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系統識別號 U0002-1408201914200700
中文論文名稱 垂直動荷載作用下樁筏基礎的有限差分分析
英文論文名稱 Finite Difference Analysis For Piled Raft Foundation under Vertical Dynamic Loading
校院名稱 淡江大學
系所名稱(中) 土木工程學系碩士班
系所名稱(英) Department of Civil Engineering
學年度 107
學期 2
出版年 108
研究生中文姓名 蔣翠莎
研究生英文姓名 Tricia John
學號 607385019
學位類別 碩士
語文別 英文
口試日期 2019-07-26
論文頁數 71頁
口試委員 指導教授-張德文
委員-葛宇甯
委員-洪勇善
中文關鍵字 樁筏基礎  有限差分分析  動態加載 
英文關鍵字 piled raft foundation  finite difference analysis  dynamic loading 
學科別分類 學科別應用科學土木工程及建築
中文摘要 本研究透過修改WERAFT-S (Wave Equation Analysis for Raft Foundation - Statics) 分析開發動態荷載條件下的有限差分分析。 此三維模型包含二維筏基的變形和一維基樁的變形,在時域中進行分析得到各種穩態荷載下筏基的位移量,進而分析樁筏基礎位移,分析結果並與三維分析軟體Midas GTS NX進行比較。
在本研究中,彈簧和阻尼器之模型選取皆有頻率相依 (frequency-dependent) 及頻率不相依 (frequency-independent) 的情況,上述兩種皆應用於模擬土壤。 所建議的分析能夠得到與有限元素法分析相似的位移量。 本研究未考慮樁與樁的互制效應。 研究結果發現,目前的分析模型在基礎共振的模擬上仍有限制。
英文摘要 In this study a finite difference analysis toolkit is developed by modifying the WERAFT-S (Wave Equation Analysis for Raft Foundation - Statics) analysis for use in dynamic loading conditions. This three-dimensional model considers the two dimensional deformations of the raft and the one-dimensional deformations of the piles. The analysis is performed in the time domain to determine the displacement of a raft foundation and subsequently a piled raft foundation, under various steady state loads. Validation of the proposed analysis model is carried out by performing a three dimensional analysis using Midas GTS NX.
Frequency-dependent and frequency-independent spring and dashpot models have been used to model the soil in this study. The proposed analysis is able to determine the order of displacement of similar magnitude as the finite element analysis. Pile to pile interaction effects have not been considered in this study. It was found that the current model is limited in its capacity to reveal the resonance of the foundation.
論文目次 Table of Contents
Abstract I
Acknowledgement III
List of Figures VI
List of Tables IX

Chapter 1 Introduction 1
1.1 Research Motivation and Objective 1
1.2 Research Method 2
1.1 Research Contents 4

Chapter 2 Literature Review 5
2.1 Raft Foundation Analysis 5
2.2 Piled Raft Foundation Analysis 6
2.3 Foundation Subject to Dynamic Loading 9
2.4 Pile Stiffness 12
2.5 Kirchhoff-Love Hypothesis 13
2.6 Summary 13

Chapter 3 Theory and Method 15
3.1 Theory 15
3.2 Governing Equation 16
3.3Nodal Equations 17
3.4 Raft Displacement Analysis: WERAFT-D 25
3.5 Piled Raft Displacement Analysis: WEAPR-D 26
3.6 Finite Difference Model 29
3.6.1 Finite Difference Model- Raft Only 30
3.6.2 Finite Difference Model - Piled Raft 32
3.7 Finite Element Model 33
3.7.1 Finite Element Model- Raft Only 33
3.7.2 Finite Difference Model- Piled Raft 36
3.8 Material Parameters 38

Chapter 4 Results 39
4.1 Raft Displacement 39
4.1.1 Raft Displacement: WERAFT-D 41
4.1.2 Raft Displacement- WERAFT-D vs. FEM Comparison 44
4.1.3 Raft Displacement- Finite Element on Linear Springs 49
4.2 Piled Raft Displacement: WEAPR-D 51

Chapter 5 Conclusion 61
5.1 Discussion and Conclusion 61
5.2 Limitations and Suggestions 62

References 63

Appendix A 67
Appendix B 68
Appendix C 70







List of Figures
Figure 1-1 Research Structure Diagram 3

Figure 2-1 Plate on Springs Model on Winkler Springs 6
Figure 2-2 Plate-Beam-Springs Modelling of a Piled Raft Foundation 8
Figure 2-2a Kitiyodom and Matsumoto (2002) 8
Figure 2-2b Randolph (1994) 8
Figure 2-3 Wolf (1995) Simplified Model 10
Figure 2-2a Disk on surface of half-space with truncated semi-infinite translational cone 10
Figure 2-2a Discrete-element model (lumped-parameter) for translational cone 10

