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

Abstract

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.

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

“…Buckingham goes back to tribological properties to explain the rheopectic behavior of the pore-fluid where the properties emerge as a result of narrow confinement of the fluid in between the asperities. While this is a subject of ongoing research, 37 we have the opinion that instead of anticipating "regular" seawater trapped in between the grains, a concentrated colloidal suspension is more likely in a marine-like environment. We would also like to add that rheopectic properties could occur due to changes in the state of aggregation or coagulation of the suspensions.…”

“…The reason can be traced back to Eqs. (37) and (44) in Ref. 1, where the acoustic pressure corresponding to a suspension without any grain-to-grain stress relaxation, is included in the expression of the stress tensor.…”

A Comparison of Three Sediment Acoustic Models Using Bayesian Inversion and Model Selection Techniques

“…According to the sediment geoacoustic model categories proposed by Jackson and Richardson [3], there are three categories, which are fluid, elastic, and poroelastic, based on the number and types of acoustic waves that can travel in sediments. We can see from the literature [4][5][6][7][8][9] that these geoacoustic models are mainly used to establish the relationship between physical and acoustic properties of sediments, such as sound speed and attenuation, and are regarded as "wave theory" or "propagation theory" to distinguish them from subsequent scattering models by Jackson and Richardson. In acoustic remote sensing, scattering models of water-seabed interface are necessary to calculate observations such as scattering strength in model-based inversion, since the speed and attenuation of sound in sediments cannot be directly measured from a distance.…”

Spring–damper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography

“…This model has been further developed to cover water‐saturated sand as well. In that case, there is also coupling between the relaxation model for the bulk modulus and that for the shear modulus; see Equation 15 of Chotiros and Isakson . The coupling term is a complex function of frequency that involves Bessel functions, but it can often be approximated with a simpler polynomial expression .…”

“…In that case, there is also coupling between the relaxation model for the bulk modulus and that for the shear modulus; see Equation 15 of Chotiros and Isakson. 43 The coupling term is a complex function of frequency that involves Bessel functions, but it can often be approximated with a simpler polynomial expression. 44 In that case, the model may also be expressed by springs and dampers, but an even more complex system than that of Figure 7.…”