Shear wave attenuation and micro-fluidics in water-saturated sand and glass beads

An improvement in the modeling of shear wave attenuation and speed in water-saturated sand and glass beads is introduced. Some dry and water-saturated materials are known to follow a constant-Q model in which the attenuation, expressed as Q(-1), is independent of frequency. The associated loss mechanism is thought to lie within the solid frame. A second loss mechanism in fluid-saturated porous materials is the viscous loss due to relative motion between pore fluid and solid frame predicted by the Biot-Stoll model. It contains a relaxation process that makes the Q(-1) change with frequency, reaching a peak at a characteristic frequency. Examination of the published measurements above 1 kHz, particularly those of Brunson (Ph.D. thesis, Oregon State University, Corvalis, 1983), shows another peak, which is explained in terms of a relaxation process associated with the squirt flow process at the grain-grain contact. In the process of deriving a model for this phenomenon, it is necessary to consider the micro-fluidic effects associated with the flow within a thin film of water confined in the gap at the grain-grain contact and the resulting increase in the effective viscosity of water. The result is an extended Biot model that is applicable over a broad band of frequencies.