Generalized Rheological Model of the Unconsolidated Marine Sediments with Internal Friction and Effective Compressibility
V. A. Lisyutin |
Sevastopol State University, Sevastopol, Russian Federation |
e-mail: nvlisiutin@mail.ru |
Abstract
Introduction. The quasi-two-phase theory of propagation of an elastic wave in the unconsolidated marine sediments is represented. The longitudinal and shear waves can propagate in marine sediments. The phase velocities, the attenuation coefficients and their frequency dependences are the acoustic properties of these waves. It is shown experimentally that the in dry granular media, the attenuation coefficient is directly proportional to frequency. Whereas in the saturated media, the deviations from this law are noted whence it follows that there are two physical loss mechanisms: the internal and viscous friction.
Data and Methods. The medium in a dry state is represented as a generalized Kelvin-Voigt element consisting of a spring and a springpot that is an element combining the spring conservative properties and the dashpot dissipative properties. The wave equation and the dispersion relation including the internal friction only are deduced using the mathematical apparatus of the fractional derivatives. Then, a new two-phase equation of state is deduced, where a part of the fluid is considered to be associated with a solid phase and another part is mobile. Substitution of the equation of state into the wave equation results in a quadratic dispersion relation whose roots yield the wave numbers of two types of the waves, namely the fast and slow ones (Grain Shearing + Effective Compressibility or GS + EC theory). According to the GS + EC theory, significant sound speed dispersion and deviations of the attenuation frequency dependence upon the linear law in the mid-frequency range occur due to a change of the medium compressibility.
Results. The results of the GS + EC theory are compared with the experimental measurement data on of phase velocity and attenuation taken from the open sources. It is shown that at low frequencies, the unconsolidated medium is of greater compressibility than at high ones that is a result of the fluid displacement from the pore space narrowing.
Discussion and Conclusions. Viscous dissipation is manifested at the medium frequencies, when the fluid is still mobile and the viscous forces are rather significant. At high frequencies, the granules and the fluid oscillate together, and attenuation in the medium arises due to the forces of the internal friction.
Keywords
unconsolidated marine sediments, intergranular friction, viscous dissipation, phase velocity dispersion, attenuation coefficient, loss tangent.
Acknowledgements
The research is carried out at the financial support of RFBR and the city of Sevastopol within the framework of the scientific project No. 18-42-920001.
Original Russian Text © V. A. Lisyutin, 2019,
published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 35, Iss. 1, pp. 85–100 (2019)
For citation
Lisyutin, V.A., 2019. Generalized Rheological Model of the Unconsolidated Marine Sediments with Internal Friction and Effective Compressibility. Physical Oceanography, [e-journal] 35(1), pp. 77-91. doi:10.22449/1573-160X-2019-1-77-91
DOI
10.22449/1573-160X-2019-1-77-91