A numerical model with high-accuracy and high-efficiency for the soil dynamic impedance of pile groups under vertical vibration

This paper develops a novel numerical model for the calculation of dynamic impedance of soil considering endbearing pile groups under vertical vibration. The soil layer is treated as a linear viscoelastic material with hysteretic damping. The vertical displacement is assumed to be uniform in each individual pile in the groups at the same embedment depth. Using separation of variables and applying proper boundary conditions at the surface and rigid bedrock, the governing equation of soil layer in three-dimensional (3D) is first transformed into a two-dimensional (2D) Helmholtz equation in xy plane, where the solution in the vertical direction is obtained analytically. To solve this problem efficiently and accurately, the whole 2D unbounded soil is then divided into a finite interior domain and an infinite exterior domain. The finite domain is discretized using the finite element method (FEM) while an exact circular artificial boundary condition (ABC) is developed to model the infinite domain. Finally, the effect of pile group interaction on the dynamic impedance of soil is investigated considering various factors, e.g., dimensionless frequency, pile number, pile slenderness ratio and relative distance between piles.