Grain-shearing Research Articles

Prediction of the shear wave speed of seafloor sediments in the northern South China Sea based on an XGBoost algorithm

Based on data on the shear wave speed and physical properties of the shallow sediment samples collected in the northwest South China Sea, the hyperparameter selection and contribution of the characteristic factors of the machine learning model for predicting the shear wave speed of seafloor sediments were studied using the eXtreme Gradient Boosting (XGBoost) algorithm. An XGBoost model for predicting the shear wave speed of seafloor sediments was established based on four physical parameters of the sediments: porosity (n), water content (w), density (ρ), and average grain size (MZ). The result reveals that: (1) The shear wave speed has a good correlation with n, w, ρ, and MZ, and their Pearson correlation coefficients are all above 0.75, indicating that they can be used as the suitable characteristic parameters for predicting the shear wave speed based on the XGBoost model; (2) When the number of weak learners (n_estimators) is 115 and the maximum depth of the tree (max_depth) is 6, the XGBoost model has a very high goodness of fit (R2) of the validation data of 0.914, the very low mean absolute error (MAE) and mean absolute percentage error (MAPE) of the predicted shear wave speed are 3.366 m/s and 9.90%, respectively; (3) Compared with grain-shearing (GS) model and single- and dual-parameter regression equation prediction models, the XGBoost model for the shear wave speed of seafloor sediments has higher fitting goodness and lower prediction error.

Characteristics of shear waves in shallow seafloor sediment in the Middle Southern Yellow Sea

The shear wave characteristics of shallow seafloor sediment are vital to marine acoustic study and ocean engineering exploration. We analyzed the shear wave speed and the physical properties of the southern Yellow Sea sediment based on the Grain-Shearing (GS) model. The results show that: (1) The shear wave speed of the high-porosity sediment is lower than that of the low-porosity sediment; (2) The shear wave speed of the fine-grained sediment is lower than that of the coarse-grained sediment; (3) The burial depth of the sediment has a significant influence on the shear wave speed of the seafloor sediment. The GS model agrees well with the measurement data from the southern Yellow Sea. However, the quantitative analysis of the impact of input parameters on the GS model requires further research.

Estimation of Compressional Wave Speed in Marine Sediments using Biot Stoll Model and Buckinghams Grain shearing Model

Acoustic properties of seafloor sediments can be estimated using theoretical models by giving geophysical properties of sediments as inputs to the respective models. Empirical relations connecting the geophysical and geoacoustic properties are available in literature. In this study an experimental assessment of two such theoretical models viz., Biot-Stoll model (BSM), a poro-elastic model and the Buckingham’s grain shearing (GS) model, a visco-elastic model is done by estimating the compressional wave speed. Compressional wave speed is measured using in-house developed sediment velocimeter and is compared with the speed estimated using both the models and a regression analysis was done. It was observed that the Coefficient of determination R2 for BSM and GS model are 0.769 and 0.729, respectively. It shows that once the constants used in GS model are evaluated for the Indian waters, then it can be used to estimate the acoustic properties of sediments.

Исследование взаимосвязи между износостойкостью при сухом трении и механическими свойствами спеченных композитов системы Al-Sn

Effect of tin-insoluble alloying elements (Zn, Si) on the mechanical and tribological properties of the Al-40Sn sintered composite has been studied. Powder mixtures with alloying additions were sintered at a temperature above the melting point of tin (232°C). Sintered specimens had residual porosity, which negatively affected the strength, ductility, and wear resistance of the composite under dry friction. Compression in a closed die and equal channel angular pressing (ECAP) at a temperature of 250°C reduced the porosity of the material and significantly increased its strength and ductility. Regardless of the pressure treatment method, the compacted specimens showed good wear resistance. The main mechanism of composite wear is the exfoliation of matrix grains in the surface layer due to their shift along the tin interlayers in the direction of friction. The shear and peeling of grains were preceded by a strong deformation of the surface layer, in which the grain boundaries with tin interlayers were stretched in the direction of friction, that is, a layered structure was formed. Composites in which most of the grain boundaries of the aluminum matrix are oriented perpendicular to the sliding direction have the maximum wear resistance. A similar structure is formed in the plane of the material flow during ECAP processing. It was found that the wear resistance of a composite with a zinc-doped matrix is higher than with a silicon-doped matrix.

