On A Solid Friction Attenuation Scheme For Dry Brittle Rock

Experimental data 1,2 on the energy dissipation in polycrystalline materials over a large frequency spectrum (10-2 cps to 106 cps) suggests that the quality factor [(e= Q )] is independent of the frequency providing both fluid-saturated and ferromagnetic materials are excluded from the test data. Additional data 3 suggest that the quality factors are less at high pressures than at low pressure, i.e., Q increases as the pressure increases. Observations on the dissipation of single quartz crystals with their polycrystalline counterparts indicate that the energy dissipation is less for the single crystal than for the aggregate .2 Both of the above observations, particularly the latter, are indicative of the fact that the dissipation increases with increasing surface contact within the polycrystal, i.e., a frictional attenuation scheme may be operative. Knopoff and MacDonald 4 have shown that a friction model gives rise to a quality factor frequency independence property. A partial listing of some values of Q, observed for both metals and non-metals, is given in Tables I, II, and III. In Tables I and II, the data all show Qs>Qp, i.e., the energy loss per cycle for compressional body waves is greater than that for shear waves of the same frequency. Most samples in Table III show the same effect. It is objective of this paper to suggest: (1) a frictional attenuation scheme may account for the observed losses incurred during the propagation of low amplitude stress waves in dry brittle rock and, in particular, that such a scheme can account for the observed relative magnitudes of the quality factors for P and S wave motion; (2) a friction scheme can readily explain the difference between the dynamic and static moduli in dry brittle rock; (3) a friction scheme, while in itself an intrinsically