Mechanical analysis of laterally-loaded piles embedded in multi-layered soils is a critical step in design. Traditional finite-element method may have deficiency in accuracy and efficiency when applied to analyze this problem. An efficient finite-element method is proposed in this paper. A “pile element” that adopts the distributed “soil springs” along the element length to reflect the nonlinear behaviors of the pile-soil interactions is developed in this method. The dominant feature of the pile element is the direct integration of soil properties into the element formulation, namely, a pile element comprises both the pile and soil properties. The pile element formulation in multi-layered soils is derived, and the Gauss-Legendre method is introduced to simplify the total potential energy summation process. The element stiffness matrix is derived and applied to Newton-Raphson incremental iterative numerical process, and the secant relations are used to minimize the cumulative errors during the numerical iteration process. Besides, the updated Lagrangian method is employed to account for the large deformation issue. Results show that: 1) the proposed method can provide predictions that match well with both the theoretical solutions and field test data; 2) using the pile element model can substantially reduce the number of elements and calculation time compared with those of the discrete element model, and thus significantly improve the calculation efficiency.
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