Simulation Analysis on P-Δ Effect for Piles Based on Energy Method
Abstract
The force analysis of piles under complex loads is one of the important contents in the design and calculation of pile foundation. In this paper, a energy control differential equation of three-dimensional pile-soil system is established according to the energy principle, considering the special case of tilting and eccentricity of pile loads as well as the layering characteristics of soils. On this basis, combined with different boundary conditions of pile and displacement conditions of pile and soil, a semi-analytical solution of pile displacement under inclined and eccentric loads is obtained based on finite difference method. The solution can fully consider the P-Δ amplification effect of pile deformation. Then, an indoor model loading test of single pile under inclined eccentric load is carried out to validate the solution. The comparison results show that the theoretical solution and the experimental test results are in good agreement, and the P-Δ amplification effect of the pile deformation under combined load is well simulated. Finally, the influencing factors affecting the P-Δ amplification effect of the piles are analyzed. The results show that the relative magnitude of the axial and lateral loads, the length of the free section of the pile, the stiffness of the pile and the stiffness of the surface soil all have a significant impact on the P-Δ amplification effect.
Keywords: single pile, inclined eccentric loads, principle of minimum potential energy, variational principle, P-Δ effect
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