Extended Biot Model Research Articles

Modeling and simulation of underwater acoustic propagation through a random distribution of ice blocks.

Acoustic propagation through a random distribution of 1 m ice cubes, from 100 to 1000 Hz, was simulated in a 3D finite element model. The effective sound speed and attenuation as functions of frequency were calculated from the simulated signals. Attempts were made to fit a number of models to the wave speed and attenuation, including single scattering, lossy water, and Biot approximations. An extended Biot model, developed for acoustic propagation in granular seabed sediments, was able to fit the simulation up to 300 Hz. Beyond this frequency, the simulation shows that multiple scattering dominates.

A porous medium model for mud.

The extended Biot model for sands and silts is repurposed to include mud, but modifications are needed. The boundary between pore water and skeletal frame needs to be redefined because a significant fraction of the pore fluid is adsorbed onto the solid frame by electrostatic forces, and a proportion of the solid particles may be suspended in the pore fluid. Revil's relationships are used to simplify the input parameters. The frame elasticity equations are corrected to accommodate the sparse skeletal frame, which is supported by electrostatic forces, and behaves differently to a mechanical packing of grains. The corrected, Revil, extended Biot model has just four fitting parameters and is compared with published measurements of wave speeds and attenuations in the literature of clay, silty clay, and clayey silt sediments including recently published measurements from the Seabed Characterization Experiment. The results indicate that the skeletal frame in clay has a high water-content and the pore water contains suspended particles. To fit all the currently available data, it was necessary to modify corrected, Revil, extended Biot by flattening the creep related relaxation loss spectrum. There is a similarity with the Viscous Grain Shearing models in the use of a fractional exponent.

A multiple relaxation interpretation of the extended Biot model.

The biphasic extended Biot poroviscoelastic model takes into account the squirt flow in grain-grain contacts and introduces the bulk and shear relaxation modes associated with it. This model has been criticized for its empirical approach, but here the constitutive equations and the time domain wave equations of the model are derived. This also makes it possible to find single phase viscoelastic equivalents for all three wave solutions of the extended Biot model. Particularly, the viscoelastic equivalents for shear wave propagation can be obtained with considerably fewer parameters than the original model. These equivalents are linear viscoelastic models with springs and dampers for the low frequencies and contain half-order spring-pots for high frequencies. For high frequencies, the non-physicality of the shear relaxation mode is highlighted. The relaxation modes of the extended Biot model are interpreted in the framework of multiple relaxation mechanisms showing that the P- and S-wave modes of the model are not much more complex than that for seawater. The model's near linear frequency dependent attenuation in the intermediate frequency range is the result of weighting each relaxation mechanism appropriately.

Linear and half order fractional viscoelastic equivalents of the extended Biot model

The extended Biot poro-viscoelastic model [Chotiros and Isakson, JASA (2014)] like the standard Biot poroelastic model is biphasic and predicts two compressional waves (fast and slow) and one shear wave. Taking squirt flow into account, the model introduces two additional relaxation modes apart from the Biot crossover relaxation mode (global flow). The frequency dependent relaxation processes and a high number of independent parameters make the finite element implementation and the inversion of parameters for reconstruction a challenge. To overcome this challenge, we identify single phase viscoelastic equivalents for all three wave solutions of the extended Biot model from its dispersion relations. Considering squirt flow and high-frequency turbulent flow, the fast compressional wave and the shear wave solutions at low frequencies are equivalent to a non-standard solid model with eight parameters (four springs and four dashpots) and six parameters (Three springs and three dashpots), respectively. At high frequencies, the Kelvin-Voigt model used for tangential contact stiffness (shear relaxation) leads to non-physical equivalents. Neglecting this shear relaxation mode, the fast compressional wave and the shear wave solutions at high frequencies are equivalent to a fractional half-order solid model of order three and two, respectively. Alternative models for tangential contact stiffness are discussed.

Geoacoustic sediment model discrimination using acoustic color comparison

Many competing geoacoustic models exist to represent sandy sediments. These models can be fluid, elastic, or poroelastic, depending on the number and types of waves the sediment is assumed to support. In this talk, a fully scattered field finite element approach is utilized to construct acoustic color templates for a buried spherical aluminum shell and a spherical bubble. The simulated results are then used to assess the ability of target strength measurements to discriminate between the predictions of the competing sediment models. Such discrimination may help determine the physical validity of a given geoacoustic model and aid in model selection. Five geoacoustic sediment models are considered: a simple fluid, constant-Q fluid model, the effective density fluid model of Williams, the viscous grain shearing model of Buckingham, the Biot-Stoll poroelastic model, and the extended Biot model of Chotiros. [Work supported by ONR, Ocean Acoustics.]

