本研究以WEAPR-S程式為分析基礎，模擬樁筏基礎在垂直均布載重下的變形量，該分析係藉二維筏基變形差分式和一維基樁變形差分式而建立。本研究另以改良之Lysmer類比模式模擬筏基底部土壤彈簧，同時使用極限強度模式模擬基樁等效彈簧勁度，並考慮群樁互制影響，完成WEAPR-S2程式之開發，其可求解線彈性樁筏基礎受力行為，具簡易分析特性。程式分析結果並與三維有限元素法Midas-GTS NX分析結果進行比較，以了解軟弱黏土地盤之樁筏沉陷量分布、應力分布、差異沉陷量、基樁折減係數、基樁受力分配情況，和相關參數影響。
研究成果顯示：1.採用改良Lysmer土壤彈簧搭配極限強度之基樁土壤彈簧，並引用群樁互制公式，可改善原WEAPR-S分析，使樁筏基礎的沉陷量與有限元素法分析結果相似。2.大型樁筏基礎的筏基下方土壤對基礎行為影響趨於明顯，基礎的沉陷以中心處最大，而受力亦以中心部位基樁較大，該受力現象與剛性基礎迴異。3.柔性樁筏基礎之基樁配置數量明顯影響基樁行為，基樁數量越多時，基樁的受力和其等效彈簧勁度愈均勻，其互制影響不明顯；但基樁數量減少時，角隅樁所受勁度之影響較其餘基樁明顯。4.研究發現：剛性樁筏基礎之基樁荷重比例將遠大於柔性基礎之基樁，其沉陷量亦將較柔性基礎低許多，故柔性樁筏中筏基下方土壤的承載力相對重要，若將剛性樁基礎之群樁設計概念套用於柔性樁筏基礎時，設計將過於保守。5.WEAPR-S2分析雖能大致掌握樁筏基礎受力行為，但仍會低估基樁的最大內力，使用時仍須謹慎。

This study, the WEAPR-S program is used as the analysis framework to simulate the deformation of the piled raft foundation under vertical uniform load. The analysis is based on two-dimensional deformations of the raft and one-dimensional deformations of the piles. In this study, a modified Lysmer analog model was used to simulate the soil spring at the bottom of the raft foundation. At the same time, the ultimate strength model was used to simulate the equivalent pile stiffness, and the pile-to-pile interactions were considered to complete the development of the WEAPR-S2 program. Validation of the proposed program was conducted with the 3D FEM analysis using Midas-GTS NX program. To understand the distribution of the piled raft foundation settlement, stress distribution, differential settlements, reduction effect, and load distribution, the effects of the structural and soil parameters in design were discussed for the applicability of such analysis.
The study reveals that: 1. The use of modified Lysmer soil springs combined with ultimate strength soil springs around the piles, and pile-to-pile interactions formula, can improve the original WEAPR-S analysis, so that the settlement of the pile raft foundation can be analyzed with the finite element method, the results are similar. 2. The soil under the raft foundation of the large pile-raft foundation is having obvious influence on the behavior of the foundation. The settlement of the foundation is the largest at the center, and the stress is also larger at the center. The stress distribution is different from the rigid foundation 3. The number of piles on the flexible pile raft foundation obviously affects the behavior of the foundation piles. The greater the number of piles, the more uniform the force of the pile and the equivalent pile stiffness it will be, and the resulting reduction effect is trivial. When the number of piles decreases, the pile-to-pile interaction influence on the stiffness of the corner pile is more obvious than rest of the piles. 4. The study reveals that the load carried by the piles of the rigid piled raft foundation will be much greater than the piles of a flexible piled raft foundation, and its settlement will be much smaller than that exerted at the flexible foundation. Therefore, the bearing capacity of the soil under the raft foundation in a flexible piled raft is relatively important. When the design concept of grouped piles with rigid pile cap is applied to flexible piled raft foundation, the design will be over conservative. 5. Although the WEAPR-S2 analysis can roughly grasp the piled raft foundation load-deformation behavior, it will underestimate the maximum internal stresses of the piles, and care must be taken when using it.

