I have performed an experiment using a shaking table to simulate the response of a soil base structure to an earthquake. A multi-floor structure was placed on a sand (90% relative density) bed and the bed was shaken horizontally at frequencies of 1-4 Hz for amplitudes of 1 mm, 2 mm and 3 mm. The acceleration of the base of the structure and of its floors was recorded, Frequency - Relative acceleration (= floor acceleration/base acceleration) graphs were drawn and the damping ratio and resonant frequency were extracted for each case.
What I found is that, as the amplitude of the shaking is increased, the damping ratio decreases, as well as the resonant frequency. Theoretically, for a linear system, the amplitude should not influence these two parameters, which led me to the conclusion that sand behaves in a non-linear way. However, I do not understand exactly what aspects of the sand's behaviour and of the sand-structure interaction lead to a lower damping ratio and resonant frequency. Any help on clarifying this would be appreciated!