Figure 3-1 Discretized Raft Model on Linear Springs 15
Figure 3-2 Single Pile Equilibrium Model 26
Figure 3-3 Discretized Pile Model 29
Figure 3-4 WERAFT-D Raft Model 30
Figure 3-5 WERAFT-D Discretized Raft Model 31
Figure 3-6 WEAPR-D Piled Raft Model 32
Figure 3-7 Finite Element Meshing 34
Figure 3-7a Isometric View 34
Figure 3-7b Top View 34
Figure 3-8 Finite Element Model Boundary Constraints 36
Figure 3-9a 3-D Finite Element Pile Model 36
Figure 3-9b 3-D Finite Element Piled Raft Model 36
Figure 3-10 Piled Raft Foundation 3-D Finite Element Mesh 37

Figure 4-1 Surface Raft Foundation 39
Figure 4-2 Raft Foundation Discretization 41

Figure 4-3a Raft Foundation Displacement vs. Frequency- Lysmer (1965) 42
Figure 4-3b Raft Foundation Displacement vs. Frequency- Gazetas (1991) 42
Figure 4-3c Raft Foundation Displacement vs. Frequency- Wolf (1995) 43

Figure 4-4 Finite Element Model Dimension 45
Figure 4-5 FEM Raft Foundation Displacement vs. Frequency 45

Figure 4-6a WERAFT-D vs. FEM Comparison (Model R1) - Vs=120m/s 46
Figure 4-6b WERAFT-D vs. FEM Comparison (Model R1) - Vs=150m/s 47
Figure 4-6c WERAFT-D vs. FEM Comparison (Model R1) - Vs=180m/s 47

Figure 4-7a WERAFT-D vs. FEM Comparison (Model R2) - Vs=120m/s 48
Figure 4-7b WERAFT-D vs. FEM Comparison (Model R2) - Vs=150m/s 48
Figure 4-7c WERAFT-D vs. FEM Comparison (Model R2) - Vs=180m/s 49

Figure 4-8 FEM on Linear Springs and Dashpots Model 50
Figure 4-9 FEM on Linear Springs and Dashpots and Proposed Finite Difference Analysis 50
Figure 4-10 Piled Raft Foundation Model 51
Figure 4-11 Piled Raft Foundation 3x3 Pile Configuration Layout 53
Figure 4-12 Piled Raft Foundation 4x4 Pile Configuration Layout 53

Figure 4-13a Piled Raft Foundation (PR1) vs. Raft Model (R1) Comparison - Vs=120m/s 54
Figure 4-13b Piled Raft Foundation (PR1) vs. Raft Model (R1) Comparison - Vs=150m/s 55
Figure 4-13c Piled Raft Foundation (PR1) vs. Raft Model (R1) Comparison - Vs=180m/s 55

Figure 4-14a Piled Raft Foundation (PR2) vs. Raft Model (R2) Comparison - Vs=120m/s 56
Figure 4-14b Piled Raft Foundation (PR2) vs. Raft Model (R2) Comparison - Vs=150m/s 56
Figure 4-14c Piled Raft Foundation (PR2) vs. Raft Model (R2) Comparison - Vs=180m/s 57

Figure 4-15a Piled Raft Foundation Model (PR2) vs. (PR1) Comparison - Vs=120m/s 58
Figure 4-15b Piled Raft Foundation Model (PR2) vs. (PR1) Comparison - Vs=150m/s 58
Figure 4-15c Piled Raft Foundation Model (PR2) vs. (PR1) Comparison - Vs=180m/s 59

Figure 4-16a Piled Raft Foundation (PR3) vs. Raft Model (R2) Comparison - Vs=150m/s 60
Figure 4-16a Piled Raft Foundation Model (PR3) vs. (PR2) Comparison - Vs=150m/s 60

Figure A-1 Graphs to determine dynamic stiffness and damping coefficients k ̃_z and c ̃_z using Gazetas, 1991 spring and dashpot model 67

Figure C-1 Sample input load- 1.5 kPa amplitude 70
Figure C-2 Sample input load- 0.222 kPa amplitude 70
Figure C-3 Sample output displacement vs. time curve - WERAFT model 71
Figure C-4 Sample output displacement vs. time curve - FEM model 71




List of Tables

Table 3-1 Spring and Dashpot Models for a disk on Homogeneous Half-space 25
Table 3-2 Pile Spring Models for a Homogeneous Half-space 28
Table 3-3 Finite Element Assigned Mesh Sizes 33
Table 3-4 Empirical Formulas for Material Parameter Calculation 38

Table 4-1 Raft Foundation Dimension and Loading 39
Table 4-2 Material Parameters (Elastic Properties) 40
Table 4-3 Finite Element Model Analysis Zone Dimension 44
Table 4-4 Piled Raft Foundation Model Parameters 52
Table 4-4 Pile Stiffness Parameters 52

Table 5-1 Analysis Time Comparison 62

Table B-1 Frequency independent soil spring and dashpot values 68
Table B-2 Frequency dependent soil spring and dashpot values 69


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