目錄
目錄	I
表目錄	IV
圖目錄	VII
第一章 緒論	1
1-1 研究動機與目的	1
1-2 研究方法	2
1-3 研究內容	3
第二章 文獻回顧	6
2-1 樁筏基礎分析方法	6
2-2 筏基變形理論	9
2-3 筏基變形之有限差分式	10
2-4 彈簧勁度	11
2-4-1 土壤彈簧勁度	12
2-4-2 基樁彈簧勁度	15
2-5 樁筏設計手冊	18
2-6 基礎之剛度與柔度	20
2-6-1 ACI336之建議公式	20
2-6-2 ECP196之建議公式	20
2-6-3 樁筏尺寸對基礎剛度影響	20
2-7 有限元素法分析	21
第三章 研究方法	24
3-1 研究工具	24
3-1-1 有限差分法程式WEAPR-S2	24
3-1-2 有限元素法軟體Midas-GTS NX	28
3-1-3 樁與樁互制因子方程式	31
3-2 研究步驟	32
第四章 標準模型分析	48
4-1 數值模型介紹	48
4-2 WEAPR-S2樁筏基礎變形分析	51
4-2-1 WEAPR-S2與WEAPR-S分析比較	51
4-2-2 WEAPR-S2標準案例之分析	54
4-3 參數研究	58
4-3-1 土壤剪力波速(Vs)	59
4-3-2 土壤柏松比(ν)	64
4-3-3 樁心距與樁徑比(S/D)	69
4-4 檢視研究成果	81
4-4-1 樁筏手冊設計之定性區間	81
4-4-2 樁筏基礎中基樁受力差異	83
4-5 剛性樁筏基礎應用	85
第五章 延伸應用	95
5-1 應用實例說明	95
5-2 小尺寸樁筏基礎變形分析	99
5-2-1 筏基位移量	99
5-2-2 樁頂位移量	102
5-2-3 基樁受力	103
5-2-4 基樁等效彈簧勁度	104
5-2-5 基樁等效彈簧勁度折減係數	106
5-2-6 樁筏建議手冊	108
5-3 大尺寸樁筏基礎變形分析	110
5-3-1 筏基位移量	110
5-3-2 樁頂位移量	115
5-3-3 基樁受力	118
5-3-4 基樁等效彈簧勁度	119
5-3-5 基樁等效彈簧勁度折減係數	123
5-3-6 樁筏建議手冊	124
第六章 結論與建議	127
6-1 結論	128
6-2 建議	130
參考文獻	131
 
表目錄
表 2 1筏基理論比較表	9
表 2 2筏基下方土壤彈簧勁度比較表	12
表 2 3土壤彈簧勁度正規化修正函數	14
表 2 4樁身與樁底土壤彈簧勁度模式比較表	17
表 2 5 Midas-GTS NX材料模式種類	23
表 2 6 Midas-GTS NX分析模式種類	23
表 3 1不同分析模式下單樁等效彈簧勁度	27
表 3 2單樁等效彈簧勁度比較表	28
表 4 1標準數值模型及參數變化	49
表 4 2 Midas-GTS NX與WEAPR-S S/D=8(未納入樁與樁互制)位移量比較表	53
表 4 3 Midas-GTS NX與WEAPR-S2 S/D=8(納入樁與樁互制)位移量比較表	54
表 4 4 Midas-GTS NX與WEAPR-S2標準案例分析之位移量比較表	56
表 4 5土壤剪力波速變化時PR26之筏基位移量比較表	60
表 4 6土壤剪力波速變化時PR26之樁頂位移量比較表	61
表 4 7土壤剪力波速變化時PR26之基樁受力占比比較表	62
表 4 8土壤剪力波速變化時PR26之基樁等效彈簧勁度比較表	63
表 4 9土壤剪力波速變化時PR26之基樁等效彈簧勁度折減係數比較表	64
表 4 10土壤柏松比變化時PR26之筏基位移量比較表	65
表 4 11柏松比變化時樁PR26之樁頂位移量比較表	67
表 4 12土壤柏松比變化時PR26之基樁受力占比比較表	67
表 4 13土壤柏松比變化時PR26之基樁等效彈簧勁度比較表	68
表 4 14土壤柏松比變化時PR26之基樁等效彈簧勁度折減係數比較表	69
表 4 15 S/D變化時PR26之筏基礎筏基位移量比較表	70
表 4 16 S/D變化時PR26角隅樁之樁頂位移量比較表	71
