A scaled boundary finite element method for soil dynamic impedance of pile groups using hybrid quadtree mesh considering horizontal vibration

Abstract

The numerical modeling of pile-soil dynamic interaction has been a challenging problem in engineering for many years because of the unbounded domain, which typically involves significant computational cost. This paper develops a novel scaled boundary finite element method (SBFEM) that can accurately calculate the soil dynamic impedance of pile groups with end bearing subjected to horizontal vibration. The three-dimensional (3D) problem is first transformed to a two-dimensional (2D) Helmholtz equation in the horizontal plane, exploiting the analytical solution for the vertical modes using separation of variables. The SBFEM is then applied to solve the 2D computational domain, which is divided into bounded and unbounded domains. Based on the SBFEM, an accurate circular artificial boundary condition (ABC) is formulated to simulate the unbounded domain of the soil. A special hybrid quadtree mesh is devised for this problem, where a high-quality structured quadrilateral mesh is generated surrounding the piles. The accuracy of the proposed method is verified using a single pile problem with known analytical solution. The effects of dimensionless frequency, pile numbers, soil depth and relative distance between piles on the soil dynamic impedance are considered.