Optimal Pile Placement for Minimization Differential Settlements
in Piled Raft Foundations
Kyeong Nam Kim
This paper presents an optimal pile placement scheme to determine the optimal location of the pile support beneath the raft which minimizes the differential settlements of the raft. The raft is subdivided into two-dimensional 'thick' plate finite elements based on the Mindlin plate theory. The raft-soil contact is lumped into an equivalent soil 'spring' at each node. The piles are modeled as springs supporting the plates based on the approximate elastic analysis method proposed by Randolph and Wroth. The piled raft combines the individual 'stiffnesses' of the pile group, the raft and the soil.
The more the differential settlements decrease, the more the area of the deflected raft decreases. An object function is defined as area of the deflected raft. Design variables are defined as pile locations and constraints are imposed to prevent the piles from escaping out of the raft. RQP(Recursive Quadratic Programming) is adopted to minimize the nonlinear object function with regard to the design variables. The sensitivity of the displacement with regard to the design variables is obtained by the direct differentiation method.
At the optimal pile location is determined by the proposed method, reliability analysis is performed to estimate the safety of the piled raft subjected to uncertainty in the shear modulus of soil. The limit state equation used in the reliability analysis is defined as the difference between the allowable differential settlement and the maximum differential settlement. Statistical properties of the raft settlements is calculated by means of stochastic finite element methods and the reliability index is obtained by the first-order second-moment method. Differential settlements are assumed to follow normal distribution and the safety of the piled raft is estimated through the probability of failure, which can be calculated from the reliability index by using tables of standardized normal variates. The proposed method which determines the optimal location of the piles is demonstrated an efficient method for minimizing differential settlements through several examples.
Differential settlements, Optimal pile placement, Object function, RQP, Reliability analysis