An analytical solution for the rotational component of the Foundation Input Motion induced by a pile group

This work investigates the effect of the rotational component of input motion induced by the kinematic interaction between a pile group and the surrounding soil on the seismic behaviour of a structure. To this end, a simple analytical model is developed by deriving the pile group behaviour from the seismic response of a single pile, taking into account equilibrium and compatibility of displacements at piles’ heads. Closed-form solutions in the frequency domain are provided for both the translational and the rotational motion of a group of unevenly distributed identical piles, rigidly connected at the top and displaced by the surrounding soil, which is subjected to purely translational oscillations. The proposed solutions, applicable to any subsoil conditions, highlight that pile group layout is the crucial parameter governing the magnitude of the foundation rotation. Further, new transfer functions from the soil surface in free field conditions to the top of a SDOF system are introduced, which take into account the translational and/or rotational kinematic effects. An application of the above concepts to a case study is presented, highlighting that the rotational component of input motion may be important for tall structures on small pile groups.