Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments

Abstract

A linear theory of wave propagation in saturated, unconsolidated granular materials, including marine sediments, is developed in this article. Since the grains are unbonded, it is assumed that the shear rigidity modulus of the medium is zero, implying the absence of a skeletal elastic frame. The analysis is based on two types of shearing, translational and radial, which occur at grain contacts during the passage of a wave. These shearing processes act as stress-relaxation mechanisms, which tend to return the material to equilibrium after the application of a dynamic strain. The stress arising from shearing is represented as a random stick-slip process, consisting of a random succession of deterministic stress pulses. Each pulse is produced when micro-asperities on opposite surfaces of a contact slide against each other. The quantity relevant to wave propagation is the average stress from all the micro-sliding events, which is shown to be a temporal convolution between the deterministic stress, h(t), from a single event and the probability, q(t), of an event occurring between times t and t+dt. This probability is proportional to the velocity gradient normal to the tangent plane of contact between grains. The pulse shape function, h(t), is derived by treating the micro-sliding as a strain-hardening process, which yields an inverse-fractional-power-law dependence on time. Based on two convolutions, one for the stress relaxation from translational and the other from radial shearing, the Navier–Stokes equation for the granular medium is derived. In a standard way, it is split into two equations representing compressional and shear wave propagation. From these wave equations, algebraic expressions are derived for the wave speeds and attenuations as functions of the porosity and frequency. Both wave speeds exhibit weak, near-logarithmic dispersion, and the attenuations scale essentially as the first power of frequency. A test of the theory shows that it is consistent with wave speed and attenuation data acquired recently from a sandy sediment in the Gulf of Mexico during the SAX99 experiment. If dispersion is neglected, the predicted expressions for the wave speeds reduce to forms which are exactly the same as those in the empirical elastic model of a sediment proposed by Hamilton. On this basis, the concept of a “skeletal elastic frame” is interpreted as an approximate, but not equivalent, representation of the rigidity introduced by grain-to-grain interactions.

Improved Description and Monitoring of Near Surface Hazardous Infiltrate Complexes by Shear Waves for Effective Containment Response

“…The anomalies may arise or evolve due to the existence of inhomogeneities of the fluid lattice complex and lattice fragmentation during the wave propagation associated response. In [4], especially such aspects as micro events of stick slip type relaxation against dynamically accumulated strain in the presence of a saturant in addition to inter granular friction are more acutely elaborated upon. The association of such micro events with a frequency dependent viscous strain hardening is also explicitly identified by drawing its implications upon either holding with or transiting from the Navier-Stokes regime.…”

“…In addition, the existence of a viscosity associated incompressible and rotational saturant boundary layer on the beads or grains, too adding to the effective diameter besides a non-rotational but viscous part. In this regard, given the context, [4,5], while theoretically examining the wave propagation through a saturated unconsolidated granular medium (i.e., marine sediments), have specifically referred, taking also frequency dependence into account, when effects of intergranular friction and shearing find consideration. Apart from the intrinsic thermodynamics of the wave phenomenon where the attenuation is due to frictional heat loss, appreciating the effective attenuation exacts the consideration of amplitude loss caused by scattering from anomalies.…”

Experimental Study of Sound Waves in Sandy Sediment

“…This assumption may not be correct for unconsolidated sand. The generalized moduli formulas appear correct when the grains are bonded [22], but the "bonding" of sand grains may include sliding friction and/or a fluid-reinforced frame [7,11]. Finding good formulas for intermediate moduli of sandy sediments is a task for future work.…”

“…The fast and slow effective density numbers in eq. (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) are at 250 kHz. As can been seen, the density of the fast wave is 89% + 3% of the total density.…”

Seabed attenuation in water saturated sands on New Jersey continental shelf in 50–3000 Hz band

“…There is not a consensus in the scientific community on the attenuation in sandy sediments, due in large measure to the scarcity of measurements. Some researchers argue that the frequency dependence of the attenuation for water-saturated sands is linear at all frequencies, and that the observed frequency dependence of the loss is caused by other mechanisms [12][13][14]. In all discussions of this debate, it is of critical importance to keep in mind not only the sediment type but also the frequency band.…”