表 4 17 S/D變化時PR26樁土之間相對位移量比較表	73
表 4 18 S/D變化時對樁與樁互制係數總和比較表	77
表 4 19 S/D變化時對PR26之基樁等效彈簧勁度折減係數(Rp)比較表	79
表 4 20 S/D變化時WEAPR-S2 PR26基樁受力占比沉陷量比值比較表	82
表 4 21 PR26之筏基底部與樁頂兩者受力比值比較表	84
表 4 22 S/D變化時WEAPR-S2 PR26基樁受力(搭配差值)沉陷量比值比較表	85
表 4 23剛性樁筏基礎之參數表	86
表 4 24 S/D變化時剛性PR26之筏基位移量比較表	87
表 4 25 S/D變化時剛性PR26之基樁受力比較表	91
表 4 26 WEAPR-S2剛性PR26之基樁等校彈簧勁度折減係數(Rp)比較表	92
表 4 27 S/D變化時WEAPR-S2 剛性PR26基樁受力占比沉陷量比值比較表	93
表 4 28剛性PR26筏基底部與樁頂兩者受力比值比較表	94
表 5 1(a)延伸應用之參數設定	96
表 5 1(b) WEAPR-S2結構尺寸參數變化	96
表 5 2 Midas-GTS NX與WEAPR-S2分析PR16之筏基位移量比較表	99
表 5 3 Midas-GTS NX與WEAPR-S2 PR16 S/D=4之樁頂位移量比較表	102
表 5 4 Midas-GTS NX與WEAPR-S2 PR16 S/D=3之樁頂位移量	103
表 5 5 Midas-GTS NX與WEAPR-S2 PR16之基樁受力比較表	104
表 5 6 WEAPR-S2 PR16之基樁等效彈簧勁度折減係數(Rp)比較表	107
表 5 7 S/D變化時WEAPR-S2 PR16基樁受力占比沉陷量比值比較表	108
表 5 8 PR16之筏基底部與樁頂兩者受力比值比較表	109
表 5 9 S/D變化時WEAPR-S2 PR16基樁受力(搭配差值)沉陷量比值比較表	109
表 5 10 Midas-GTS NX與WEAPR-S2分析PR34之筏基位移量比較表	111
表 5 11(a) Midas-GTS NX與WEAPR-S2 PR34 S/D=8之樁頂位移量比較表	115
表 5 11(b) Midas-GTS NX與WEAPR-S2 PR34 S/D=6之樁頂位移量比較表	116
表 5 11(c) Midas-GTS NX與WEAPR-S2 PR34 S/D=4之樁頂位移量比較表	117
表 5 12 Midas-GTS NX與WEAPR-S2 PR34之基樁受力比較表	118
表 5 13 S/D變化時 PR34樁土之間相對位移量比較表	119
表 5 14 WEAPR-S2 PR34之基樁等效彈簧勁度折減係數(Rp)比較表	123
表 5 15 S/D變化時WEAPR-S2 PR34基樁受力占比沉陷量比值比較表	124
表 5 16 PR34筏基底部與樁頂兩者受力比值比較表	125
表 5 17 S/D變化時WEAPR-S2 PR34基樁受力(搭配差值)沉陷量比值比較表	126
 
圖目錄
圖 1 1研究流程圖	5
圖 2 1筏基各節點相對位置(摘自Bowles,1982)	10
圖 2 2基礎下方土壤彈簧模擬(a)剛性基礎(b)柔性基礎 (from Chang et al.2018)	12
圖 2 3土壤彈簧勁度正規化函數	13
圖 2 4土壤彈簧勁度正規化函數和適用範圍	14
圖 2 5土壤彈簧勁度正規化修正函數	15
圖 2 6基樁周圍土壤不排水剪力強度完全發揮所需位移量(a)樁身(b)樁底	16
圖 2 7樁筏基礎與土壤互制關係(from Katzenbach and Choudhury, 2013)	18
圖 2 8規範樁筏基礎設計定性區間(from Katzenbach and Choudhury, 2013)	19
圖 2 9有限元素法分析流程	22
