. The motivations for building the Dayanta were clearly described by Xuanzeng in AD 647—three years after his return from India—and are summarized by the following three points:

 To build a permanent location for preserving the Buddhist texts and josses

which were taken by Xuanzeng to guard against them being stolen or

destroyed by fire;

 To symbolize the indestructible foundation of the Tang Empire;

 To reconstruct the ancient Sakyamuni worship site for the people

Before the Dayanta was built, the Ci’en Temple was constructed on the same site in AD 648 by Zhi Li, the third emperor of the Tang Dynasty, as a memorial for his mother. Hence, as an attached building of the Ci’en Temple, the Dayanta shared the same center axis line with the temple in plane—in other words, it was built just behind the temple. This configuration was primarily based on the following four considerations:

(Li, 2012)

 There was insufficient space to build a huge pagoda in the center of the

Ci’en temple; therefore, the Dayanta was built along the center axis line of

the original building;

 Visually, the Dayanta was considerably higher than the building of Ci’en

Temple; this was designed to demonstrate the achievement of Xuanzeng’s

visit to India;

 From a spatial perspective, the relatively large Dayanta increased the

subjective size of the Ci’en Temple.

At the societal and cultural levels, the Dayanta was most popular at two time points. The first popularity peak occurred just after the building was finished in approximately AD 652 and it served as a place for the preservation of Buddhist classics where Xuanzeng led a team of monks to translate the Buddhist texts he had taken from

India; the second started at approximately AD 705–707, when the concept of “Yanta

Timing,” in which the winner of the imperial examination was authorized engrave his name on the Dayanta to record his achievement. Therefore, to some extent, the

Dayanta was actually the Mecca for all Chinese intellectuals that time because engraving their names on the Dayanta was a supreme honor they could achieve during their lifetimes.

Although it was not directly mentioned in historical documents, considering the huge structure and the fine design of the Dayanta, the funding of its construction must have been financially supported by the Tang Dynasty government or privately by the emperor himself. However, Wang’s research about the Dayanta (Wang, 1998) revealed 33

that its construction cost was raised by selling the belongings of dead servants in the imperial palace. Considering the near-zero value of the properties owned by people who served in the imperial palace during the Tang Dynasty, in the author’s opinion, it is hard to believe that the construction costs of the Dayanta could have been raised by money obtained from selling the property of dead servants. The investigation of the construction of the Dayanta may require more and deeper verification based on both historical records and civil engineering common sense.

Throughout its history, the Dayanta has been renovated or reconstructed several times due to damage caused by wars, earthquakes and weathering. Moreover, the appearance of the Dayanta changed significantly over these different versions. The four versions of the Dayanta are discussed in detail in the rest of this chapter. Figure 3.1 shows 3-D models of the four versions of the Dayanta (created in Autodesk 3DS MAX).

Although not all the details could be fully restored to make these models look exactly as the Dayanta would have looked at the time, these 3-D graphical models are built to a comparative scale, as shown in the right-top view in the Autodesk 3DS MAX view pane.

Therefore, they reflect the radical changes in the appearance of the Dayanta such as its height and general architectural style.

Figure 3.1 Four versions of the Dayanta in Autodesk 3DS MAX: Overview

Figure 3.2 Four versions of the Dayanta in Autodesk 3DS MAX: Multi-view

3.2 First Version of the Dayanta (AD 652–704)

As introduced in previous sections, the first version of the Dayanta refers to the version built in AD 652 by Xuanzeng. This version lasted until AD 704, when it was totally renovated. The architectural style of this version of the Dayanta was basically an imitation of the Indian Bodh Gaya pagoda, which was carefully recorded and studied by

Xuanzeng when he was there. After returning to Chang’an (the old name for Xi’an), he was authorized to build a pagoda to both preserve the Buddhist texts he had brought with him and to facilitate worship by the Zhi Li, the third emperor of the Tang Dynasty.

Unlike Bodh Gaya pagodas in India, which were usually made of stone, based on cost considerations, the structure of the original Dayanta was rammed earth faced with brick.

As was fully discussed in Section 2.1.2, the first version of the Dayanta stemmed directly from the influence of Indian Buddhist culture in the Tang Dynasty. From Figures

3.1 and 3.2, its disparate architecture style compared with its successors can be detected even at first glance. Another noteworthy feature of the first version of the

Dayanta is that the ratio of the height of its spires to the total height of the building is relatively large. Moreover, a horizontal structural component was consistently constructed on the exterior, forming connected parts between levels. Both of these features were adaptations of an Indian tradition in pagoda design during that period.

According to the official record, the first version of the Dayanta was 180 Chi in height, had five levels, and the length of each side of its square base was 140 Chi. Chi was a length measurement unit used in the Tang Dynasty: one Chi equals 30.7 centimeters. Therefore, the dimensions of the original Dayanta are approximately 42.98 meters on each side for the square base and the tower was 55.26 meters in height. It has five levels that taper from the bottom to the top, on which many delicate Buddhist figures and frescos were engraved, as shown in Figure 3.3 (the refabricated hand-drawn

picture of the original Dayanta), taken from the original painting of Hongxun Yang

(2007).

Figure 3.3 First version00 of the Dayanta (AD 652–704), redrawn by the author from Yang (2007)

3.3 Second Version of the Dayanta (AD 704–930)

Approximately 50 years after the first version of the Dayanta was built, the main body of the building was seriously damaged by weathering of the façade. Plants had grown within the walls and the construction materials had aged. Therefore, the Dayanta was reconstructed in AD 704. This reconstruction totally changed the architectural style of the Dayan Pagoda—from a copy of the Indian Buddhist style to a Chinese local pavilion pagoda style. In this reconstruction, the façade of the Dayanta was redesigned to five compartments divided by exterior columns for each level, without the engraved

Buddhist figures, as shown in 3.4, which is a refabricated hand-drawn image of the second version of the Dayanta.

Figure 3.4 Second version of the Dayanta (AD 740–933), redrawn by the author from Yang (2007)

Another big difference between the second version of the Dayanta and its predecessors and successors is that it had ten levels. This even number is extraordinarily rare in ancient Chinese pagodas, all of which have an odd number of levels (e.g., the first version of the Dayanta had five levels and today’s Dayanta has seven levels.

Yang (2007) expounded on the unique design of the second version of the

Dayanta by concluding that it was actually a product of the transitory feminism of that time. The second version of the Dayanta was built in AD 704. During that time, China was ruled by the only female emperor in Chinese history, the Emperor Wuzetian, who was the queen of Zhi Li, the third emperor of the Tang Dynasty. Wuzetian established a new dynasty called the Zhou Dynasty, which lasted from AD 684–705, the only period during which gender equality was accepted in ancient Chinese history prior to AD 1912.

In the binary philosophy in Chinese traditional culture, everything in the universe can be categorized as Yin and Yang, in which Yin stands for female and obedience while

Yang symbolizes male and governance, such as the pervasive male chauvinism among ancient empires, dynasties, tribes and civilizations around the world. In ancient Chinese architecture, Yin corresponds with even numbers while Yang corresponds to odd numbers; making it easy to understand the dominance of ancient Chinese pagodas with an odd number of levels, which is a chauvinistic reflection of the dominance of men.

However, as the only female ruler in ancient China, the rebellious spirit against the patriarchy represented by the Emperor Wuzetian can be seen not merely from a series of political revolutions in governmental organization but also in the fact that she built

the only pagoda building with an even number of levels in the history of ancient Chinese architecture. This second version of the Dayanta, with its ten 10 levels, was completed in AD 704, just one year before her death and the end of the Zhou Dynasty.

3.4 Third Version of the Dayanta (AD 933–1604)

The ten-level Dayanta built by the Emperor Wuzetian was destroyed during the continuous wars that occurred in the middle of the Tang Dynasty, especially during the

An-Shi Rebellion (AD 755–763) and the Chao Huang Rebellion (AD 875–884), during which the rebellious army once invaded Chang’an repeatedly and nearly ruined the entire city. Additionally, due to the unstable political conditions, a grim economy, a corrupt government and restrictions on the dissemination of Buddhism, for nearly two hundred subsequent years the Dayanta was neither renovated nor preserved, until, by the late Tang Dynasty, only seven levels of the Dayanta survived. Finally, in AD 933, during the period of the Five Dynasties in the tenth century (AD 907–960), the official

Chongba An of Chang’An city repaired the Dayanta, forming the third version of the

Dayan pagoda.

Because in AD 933 the area of Chang’An was still subject to frequent wars and limited financial resources were available to Chongba An, the third version of the Dayan pagoda retained its seven levels. Otherwise, it and basically followed the architectural design of the second version, in which the elements of Buddhism were thoroughly eliminated. Moreover, to avoid an overly monotonous appearance in its façade, leaning columns and additional horizontal beam-like decorative components were employed, as

shown in 3.5, which is a refabricated hand-drawn picture of the third version of the

Dayanta.

Figure 3.5 Third version of the Dayanta (AD 933–1604), redrawn by the author from Yang (2007)

3.5 Fourth Version of the Dayanta (AD 1604–present)

With the migration of the political and economic center from Xi’an to southern and eastern China, wars rarely affected the Dayanta, and it maintained its current appearance from AD 933–1640; therefore, it has lasted through the Five Dynasties and the tenth century (AD 907–960), the Song Dynasty (AD 960–1279), the Yuan Dynasty

(AD 1271–1368) and the Ming Dynasty (AD 1368–1644). The only threat to the Dayanta was an official record of an earthquake that occurred in January 3rd, AD 1556 in nearby

Xi’an. According to an investigation by Bao (1985), that earthquake reached 8.3 on the

Richter scale and more than 82,000 people died. Some 48 years later, in AD 1604, during the Wuli period in the Ming Dynasty, the Dayanta was again renovated. This fourth version of the Dayanta is the one that still stands today (Figure 3.6).

Figure 3.6 Fourth version of the Dayanta from (AD 1604–present), redrawn by the author from Yang (2007)

This renovation project added an additional layer of bricks to the outside of the original building, making it stouter than its predecessors. The materials used were

Chinese local gray bricks. During this renovation, the wooden structures inside the pagoda, including the stairs and floors of the monks' cells were also replaced. The decorative leaning columns were kept but the style of the pagoda was modified to more closely resemble the wooden structures of Chinese buildings during that period.

Since the 1604 renovation, the Dayanta has retained the same appearance until the present. The Dayanta is now 59.05 meters tall, and the sides of its base are each

25.35 meters. Today, the Dayanta has been developed into a tourist site in Xi’an, along with the Great Ci’en Temple, North Square with the largest fountain in Asia, and the

Tang Dynasty's Furong Park, which has an artificial lake and other auxiliary tourism facilities, as shown in Figure 3.7, which shows a view of the Dayanta and the Great Ci’en

Temple.

Figure 3.7 Tourism at the Dayanta and the Great Ci’en Temple

Chapter 4 Substructure

This chapter reviews the condition of the Dayanta's substructure, including the underground water table, the soil type, settlement of the foundation and the leaning problem of the Dayanta. It must be noted that the research here has been conducted based on the current conditions around today’s Dayanta, not those conditions that may have prevailed during the previous versions of the Dayanta introduced in Chapter 3.

After performing an analysis of the current potential failure risks and substructure problems, some protection and precaution procedures are proposed in the end of this chapter.

4.1 Water Table

The area in which the Dayanta is located is geographically classified as the Loess

Plateau in the northwestern part of China. Specifically, the soil condition in Xi’an is complex and consists of shallow soft soil, loess and backfill. Xi’an is also located in a seismic zone in which geological activity has occurred relatively frequently throughout history, such as the 8.3 Richter degree earthquake that occurred in 1556, as mentioned in Chapter 3. Therefore, the stability of the Dayanta's foundation is highly related to the underground natural conditions below it. This section discusses the water table under the substructure of the Dayanta in detail.

In general, the depth of water table mainly depends on the following factors: the original amount of groundwater, including phreatic water and confined groundwater, precipitation, and external influx and runoffs. Duan and Xue (2009) conducted a study that investigated the changes in the water table and collected data concerning phreatic water and confined groundwater from 1986 to 2002 and from 1982 to 2004 in the Xi’an area, as shown in Figure 4.1 and 4.2, respectively.

Figure 4.1 Changes of phreatic water levels in the water table of Xi’an from 1986 to 2002

Figure 4.2 Changes of confined groundwater levels in the water table of Xi’an from 1982 to 2004

As shown in Figure 4.1 and 4.2, the depth of both phreatic water and confined underground water have increased over the last 30 years, reflecting the overexploitation of groundwater resources since the 1970s. The decreasing level of the water table has inevitably caused soil settlement in the area of Xi’an. In addition to the overexploitation of groundwater, especially the pumping of confined groundwater from a number of deep wells drilled in the suburban areas around Xi’an since 1975, the decreasing influx of the Weihe River has also participated in lowering the water table.

