Optimal pile placement for minimizing differential settlements

             in piled raft foundations


K. N. Kim, S.H. Lee, C.K. Chung, H.S. Lee



 This paper presents an optimal pile placement scheme to minimize the differential settlements of piled raft systems. A raft is modeled as a plate based on the Mindlin theory, and soils and piles are modeled as the Winkler springs and single springs, respectively. Interactions between piles are neglected. The pile spring constant is obtained by the method proposed by Randolph and Wroth, and the Vesic formula is adopted to obtain the Winkler spring constant. The raft is discretized by isoparameteric finite element. The object function for the optimization is derived from the area of the deflected surface of a raft, and the locations of piles are selected as design variables. Inequality constraints are imposed to keep all piles completely inside of the raft. The recursive quadratic programming is adopted to minimize the nonlinear object function with respect to the design variables. The direct differentiation method is used to obtain the sensitivity of displacement. The validity and effectiveness of the proposed method are demonstrated by three numerical examples.

KEY WORDS : differential settlements, piled raft, optimal pile placement, deflected surface, recursive quadratic programming, sensitivity, optimization

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