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。 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.