圖 3 1樁筏基礎受垂直作用力的簡易模型示意圖(摘自 張德文，2017)	25
圖 3 2筏基節點示意圖(a)一般點 (b)邊緣點 (c)邊緣角隅鄰近點 (d)邊緣內側第一排點 (e)角隅點 (f)角隅內側臨近點 (摘自張德文，2017)	26
圖 3 3 Midas-GTS NX網格布置之實況	30
圖 3 4 Midas-GTS NX三維模型邊界條件示意圖	31
圖 3 5沉陷量對稱趨勢圖	33
圖 3 6 S/D=8基樁編號配置圖	33
圖 3 7 S/D=6基樁編號配置圖	35
圖 3 8 S/D=4基樁編號配置圖	38
圖 3 9研究步驟流程圖	47
圖 4 1 Midas-GTS NX 26m筏基之樁筏基礎數值模型S/D=4	50
圖 4 2 Midas-GTS NX PR26 S/D=8之筏基位移量俯瞰圖	52
圖 4 3 WEAPR-S PR26 S/D=8之筏基位移量俯瞰圖(摘自 連心維，2018)	52
圖 4 4 WEAPR-S2 PR26 S/D=8之筏基位移量俯瞰圖	53
圖 4 5 WEAPR-S2、WEAPR-S和Midas-GTS NX分析結果之比較圖	54
圖 4 6 Midas-GTS NX PR26標準案例之筏基位移量俯瞰圖	55
圖 4 7 WEAPR-S2 PR26標準案例之筏基位移量俯瞰圖	55
圖 4 8(a) Midas-GTS NX PR26標準案例之筏基應力	56
圖 4 8 (b) WEAPR-S2 PR26標準案例之筏基應力	57
圖 4 9 PR26 S/D=4樁土之間相對位移量分布圖	57
圖 4 10 PR26 S/D=8筏基位移量之相對概略誤差與疊代次數關係圖	58
圖 4 11土壤剪力波速變化時PR26之筏基位移量比較圖	59
圖 4 12土壤剪力波速變化時PR26之樁頂位移量比較圖	61
圖 4 13土壤柏松比變化時PR26之筏基位移量比較圖	65
圖 4 14土壤柏松比變化時PR26樁頂位移量比較圖	66
圖 4 15 S/D變化時PR26筏基位移量比較圖	70
圖 4 16 S/D變化時PR26不同土壤剪力波速之基樁總荷重占外力百分比	72
圖 4 17(a) Midas-GTS NX PR26 S/D=8基樁等效彈簧勁度等高線圖	74
圖 4 18(a) WEAPR-S2 PR26 S/D=8基樁等效彈簧勁度等高線圖	74
圖 4 17(b) Midas-GTS NX PR26 S/D=6基樁等效彈簧勁度等高線圖	75
圖 4 18(b) WEAPR-S2 PR26 S/D=6基樁等效彈簧勁度等高線圖	75
圖 4 17(c) Midas-GTS NX PR26 S/D=4基樁等效彈簧勁度等高線圖	76
圖 4 18(c) WEAPR-S2 PR26 S/D=4基樁等效彈簧勁度等高線圖	76
圖 4 19(a) PR26 S/D=8基樁編號與基樁名稱	78
圖 4 19(b) PR26 S/D=6基樁編號與基樁名稱	78
圖 4 19(c) PR26 S/D=4基樁編號與基樁名稱	79
圖 4 20 S/D變化時PR26基樁等效彈簧勁度折減係數關係圖	80
圖 4 21樁筏基礎與土壤互制關係(from Katzenbach and Choudhury, 2013)	81
圖 4 22規範樁筏基礎設計定性區間(from Katzenbach and Choudhury, 2013)	82
圖 4 23 WEAPR-S2 PR26分析結果繪製於ISSMGE樁筏設計手冊	83
圖 4 24 PR26 S/D=4應力分布透視圖	84
圖 4 25 WEAPR-S2 PR26分析結果搭配受力差值繪製於樁筏設計手冊	85
圖 4 26(a) Midas-GTS NX剛性PR26 S/D=4之筏基位移量	88
圖 4 27(a) WEAPR-S2剛性PR26 S/D=4之筏基位移量	88
圖 4 26(b) Midas-GTS NX剛性PR26 S/D=6之筏基位移量	89
圖 4 27(b) WEAPR-S2剛性PR26 S/D=6之筏基位移量	89