According to the data from several hydrological observatories of the Weihe River around Xi’an city, the runoff from the Weihe has been decreasing since 1992; with a maximum reduction as high as 54.2% (observed in the Fenggelin Station). If continued, this decline will permanently affect the water table (Duan and Xue, 2009). Li et al. (2016)

reviewed the historical groundwater data for Xi’an and calculated that the average groundwater level has decreased by 4100 millimeters from 1965 to 2010, a result that both verified Duan and Xue (2009) and indicated that the water table in Xi’an area has clearly decreased over the last half-century.

As another major supplement of groundwater, precipitation in the Xi’an area also significantly decreased in the 1990s. By analyzing precipitation records for Xi’an from

1951 to 2007 (collected from second-degree national meteorological stations by Deng

(2008)), the average precipitation is 573 millimeters, the maximum precipitation was

903.2 millimeters in 1983 and the minimum was 312.2 millimeters in 1995. In general, the greatest trend of precipitation reduction emerged in the 1990s: statistically, the average precipitation from 1991 to 2007 fell to 544.3 millimeters, which is lower than the average precipitation from 1951 to 2007 (573 millimeters) and considerably below that of the 1951–1990 period (585.2 millimeters). Therefore, the gradually decreasing depth of groundwater has also been affected by reduced precipitation.

The third factor concerning the changes in the water table change is the overexploitation of groundwater in Xi’an city, which will be discussed further in Section

4.4, which investigates the leaning condition of the Dayanta. In addition, Liu and Liu

(2007) noted the largest fountain in Asia is located north of the Dayanta. This fountain consumes approximately 10,000 cubic meters of water for its display. Moreover, there is an artificial lake with 200,000 square meters of water in the Datang Furong Park, which is less than 1 kilometer from the Dayanta. Both these tourist facilities with their large water consumption also affect the water table under the substructure of the Dayanta. 51

4.2 Soil Condition

In foundation construction in civil engineering, the design of a building's foundation, which involves its type, material, bearing capacity and burial depth, is highly related to the geological condition of the site on which the building will be built. Usually, the geological factors in terrain that are considered in civil engineering practice are the water table and soil conditions. The former was discussed in the previous section, while this section examines the latter.

Man and Lai (2004) evaluated the soil conditions under the substructure of the

Dayanta. They showed there are two primary soil levels and measured the average elevation, major soil types and current conditions, as shown in Table 4.1.

Table 4.1 Soil conditions of the Great Wild Goose Pagoda Level Ave. Elevation Soil Type Soil Condition Level I 0. 8 m–5.5 m Artificial backfill, plain fill Loose soil texture Level II 2.50 m–3.60 m - Quaternary, upper Pleistocene Collapsible under its own Loess weight with a - Quaternary, middle collapsibility degree of Pleistocene Loess II~III - residual paleo-soil

From Table 4.1, it was found that the bearing capacity of the pure and mixed backfill in the upper level of the foundation is quite low. More importantly, considering that both types of backfill are highly inhomogeneous and relatively porous, they will

settle significantly under even very small loads. In addition, if this area is soaked in water, the settlement will be even larger.

In contrast, the lower level of the soil under the Dayanta primarily consists of loess, which does not constitute a solid medium for foundation construction due to its collapsibility. The four elements that compose the loess are complex, including more than 60 different types of minerals, igneous sedimentary and metamorphous rocks.

Although loess in different regions has different compositions, the common feature of loess that it weathers easily and is very unstable, particularly when it is contact with water (Pye, 1995). The physical properties and granular composition of the loess in the

Loess Plateau in northwestern China is shown in Table 4.2 and Table 4.3.

Table 4.2 Physical properties of the loess in the Loess Plateau in northwestern China

Water content Compactness Maximum Optimum dry Specific Liquid Plastic Plastic Liquid water specific gravity Limit Limit Index content Index gravity (%) (g/cm3) 26.70 17.65 9.05 0.287 12 1.82 2.70

Table 4.3 Granular composition of the loess in the Loess Plateau in northwestern China

Diameter Granular (mm) composition (mm) 1-0.25 0.25- 0.05-0.01 0.01-0.005 0.005- <0.001 0.05 0.001 Percentage 0.001 3.47 29.65 16.22 10.71 39.94 (%)

One assumption which must be made here is that, considering the fact that the composition and the physical properties of loess are highly diverse around the northwestern area of China, this thesis assumes that the loess under the substructure of the Dayanta has the same physical properties and granular composition as the loess studied by Pye (1995) and shown in the tables 4.2 and 4.3. From the data shown in

Table 4.1 and 4.2, it can be seen that loess is poor soil in which to construct foundations.

In civil engineering, the mechanical properties of loess (which refer mostly to its stability and load-bearing capacity) are highly sensitive to the amount of water it is in contact with. Due to its relatively large porosity, when water infiltrates, the stiffness of the loess falls dramatically, causing the loess to collapse disastrously, a condition termed the collapsibility of loess. It has been verified that an increase in compactness can overcome the collapsibility of loess in civil engineering practice; so it can be deduced that the soil must have been rammed before the foundation of the Dayanta was built.

On the other hand, the soil condition under the Dayanta also has been affected by the construction of the modern municipal transportation system, especially the project to build the No. 4 Subway of Xi’an, one station of which was built near the Dayanta. Wu and Chen (2012) analyzed the influence of the construction of the No. 4 Subway of Xi’an on the soil condition of the Dayanta and estimated the amount of settlement it caused.

Their conclusions are presented as follows:

 The distance between the construction site of the Dayanta North Station

of the No. 4 Subway and the location of the Dayanta is 164.7 meters, This

has been verified to be a distance far beyond the width of the settlement 54

trench caused by the subway's construction according to the national

specifications of underground facilities in China. Therefore, the

construction basically has no impact on the Dayanta.

 During construction of the Dayanta North Station, by adopting the

methods of rotating and spraying piles surrounded by a waterproof curtain

and trench drainage, the radius of the loess settlement caused by the

subway station construction is smaller than its distance from the Dayanta.

So the Dayanta was not affected by the settlement caused by drainage on

the construction site.

 The vibration velocity generated by the train running on the railway was

measured to be below the limit of 0.15 mm/s according to the building

code; however, considering the differences between ancient and modern

buildings and the importance of ancient heritage protection, procedures

for abating the vibration from the railway have been performed as a

redundant precaution.

 After a review of the underground water conditions by professional

surveyors, the route of No. 4 Subway was determined not to block the flow

of underground water near the Dayanta; consequently it will not be

significantly affected by the groundwater table.

From the case study of the construction of the Dayanta North Station of No. 4

Subway is Xi’an, it can be seen that sometimes influences caused by the construction of modern facilities around ancient buildings in the process of city planning and

development are inevitable and that during their construction, the soil condition, water table and other possible negative impacts must be carefully considered to protect and preserve these ancient heritages.

4.3 Foundation

There is no direct documentation on the style of the foundation used for the

Dayanta. By reviewing the records related to its construction from ancient official annals and from ancient building codes, most describe only the appearances of ancient buildings or records of their repair and renovation; however, the descriptions rarely cover their exact construction methods or activities. Therefore, because the substructure of the Dayanta is buried underground and invisible, the foundation style of the Dayanta must be deduced from general engineering knowledge and experience.

We can make three possible assumptions about the style of the foundation of the

Dayanta: that it is either a rammed earth foundation, a timber pile foundation or a strip foundation. These are simulated graphically in Autodesk 3DS MAX in Figures 4.3–4.5.

Figure 4.3 Rammed earth foundation of the Dayanta

Figure 4.4 Timber pile foundation of the Dayanta

Figure 4.5 Strip foundation of the Dayanta

First, we can probably exclude the rammed earth foundation, because such foundations were usually applied to halls, palaces, and to Great Wall watchtowers

(Yang, 2016). The common architectural characteristics of all these structures is that they usually are less than two stories in height and occupy a relatively large area in a plane, over which the weight of the entire building can be distributed uniformly, rather than being concentrating in a small area. However, for a pagoda, which is often quite tall with multiple stories but based on a comparatively small area—precisely the area of its base in a plane—the total weight of entire building rests on that small area, creating a large concentrated load stress on the foundation. The base dimensions of the Dayanta are approximately 25 m × 25 m, while the total weight of the Dayanta has been estimated at 36,000 tons. Consequently, the stress acting on the foundation will be 58

14.112 MPa (Liu and Liu, 2007), which is beyond the bearing capacity of common rammed earth foundations. Although based on the fact that the foundation was initially designed for the first version of the Dayanta (the Buddhist version with only five stories and a weight thought to be much lighter than that of today’s Dayanta, and—assuming that the substructure has never been renovated since the original construction—the rammed earth foundation hypothesis is not sufficiently convincing from a civil engineering perspective.

Second, for the timber pile foundation, the problem is not in the load bearing capacity but in the durability. Under the assumption that the substructure has never been reconstructed since the Dayanta was first built in AD 652, the material with which the pile foundation was constructed can safely be assumed to be timber—no other possible substitute was available given the limitations of science and technology at that time. The damage and deterioration to timber materials occurs mainly from decomposition by microorganisms that live underground, especially fungi. Given the appropriate temperature, humidity and oxygen, some fungi propagate by extracting nutrients from chemically decomposing wooden materials. Therefore, typically, according to the civil engineering observations of other ancient buildings, the lifetime of timber pile foundations is usually less than 50 years. Even if the wood had been well- treated with preservatives, in most cases it would not last more than 100 years.

Therefore, considering the Dayanta has been standing there for close to 1400 years, it is hardly to believe that it stands on a timber pile foundation.

Consequently, a strip foundation is the most likely foundation type employed in the construction of the Dayanta. Unlike rammed earth and timber pile foundations, strip foundation has sufficient load bearing capacity and is sufficiently durable. The cross section of the strip foundation is assumed to be an inverse “T” form and would have been built continuously along the four directions of the foundation, as shown in Figure

4.5. The construction materials of which strip foundations were made at that time were stone, sand and lime, all of which were available in ancient China. By mixing the sand and lime together to make mortar, stones could be laid closely and affixed strongly for the strip foundation of the Dayanta. Furthermore, another possible deduction about the strip foundation of the Dayanta is that there may be more than two layers of strip foundation—an exterior and an interior layer. Moreover, rammed earth would have filled in the space between them to construct a mixed foundation of both rammed earth and a strip foundation, as shown in Figure 4.6. This conclusion not only explains the load bearing capacity but also accords with observations of how the Dayanta began to lean when its underground soil condition was altered in recent years, which will be discussed in the next section.

Figure 4.6 Mixed foundation of rammed earth and two layers of strip foundation of the Dayanta

4.4 Leaning

The leaning of the Dayanta was first detected by surveyors in AD 1719, during the

Qing Dynasty in China. At that time, the lean was measured at 198 millimeters.

Subsequently, according to the available data, the leaning of the Dayanta accelerated from 1941 to 1985. Specifically, the lean grew from 413 millimeters in 1941 to 894 millimeters in 1983, 998 millimeters in 1985, and to its greatest extent of 1010.5 millimeters in 1996, as shown in Figure 4.7 (Li, 2007) (Liu and Liu, 2007).

Figure 4.7 Change in the lean of the Dayanta in recent years

In fact, leaning is a common problem among many ancient Chinese pagodas including the Yingxian Wooden Pagoda in Shanxi Province and the Songyue Pagoda in

Henan Province (Dou, 2005). The leaning of the Dayanta is a complex problem that involves factors such as the settlement caused by the altered water table, the collapse of the loess layer, climate change, human activities, foundation load bearing capacity and the like. Gong (2008) completed a monograph on the leaning condition of the

Dayanta and reached the following conclusions:

 Structurally, the common features in ancient Chinese pagodas are a

relatively small cross section and a very tall main body, thereby causing

large compressive stresses on their foundations. As was discussed in the

previous section, the current foundation might have initially been designed

for the first version of the Dayanta—the one built in AD 652 with only five

stories. After at least three major renovations, the levels of the Dayanta

had been increased to ten levels in AD 704 and then reduced to seven

levels in AD 933, but both renovations definitely added more weight on

the foundation. It is noteworthy that only the superstructure of the

Dayanta has been renovated; its foundation actually remained as it was

built in AD 652. The increasing weight of the superstructure may have

exceeded the load bearing capacity of the original foundation.

Consequently, any non-uniform load would cause a non-uniform

foundation settlement, thus triggering the leaning problem, as has been

observed in recent years.

 Structural eccentricities caused by heterogeneous underground settling.

 The amount of sunlight (and thus evaporation) differs between the north

and south sides of the Dayanta. This causes a difference in the mechanical

properties of the soils on the two sides, such as the porosity, water

content, void ratio and dry density, which may also bear responsibility for

the leaning problem.