Grain shearing models and relevance beyond sediment acoustics

The grain shearing (GS) and viscous grain shearing (VGS) models for saturated, unconsolidated marine sediments fit well to real data. But the models have much further relevance. The inherent convolution is in fact the definition of a non-integer derivative. Therefore, the GS theory is exactly described by the fractional diffusion-wave equation for shear waves and the fractional Kelvin-Voigt wave equation for the compressional mode. Both have been studied extensively in fractional calculus [Pandey and Holm, “Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations,” JASA (2016)]. The GS theory demonstrates that fractional derivatives arise naturally from physical processes and thus are more than just clever mathematics. These derivatives appear in the relaxation modulus, the stress response to a strain step, of the GS process. The variation in time of the viscosity makes it a time variant non-Newtonian process. But when strain and stress change roles, a surprising result appears. The creep response is the Lomnitz law, an empirically defined logarithmic relationship for such diverse materials as igneous rocks and wood [Pandey and Holm, “Linking the fractional derivative and the Lomnitz…,” Phys. Rev. E (2016)]. In the VGS model, the power-law response is exponentially tempered. The relaxation modulus is then that of the Cole-Davidson model, known from dielectric materials. This relationship has yet to be explored [Holm, Waves with Power-Law Attenuation (Springer, 2019), Chap. 8].

An overview of the sediment acoustic models and their experimental validations

The Biot theory of acoustic wave propagation in porous media was first adapted to marine sediments by Stoll (1969). To describe the response of a slightly inelastic skeletal frame over a wide frequency range, Stoll introduced the notion of constant complex bulk and shear moduli with small imaginary parts. Stoll’s model predicts f1 frequency-dependence of attenuation at low frequencies and nearly f2 and f1/2 frequency-dependence at frequencies where maximum velocity dispersion occurs. Although the theory well reproduces the velocity and attenuation measurements in marine sediments, the assumption of constant complex moduli slightly violates the causality (Turgut, 1990). The more recent Grain-Shearing (GS) and Viscous Grain-Shearing (VGS) models (Buckingham, 2000 and 2007) are causal and the VGS model also predicts a frequency-dependence of attenuation like that of the Stoll model. With the selection of proper parameter values, both models predict compressional and shear-wave dispersions that are in agreement with those of previous in-situ and laboratory measurements. In addition, the Stoll model predicts the existence of slow compressional waves that have been observed in synthetic porous media (Plona, 1980) but not in natural marine sediments. Several reflection and in-sediment transmission experiments are discussed to facilitate the detection of slow compressional waves in marine sediments. [Work supported by ONR.]

Fractional viscoelastic modelling of wave propagation in fluid-saturated marine sediments

It is shown that Buckingham's grain-shearing (GS) model [JASA (2000)] as well as its improved viscous-GS (VGS) model [JASA (2007)] can be expressed using the mathematical framework of fractional calculus. The fractional version of the standard fluid model is adopted to independently arrive at the wave equations and dispersion relations derived by Buckingham. The fractional-order wave equations obtained for the compressional waves and shear waves are relatively easier to analyse due to their closed-form representation in the fractional framework. It is also shown that the fractional calculus approach may help in bridging the disparate fields of non-Newtonian rheology and sediment acoustics, which may have actually developed independently of each other. Further, the experimental data relating wave dispersion and attenuation in marine sediments is found to match with the predictions from the fractional framework. The overall goal is to show that fractional calculus is not just a mathematical framework that can only be applied to curve-fit the observational data for complex media. In fact, it has an inherent connection to real physical processes that needs to be explored more.