圖 4 26(c) Midas-GTS NX剛性PR26 S/D=8之筏基位移量	90
圖 4 27(c) WEAPR-S2剛性PR26 S/D=8之筏基位移量	90
圖 4 28 S/D變化時剛性PR26基樁等效彈簧勁度折減係數關係圖	93
圖 4 29 WEAPR-S2剛性PR26分析結果繪製於ISSMGE樁筏手冊	93
圖 4 30 WEAPR-S2 PR26剛柔性樁筏基礎分析結果比較(ISSMGE樁筏手冊)	94
圖 5 1 Midas-GTS NX 16m筏基樁筏基礎數值模型S/D=4	97
圖 5 2 Midas-GTS NX 34m筏基樁筏基礎數值模型S/D=8	98
圖 5 3(a) Midas-GTS NX PR16 S/D=4之筏基位移量	100
圖 5 4(a) WEAPR-S2 PR16 S/D=4之筏基位移量	100
圖 5 3(b) Midas-GTS NX PR16 S/D=3之筏基位移量	101
圖 5 4(b) WEAPR-S2 PR16 S/D=3之筏基位移量	101
圖 5 5(a) PR16 S/D=4基樁編號與基樁名稱	102
圖 5 5(b) PR16 S/D=3基樁編號與基樁名稱	103
圖 5 6(a) Midas-GTS NX PR16 S/D=4之基樁等效彈簧勁度等高線圖	105
圖 5 7(a) WEAPR-S2 PR16 S/D=4之基樁等效彈簧勁度等高線圖	105
圖 5 6(b) Midas-GTS NX PR16 S/D=3之基樁等效彈簧勁度等高線圖	106
圖 5 7 (b) WEAPR-S2 PR16 S/D=3之基樁等效彈簧勁度等高線圖	106
圖 5 8 S/D變化時PR16基樁等效彈簧勁度折減係數關係圖	107
圖 5 9(a) WEAPR-S2 PR16分析結果繪製於ISSMGE樁筏設計手冊	108
圖 5 9(b) WEAPR-S2 PR16分析結果搭配受力差值繪製於樁筏設計手冊	109
圖 5 10(a) Midas-GTS NX PR34 S/D=8之筏基位移量	112
圖 5 11(a) WEAPR-S2 PR34 S/D=8之筏基位移量	112
圖 5 10(b) Midas-GTS NX PR34 S/D=6之筏基位移量	113
圖 5 11(b) WEAPR-S2 PR34 S/D=6之筏基位移量	113
圖 5 10(c) Midas-GTS NX PR34 S/D=4之筏基位移量	114
圖 5 11(c) WEAPR-S2 PR34 S/D=4之筏基位移量	114
圖 5 12(a) PR34 S/D=8基樁編號與基樁名稱	115
圖 5 12(b) PR34 S/D=6基樁編號與基樁名稱	116
圖 5 12(c) PR34 S/D=4基樁編號與基樁名稱	117
圖 5 13(a) Midas-GTS NX PR34 S/D=8之基樁等效彈簧勁度等高線圖	120
圖 5 14(a) WEAPR-S2 PR34 S/D=8之基樁等效彈簧勁度等高線圖	120
圖 5 13(b) Midas-GTS NX PR34 S/D=6之基樁等效彈簧勁度等高線圖	121
圖 5 14(b) WEAPR-S2 PR34 S/D=6之基樁等效彈簧勁度等高線圖	121
圖 5 13(c) Midas-GTS NX PR34 S/D=4之基樁等效彈簧勁度等高線圖	122
圖 5 14(c) WEAPR-S2 PR34 S/D=4之基樁等效彈簧勁度等高線圖	122
圖 5 15 S/D變化時PR34基樁等效彈簧勁度折減係數關係圖	124
圖 5 16(a) WEAPR-S2 PR34分析結果繪製於ISSMGE樁筏設計手冊	125
圖 5 16(b) WEAPR-S2 PR34分析結果搭配受力差值繪製於樁筏設計手冊	126

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