 The overexploitation of groundwater near the Dayanta since 1964 has

altered the depth of confined underground water, a reduction of which

would cause the soil to settle and thus cause the leaning problem.

 Human activities have affected the water environment around the

Dayanta. These include the largest fountain square in Asia to the north of

the Dayanta, the nearby subway construction, overdevelopment of

tourism facilities and the construction of residential buildings in the

neighborhood. For any of these inappropriate drainage may influence the

stability of Dayanta's foundation.

 The weathering and deterioration of foundation construction materials,

some parts of which may be failing and collapsing after nearly 1400 years.

Such deterioration would cause the foundation to become unstable, which

would facilitate the leaning problem.

Considering these possible explanations for the leaning problem of the Dayanta,

Gong (2008) discussed and proposed procedures and precautions that could be employed to correct the leaning problem and improve the protection of the Dayanta.

First, stricter supervision and control of tourism development for the Dayanta should be carried out, minimizing the negative effects caused by excessive tourist activities.

Indeed, the site of the Dayanta has been closed from time to time for inspection and repair, and some zones of the pagoda have been off-limits to visitors. The most recent closing of the Dayanta was in June, 2016.

Second, the groundwater exploitation has been effectively controlled by establishing more sustainable policies and plans. From Figure 4.7 it can be seen that there is an outstanding decreasing lean trend since 1996—the very time at which the government of Xi’an began to enforce severe restrictions prohibiting the exploitation of groundwater and implemented water resource protections. These have been shown to be effective in alleviating the leaning condition of the Dayanta.

Third, more advanced technologies could be employed to detect, measure, renovate and reinforce the structure of the Dayanta. Because adopting grouting methods to reinforce the foundation of ancient pagodas has been successful in some cases (Dou, 2005), it is promising to employ similar techniques to correct the leaning problem immediately and to help prevent any other possible structural failure of the

Dayanta in the future.

However, as Li (2007) speculated, although some precautions have been carried out since 1982, even assuming that all of them can be executed effectively, it would still require at least 1000 years for the Dayanta to return to its original position and stand straight again. Therefore, efforts to protect the Dayanta must be organized and planned by considering sustainability.

Chapter 5 Superstructure

This chapter, before discussing the superstructure of the Dayanta, introduces a definition and a classification scheme for ancient Chinese pagodas. Then it covers the planning, materials, repair history and supporting components to provide a thorough overview of the superstructure of the Dayanta. Additionally, as was done in Chapter 4, some suggestions for protection and damage prevention methods are proposed to preserve the superstructure of the Dayanta.

5.1 Introduction of Chinese ancient pagoda

As mentioned in Chapter 3, as an architectural form, pagodas do not originate from Chinese culture; instead they are a product of the dissemination of Buddhism into

China, which began approximately in the 3rd century, during the Eastern Han Dynasty

(AD 38–220). Almost all the pagodas were built for Buddhist worship or as memorials, such as the Yingxian Wooden Pagoda in Shanxi Province and the Dayanta in Xi’an.

Although early-stage pagodas were similar to Indian architectural styles, later pagodas were gradually localized to form a unique Chinese pagoda style. Examples include the

Yingxian Wooden Pagoda, a timber pagoda in which the unique architectural components called dougong are intensively employed, as shown in Figure 5.1. Another example of the pagoda evolution or localization can be seen by the changes in the

appearance of the Dayanta, as discussed in Chapter 3, which gradually evolved from its initial obvious Indian Buddhist style into a wholly localized Chinese pagoda in its present form.

Figure 5.1 Yingxian Wooden Pagoda in Shanxi Province, built using the unique Chinese dougong architectural component

A typical Chinese pagoda structure is shown in Figure 5.2. These structures usually consist of four major parts: spire, main body, base and an underground chamber. The

spire, called Tasha in Chinese, which, literally translated from the ancient Indian Sanskrit means “the country of Buddhism,” refers to the top part of a pagoda. As the most important feature of a pagoda, no matter what materials or what architectural style it employs, the spire is always located at the highest position of a pagoda, forming a common symbol for all Buddhist buildings.

Figure 5.2 Composition of a typical Chinese pagoda

Below the spire is the main body. Except for the second version of the Dayanta, built by the Emperor Wuzetian, the only female emperor in Chinese history, which had ten levels, all the pagodas in ancient China have an odd number of levels: seven, nine , etc., reflecting the dominant male chauvinism in Chinese tradition culture. The base of a pagoda is the foundation of the entire building on the ground, transferring the load from the weight of the main body and spire to the substructure. Typically, base area is larger than that of the first floor of the pagoda for the sake of structural stability. Access facilities such as stairs are installed on the base. In some cases, there is an underground

chamber beneath the pagoda—a small basement area used specifically to preserve relics of the Buddha, bone ash of previous Buddhist monks or to preserve precious

Buddhist texts to protect them from being destroyed by fire or war.

According to a study of ancient Chinese pagodas made by Yang (2009), pagodas can be classified by their superstructure styles—their main body parts. The first type of pagoda is the pavilion-style pagoda, the main body of which is a collection of equally sized square pavilion structures with extended eaves and walls from the bottom to the top. Among ancient Chinese pagodas, pavilion-style pagodas have the longest history.

They are usually relatively large and represent most of the best-preserved pagodas.

Pavilion-style pagodas are usually constructed of bricks and stone, sometimes with timber supports and access. The Dayanta is representative of this type. Its superstructure is masonry and the style of each level follows the same design in terms of walls and extended eaves, as shown in Figure 5.3.

Figure 5.3. Pavilion-style pagoda: The Dayanta in Xi’an

The second type is the timber pagoda. These are characterized by their timber construction and the use of dougong, an important indicator of Chinese localization.

There are two major types of timber pagodas. In the first type, both the spire and the eaves in each levels use the dougong structure. In the second type, the main superstructure is constructed primarily from timber. Compared with pavilion-style pagodas, the eaves of timber pagoda are more prominent and involve placing many dougong. For example, Figure 5.4 shows the eaves with dougong of the Yingxian

Wooden Pagoda. Other examples of timber pagodas are the pagoda at Hanshan Temple and the Beisi Pagoda of the Baoen Temple in Suzhou, Jiangsu Province, as shown in

Figures 5.5 and 5.6, respectively.

Figure 5.4 Intensive eaves with dougong of Yingxian Wooden Pagoda.

Figure 5.5 Timber pagoda at Hanshan Temple, Suzhou, Jiangsu Province

Figure 5.6 Beisi Pagoda of Baoen Temple, Suzhou, Jiangsu Province

The third type is the Lamaism pagoda, which was influenced by Tibetan Buddhism or Lamaism. Lamaism originated during the Yuan Dynasty (AD 1271–1368). The most obvious features are the short, white main body and the relatively tall metal spire.

Lamaist pagodas preserved most of the typical style of the dagoba or "stupa" in India, which were initially designed to preserve Buddhist relics. One famous Lamaist pagoda is the White Pagoda of Miaoying Temple in Beijing, which was built in AD 1279 and still stands today, as shown in Figure 5.7.

Figure 5.7 Lamaist pagoda: White Pagoda of Miaoying Temple in Beijing

5.2 Planning

The total height of today’s Dayanta is 63.25 meters, with a square base whose perimeter is 100 meters. The dimensions of the area of the cross section of each floor, the height and thickness of the exterior walls of each floor gradually diminish from the base level to the spire, as shown in Table 5.1 (based on data collected by Shen (2005) in

2004). Given these dimensions, the entire main body of the Dayanta tapers from the bottom to the top, which both improves the structure's stability and is aesthetically

pleasing. As mentioned in Chapter, today’s Dayanta is the version that was renovated during the Ming Dynasty, by adding an extra single layer of brick that encompassed the original pagoda body, the total weight of which is estimated to be approximately 70,000 tons (Yang, 2016).

On each of the four facades of each level of the Dayanta, there is an arched door located in the middle on the wall. This door is also an architectural tradition adopted from Indian Buddhist pagoda design. On each level, except for the area occupied by the spiral stairs in the center, the space is called the pagoda cell. The width of the cells decreases from the ground level to the top. There is no floor slab between the first and second level, but starting at level 3 and continuing to level 7, the pagoda is divided into several cells on each level. These cells can be accessed by climbing the spiral stairs constructed vertically in the center of the Dayanta. The cells were used by the Buddhist monks for their daily work and lives. Initially, these monks were assembled to translate the Buddhist texts brought by Xuanzeng from India in AD 648. Later, some cells were used to store and preserve the precious calligraphy and paintings by prestigious emperors and artists in dynasties. Dimensions for each level of the Dayanta are shown in Table 5.2.

Table 5.1 General dimensions of the Dayanta

No. of Levels Length of each Height of each Wall thickness Floor area (m2) side (m) level (m) (m) One 25.20 10.36 9.15 635.04 Two 22.69 7.73 8.31 514.84 Three 20.33 7.15 7.49 413.31 Four 18.20 6.65 6.50 331.24 Five 16.23 6.70 5.78 263.41 Six 13.92 6.40 4.80 193.77 Seven 11.60 5.20 4.22 134.56

Table 5.2 Detailed dimensions of the Dayanta

No. of Levels Width of pagoda Cross sectional Width of arched Height of arched cell on each floor area of each door on each door on each (m) floor (m2) floor (m) floor (m) One 6.90 587.40 1.90 2.70 Two 6.07 478.00 1.85 2.70 Three 5.35 384.70 1.80 2.60 Four 5.20 304.20 1.70 2.60 Five 4.67 241.60 1.50 2.50 Six 4.32 175.10 1.50 2.40 Seven 3.17 124.50 1.40 2.30

5.3 Materials

The exterior structure, including the façade walls, arched doors, leaning pillars, base and spire are primarily constructed of masonry—specifically, bricks—while the interior structures, including the stairs, cells, floor slabs and indoor facilities are made from timber. The mineral composition of the bricks used to construct the exterior walls, leaning pillars and arched doors is shown in Figure 5.9. Based on an examination conducted by He et al. (2004), it has been found that the bricks of the Dayanta have a porosity as high as 35%; consequently, they have seriously weathered over the years under the influence of rain, humidity, acid rain, etc., and some parts of the exterior walls were peeling away or pulverized, with many fissures, broken bricks and collapsed bricks.

To protect and repair the bricks of the Dayanta, they used a fluorine-containing polymer to reinforce the bricks, increasing their compressive strength and resistance to permeability, thereby enhancing the durability and stability of the construction materials of the Dayanta.

Figure 5.9 Mineral composition of the bricks used in the Dayanta

In addition, regarding research about the construction materials of ancient

Chinese buildings, considering that taking samples from the original building to conduct destructive materials tests and studies is forbidden, Shen (2005) proposed a Periodic

Table of Ancient Building Materials (PTABM) to provide reference data for the material properties of all the ancient Chinese pagodas, thus solving this problem over the long run. The accuracy of the Periodic Table of Ancient Building Materials (PTABM) can be ensured by continuously updating its database. Then, it can serve as a guide for the renovation and repair of ancient Chinese pagodas.

Yang (2009) discussed classifying Chinese pagodas according to their construction materials. Apart from the masonry pagoda and timber pagodas discussed in Section 5.1, there are also stone pagodas, colored glaze pagodas and metal pagodas. Due to the relatively large density of stone materials, stone pagodas are typically short—usually less than 10 meters in height. In most cases, these pagodas function as memorial buildings and places for the preservation of Buddhist relics in temples. Colored glaze pagodas refer to pagodas whose inner structures are usually made of masonry but with a colorful glaze applied to the exterior surface of the building for decorative purposes. In ancient China, only the privileged classes were allowed to use glaze to build pagodas; consequently, only a few of these pagodas have been preserved, and all of them were built as royal or aristocratic private buildings. Metal pagodas are common in may

Chinese temples because of the use of thurification, or burning joss sticks as part of

Buddhist worship practices. Metal pagodas are often not as large as masonry pagodas:

some are no taller than an adult man. Figure 5.10 shows a metal pagoda in front of

Sanqing Hall at the Xuanmiao Temple in Suzhou, Jiangsu Province.

Figure 5.10 A metal pagoda in front of Sanqing Hall at the Xuanmiao Temple

5.4 Repairing history

According to the available documentation concerning the destruction and repair history of the Dayanta by Shen (2005) and Dou (2005), in total, the building has been destroyed five times and renovated sixteen times over its history, as listed in Tables 5.3 and 5.4, respectively.

