樁基礎最佳化設計之研究

Optimum Design of Piled Foundations

鍾明劍(Ming-Chien Chung)

指導教授 ： 黃俊鴻 ； 莊德興

國立中央大學/工學院/土木工程學系/博士(2006年)

摘要

本研究針對場鑄式群樁基礎進行最佳化設計之研究，群樁基礎設計的最佳化數學模型包含七個獨立之離散設計變數，依設計規範要求建立設計變數之束制條件，以工程造價為目標函數進行最低價可行解之搜尋。文中分別以離散拉格朗日法、修正相對差商法、實數編碼遺傳演算法、以及混合式GA演算法進行最佳解之搜尋，並以竭盡搜尋法所得全域最佳解來檢驗各演算法之搜尋性能。透過七個實際案例分析，顯示離散拉格朗日法、修正相對差商法的搜尋成效良好，可穩定地求得一個合理、可靠的近似最佳解，甚至為全域最佳解，且所需時間甚短。實數編碼遺傳演算法及混合式GA演算法於各案例均有機會搜尋至全域最佳解，且其與最佳解之差距較上述兩方法為小，惟所需時間較多。
此外，本文提出一套非線性靜力側推程序，可應用於分析地盤液化流動壓力或位移作用下基樁之非線性側向承載行為，可分析不同液化程度下基樁之側向承載性能狀態，供基樁耐震性能設計之用。文中分別以流動土壓與流動變位兩種加載模式進行現地損害案例的分析比較，探討兩者於非線性靜力側推應用上之差異，結果顯示兩種分析模式皆可合理地掌握基樁於液化流動地盤之受力與變形行為，惟流動土壓分析模式可較簡單地應用於性能設計法。文中以流動土壓分析模式為基礎，提出基樁抵抗液化流動之耐震性能分析流程，可供工程界參考應用。文末則以流動土壓為基礎，提出此問題之簡化分析模式，推導出解析解，並以現地基樁損害案例進行驗證與比較，結果顯示此解析解可合理地掌握側向樁的受力與變形行為，最後以實際案例為例，透過此解析解進行參數研究，探討不同參數之變化對側向樁變形與受力行為之影響。

關鍵字

最佳化設計 ； 解析解 ； 性能設計 ； 側推分析 ； 最佳化演算法 ； 樁基礎

並列摘要

This thesis presents the application of optimal algorithms to the least cost design of bored piled foundations. The objective function is the combined costs of soil excavation, pile cap, piles, and soil backfill. The design variables, including pile length, pile diameter, depth of pile cap, pile spacing, and pile number, are all discrete. The optimal algorithms include discrete Lagrangian method (DLM), modified relative difference quotient algorithm (MRDQA), real-coded genetic algorithm (RGA), and hybrid genetic algorithm (HGA). The efficiency and validity of the above algorithms have been verified by comparing the solutions with the global optimum solutions obtained from exhaustive search method (ESM).
The comparative results of seven design cases have shown that the mean errors of DLM and MRDQA solutions are around 1.86%, respectively. RGA and HGA can find the optimum solutions from ESM, but they spend more time than DLM or MRDQA. The influences of the unit price of the constructive materials, soil liquefaction, the resistance of pile cap, and the pile-group effect on the optimum solutions are discussed in the thesis.
Furthermore, the thesis presents a simplified nonlinear pushover analysis for the lateral response of the pile subjected to liquefaction-induced flow earth pressure. The pushover analysis can be carried out by incrementally imposing flow pressure or flow displacement on the pile. The capacity curve of the lateral pile was expressed in terms of the total flow forces and the displacement of pile top. The seismic performances corresponding to different liquefaction extents can be clearly identified on the curve. The field damage case was analyzed by both of the flow pressure and displacement methods. A comparison was made between the results of these two methods. It shows that both two
methods can reasonably capture the lateral pile response when subjected the flow pressure due to ground liquefaction. However, the flow pressure method seems more suitable to be used in the area of seismic performance-based design of pile foundation.
Although pushover analysis can capture the pile response very well, it is so complicated that the analyses usually have to be solved by numerical methods. Based on some reasonable assumptions, the thesis presents a simplified closed-form solution for the analysis. It is a combination of the solutions of an Euler’s beam and an elastic lateral pile. The solution is used to analyze two cases of damaged pile due to lateral spreading. The calculated result by the solution agrees the field performance well. Based on the simplified closed-form solution, the influences of pile diameter, pile spacing, peak ground acceleration, the SPT-N value of liquefying layer, and the SPT-N value of non-liquefying layer on the lateral pile responses are discussed in the thesis.

並列關鍵字

piled foundation ； performance-based design ； optimum design ； closed-form solution ； algorithms ； pushover analysis

參考文獻

43. 冀樹勇、陳錦清、王建智，「RIDO程式之最佳化土壤參數之探討」，地工技術，第七十五期，第61-76頁 (1999)。

49. 鍾明劍、黃俊鴻、莊德興，「群樁基礎設計模式與全域最佳解之應用」，結構工程，第二十一卷，第一期，第122-139頁 (2006)。

37. 黃俊鴻、鍾明劍，「液化流動壓作用下側向樁之簡化解析解」，中國土木水利工程學刊 (已接受)。

29. 莊德興、吳朗益，「離散拉格朗日法於群樁基礎低價化設計之應用」，中國土木水利工程學刊，第十五卷，第二期，第303-314頁 (2003)。

30. 莊德興、張慰慈，「離散拉格朗日法於大型桁架輕量化設計之加速搜尋策略」，中國土木水利工程學刊，第十七卷，第一期，第143-151頁 (2005)。