Biological effects and the Grain-Shearing model of wave propagation in unconsolidated sediments

The Grain-Shearing (GS) model of wave propagation in unconsolidated sediments is embodied in two sets of dispersion relations, one for the compressional wave and the other for the shear wave. Besides frequency, these expressions for the wave speed and attenuation depend on the physical properties of the sediment, notably the bulk density and porosity. They also involve a material exponent, n, and grain shearing coefficients that are associated with the sliding of grains against one another, which is a non-linear, stick-slip type of process that is controlled by micro-asperities on the surface of the grains. Bioturbation is known to affect both the bulk density and porosity of sediments, while biogenic coatings of mineral grains modify the surface roughness, which alters the grain-shearing coefficients. The magnitude of the effects of bioturbation and biogenic coatings on the wave speeds and attenuations predicted by the GS theory will be discussed, based on available biological information in the literatu...

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

The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815 (2000)] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown to take the form of the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation, respectively. Therefore, an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the GS model to establish the equivalence of the respective wave equations. Further, a physical interpretation of the characteristic fractional order present in the wave equations is inferred from the GS model. The overall goal is to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials. Rather, it can also be derived from real physical processes as illustrated in this work by the example of GS.

Linking the viscous grain-shearing mechanism of wave propagation in marine sediments to fractional calculus

An analogy is drawn between the diffusion-wave equations derived from the fractional Kelvin-Voigt model and those obtained from Buckingham's grain-shearing (GS) model [J. Acoust. Soc. Am. 108, 2796-2815 (2000)] of wave propagation in saturated, unconsolidated granular materials. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and shear wave equation derived from the GS model turn out to be the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation respectively. Also, a physical interpretation of the characteristic fractional-order present in the Kelvin-Voigt fractional derivative wave equation and time-fractional diffusion-wave equation is inferred from the GS model. The shear wave equation from the GS model predicts both diffusion and wave propagation in the fractional framework. The overall goal is intended to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials, but rather it can be justified from real physical process of grain-shearing as well.

Estimation of Seabed Properties Using Ambient Noise from Shallow Water Sites of the Indian Continental Shelf

ABSTRACTIn this study an attempt has been made to extract sediment geoacoustic properties using ambient noise measured from a vertical hydrophone array. Time series noise data recorded from three shallow water sites (Chennai, Cuddalore and Cochin) along the Indian continental shelf were used for the analysis. The compressional sound speed of sediment for all the sites was estimated from the vertical directionality of ambient noise. Using the value of the compressional sound speed remaining wave properties and material properties were deduced from the Grain-Shearing (G-S) theory of wave propagation in saturated granular media. The type of sediment extracted from the G-S theory correlates well with the results obtained from sieve and particle size analysis of grab samples, collected from all the sites. The study clearly shows the application of ambient noise in extracting environmental information in shallow water, and further applying it to improve sonar performance modeling.

A fractional calculus approach to the propagation of waves in an unconsolidated granular medium

Our study builds on the work of Buckingham [JASA (2000)] which employed a grain-shearing (GS) model to describe the propagation of elastic waves in saturated, unconsolidated granular materials. He ensemble averages the random stick-slip process which follows the velocity gradient set up by the wave. The stick-slip process is due to the presence of micro-asperities between the contact surfaces of the grains. This is a strain hardening process which is represented by a time-dependent coefficient in the Maxwell element, besides the coefficient also gives the order of the loss term in the wave equations. We find that the material impulse response derived from the GS model is similar to the power-law memory kernel of fractional calculus. The GS model then gives two equations; a fractional Kelvin-Voigt wave equation for the compressional wave and a fractional diffusion equation for the shear wave. These equations have already been analyzed extensively in the framework of fractional calculus. Since the Kelvin-Voigt model is used in biomechanics of living tissue, we believe the GS theory could offer insights into ultrasound and elastography as well. The overall goal is to understand the role of different material parameters which affect wave propagation.

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.

