Filtering effect induced by rigid massless embedded foundations

It is well recognised that the dynamic interaction between structure, foundation and supporting soil can affect significantly the seismic behaviour of buildings. Among other effects, embedded and deep foundations can filter the seismic excitation, causing the foundation input motion (FIM) to differ substantially from the free-field motion. This paper presents a theoretical and numerical investigation on the filtering effect induced by rigid massless embedded foundations. Based on the results of dimensional analysis and numerical simulations, it is shown that the problem can be reasonably described by two sole dimensionless groups, namely: (1) ωH/VS, relating the wave length of the signal to the embedment depth of the foundation, and (2) the aspect ratio of the foundation, B/H, where B is the foundation width in the polarization plane. New simplified and physically sound expressions are derived for the kinematic interaction factors, $$ I_{u} = u_{\text{FIM}} /u_{{{\text{ff}}0}} $$Iu=uFIM/uff0 and $$ I_{\theta } = \theta_{\text{FIM}} H/u_{{{\text{ff}}0}} $$Iθ=θFIMH/uff0, which are frequency-dependent transfer functions relating the harmonic steady-state motion experienced by the foundation to the amplitude of the corresponding free-field surface motion. Standard methods for using these functions in the evaluation of the FIM are critically reviewed, with reference to both static and dynamic procedures for the seismic design of structures.