An application of Bayesian inference techniques to compare three competing sandy sediment models

Many competing geoacoustic models exist to represent sandy sediments. In this work, Bayesian inference is employed to compare the sensitivity of the physical input parameters of three competing models: the viscous grain shearing model of Buckingham, the Biot-Stoll model, and the extended Biot model of Chotiros, using previously taken wave speed and attenuation laboratory measurements. Bayesian model selection techniques are then employed to assess the degree to which the predictions of these models can be used to explain the observed data. Since all three geoacoustic models require a large number of input parameters and many of these input parameters are difficult to measure, a main goal of this work is to use Bayesian techniques to determine which parameters can be resolved via inversion and what kinds of data are required for parameter resolution. [Work supported by ONR, Ocean Acoustics.]

In situ measurements of sediment acoustic properties in Currituck Sound and comparison to models.

In situ measurements of compressional and shear wave speed and attenuation were collected 30 cm below the water-sediment interface in Currituck Sound, North Carolina at two field locations having distinctly different sediment types: medium-to-fine-grained sand and fine-grained sand with approximately 10% mud content. Shear wave measurements were performed with bimorph transducers to generate and receive horizontally polarized shear waves in the 300 Hz to 1 kHz band, and compressional wave measurements were performed using hydrophones operated in the 5 kHz to 100 kHz band. Sediment samples were collected at both measurement sites and later analyzed in the laboratory to characterize the sediment grain size distribution for each field location. Compressional and shear wave speed and attenuation were estimated from the acoustic measurements, and preliminary comparisons to the extended Biot model by Chotiros and Isakson [J. Acoust. Soc. 135, 3264-3279 (2014)] and the viscous grain-shearing theory by Buckingham [J. Acoust. Soc. 136, 2478-2488 (2014)] were performed.

Analysis of shear-wave attenuation in unconsolidated sands and glass beads.

Chotiros and Isakson [J. Acoust. Soc. Am. 135, 3264-3279 (2014)] contend that the physics-based grain-shearing (GS) theories of wave propagation in granular materials are not consistent with one particular shear-attenuation data set for water-saturated angular sand that has appeared in the literature. This provides them with the rationale for developing their own model, an extension of the empirical Biot-Stoll model, which they designate the Extended Biot (EB) model. In this article, the EB model and the grain-shearing theories are briefly reviewed, and it is demonstrated that, in fact, the original GS theory accurately matches the frequency-dependent trends of all the shear attenuation data sets that are currently available, including those for saturated angular sands after random fluctuations are suppressed by averaging over several realizations of the medium. It is also pointed out that Chotiros and Isakson's treatment of the available shear-attenuation data is highly selective, and that the format in which they present the selected data makes their comparisons with theoretical models difficult to interpret. Thus, their attempts at validating the EB model and their conclusions concerning alternative theories should be treated with caution.

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.

Model parameter estimation of a porous seabed using in situ acoustic‐probe and chirp‐sonar reflection data.

The velocity dispersion and frequency dependency of attenuation in marine sediments are two important measures that provide the ability to test the validity of geoacoustic models as well as to estimate physical properties from the acoustic data. A widely‐used Biot–Stoll theory for elastic‐wave propagation in porous marine sediments seems to predict a narrow band of dispersion that was measured only in well‐sorted granular marine sediments [A. Turgut and T. Yamamoto, J. Acoust. Soc. Am. 87, 2376–2382 (1990)]. Recent measurements in silty‐sand sediments show almost linear frequency dependency of attenuation and mild velocity dispersion within the 3–80 kHz frequency band. The newly measured attenuation and velocity dispersion curves are in good agreement with those predicted by an extended Biot theory for sediments with a distribution of pore sizes [T. Yamamoto and A. Turgut, J. Acoust. Soc. Am. 83, 1744–1751 (1988)]. Simultaneous measurements of in situ acoustic‐probe data and chirp‐sonar reflection data are also used to estimate the model parameters of the extended Biot model. [Work supported by the Office of Naval Research.]