應用Discrete Lagrangian Method於群樁基礎低價化設計

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姓名

吳朗益(Lang-Yi Wu ) 查詢紙本館藏

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土木工程研究所

論文名稱

應用Discrete Lagrangian Method於群樁基礎低價化設計

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摘要(中)

傳統的群樁設計程序均採用試誤法，結果雖可滿足安全的考量，但卻無法保證工程造價最低。本研究之主要目的便是針對群樁設計中不連續的變數，利用離散式拉格朗日法，來進行預鑄混凝土群樁基礎的最低價設計，使設計結果同時滿足經濟與安全的考量。
群樁的工程造價包含土方開挖費用、樁帽費用及基樁打設費用等，而設計變數則為樁數、樁徑、樁長、基樁間距與樁帽的有效深度。群樁的設計結果必須滿足規範的檢核條件，如垂直承載力、水平力、拉拔力、容許變位等，同時亦須考慮樁距、樁徑、樁長及樁帽尺寸等束制條件。
離散式拉格朗日法的應用與效率將透過多個群樁設計案例來說明，而不同設計變數對工程造價的影響亦將在參數研究中詳加探討。

摘要(英)

Conventional design of pile groups is based on the trial-and-error procedures. Although the design results can satisfy safety requirements, it is not a minimum cost design. The purpose of this study is to apply the Discrete Lagrangian Method for finding the minimum cost design of precast concrete pile groups with discrete design variables. The objective function of the problem is the total cost of a pile group, which includes the costs of soil excavation, cap, and piles. The design variables will be the diameter of piles, length of piles, distances between piles and dimensions of cap.
The stress and deformation constrains of the pile group design are formulated according to the code provisions. Size constrains, such as the length of piles, the diameter of piles, distance between piles are also considered in the optimization formulation.
Several numerical examples for minimum cost design of pile groups are used to illustrate the efficiency of the Discrete Lagrangian Method. The influences of design variables on the cost of pile groups are also discussed in this report.

關鍵字(中)

★ 不連續變數
★ 低價化設計
★ 群樁基礎
★ 離散式拉格朗日法

關鍵字(英)

★ Pile Groups
★ Discrete Design Variables

論文目次

目錄
誌謝
中文摘要I
英文摘要II
目錄III
表目錄VI
圖目錄VII
第一章緒論……………………………………………………………………….. 1
1.1 研究動機………………………………………………………...…………. 1
1.2文獻回顧………………………………………………………..………….. 2
1.3研究方法與內容………………………………………………...…………. 5
第二章理論推導……………………………………………….……...…………. 7
2.1 Lagrangian Method的回顧……………………………………..…………. 7
2.2 DLM (Discrete Lagrangian Method)…………………………… …………10
2.2.1最大可能下降方向DMPD………………………….………………11
2.2.2不連續最佳化問題的一階必要條件……………….………………12
2.2.3不連續空間一階搜尋法………………………………….…………16
2.2.4不等式束制條件…………………………………….………………18
2.3 Lagrange 乘子的更新…………………………………………..…………19
第三章目標函數與束制條件的建立………………………………...…………23
3.1目標函數的建立………………………………………………..…………23
3.1.1土方開挖費用 ………………………………………………………23
3.1.2基樁打設費用 ………………………………………………………24
3.1.3樁帽費用………………………………….…………………………24
3.2束制條件的建立………………………………………………..…………25
3.2.1基樁的間距……………………………………………….…………26
3.2.2 樁頂位移量……………………………………………….…………27
3.2.3 基樁承載力……………………………………………….…………29
3.2.4 拉拔力檢核…………………………………………………………30
3.2.5穿孔剪力檢核…………………………………………….…………31
3.2.6基樁強度………………………………………………….…………33
3.2.7土地的限制……………………………………………….…………34
第四章參數研究與案例分析………………………………………..………….35
4.1 Lagrange乘子更新之比較……………………………………..…………35
4.2群樁設計之參數研究…………………………………………..…………36
4.2.1不同外力之影響……………………………………………………37
4.2.2基樁打設方式之影響………………………………………………39
4.2.3土壤參數之影響……………………………………………………39
4.2.4雙向樁距不同之影響………………………………………………41
4.2.5土地面積限制之影響………………………………………………41
4.2.6固定樁數之比較……………………………………………………42
4.2.7實際設計案例比較…………………………………………………43
第五章結論及建議…………………………………………………..…………44
5.1結論……………………………………………………….…….…………44
5.2建議……………………………………………………….…….…………45
參考文獻……………………………………………………….……...…………47
附錄一……………………………………………………….……...………….…75

參考文獻

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指導教授

莊德興(Der-Shin Juang)

審核日期

2001-7-16

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