The Dependence of Q with Seismic-induced Strains and Frequencies for Surface Layers from Resonant Columns

Abstract

—The gross effect of internal friction is summarized by the dimensionless quantity Q, defined in various ways. If a volume of soil is cycled in stress at a frequency ω, physically, the Q factor is equal to the ratio of energy dissipated per cycle to the total energy Q ⁻¹ = δE/(2πE). The authors used Hardin and Drnevich resonant columns to determine the damping capacity 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 shear 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 in these resonant columns will correspond to the area of the hysteresis loop stress strain relation divided by 4π times the elastic strain energy stored in the specimen at maximum strain. Consequently, we can express D in the 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 nonlinear function ω and γ. The nonlinear dependence of Q with seismic induced strains and frequencies for large deformations has an important influence on the propagation of the seismic waves in the hazard and microzonation studies.