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利用非線性數學規劃法，來進行預鑄混凝土群樁基礎的低價設計，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、基樁打設費用及樁帽費用等，而設計變數則為樁徑、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。群樁的分析則採用彈性分析法。 由於基樁數量為整數，故最佳化的程序分兩階段進行，首先根據群樁配置形態選取不同群樁數量，分別進行最佳化設計，最後再由這些設計結果選出最低價的設計。 在最佳化的設計過程，經由敏感度分析，可了解各個變數對工程造價的影響程度，而參數設計研究結果與設計結果亦可供工程界作為群樁設計的參考。 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 nonlinear programming methods for finding the minimum cost design of precast concrete pile groups. The objective function of the problem includes the cost of soil excavation, the cost of cap and the cost of piles. The design variables will be the diameter of piles, length of piles, distances between piles and dimension of cap. The stress and deformation constrains of the pile group design are to be 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. The pile groups are arranged as rectangular or square in the study. It causes the number of piles are integer and discrete. Therefore, the number of piles in the optimal design is pre-selected. All the design results of various arrangements of pile groups are then compared and a least cost design can be found. In the optimization processes, the influences of design variables on the cost function can be studied by using sensitivity analyses. The parametric studies and the minimum cost design results can be used in engineering practice.
