Structure-foundation dynamic interaction plays an important role in the earthquake response analysis and safety assessment of structures. A novel computational model for structure-foundation dynamic interaction in the time domain based on the scaled boundary finite element method is presented. The near field bounded domain is modelled by the subdomains of the scaled boundary finite element method; and the far-field unbounded domain is represented by the high order transmitting boundary. By using the continued-fraction expansion and introducing auxiliary variables

the dynamic equation of the bounded domain is expressed in high order static stiffness and mass matrices. The high order transmitting boundary can exactly satisfy the radiation boundary condition at infinity. This open boundary is global in space

local in time and converges rapidly as the order increases. The high order transmitting boundary is based on the improved continued-fraction solution for the dynamic stiffness matrix of the unbounded domain; and the equation is a system of first-order ordinary differential equations in the time domain. Then the standard equation of structure-foundation interaction in the time domain is obtained by combining the dynamic equations of the bounded and unbounded domains

which can be solved by the Newmark method directly. The results of three numerical examples demonstrate that the proposed method is more accurate and efficient than the viscoelastic boundary in the time domain.