Table 5.3 Destruction history of the Dayanta

Year Reason Comments AD 680~690 Aging of structure The first version of the Dayanta was component destroyed by weathering AD 755~763 War of An-Shi Rebellion The second version of the Dayanta was once burned

AD 875~763 War of Chao Huang The second version of the Dayanta Rebellion was basically destroyed, losing its top three stories AD 1068~1077 Fire Visitors were not allowed to enter the Dayanta during this period AD 1556 Earthquake with 8.3 Richter The spire of the Dayanta collapsed, degree causing serious injury to the supporting structure

Table 5.4 Repair history of the Dayanta

Year Period / Dynasty Repairing details AD 704 Tang Dynasty Emperor Wuzetian reconstructed the Dayanta with ten levels, forming the second version of the Dayanta AD 933 Tang Dynasty The Major of Xi’an, Chongba An, reconstructed the Dayanta with seven levels AD 1466 Ming Dynasty One layer of bricks was added to cover the original outside wall of the Dayanta, forming “a pagoda in a pagoda” AD 1604 Ming Dynasty The local government of Xianning County organized a comprehensive renovation project that included reinforcing the structural components and installation of new inside stairs AD 1746 Qing Dynasty The Emperor Qianlong organized a minor renovation of the Dayanta AD 1931 Republic of China The government of Republic of China organized a

comprehensive renovation project AD 1941 Republic of China A philanthropist, General Ziqiao Zhu, raised funds to repair the Dayanta AD 1950 People Republic of The interior walls of the Dayanta were China renovated AD 1954 People Republic of Installed guard rails on the stairs inside the China Dayanta AD 1955 People Republic of Repaired the base and eaves of the Dayanta and China constructed neighboring roads AD 1956 People Republic of Established the Committee for the Protection of China the Dayanta, an agency authorized to supervise archaeological protective measures and tourist development of the Dayanta AD 1963 People Republic of Repaired the spire of the Dayanta China AD 1991 People Republic of Inspected and renovated the spire of the China Dayanta AD 1994 People Republic of Renewed the lightning rod system of the China Dayanta

It is noteworthy that all the destruction and repair projects were conducted only on the superstructure (the aboveground structure of the Dayanta, including its base, main body and spire) and did not include any substructures such as the foundation. The outer appearance of the Dayanta has been significantly changed three times (during the renovations of AD 704, AD 933 and AD 1604). Counting the original Buddhist pagoda version, there are four historical versions of the Dayanta, as discussed in Chapter 3.

Recently, the major problem of the Dayanta is that it began leaning more severely in the last 30 years, as discussed in Section 4.4. Therefore, the next renovation of the Dayanta is expected to correct its current leaning condition, reinforce its foundation, limit excessive tourist development and further reduce groundwater exploitation.

5.5 Support System

In general, the support system of the Dayanta consists of its exterior walls, interior walls, the pillars and horizontal beams. Specifically, the masonry exterior walls and the wooden interior walls function as the skeleton of the Dayanta. At each level, the pillars bear the vertical loads from the upper structure, and horizontal beams connect these three structural components to increase the integrity and stability of the support at each level. An example of the support system for the fourth level of the

Dayanta is shown in Figure 5.11 (a 3-D graphical simulation created in Autodesk 3DS

MAX), in which the major support system components have been labeled: the exterior masonry walls and interior timber walls, the interior pillars (red) and the horizontal

beams (green). Other features of each floor of the Dayanta can also be seen in Figure

5.11, such as the pagoda cell, the space between the exterior and interior walls, the floor slab, stairs and decorative components such as the leaning pillars and arched door on the façades of each exterior wall.

Figure 5.11 Support system of the fourth floor of the Dayanta in 3-D simulation

It is noteworthy that the number of pillars used to construct the Dayanta varies by level. This variation was probably designed to conserve building materials. The first and second levels, each have ten pillars and nine cells; the third and fourth levels have eight pillars and seven cells; and the fifth through the seventh levels have six pillars and five cells, as shown in Figure 5.12. In Figure 5.12, the pillars in the 3-D simulation look as if they are made of a single log that extends continuously from the bottom to the top, but in reality, they were built by splicing several short timber log together. Another inconsistency in the 3-D model is in the configuration of the stairs. Figure 5.12 shows only one staircase connecting any two levels. This is not the case at all; there are two or three staircases connecting any two levels. There is no floor slab on the second floor; instead, a caisson celling was built, a typical design in ancient Chinese pagodas, as shown in Figure 5.13.

Figure 5.12 Pillar system of the Dayanta in the 3-D simulation

Figure 5.13 Caisson ceiling on the second floor of the Dayanta

In the Dayanta, the stairs were constructed spirally, moving upward from the ground level to the spire by encircling the four pillars in the center of the Dayanta. The current stairs were built in 1954 and have been renovated several times since then. A comparison of the real stairs and the stairs used in the 3-D simulation is shown in Figure

5.14. The obvious differences between the real stairs and the simulated stairs include the number of staircases and the style of the handrails. The spiral configuration of the stairs will be discussed in Section 6.2, which addresses the modeling inaccuracies.

Additionally, other pertinent information concerning the configuration and construction sequence of the stairs on each level will be discussed in Chapter 6.

Figure 5.14 Comparison between the modeled stairs and the real stairs of the Dayanta

Chapter 6 Graphical Simulation

This chapter describes the 3-D graphical simulation of the structure and construction sequence of the Dayanta conducted in Autodesk 3DS MAX, including the models for the foundation, base, exterior walls, interior walls, pillars, beams, stairs and other decorative components. According to the available references and assumptions based on engineering knowledge, the level-by-level construction sequence of the

Dayanta is presented both through graphical models and descriptive text. In addition, the significance of creating 3-D graphical simulations of ancient building will be discussed and the modeling methodology, called the graphical pipeline, and its three stages (modeling, assigning materials and rendering) will be defined and illustrated. As mentioned, all the graphical models were created in Autodesk 3DS MAX; the reasons for choosing this package as the modeling tool will be described from a software selection viewpoint as a reference for the further graphical simulation studies in Section 6.2.

Additionally, the inconsistencies between the graphical models and reality will be examined in Section 6.3.

6.1 Overview

As defined in Chapter 1, graphical simulations of ancient buildings can be regarded as one application of advanced technology to a traditional discipline. With the help of

graphical simulations realized by adopting computer modeling techniques, records and descriptions of the ancient building that have hitherto been recounted only in the form of texts and static illustrations can be reinterpreted in 3-D graphics models. This process actually entails a full-scale visualization of ancient documents in graphics format, providing a brand-new approach to reviewing and presenting knowledge preserved in ancient records. In this thesis, this was done in a civil engineering context: by reinterpreting the construction details of the Dayanta in 3-D models based on historical references.

The graphics pipeline used to conduct the 3-D graphical simulation of the Dayanta is shown in Figure 6.1. The first stage of the graphics pipeline involves creating the basic components of the Dayanta, such as the walls and pillars. Using photographs as references, the basic shapes of components are obtained by combining primitives such as cubes, boxes and cylinders and then adding proper modifiers to change the vertexes, edges and polygons of the edited primitives to obtain the desired shapes for the component models. The basic model of the exterior walls of the Dayanta is illustrated in

Figure 6.2. This figure shows that the leaning pillars and wall sections are modeled from modified boxes, which are deformed by adding an FFD 3 × 3 × 3 modifier and rotated 5 ° inward from the wall plane. Similarly, all the other components of the Dayanta are modeled in a similar fashion—by combinations of modified geometrical primitives.

Figure 6.1 Graphics pipeline of the Dayanta

Figure 6.2 Basic modeling of exterior wall of level on of the Dayanta

The next task in the modeling stage is to assemble the separate components as parts of the full composition, for example, by grouping the exterior walls along the four directions. In the previous examples, the exterior walls of level one were assembled.

Then, by combining the assembled exterior walls, extended masonry eaves and horizontal decorative components, all the parts can be assembled into a more complex assembly—the outer structure of level one, as shown in Figure 6.3. The entire assembly

procedure for the Dayanta is illustrated in the hierarchical tree-like diagram in Figure

6.4, in which the structural organization of 3-D graphical models of the Dayanta can be clearly seen. Based on this hierarchy, the construction sequence of the Dayanta can be deduced and interpreted from a 3-D graphics perspective—as the reverse-engineered process simulating the construction activities and details required to build the Dayanta in the first place.

Figure 6.3 Assembled outer structure of level one, including the exterior wall, extended eaves and hanging decorative components.

Figure 6.4 Assembly hierarchy of the Dayanta

The next stage is to assign materials to the assembled structure to make it appear more realistic. There are several channels in the maps panel in the material editor in

Autodesk 3DS MAX that can maximize the reality of a texture by selecting appropriate settings and configurations. The results can be previewed immediately by selecting a texture from the sample "ball panels" above the maps panel, as shown in Figure 6.5. The material assigning procedure in this stage is illustrated by taking the exterior wall as an instance in the following statement. First, a bitmap of yellow masonry wall is added to the diffuse channel of the 3-D models, showing the textures on the surface of which, as shown in Figure 6.6. Then, by adding the same bitmap to the bump channel and setting a proper parameter for the bump, the bumping effects can be clearly seen in the sample ball and on the graphical models, as shown in Figure 6.7.

Figure 6.5 Maps panel and sample textures in the materials editor in Autodesk 3DS Max

Figure 6.6 Selecting a bitmap in the diffuse channel in the materials editor and assigning it to the exterior walls

Figure 6.7 Adding bump effects to the texture, which can be previewed in the sample ball

After the graphical models have been assigned and the textures and materials corrected based on the UVW coordinates with respect to the surface geometry, the next stage is the rendering stage, in which light and shadow effects are added and the environment is set, including the sky and ground, as shown in Figure 6.8. Based on the rendered model, an animation can be created by moving the camera position and angle for each frame along the timeline to create the final product in a rendering stage. Figure

6.9 shows the camera viewpoint at the 172nd frame in an animation with a duration of

2400 frames.

One consideration that must be taken into account is the tradeoff between rendering spend and rendering quality, which are mutually exclusive. In short, it is impossible to achieve high rendering speed while at the same time maintaining high rendering quality and vice versa. The dominant factors that influence the rendering speed and rendering quality are the number of geometries to be rendered, the quality of the materials used, the complexity of the rendering process, whether light tracing has been employed, and the number of light sources that must be rendered. First, the number of primitives used in the modeling stage is directly related to the rendering process because the Graphics Processing Unit (GPU) used to render the primitives has limited computing ability, and it can render only a certain number of geometry objects simultaneously. Therefore, the fewer geometric objects there are that must be rendered, the faster and more accurately they can theoretically be rendered within a given duration. The 3-D graphical model of the Dayanta in this thesis involves a total of

1882 modeled geometric elements. In the rendering process in Autodesk 3DS Max, using only the diffuse and bump channels in the material assignment and adding two target lights and one omni light, setting the final gathering to “low” and activating light tracing with a quality of 4 and an output size of 640 × 480, and using rendering hardware consisting of an Intel® Core™ i7-4700 MQ CPU @ 2.40 GHz with eight cores and an NVIDIA Quadro K1100 M graphics card as the GPU, the total rendering time is 1 minute and 33 seconds, as shown in Figure 6.10. From the example described above it can be deduced that the speed of the rendering process depends on the capability of the available hardware and on optimizing the 3-D models, both of which are important considerations during the last stage of the graphics pipeline—the rendering stage.

Figure 6.8 Rendered indoor scene of the Dayanta with adding light effects

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Figure 6.9 The 172nd frame from the animation of the rendered Dayanta

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Figure 6.10 Rendering settings panel and the final rendering results in Autodesk 3DS MAX at an output size of 640 × 480, requiring 00:01:33 for rendering

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6.2 Software Selection

As per the graphics pipeline defined in the previous section, the modeling quality, material assignment and the rendering settings determine the final output of the graphical simulation of the Dayanta. In this thesis, the application used to complete the

3-D models of the Dayanta for all three stages of the graphics pipeline is Autodesk 3DS

MAX, the Student Version. Examples of the output are shown in several of the figures above. This section discusses the considerations and criteria for selecting modeling and rendering software and details why Autodesk 3DS MAX Student Version was chosen for this project—a 3-D graphical simulation of the Dayanta.

A few similar graphical simulation studies hav e been conducted by people in the same graduate program as this author. Dr. Adrian Tan employed Autodesk Inventor,

Google SketchUp and Cinema 4-D to simulate the construction sequence of the Roman

Colosseum using a top-down approach in 2012 (Tan, 2012) and using a bottom-up approach in 2015 (Tan, 2015), as illustrated in Figure 6.11 (Google SketchUp) and Figure

6.12 (Cinema 4D), respectively. Li (2015) used Autodesk Inventor to model a typical

Chinese temple with a Wudian-style roof, as illustrated in Figure 6.13. Yang (2016) and

Ridgrill (2016) used Solidworks to graphically model sections of the Great Wall, the

Jinshanling and Lalibela Rock Hewn Church, as illustrated in Figures 6.14 and 6.15, respectively. Hao (2014) used Autodesk Inventor and Autodesk 3DS MAX to simulate the complex structures and the construction sequence of dougong, as illustrated in Figure

6.16. Liang (2016) applied Lumion to create a as a VR graphical simulation that supports

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a real-time virtual exploration of the Humble Administrative Garden, as illustrated in

Figure 6.17.

