Analysis of foundation damping from theoretical models and forced vibration testing

Foundation damping incorporates the combined effects of energy loss due to waves propagating away from the vibrating foundation (radiation damping), as well as hysteretic action in the soil (material damping). Two closed-form solutions for foundation damping of a flexible-based single degree-of-freedom oscillator were derived from first principles where the inherent (structural) damping ratio, radiation damping and the soil hysteretic damping ratio appear as variables. Since both formulations are theoretically defensible, yet provide numerically distinct results, we look to case histories for validation. In addition to previously established case histories we evaluated data derived from forced vibration testing of a field test structure installed at two sites in California. Parametric system identification was employed to evaluate the fixed-base and flexible-base first mode period and damping ratio during tests performed across a wide frequency range and multiple load amplitudes. Foundation damping derived from these results is shown to favor one of the theoretical models over the other.