Based on the Biot's dynamic coupled consolidation theory, the scaled boundary finite-element method was developed to correctly model the dynamic unbounded far-field boundary of three-dimensional (3D) fully saturated soil in this paper. Body forces and surface tractions were considered in the derivation. The concept of similarity, the compatibility equation, Biot's coupled consolidation equations, and the Galerkin's weighted-residual method were used to derive the formulation for the governing equations. The main difference from the single-phase version was the presence of pore water pressures as additional parameters to be solved, in addition to the displacements, strain and stress which were incorporated into the static-stiffness matrices by producing fully coupled matrices. Solving the resulting equations yielded a boundary condition satisfying the far-field radiation condition exactly. The computed solutions were exact in a radial direction (perpendicular to the boundary and pointing towards infinity), while converging to the exact solution in the finite element sense in the circumferential direction parallel to the soil-structure boundary interface.