Figure 6.11 Simulation of Roman Colosseum in Google SketchUp (courtesy of Tan 2015)

Figure 6.12 Simulation of Roman Colosseum in Cinema 4-D (courtesy of Tan 2015)

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Figure 6.13 Simulation of Chinese temple with Wudian in Autodesk Inventor (courtesy of Li 2014)

Figure 6.14 Simulation of the Jinshanling section of the Great Wall in SolidWorks(courtesy of Yang 2016)

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Figure 6.15 Simulation of the Lalibela Rock Hewn Church in SolidWorks (courtesy of Ridgill 2016)

Figure 6.16 Simulation of Chinese dougong in Autodesk 3DS MAX (courtesy of Hao 2016)

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Figure 6.17 Simulation of Humble Administrative Garden in Lumion (courtesy of Liang 2016)

By capitalizing on the experience of these uses of 3-D modeling software and considering the structure of the Dayanta, the criteria considered for software selection in this thesis include the following aspects: cost, functionality, ease of use, flexibility, and rendering effect. The evaluated software packages include those employed in the previous examples: Autodesk Inventor, Autodesk 3DS MAX, Google SketchUp, Cinema

4D, SolidWorks and Lumion.

Autodesk Inventor is a mechanical engineering oriented 3-D modeling application in which all the graphical features, such as spheres, cylinders or boxes must be modeled based on a predawn sketch. This process closely resembles real practices in mechanical engineering design—that is, sketching first and manufacturing (modeling) second.

However, it is not merely a 3-D modeling application; Autodesk Inventor also has

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powerful features that can be used to simulate static conditions or dynamic motion based on the modeled components, similar to real machinery running in the real world.

The rendering quality produced by Autodesk Inventor can be rated as “medium,” because its default materials library contains only finite textures; there is no advanced renderer setting as is available in Autodesk 3DS MAX. The hardware requirements to run

Autodesk Inventor are not particularly high; any normal workstation with an average

CPU and graphics card can run it quite efficiently, given that only 3-D modeling and simple kinetic simulations are conducted. Typically, the student version of Autodesk

Inventor (which has some limitations in functionality) is adequate to be used to complete most modeling work. Hao (2014) and Li (2015) used Autodesk Inventor in their digital reconstructions of ancient Chinese buildings .

Compared with Autodesk Inventor, Autodesk 3DS MAX is a purely art-design oriented graphical modeling application. This package includes numerous materials that can be selected and applies. Moreover, for each material, there are more than 10 channels that can be added and adjusted to maximize the final effects of texture and materials during the rendering process, mixed with light and shadow effects. The creation of graphical models in Autodesk 3DS MAX is sketch free; instead, objects are created based on primitives and then applying various types of modifiers to change the geometries to the desired shape. Under the highest rendering quality setting, graphical models can be rendered exquisitely, with extraordinarily high quality details. However, to achieve that capability the hardware requirement is also quite high, involving the

CPU, CPU cooler, RAM memory, graphics card computing capability, and the overall

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stability of the entire workstation. Therefore, for commercial purposes, the cost of

Autodesk 3DS MAX is usually quite high. Fortunately, Autodesk 3DS MAX has a student version that is free for educational purposes. The student version's basic modeling and rendering functions are sufficiently powerful for students to create graphical building simulations, as shown in the previous example research. Another advantage of

Autodesk 3DS MAX is that it is both easy to learn and easy to use—for beginners the modeling process is “What You See Is What You Get (WYSIWYG),” making it convenient for entry-level engineering students to learn and use for educational purposes. In addition, after graphical models have been completed, creating an animation is quick and simple. Animations are realized by moving the position and angle of cameras or moving objects on key frames.

Google SketchUp is a graphical simulation application developed by the Google corporation. There are several versions of SketchUp that include Basic Google SketchUp,

Google SketchUp for Site Design, Google SketchUp Pro, and so on. The version discussed in this section is the basic SketchUp version that was used by Tan (2015) to complete an initial 3-D graphical model of the Roman Colosseum (see Figure 6.11). The popularity of

Google SketchUp among architecture designers is based on its low hardware requirements; a typical office computer with an integrated graphics card can run the basic version of Google SketchUp of quite adequately. The 3-D models made in Google

SketchUp are relatively simple and preliminary. More advanced modeling and rendering effects in Google SketchUp can be achieved by installing various add-ons. The add-ons are independent modules that integrate with Google SketchUp and typically perform a

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single specific function. An example is the Metalray renderer which can be plugged in

Google SketchUp to augment its rendering quality. Although it has limited functionality,

Google SketchUp can be used to create preliminary 3-D models during the first step of the graphics pipeline. The size and complexity of the geometry objects created by

Google SketchUp are quite small, which is significant for reducing the computing load required by the rendering process.

Cinema 4-D R18 is a multi-purpose modeling application developed by MAXON that employs a popular graphics engine often used in modern video and cellphone games. One characteristic of Cinema 4-D is that it models complex geometric features using hierarchical relationships, in which the geometric objects, including the basic primitives and modifiers, are classified as child objects and parent objects. By designating the combinations and deformations of child objects, the parent object can be modeled as desired, and modifications can be made easily by simply adjusting the properties of the child objects. Cinema 4-D has moderate hardware requirements; a single computer with an average stand-alone (non-integrated) graphics card can run it sufficiently well. Additionally, the output format of graphics files exported from Cinema

4-D are compatible with other modeling packages: as the typical output file types have extensions such as “.fbx” or “.stl.”

SolidWorks is an engineering-education oriented modeling application that has been broadly applied in engineering colleges and universities in the United States. In

SolidWorks, all the geometric features are based on engineering drawings, which accords with the typical work procedures in real-world engineering design. When the 109

modeling of an assembly, for example, an engine, has been completed, the standard multi-view engineering drawings showing the dimensions of all the engine components can be produced together or separately. Moreover, an animation clip to show how this complex motor engine should be assembled can be created based on a specified assembly sequence and by setting some constraints. The rendering speed and output quality of SolidWorks is acceptable in most scenarios, and its hardware requirements are compatible with most computers found in college computer laboratories. Finally, it is available for a low price—only $40 for the full version, making it affordable by college students. SolidWorks is the prime choice for engineering education software for most universities. However, its limited functions compared with other modeling software such as Cinema 4-D and Autodesk 3DS MAX hinder the application of SolidWorks in professional design situations.

In contrast to SolidWorks, Lumion is a common modeling application used in professional architectural design. Lumion supports beautiful and vivid real-time rendering of landscaping and architectural design simulations. The rendering quality produced by Lumion is quite high; consequently, its hardware requirements are also rigorous: only computers with recent Intel Core i7 series CPUs and professional-level graphics cards (such as the NVIDIA Quadro series GPU) can meet the basic requirement for real-time rendering (i.e., maintaining a rendering frame rate of 30 or more frames per second during a simulation). Lumion is an application solely intended for rendering—the last stage of the defined graphics pipeline; consequently its functionality mostly involves choosing settings for real-time rendering, including such things as

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changes in lighting and shadows. The models used in Lumion's rendering process are often prefabricated by being assigned materials in some other modeling application

(such as Autodesk 3DS MAX) and then importing the results in an appropriate graphical format. Then, the imported graphical objects can be rendered in Lumion. Lumion is costly for conducting graphical simulations; both its full-version price and its hardware requirements exceed most individual's budgets. In most cases, Lumion is used by professional studios and architectural design companies.

A summary of the six software packages discussed above is shown in Table 6.1.

Note that this table lists the author’s personal evaluation of the user experience, including the categories availability, cost, functionality, sketch-based features, rendering quality and required hardware. Also note that the “Full Version Cost” in the table below refers to the latest commercial or professional standalone version (usually with the suffix “PRO” in its name, such as “Google SketchUp PRO.” The PRO versions are typically the most expensive versions available for any given software package.

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Table 6.1 Software selection evaluation

Software Free Version Full Sketch Functionality Rendering Hardware Availability Version Based Quality Requirement Cost Autodesk Student $1,890 Yes High Medium High Inventor Version Autodesk Student $1,470 No High High High 3DS MAX Version Google Basic Version $695 Yes Low Very Low Low SketchUp Free Cinema 4D Trial Version $3,495 No Medium Medium Medium SolidWorks Student $40 Yes Medium Medium Medium Version Lumion Trail Version $2,292 No Medium Very High Very High

6.3 Model Inaccuracies

The graphical modeling of the Dayanta in this thesis was conducted in Autodesk

3DS MAX, and the major references for this modeling work were photographs taken during field trips to the site. Unfortunately, during the summer of 2016 when the author visited the Dayanta in Xi’an, the building was undergoing some renovation work, and only part of it was open to visitors for sightseeing. Therefore, the author was able to obtain adequate photographs for only some parts of the Dayanta. Specifically, from the first to the third levels the obtained photographs were adequate to be used as references; however, for the parts that the author was unable to see in person on site, only other documentation about the Dayanta was used as the basis for the modeling work. Therefore, one source of model inaccuracies stems from the inconsistencies

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between the old document descriptions and the true current condition of the Dayanta after several renovations. Another source involved deliberate simplification of the graphical model to reduce the computing load during the rendering process. A third source involved assumptions made about invisible structural components, such as the beams and pillars inside the walls. These were modeled based on civil engineering specifications and rational deduction. Finally, some decorative components are not fully modeled to be identical as they appear in the Dayanta. This omission was made largely because of the need to optimize the rendering process and includes such features as the horizontal decorative components on the exterior wall, the guard rails on the base and the spirally constructed stairs around the pillars in the second level, as shown in Figures

6.18, 6.19 and 6.20, respectively. However, the focus of this thesis is to graphically simulate the construction sequence of the Dayanta; therefore, minor model inaccuracies of the non-structural components were ignored. For structural stability, the dimensions of some structural components such as the horizontal beams are assumed and simulated according to deductions based on civil engineering knowledge. The author believes that these model inaccuracies could eventually be eliminated by accumulating more accurate information—both in the form of photographs and through engineering investigation. The Dayanta could be fully and precisely modeled in future studies, as recommended in Chapter 8.

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Figure 6.18 Model inaccuracies of the decorative components on the exterior walls

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Figure 6.19 Model inaccuracies of the masonry guard rails at the base

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Figure 6.20 Model inaccuracies of the spirally constructed stairs around the pillars

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6.4 Simulation of the Construction sequence

This section discusses the construction sequence of the Dayanta simulation, including the substructure, superstructure and spire. Specifically, the assumed strip foundation, artificial backfill, base, the exterior walls, pillars, stairs, horizontal beams, interior walls and the pagoda cells from the first level to the top level and the access stairway will be graphically simulated based on the 3-D models conducted in Autodesk

3DS MAX in a step-by-step manner. The assumptions made and the model inaccuracies have been defined and discussed in Chapter 1 and in the preceding section of this chapter, respectively. The construction sequence was determined by referring to construction considerations and methods from modern civil engineering practices.

Although inconsistencies will inevitably exist, the author believes this simulation of the construction sequence of the Dayanta, achieved through reverse engineering and digital reconstruction, is adequate for display purposes. In addition, the entire construction sequence can be simulated in the form of an animation clip in Autodesk 3DS MAX, which is a dynamic way to show such assembly procedures.

Step 1: Excavate the earth with a slope of 3:1 (length: height) for safety. According to the assumptions and deductions discussed in Chapter 4, build the two layers of the strip foundation, exterior and interior, as illustrated in Figure 6.21.

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Figure 6.21 Excavate and build the dual layer strip foundation

Step 2: Backfill earth into the space between the exterior and interior strip foundation built in Step 1, and then compact it intensively (the rammed earth part of the foundation), as illustrated in Figure 6.22. The composition of the backfill soil mainly includes loess and clay. In the Tang Dynasty, these tasks would have been performed manually by laborers using heavy stone equipment to compact the soil of the foundation. This type of hybrid foundation (masonry strip foundation and rammed earth) was assumed to be the substructure of the Dayanta at the time it was built in AD

652. It was also assumed that the substructure of the Dayanta has remained intact and has never been reconstructed during the several major renovations in its history, which are listed in Table 5.4.

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Figure 6.22 Backfill and compact the rammed earth into the strip foundation

Step 3: Build the base of the Dayanta upon the substructure on the ground, as illustrated in Figure 6.23. Although the base that exists today was built in the 1920s according to historical records (Yang, 2005), to maintain the completeness and continuousness of this simulation, it is shown as being built first.

Figure 6.23 Build the base of the Dayanta

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Step 4: Build the exterior walls and leaning pillars for the ground floor or Level 1.

