The dependence of Q with seismic-induced strains and frequencies for surface layers from resonant columns

The gross effect of internal friction is summarized by the dimensionless qu antity Q, defined in various ways. If a volume of soil is cycled in stress at a frequency w, physically, the Q factor is equal to the ratio of energy dissipated per cycle to the total energy Q(-1) = Delta E/(2 pi E). The auth ors used Hardin and Drnevich resonant columns to determine the damping capa city of cylindrical specimens from surface soil layers during torsional and longitudinal vibrations. The energy dissipated by the system is a measure of the damping capacity of the soil. The damping will be defined by the she ar damping ratio for the soil D, analogous to the critical viscous damping ratio for a single degree of Freedom c/c(0). Values of damping determined i n these resonant columns will correspond to the area of the hysteresis loop stress strain relation divided by 4 pi times the elastic strain energy sto red in the specimen at maximum strain. Consequently, we can express D in th e form of quality factor Q, that is Q = 1/(2D), where Q is defined in terms of the fractional loss of energy per cycle of oscillation and D is a nonli near function w and gamma. The nonlinear dependence of Q with seismic induc ed strains and frequencies for large deformations has an important influenc e on the propagation of the seismic waves in the hazard and microzonation s tudies.