Evaluation of interaction effects on the system period and the system damping due to foundation embedment and layer depth

On the basis of some simplifying assumptions, a parametric analysis is made of the interaction effects on the effective period and damping of structures with embedded foundation in a soil layer, A simplified three-dimensional interaction model is used, in which the depth of a cylindrical foundation, the degree of contact between the ground and the footing walls and the depth of a homogeneous stratum over rigid rock are considered variable. The soil is replaced with impedance functions that are taken from a data base obtained with an appropriate numerical technique, so that suitable springs and dashpots dependent on the excitation frequency are used. The system period and system damping are determined from the steady-state response of an equivalent single oscillator with flexible base subjected to a harmonic motion with constant amplitude, by equating its resonant response with that of a replacement oscillator with rigid base excited with the same motion. The influence of the foundation embedment and soil layer is investigated for several depths of both the footing and the stratum. It is confirmed that the system period decreases and the system damping increases with the foundation embedment only for sidewalls extending along the entire foundation depth. For embedded footings without sidewall or with sidewall in null contact with the surrounding soil, the effective system parameters behave opposite to those corresponding to the interface condition of total contact. Also, the system damping increases significantly with the layer depth, while the system period is practically insensitive to variations of this characteristic parameter. Finally, introducing additional permissible simplifications, an improved approximate solution for the effective period and damping of coupled systems is presented, which differs from previous analogous approximations in that damping factors of second order are not neglected and the foundation depth is explicitly considered.