The walls were built of masonry blocks. In this simulation, it is assumed that they were assembled from prefabricated stones (at least on Level 1). Then, build the three arched doors on the facades of the exterior walls in the four directions as illustrated in Figure

6.24.

Figure 6.24 Build exterior walls for Level 1 in the four directions

Step 5: Erect the pillars on the ground floor as the basis of the support system, as shown in Figure 6.23. There are 10 pillars constructing two square layers in the plane; four of these pillars are placed at the four corner points on the inner square and the other six pillars are placed at the corner points and along the edges of the outer square, as illustrated in the plane view in Figure 6.25 and in the 3-D graphical model view in

Figure 6.26.

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Figure 6.25 Pillar configuration on the Level 1 in a plane view

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Figure 6.26 Building the supporting pillars on Level 1 in the 3-D graphical model

Step 6: Add the horizontal decorative components on the top of exterior walls on

Level 1, as illustrated in Figure 6.27. The horizontal decorative components are rectangular bricks placed vertically or horizontally in two layers. These are built only on the walls on the ground floor. The functionality and decorativeness of these components resembles that of dougong in the timber structures of ancient Chinese architecture (Li et al. 2016).

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Figure 6.27 Add the horizontal decorative components on the top of exterior wall on Level 1

Step 7: Build the eaves on the exterior wall on Level 1, as illustrated in Figure 6.28.

The eaves are made from bricks and extend toward the outside in the middle. The eaves act to drain rainwater along the slope of the eave, preventing the wall from becoming soaked by water, thereby protecting the exterior walls and prolonging their lifetime.

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Figure 6.28 Build the eaves extending toward the outside in the middle on Level 1

Step 8: Build the horizontal beams connecting the pillars and exterior walls to complete the support system for Level 1. In particular, there is a caisson celling on Level

1, a square timber structure like a Sudoku puzzle that sits on top of the inner-square pillars, as shown in Figure 6.29. All the pillars are connected by beams to reinforce the integrity and stability of the pillar support system, and the exterior walls and the eaves in all four directions (as well as the four top edges on Level 1) are connected by the pillars and the beams via diagonal beams anchored at the corner points. Next, the stairs are constructed spirally around the inner square (consisting of the four inner pillars at the four corner points in the plane view), providing access to the upper floors. There is no floor slab or pagoda cells on the first level; instead, the vertical space is kept to build the caisson celling.

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Figure 6.29 Build the stairs, pillars, beams, and caisson ceiling for Level 1

Step 9: For Levels 2–7, the construction procedures are basically the same as those described for Level 1. For example, the first step is to build the exterior walls and eaves on Level 2, as illustrated in Figure 6.30. It is believed that scaffolding was used as a temporary structure to build the upper levels of the Dayanta. Although there is no corroborating historical document or reference, the scaffolding was likely made of local bamboo or timbers connected by knotted rope and iron nails. To transporting heavy components such as the large bricks for the walls and large pieces of timber, a pulley system was likely used on the construction site. Unfortunately, the official documents of the government of the Tang Dynasty omitted any details of the construction sequence; consequently, the detailed construction activities can only be assumed based on modern civil engineering practices, as illustrated in the following statements and figures.

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Additionally, it is noteworthy that from Level 2 onward, there is only one arched door in each direction on the exterior walls.

Figure 6.30 Build the exterior walls and eaves for Level 2

Step 10: Similarly, build the stairs, pillars, beams, and the caisson ceiling for Level

2, as illustrated in Figure 6.31.

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Figure 6.31 Build the stairs, pillars and beams for Level 2

Step 11: On Level 3, follow the same procedures as for Level 2; build the exterior walls and eaves, as illustrated in Figure 6.32.

Figure 6.32 Build the exterior walls and eaves for Level 3

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Step 12: For Level 3, follow the same procedures used for Level 2: build the stairs, pillars and beams, as shown in Figure 6.33.

Figure 6.33 Build the stairs, pillars and beams for Level 3

Step 13: for Level 4, follow the same procedures used for Level 3: build the exterior walls and eaves. However, note that there is one difference. Level 4 has interior walls and a floor slab with a square hole for the stairs going upward, as illustrated in

Figure 6.34.

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Figure 6.34 Build the floor slab, interior wall, exterior wall and eaves for Level 4

Step 14: Then, followed the same procedures for Level 4 as for Level 3: build the stairs, pillars and beams, as shown in Figure 6.35.

Figure 6.35 Build the stairs, pillars and beams for Level 4

Step 15: For Level 5, follow the same procedures as for Level 4: build the floor slab, interior walls, exterior walls and eaves, as illustrated in Figure 6.36.

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Figure 6.36 Build the floor slab, interior wall, exterior wall and eaves for Level 5

Step 16: Similarly, for Level 5, follow the same procedures as for Level 4: build the stairs, pillars and beams, as illustrated in Figure 6.37.

Figure 6.37 Build the stairs, pillars and beams for Level 5

Step 17: For Level 6, follow the same procedures used for Level 5: build the floor slab, interior walls, exterior walls and eaves, as illustrated in Figure 6.38.

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Figure 6.38 Build the floor slab, interior walls, exterior walls and eaves for Level 6

Step 18: Similarly, for Level 6, follow the same procedures used for Level 5: build the stairs, pillars and beams, as illustrated in Figure 6.39.

Figure 6.39 Build the stairs, pillars and beams for Level 6

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Step 19: Then, for Level 7, the top floor, follow the same procedures used for

Level 6: build the floor slab, the interior walls, the exterior walls and eaves, as illustrated in Figure 6.40.

Figure 6.40 Build the floor slab and exterior walls for Level 7

Step 20: Similarly, for Level 7, follow the same procedures used for Level 6, build the stairs, pillars and beams, as illustrated in Figure 6.41.

Figure 6.41 Build the stairs, pillars and beams for Level 7 132

Step 21: Build the roof on the top of the Dayanta, the shape of which is a square pyramid, as illustrated in Figure 6.42.

Figure 6.42 Build the roof on the top level of the Dayanta

Step 22: Add the spire upon the roof at the top of the Dayanta. The spire is an architectural tradition that was kept from Indian Buddhist buildings. It points toward the sky, symbolizing the direction to access heaven in Buddhism, as illustrated in Figure

6.43.

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Figure 6.43 Build the spire on the top level of the Dayanta

Step 23: Go back to the base, and build the guard rails around the ground floor, keeping the access point for the front entrance of the Dayanta, as illustrated in Figure

6.44.

Figure 6.44 Build the guard rails around the ground floor

Step 24: Build the access stairs at the front entrance of the Dayanta so visitors can climb from the lower base to the upper base, as illustrated in Figure 6.45.

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Figure 6.45 Build the access stairs from the lower base to the upper base of the Dayanta

Step 25: Finally, the finished structure of the Dayanta is shown in Figure 6.46.

Figure 6.46 Finished structure of the Dayanta

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6.5 Animation

The construction sequence graphically simulated in Section 6.4 can be represented in animation with a more straightforward and clear construction sequence.

The animation can be produced in Autodesk 3DS MAX easily and quickly: after setting the textures for the ground and sky, a target camera can be added to the scene, in which the length of lens and focus of view can be finely adjusted. To achieve better light and shadow effects, lights can be set at appropriate positions to cast shadows on certain portions of the Dayanta to reinforce the realism of the animation. Then, by setting key frames on the timeline to change the position of the camera and control the point of view during the assembly of the components, a step-by-step animation that showcases the construction sequence of the Dayanta and a visual walk-through can be produced, as shown from Figures 6.47–6.54. These animations are highly suitable for playing in educational scenarios, both for the public and for college students.

After completing the graphical simulation of the Dayanta, the author began to consider the real performance of the Dayanta from a modern engineer’s perspective.

However, the evaluations for specific construction issues are often provided in linguistic

(text) form. Thus, in the following Chapter 7, the author will continue to evaluate the performance of the Dayanta by using Fuzzy Fault Tree Analysis, which can be used to translate the linguistic expressions to valid data. Using the models created in this chapter, the author will import the model shapes generated using Autodesk 3DS MAX

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into Microsoft Visual Studio to better educate the audience concerning the current safety issues facing the Dayanta.

Figure 6.48 Step-by-step animation of the construction sequence of the Dayanta: Foundation

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Figure 6.49 Step-by-step animation of the construction sequence of the Dayanta: Level 1

Figure 6.50 Step-by-step animation of the construction sequence of the Dayanta: Level 3

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Figure 6.51 Step-by-step animation of the construction sequence of the Dayanta: Level 6

Figure 6.52 Visual walk-through of the Dayanta: Overview

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Figure 6.53 Visual walk-through of the Dayanta: Guard rails and access stairs

Figure 6.54 Visual walk-through of the Dayanta: Inside the Dayanta

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Chapter 7 Fuzzy Fault Tree Analysis

This chapter provides a brief introduction to Fault Tree Analysis (FTA), fuzzy logic concepts and the combination of the two, Fuzzy Fault Tree Analysis (FFTA) methods.

Then, the angular model based on fuzzy set theory are introduced, including their basic algorithms and principles. The angular model is used in a Windows-based FFTA system

(programmed in the C# language) to investigate the performance of the Dayanta.

Additionally, the reasons and factors for the performance of the Dayanta, including substructure, structural components and non-structural component will be examined, defined and rated, and an integrated FFTA system adopting the angular model will be used to evaluate the performance of the Dayanta through an interactive graphical user interface (GUI) running in a C# Windows Forms application. The considerations of that the author chooses FFTA to assess the performance of the Dayanta, instead of other statistical models, include insufficient data available. Hence, to investigate the performance of each component of the Dayanta, the accurate dimensions of each part and mechanical properties of construction materials obtained from on-site surveys and related studies. However, due to the technical limitation, those kinds of data are not accessible for now. Thus, statistical models cannot be employed appropriately to yield satisfactory evaluation results. Accordingly, the author uses FFTA to serve as a tool to evaluate the performance of the Dayanta. Firstly, models of FFTA have the advantages of allowing to input insufficient data to get relatively accurate evaluation result of the

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performance of the Dayanta. On the other hand, FFTA could be in favor of translation of linguistic values from experts or professors when they were asked to provide their professional opinions to valid data used for modeling towards a relatively subjective topic, as shown in the example of the evaluation of the performance of the Dayanta in this thesis. Also, the graphical simulation of the step-by-step construction sequence of

Dayanta will integrated in the Windows-based application.

7.1 Introduction

The structure and procedure of modern industrial facilities is well-known as its notoriously complexity. Along with the increasing concerns about safety problems during the production and operation process in industrial fields, for example, the construction engineering field, a question arises of how to most effectively investigate the failure modes or failure mechanisms of structures. Thanks to the rapid development of computer science, several risk analysis methods such as Fault Tree Analysis (FTA) and

Decision Tree Analysis (DTA) along with mathematical theories such as probability theory and fuzzy set concepts have been applied to the decision-making processes of civil engineering with some success.

It is common sense that the essential property of a construction project is its complexity. Philosophically, the meanings of the word “composite” and “complex” are different. The former describes a system that consists of multiple components in which the number or types of the components may be diverse, but the inner relationships between the individual components and the inter relationships between each individual

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component and the whole system can be simply calculated as static and linear. In contrast, a complex system not only contains many subsets or components but both the inner and inter-relationships within it are complex, dynamic and usually non-linear. For example, a hamburger consists of toasted bread, vegetables, beef and cheese is composite, not complex, because these ingredients are simply combined together and the relationships between the components are static. This means that property changes occurring to one of these ingredients individually and separately, does not affect the property of the others ingredients. On the other hand, a human body is a complex system in which various parts work cooperatively. The relationships within this system are dynamic and nonlinear: a breakdown of one component can lead to a collapse of the whole system.

Obviously, based on these definitions for complex given above, a construction project and it related events are complex. The overall performance of a constructed structure depends on the materials used, its designed properties, the effectiveness of its project management, the considerations of economics and the environment, and its true function. It is clear that these subprojects influence the entire project in complex ways. The traditional mathematical methods such as Boolean logic, in which bi-valued linguistic values such as “good” or “poor” are used as the assessment always fail to evaluate a complex system precisely. Moreover, due to system complexity most linguistic evaluations of such systems are vague, ambiguous or fuzzy such as “fairly good” or “very poor.” However, such fuzzy analysis is exactly the type of pattern that our brains work with, where we rarely judge a certain object absolutely, using such

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terms as “good” or “bad” but use subjective assessment terms such as “fairly good,” qualitatively, or “70% positive,” quantitatively. Dr. Zadeh proposed the Fuzzy Set

Concept in 1965 to extend bi-valued Boolean logic to fuzzy logic, where the output value is continual and varies gradually rather than being discrete and fixed, as in Boolean logic. Full discussions of Boolean Logic and Fuzzy Logic will be presented in a later section.