Friction versus dilation revisited: Insights from theoretical and numerical models

[1] The stability and dynamics of geological faults are often controlled by the frictional strength of the fault gouge, a granular layer that accumulates between the fault blocks due to wear. One of the main factors controlling the shear strength (as measured by an apparent friction coefficient) of such granular layers is the systems resistance to dilation, a by-process accompanying granular shear. This paper develops theoretical models connecting shear resistance and dilation during the different types of motions that occur in shear of uniform grains and compares theoretical predictions to results from two-dimensional discrete element simulations. We find that minimization of dilation-associated work (and thus minimization of apparent friction) is the factor that determines whether granular deformation will be localized or distributed and whether grains will predominantly slide or roll. Simulations of more realistic systems, with heterogeneous grain sizes, suggest that the apparent friction and dilation rate follow a physical picture consisting of two of the deformation mechanisms identified in shear of uniform grain systems: (1) shear localization onto a few layers of rolling grains and (2) brief compaction events in which dilated regions outside the shear zone compact. The first mechanism provides a nearly linear relationship between apparent friction and dilation rate. The second mechanism produces significant deviations from the linear relationship, with strongly negative dilation rates reflecting compaction events. Because observed compaction events occur outside of shear zones, dilation rate is not always simply related to apparent friction.

Variability of parameter estimates used in the Buckingham viscous grain shearing model.

A compilation of 54 sets of geoacoustic measurements of marine sediments was reviewed in order to bound estimates of parameters for use in Buckingham’s grain shearing (GS) theory of acoustic propagation. These data, for unconsolidated sands (siliciclastic and carbonate) with grain sizes between 0.0156 and 0.57 mm, were all made in shallow water (maximum depth of 60 m) sites at diverse locales. In each data set, measurements of the speed and attenuation of the compressional wave at high frequency, the shear wave speed at 1 kHz, porosity, and bulk density are sufficient to calculate the three free parameters in GS theory (a material exponent, a compressional coefficient, and a shear coefficient). The spread of the values calculated for GS parameters, combined with a sensitivity analysis, does not support the use of a single material exponent value for all sediments. Shear wave attenuation measured at 18 sites was compared to the predictions of Buckingham’s (2010) most recent version of the VGS model. In this model the shear viscoelastic time constant is based on the wavelength of the propagating shear wave rather than shear speed.

Comments on “On pore fluid viscosity and the wave properties of saturated granular materials including marine sediments” [J. Acoust. Soc. Am. 122, 1486–1501 (2007)

The ability of the grain shearing (GS) and viscous grain shearing (VGS) models to relate geophysical and acoustic properties is tested by a method based on the claimed tight coupling between compressional and shear wave speeds and attenuations, which allows the test result to be quantified in a single parameter. The VGS model is claimed to provide a better fit to the measured sound speed and attenuation in sandy sediments below 10 kHz. In situ measurements of wave speeds and attenuations from the Sediment Acoustics Experiment 1999 (SAX99) and published laboratory measurements by Prasad and Meissner [Geophysics 57, 710-719 (1992)] on a number of sand samples were used to test the models. By this metric, the SAX99 data show that the VGS model is no better than the original GS model because the improved agreement of compressional wave speeds at low frequencies is achieved at the expense of gross overestimation of the shear wave attenuation. When applied to the measurements by Prasad and Meissner, it is shown that the GS models are not applicable at any significant confining pressures, and at zero pressure they may only be applicable to a small subset of the sand samples.

