Approximate dynamic model of embedded foundation in time domain

A discrete model to represent the unbounded soil (halfspace) in a soil–structure interaction analysis in the time domain is developed. For each dynamic degree of freedom of the foundation node, the discrete model consists of a mass M0 which is attached to a rigid support with a spring K and with a damper C0. In addition, a free node with the mass M1 is introduced, which is connected to the foundation node with a damper C1. All coefficients are frequency‐independent. The discrete model is semi‐empirical. It is based on a semi‐infinite truncated cone, whereby, after enforcing the static stiffness, the remaining parameters are modified to achieve an optimal fit of the dynamic‐stiffness coefficient in the frequency domain. The spring K is equal to the static stiffness. The coefficients appearing in the equations for the dampers C0, C1 and the masses M0, M1 are specified (assuming a homogeneous halfspace) for the disc, the embedded cylinder, the rectangle (also embedded) and the strip. A square on a layer whose stiffness increases with depth resting on a homogeneous halfspace is also treated. For an embedded foundation, eccentricities arise. Material damping increases the damper C0 and the mass M0.