Fault Tree Analysis, a term originally coined in 1962 at Bell Laboratories, is a deductive failure analysis method to evaluate the reliability and safety of a system and used primarily in the engineering field. According to the Guidelines for Hazard

Evaluation Procedures (3rd Edition), the definition of FTA is as follows:

“FTA (FTA) is a top down, deductive failure analysis in which an

undesired state of a system is analyzed using Boolean Logic to combine a series

of lower-level events.”

This definition unequivocally states that FTA is based on Boolean Logic, but even though a construction project can be regarded as a complex system, we can still use FTA in conjunction with the Fuzzy Logic Concept (i.e., Fuzzy FTA or FFTA) to evaluate the project's performance and diagnose its problems. That is the topic this part of the thesis primarily discusses. A more in-depth introduction of FTA will be presented in a later section. Two fault-detection approaches that have been utilized in engineering to detect system problems: the inductive method and the deductive method, which are compared in Table 7.1

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Table 7.1 Comparison using the inductive and deductive methods

Name Inductive Method Deductive Method Advantages All the possible states can be Easier to find which component examined failure leads to a systematic failure; Disadvantages Must consider all the possible Might omit other states of states of its components; the components in a system; number of failure state may be very large; it is difficult to diagnose the causes of failures Examples Preliminary Hazard Analysis Fault Tree Analysis (FTA), Fuzzy (PHA); Failure Mode Effect and Fault Tree Analysis (FFTA) Criticality Analysis (FMECA)

To seek failure mechanisms and the cause-and-effect relationships in a construction project, a deductive method, FTA, will be used in this thesis. FTA is a deductive method that represents the logical structure of a composite system graphically. FTA can clearly express how the components in a system are connected using AND or OR gates and its failure sequences using a diagram, in which all the logic relationships between the causes and effects of a certain failure scenario, which are denoted as “basic events” and “top events,” are connected with various types of gates

(AND gates for intersection logic and OR gates for union logic). The basic concepts of

FTA gates used in this thesis are shown in Table 7.2.

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Table 7.2 The components of FTA

Name Illustration Description Top Event A type of result event, the terminal consequence a system state

Intermediate A type of result event, the Event intermediate consequence of a system Basic Event Basic event is a possible failure which requires no further development, usually it is an internal cause for the failure of its upper event AND Gate Shows the contributions of either one of the lower events to the upper event OR Gate Shows the contributions of all the lower events to the upper event

Sum Gate Represents the contribution of either one or both of the lower events to the upper event Mean Gate Considers the average value of all fuzzy set values of the lower events that contribute to the upper event Weight Denotes the weight when more than two basic events are being averaged or summed to obtain the upper event using a certain algorithm

After a fault tree has been constructed, it can be used to evaluate the risk and the possible failure patterns of a system both qualitatively and quantitatively. The aim of the qualitative analysis of a fault tree is to discover its Minimal Cut Sets (MCSs), which are the smallest combinations of component failures that could result in the occurrence

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of a higher failure event by using Boolean Logic. By analyzing the MCS paths, the weakest links in a system can easily be identified and, therefore, some appropriate prevention procedures can be applied and constructive improvement can be considered. In addition, only two terms, “fault” and “normal,” are used to denote the current status of each event (Fujino, 1994).

In contrast to the qualitative analysis, which mainly determines the status of events, the quantitative analysis can be used to calculate the probabilities of failure from the top event to every basic event, using probability theory. The arithmetic properties of AND and OR gates are presented below:

푛 푃 = ∏ 푝 퐴푁퐷 푖 Equation 7-1 푖=1

where PAND is the probability of an event through an AND gate and 푝푖 is the probability of each of its basic events occurring. For an OR gate,

푛

푃푂푅 = ∑ 푝푖 Equation 7-2 푖=1

where POR is the probability value of an event occurring through the OR gate and

푝푖 is the probability value of each of its basic events occurring.

An example of a “Triggering Cause,” all of which are intermediate events in this fault tree. For every intermediate event, several independent causes can be deduced.

For example, “Enabling Events” are considered to be triggered by these five aspects:

“Construction,” “Materials,” “Design,” “Detailing” and “Maintenance.” All five causes

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are regarded as basic events (denoted by circles). Similarly, both “Human-related Cause” and “Triggering Cause” are divided into several undeveloped events denoted by diamonds. After obtaining the logic structure of the fault tree, the occurrence probability of each event can be calculated according to the probability theory algorithm. The calculation procedures are listed in Table 7.3.

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Figure 7.1 An example of fault tree to investigate the failure of scaffolding

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Table 7.3 The calculation procedures of FTA using probability theory Level 1 Level 2 Level 3

Scaffolding Failure Enabling Cause Construction p1 = 0 p= P1 × P2× P3 = P1= p1 + p2 + p3 + p4 + p5= 0.21 Material p2 = 0.1 0.097 Design p3 = 0.01

Detailing p4 = 0

Maintenance p5 = 0.1

Human-related Cause Deviation p6 = 0.3

P2= p6 + p7 + p8 + p9 = 0.9 Improper Operation p7 = 0.3

Alcohol Abuse p8 = 0

Distraction p9 = 0.3

Triggering Cause Temperature p10 = 0.013

P3 = p10 + p11 + p12 = 0.512 Wind p11 = 0.1

Heavy Rain p12 = 0.4

where pi is the occurrence probability of failure, Pi is the occurrence probability of an intermediate event and P is the occurrence probability of scaffolding failure (the top event).

From the axioms and the example of FTA with probability theory, it can be seen that the probability value of the top event is a linear combination of all of its basic events, based on probability theory. Through the quantitative analysis, the occurrence probability for each event can be obtained, and the MCSs can also be obtained quite easily by sorting the probability values.

The interactions between the basic events and their top event are linear, which indicates that the system being represented as a fault tree is composite rather than complex. Consequently, the reliability of the results largely depends on the

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completeness and accuracy of the lower events. In other words, there are limitations of

FTA with traditional probability theory, and that is why fuzzy logic is substituted for probability theory in FFTA—to enable the evaluation of complex systems such as construction projects, in which the relationships between elements are non-linear.

Consequently, the results, which are calculated based on fuzzy set concepts are more reliable and closer to real-world conditions. This thesis uses FFTA as a tool to evaluate the performance of the Dayanta.

As mentioned previously, to evaluate complex systems such as construction projects, traditional FTA based on probability theory is inadequate. In 1965, Dr. Zadeh proposed an expansion of the traditional set theory introduced by Cantor called fuzzy set theory, in which the sets have unclear and “fuzzy” boundaries. The definition of a fuzzy set provided by Zadeh is presented below (Zadeh, 1965):

“Let X be a space of points (objects), with a generic element of X denoted by x.

Thus, X={x}. A Fuzzy Set (class) A in X is characterized by a membership

(characteristic) function fA(x) which associates with each point in X a real number

in the interval [0,1], with the value of fA(x) at x representing the “grade of

membership” of x in A.”

To understand the differences between Cantor’s set theory and Zadeh’s fuzzy set theory, suppose that X is a universe of discourse of a certain object, and the elements belonging to it are denoted as x. Assuming that A is subset of X, then the membership function fA can be examined. In Cantor’s set theory, an element must Equation 7-3

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either be in or not in a certain set. Consequently, the membership function for such a set can be presented as:

1 푥 ∈ 퐴 푓 (푥) = { 퐴 0 푥 ∉ 퐴

Based on the function presented above, the value of the membership function fA can result only in either 0 or 1, corresponding to “true” or “false” in Boolean logic.

Hence, the discussion of membership in set theory is similar to the famous line “to be or not to be” in Shakespeare's Hamlet, while in fuzzy set theory, this line is rewritten as “to be or not to be, which can—to some degree—occur concurrently.” In contrast to the set of the values of the membership function fA in set theory, which is finite, discrete and has only two elements (0 and 1), a set in fuzzy set theory is continuous and infinite, in which the value of the membership function fA can be taken as a value of the real interval from 0 to 1. Unlike in set theory, in which the value of the corresponding element represents only whether or not it belongs to the defined set, in fuzzy set theory, the value of an element stands for the probability that it belongs to the defined set. For example, “fA(x) = 1” means “x completely belongs to A,” “fA(x) = 0” means “x completely does not belong to A,” and “fA(x) = 0.6” means “x belongs to A with the probability of 60%.”

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7.2 Angular Fuzzy Model

This thesis uses the angular model to construct the FFTA to investigate the performance of the Dayanta, which has been defined as the top event in the FFTA structure. The angular model is simple and effective in which the fuzzy elements and membership functions are defined in a semicircle, as shown in Figure 7.2. Therefore, the value of the membership function of fuzzy set A can be represented by angle A according to the geometric relationship, which is defined as follows:

푓퐴(푎) = 푎 tan 퐴 , 퐴 ⊂ 풜, 푎 ∈ 풜.

Figure 7.2 Angular fuzzy model

The fuzzy membership function associating the linguistic value with the degree of the rotating angle from the horizontal benchmark in the semicircle defines counterclockwise as positive and clockwise as negative, as shown in Table 7.4.

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Table 7.4 Definitions of membership functions in angular model

Linguistic Values Degrees of Angle Absolutely Positive 1 휋 = 90° 2 Extremely Positive 7 휋 = 78.75° 16 Very Positive 3 휋 = 67.5° 4 Positive 1 휋 = 45° 4 Fairly Positive 1 휋 = 22.5° 8 Undecided 0° Fairly Negative 1 − 휋 = −22.5° 8 Negative 1 − 휋 = −45° 4

Very Negative 3 − 휋 = −67.5° 4 Extremely Negative 7 − 휋 = −78.75° 16 Absolutely Negative 1 − 휋 = −90° 2

By adopting the membership functions defined in Table 7.4, the subjective judgments such as “very good” and “fairly poor” can be converted into a numerical value in the form of an angle and be presented straightforwardly in a semicircle. In this thesis, the basic events, which include five structural components, five non-structural components in the superstructure of Dayanta, and three foundation factors in the substructure of Dayanta, will be assessed using the membership functions in the angular models. Based on the literature reviews as well as discussions about

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substructure and superstructure in Chapters 2, 4, and 5, respectively, and using the author’s personal expertise, the evaluation of basic events in the FFTA about the performance of Dayanta is shown in Table 7.5.

Table 7.5 Evaluations of basic events in the angular FFTA

Intermediate Events Basic Events Evaluation Degree of the Angle Superstructure Structural Interior Wall Extremely 78.75° System Positive Horizontal Beams Positive 45° Pillars Fairly Positive 22.5° Floor Slab Fairly Positive 22.5° Exterior Wall Very Positive 67.5° Non- Arch Door Positive 45° Structural Decorative Very Positive 67.5° System Components Eave Fairly Positive 22.5° Pagoda Cells Positive 45° Stairs Positive 45° Substructure Strip Foundation Fairly Positive 22.5° Base Very Positive 67.5° Rammed Earth Positive 45°

The middle level of the FFTA includes three intermediate events: the structure system integrating the interior wall, horizontal beams, pillars, floor slab, and exterior wall via an OR gate; the non-structure system integrating the arch door, decorative components, eaves, pagoda cells, and stairs via an OR gate; and the substructure integrating the strip foundation, base, and rammed earth via another OR gate. The

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reason for using an OR gate in the analysis of FFTA is that each of the basic events can affect the performance of the intermediate events independently, and the one with the dominant influence will influence its upper events most apparently. Thus, in accordance with the deduction made above, the algorithms of the OR gate defined in the angular

FFTA are shown in Equation 7-4, highlighting the maximum value among the degree of angles in the basic events.

푂푅 퐺푎푡푒: 훼푈푃푃퐸푅 = 푀푎푥 (훼퐵퐴푆퐼퐶 1, 훼퐵퐴푆퐼퐶 2, 훼퐵퐴푆퐼퐶 3, … 훼퐵퐴푆퐼퐶 푛) Equation 7-4 Using the data presented in Table 7.5, the value of the intermediate events in the angular FFTA can be calculated using Equations 7-5 to 7-7 as follows:

Equation 7-5 푆푡푟푢푐푡푢푟푎푙 퐶표푚푝표푛푒푛푡푠: 훼푆퐶

= 푀푎푥 (78.75°, 45°, 22.5°, 22.5°, 67.5°) = 78.75°

푁표푛 − 푠푡푟푢푐푡푢푟푎푙 퐶표푚푝표푛푒푛푡푠: 훼푁퐶 Equation 7-6

= 푀푎푥 (45°, 67.5°, 22.5°, 45°, 45°) = 67.5°

푆푢푏푠푡푟푢푐푡푢푟푒: 훼푆푈퐵 = 푀푎푥 (22.25°, 67.5°, 45°) = 67.5° Equation 7-7

Based on the calculation defined, a Windows-based application was programmed using C# programming language to integrate the angular FFTA and graphical simulation.

