Behaviors of pile-column piers based on modified pasternak foundation model

The analysis of behaviors of pile-column piers in layered soils under inclined loads is extremely complicated. An improved Pasternak foundation reaction model considering the plastic yield characteristics of soils is proposed. Considering the influences of 'P-Δ effect', shear deformation and axial force distribution of piles, the governing equations for displacements of free section, elastic section and plastic section of the pile-column pier are respectively established based on the Timoshenko beam theory. Then, the semi-analytical solutions to the internal forces and deformations of the pier in the layered foundation under inclined loads are obtained by using the Laplace transform and the matrix transfer method. On this basis, the influences of shear stiffnesses and foundation stratification are discussed and analyzed in a parametric study. It can be concluded as follows: (1) For the cases with different length-diameter ratios, the horizontal displacement of the piles increases with the increasing shear stiffness of the piles, but the tendency is opposite for the results of bending moment, and the influences of shear stiffness reaches the maximum when the length-diameter ratio reaches approximately 5. (2) Unlike the influences of the 'P – Δ effect', the shear modulus of the soils significantly inhibits the horizontal displacement and the bending moment of the piles. (3) In a multi-layer foundation, the strength of upper soil layers has the greatest influences on the horizontal displacement and the bending moment of the piles, and increasing their strength will significantly reduce the horizontal displacement and bending moment.