Compressional Wave Speed Dispersion and Attenuation in Carbonate Sediments, Kaneohe Bay, Oahu, HI

In situ compressional wave speed and attenuation measurements between 20 and 100 kHz were made at two carbonate sediment sites in Kaneohe Bay, on the windward side of the Hawaiian island of Oahu. Velocities increased with frequency from 1691 to 1708 m/s at a coarse sediment site (HC, porosity=0.45) and from 1579 to 1585 m/s at a fine-grained sediment site (HF, porosity=0.56). Effective attenuation increased with frequency from 15 to 75 dB/m at HC and from 22 to 62 dB/m at HF. Values of sound speed at these sites are within the range of those reported in the literature for silicate sands of the same porosity. Attenuation values of these reef-derived carbonate sands are higher than many of those reported in the literature for silicate sands and they appear to be linearly related to frequency (?=0.65f). Sound-speed and attenuation data were compared to predictions of two sediment geoacoustic models, Biot-Stoll and grain shearing (GS). In both models, two unknown parameters were varied to find best fits at each site to: 1) both attenuation and sound-speed data and 2) sound-speed data only. Both models yielded similar fits, which differ significantly from the measured data.

The Viscous-Grain-Shearing (VGS) theory of wave propagation in marine sediments

The grain-shearing (GS) theory of wave propagation in a marine sediment is based upon the idea that, as grains slide against one another, the dissipation becomes progressively stronger, a phenomenon known as strain hardening. The GS theory predicts a sound speed showing weak, logarithmic dispersion and an attenuation that scales linearly with frequency. At frequencies above about 10 kHz, such behavior matches the sound speed and attenuation data obtained during the SAX99 experiment in the Gulf of Mexico. But at lower frequencies, the measured dispersion curves show a lower sound speed and higher attenuation than predicted by the GS theory. A generalized version of the GS theory, designated the VGS theory, takes account of the effective viscosity of the molecularly thin layer of pore fluid between contiguous grains, which limits the degree of strain hardening that can occur during sliding. The VGS dispersion expressions are the same as those of the GS theory, except for the appearance of a simple algebraic function that has an effect only at low frequencies, below 10 kHz. The resultant VGS curves match the sound speed and attenuation measurements from SAX99 over the measurement frequency band from 1 to 400 kHz. (Research supported by ONR.)

On pore-fluid viscosity and the wave properties of saturated granular materials including marine sediments

The grain-shearing (GS) theory of wave propagation in a saturated granular material, such as a marine sediment, is extended to include the effects of the viscosity of the molecularly thin layer of pore fluid separating contiguous grains. An equivalent mechanical system consisting of a saturating, strain-hardening dashpot in series with a Hookean spring represents the intergranular interactions. Designated the VGS theory, the new model returns dispersion curves that differ mildly from those of the GS theory at lower frequencies, below 10 kHz, where effects due to the viscosity of the pore fluid may be non-negligible. At higher frequencies, the VGS dispersion curves approach those of the GS theory asymptotically. The VGS theory is shown to match the SAX99 dispersion curves reasonably well over the broad frequency band of the measurements, from 1 to 400 kHz. This includes the frequency regime between 1 and 10 kHz occupied by Schock's chirp sonar data, where the viscosity of the pore fluid appears to have a discernible effect on the dispersion curves.

Frequency dependencies of phase velocity and attenuation coefficient in a water-saturated sandy sediment from 0.3to1.0MHz

The frequency-dependent phase velocity and attenuation coefficient for the fast longitudinal wave in a water-saturated sandy sediment were measured over the frequency range from 0.3 to 1.0 MHz. The experimental data of phase velocity exhibited the significant negative dispersion, with the mean rate of decline of 120 +/- 20 m/s/MHz. The Biot model predicted the approximately nondispersive phase velocity and the grain-shearing (GS) model exhibited the slightly positive dispersion. In contrast, the predictions of the multiple scattering models for the negative dispersion in the glass-grain composite were in general agreement with the experimental data for the water-saturated sandy sediment measured here. The experimental data of attenuation coefficient was found to increase nonlinearly with frequency from 0.3 to 1.0 MHz. However, both the Biot and the GS models yielded the attenuation coefficient increasing almost linearly with frequency. The total attenuation coefficient given by the algebraic sum of absorption and scattering components showed a reasonable agreement with the experimental data for overall frequencies. This study suggests that the scattering is the principal mechanism responsible for the variations of phase velocity and attenuation coefficient with frequency in water-saturated sandy sediments at high frequencies.