The welcome page of this application is shown in Figure 7.3, and the interface of the results of assigned basic events in FFTA in the Windows-based application is shown in

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Figure 7.4. Please note the angles of basic events are presented in blue whereas the green angles represent the angles of weights in the interface of the Windows-based application.

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Figure 7.3 Welcome page of the Windows-based application

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Figure 7.4 Basic events of FFTA in the Windows-based application

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The intermediate events will then be assigned the different weights to obtain the evolution of the top events via a fuzzy mean gate. The algorithm of the fuzzy mean gate is defined in Equation 7-5, and the weights assigned for the intermediate events are shown in Table 7.6. The interfaces of the results of weighed intermediate events and the result of the top event in FFTA in the Windows-based application are shown in Figures

7.5 and 7.6, respectively. After completing the calculation programmed in the Windows- based application, the final evaluation of the top event is 73.13°; comparing this with the membership function defined in Table 7.4 indicates that the performance of

Dayanta ranges from very positive (67.5°) to extremely positive (78.75°), given the initial inputs in the evaluation of basic events.

∑푛 푖 훼푖 × 푤푖 Equation 7-8 푀푒푎푛 퐺푎푡푒: 훼푈푃푃퐸푅 = 푛 ∑푖 푤푖

Table 7.6 Weights assigned for the intermediate events in the angular FFTA

Intermediate events Weight Degree of the Angle Structural System Very Positive 67.5° Non-structural System Positive 45° Substructure Fairly Positive 22.5°

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3 ∑1 훼푖 × 푤푖 푃푒푟푓표푟푚푎푛푐푒 표푓 퐷푎푦푎푛푡푎: 훼푇푂푃 = 3 ∑1 푤푖

78.75° × 67.5° + 67.5° × 45° + 67.5° × 22.5° Equation 7-9 = 67.5° + 45° + 22.5°

= 73.13°

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Figure 7.5 Results of the intermediate events of FFTA in the Windows-based application

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Figure 7.6 Result of top events of FFTA in the Windows-based application

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It is noteworthy that the results produced by the FFTA in the Windows-based application presented in Figure 7.6 are just a demonstration to show how to use the method of angular FFTA to evaluate the performance of Dayanta. In fact, as previously discussed, the angular FFTA values can be customized by the users, allowing the collection of different opinions to update the evaluations of the conditions of structural components, non-structural components, and substructures based on the latest research results.

This flexibility highlights the applications’ versatility and ensures that the angular

FFTA application can remains accurate to investigate the performance of the Dayanta over time. When conditions change in the user selection interface, as shown in Figure

7.7, the final evaluation will update to 56.25°, as shown in Figure 7.8, by repeating the calculation process used in the previous example, which can be defuzzified as a less positive evaluation than that obtained in the previous example and can be interpreted as ranging from positive (45°) to very positive (67.5°). The significance of the customization of the angular FFTA lies in the fact that it can integrate new information and evidence investigated by other scholars to reevaluate the structural components, non-structural components, and substructures as well as the top event when new and different opinions are available. Thus, the angular FFTA application constructed as part of this thesis is a dynamic and robust system, rather than a static analysis tool.

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Figure 7.7 Customized basis events of FFTA in the Windows-based application

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Figure 7.8 Less positive evaluation of the top events of FFTA in the Windows-based application

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Rather than merely integrating the angular FFTA evaluation system in the

Windows-based application, the graphical simulations of the construction sequence of

Dayanta presented in Chapter 6 were integrated as well. By clicking the buttons with green icons near the label of basic event, the graphic model of the corresponding components can be reviewed in a pop-up window, as shown in Figure 7.9, as well as the graphical model of the interior wall after clicking the green button and, in Figure 7.10, the strip foundation. Furthermore, by clicking the “Structure” button on the upper-right corner in the FFTA interface, a tree-diagram of the Dayanta structure can be reviewed, in which the hierarchy of structural components is organized from the left to the right and the construction sequence is illustrated from the bottom to the top, indicating the connection between the structural components evaluated in Chapter 7 with the graphically simulated construction sequence conducted in Chapter 6 (see Figure 7.11).

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Figure 7.9 Graphics model of interior wall in the pop-up window

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Figure 7.10 Graphics model of strip foundation in the pop-up window

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Figure 7.11 Tree-diagram of the structure of Dayanta

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Then, by clicking the “Construction sequence” button, the graphical models of the

Dayanta construction sequence can be seen in an interface, which is like a gallery, to illustrate the complete simulation of the Dayanta in three stages, as shown in Figure

7.12. If a larger size of the picture of each single step is needed, the picture of graphical models of the construction sequence can be zoomed out in a pop-up window by clicking on the picture itself, as shown in Figure 7.13. Also, other graphical simulations, such as the three possible assumptions of the foundation style of Dayanta, can be seen in other interfaces, as shown in Figure 7.14.

In the education level, the entire system is a prototype of the integrated system to investigate one ancient building in the civil engineering perspectives, which can be employed as a learning tool to introduce one method to evaluate the performance of an ancient, as the angular FFTA applied in this case, and to present the step-by-step graphically modeled construction sequence of the ancient building, as Dayanta in this thesis.

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Figure 7.12 Graphical simulation of the construction sequence of the Dayanta

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Figure 7.13 A zoomed out view of construction sequence

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Figure 7.14 Graphical simulation of foundation assumptions of the Dayanta

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In summary, the FFTA method was adopted to investigate the performance of the

Dayanta. Based on the available research, the performance of Dayanta in the aspects of superstructure and substructure involves environmental factors, structural factors, materials, and other considerations, as discussed in Chapters 4 and 5. The evaluation of the performance of the Dayanta was visualized in the form of a fault tree with a fuzzy angle that can be easily and readily comprehended. One Windows Forms application built in the C# programming language was created to integrate angular FFTA and the graphical simulation of the construction sequence of Dayanta, with customized user selections. These applications can serve as effective investigating tools when new information is introduced. The Windows-based application can be regarded as a prototype of a learning platform to introduce and evaluate an ancient building by using the FFTA method and graphical simulation, as has been done with Dayanta in this thesis.

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Chapter 8 Summary, Conclusion and

Recommendations

8.1 Summary and Conclusion

In summary, this thesis presented visualized investigation of the Dayanta, including its history, discussions and visualizations of its substructure, superstructure, construction sequence and an evaluation of its performance that uses Fuzzy Fault Tree

Analysis the angular fuzzy model. The visualizations in this study are predicated on three aspects. The first aspect involves the four different versions of the Dayanta in history.

The second aspect of this visualization involved the creation of 3-D models of the

Dayanta using Autodesk 3DS MAX. These efforts included the digital reconstruction of the different versions of the Dayanta, simulating its foundation style, modeling the structural components including the stairs, pillars, walls and the configuration of the superstructure of the Dayanta, and a complete, step-by-step graphical simulation of the construction sequence of the Dayanta, including its strip foundation, base, exterior and interior walls on each floor, spirally ascending stairs, supporting system and decorative components.

By following the graphics pipeline, the modeling work was accomplished in three stages, a modeling stage, a material assignment stage and a rendering stage. All the preliminary modeling work, such as creating the basic geometric objects for the 176

structural components of the Dayanta, was performed during the modeling stage and formed the basis for further graphical simulation. In the materials assigning stage, textures were mapped onto the surfaces of the graphical models of the Dayanta. By setting the proper parameters for some channels of the assigned materials, such as the diffuse, ray tracing and bump channels, the effects of light and shadow were maximized, making the graphical simulation much more realistic. In the third stage, the graphical model of the Dayanta was rendered by configuring the environmental conditions.

Finally, two animation clips were produced in Autodesk 3DS MAX that, respectively, showcase the construction sequence of the Dayanta and provide a virtual tour of the

Dayanta. The graphics pipeline adopted in this thesis is an effective method for digitally reconstructing ancient buildings and creating graphical simulations that reveal their structures and construction activities. Autodesk 3DS MAX was shown to be appropriate software to use for the 3-D modeling work in this graphics pipeline. The significance of the modeling work in this thesis is that it provides a prototype for constructing a 3-D database of ancient buildings—in this case, the Dayanta—in which all the information pertinent to an ancient building, including its historical studies, structural analysis, construction procedures, materials and architectural design can be visualized using 3-D graphical models. These models can be shared with people from all over the world via the Internet; no matter what language they speak or understand, people can learn about and appreciate the beauty of ancient buildings by viewing their 3-D visualized models and illustrations. Such a capability can contribute greatly to the preservation, documentation and protection of ancient buildings.

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The third aspect of the visualization in this thesis concerns the application of Fuzzy

Fault Tree Analysis to investigate the performance of Dayanta. In this visualization, both the problem evaluation processes and the results are presented in the form of graphics defined using fuzzy models. The angular fuzzy model was employed for the FFTA in this thesis, and one Windows Forms applications were developed using the C# language and

Microsoft Visual Studio 2015 to integrate the FFTA analysis with the ability for users to make customized selections and graphical simulation of the construction sequence. This application serve as prototypes to show how fuzzy logic methods can be applied to the investigation of ancient building problems, which is particularly important given that the records and data for such buildings are unavailable in some cases, and how efficient the graphical models can facilitate the readers to understand the complex structure and construction sequence of Dayanta in 3-D graphics. The conclusions produced by the

FFTA approaches agree with real observations of the Dayanta and range from

“Extremely Good” to “Very Good,” verifying the effectiveness of using FFTA to investigate the performance of Dayanta. The accuracy and validity of the FFTA method can be continuously enhanced by updating the applications using new data and by increasing the number of experts participating in the evaluation process.

The visualized investigation of an ancient building described in this thesis can be regarded as an exploration of the application of new techniques to old disciplines—in this case, the application of modern computer graphics techniques to ancient architectural fields, and the adoption of fuzzy logic methods to investigate the performance of the Dayanta, which has stood for nearly 1500 years. The practices of the

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visualization studies conducted in this thesis have multifold meanings: at an archaeological level, the method for 3-D graphical reconstruction of ancient buildings can be used as a standard model to document additional ancient architecture around the world for educational purposes and heritage preservation; at an engineering level, the application of FFTA usi and the angular model can be repurposed to evaluate the performance of other buildings and infrastructures; at an educational level, 3-D modeling is a useful approach for teaching college student about complex building structures and construction sequences; and, finally, from at a historical level, investigating and visualizing the development, structure, renovation and the complete construction sequence of the Dayanta provides a great experience for learning the wisdom and ideas hidden in ancient building design s and for acquiring cultural, political, economic and societal knowledge of the periods the Dayanta has served.

8.2 Recommendations

The recommendations of this thesis are targeted to cover the aspects of this effort that were not fully accomplished in this thesis. From the aspect of graphical simulation, only the most recent version of the Dayanta was comprehensively modeled. For the other three versions of the Dayanta, lack of required data—specifically the dimensions of the no-longer-existing versions of this pagoda—prevented their complete and accurate modeling in this thesis. In the future, as new discoveries accumulate in

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archaeology and with new studies in history, the modeling work of all the versions of the Dayanta may be completed should sufficient and usable data surface.

The systems to evaluate the performance of the Dayanta using FFTA currently form only a prototype showing a preliminary application of fuzzy logic in evaluating the structural performance of ancient building—in this case, the Dayanta. More complex and precise algorithms and models should be introduced and other types of FFTA can be developed, forming a set of assessment systems that can be used to examine additional aspects of the Dayanta, such as its structural stability, materials, and so on. Most importantly, such systems show promise for the evaluation of other ancient buildings using criteria based on fuzzy logic methods.

Also, to evaluate the effectiveness of the result produced in FFTA, Institutional

Review Board (IRB) could be employed as an important approach to verify the evaluation concluded in the models of FFTA. Additionally, with increasing development of the on-site surveying technology, data collection will contribute to a more accurate and comprehensive study of the Dayanta, based on which statistical models can be applied to verify the performance of the Dayanta more accurately.

Furthermore, the file format interoperability between Autodesk 3DS MAX and

Visual Studio makes it possible to use the 3-D models from wider fields such as construction and industry in the flexible development environment of Visual Studio, which supports multiple programming languages. The compatibility of the models from these two software tools can be evaluated based on the results of this thesis. In the

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future, 2-D or 3-D models can be connected to Visual Studio from diverse software modeling tools and used widely in applications.

Virtual Reality (VR) is pivotal in today’s technology, and it is regarded as the next- generation form of man-to-machine interaction. In a VR environment, all the objects are graphically modeled and intelligently programmed, and users can interact with them freely in an immersive manner. Developing VR requires 3-D modeling and utilizes VR devices such as VR glasses to connect the virtual modeled world stored and rendered by a computer with a VR environment where users experience immersive exploration.

Therefore, the modeling work performed in this thesis can be used as a basis of the establishment of a VR system to simulate the construction sequence of the Dayanta.

This VR system is one of the recommendations for extending this research in the future.

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