Mj. Buckingham, Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments, J ACOUST SO, 108(6), 2000, pp. 2796-2815
A linear theory of wave propagation in saturated, unconsolidated granular m
aterials, including marine sediments, is developed in this article. Since t
he grains are unbonded, it is assumed that the shear rigidity modulus of th
e medium is zero, implying the absence of a skeletal elastic frame. The ana
lysis is based on two types of shearing, translational and radial, which oc
cur at grain contacts during the passage of a wave. These shearing processe
s 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 probabi
lity, q(t), of an event occurring between times t and t + dt. This probabil
ity is proportional to the velocity gradient normal to the tangent plane of
contact between grains. The pulse shape function, h(t), is derived by trea
ting the micro-sliding as a strain-hardening process, which yields an inver
se-fractional-power-law dependence on time. Based on two convolutions, one
for the stress relaxation from translational and the other from radial shea
ring, the Navier-Stokes equation for the granular medium is derived. In a s
tandard way, it is split into two equations representing compressional and
shear wave propagation. From these wave equations, algebraic expressions ar
e 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 attenuat
ion data acquired recently from a sandy sediment in the Gulf of Mexico duri
ng the SAX99 experiment. If dispersion is neglected, the predicted expressi
ons 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 appr
oximate, but not equivalent, representation of the rigidity introduced by g
rain-to-grain interactions. (C) 2000 Acoustical Society of America. [S0001-
4966(00)01112-7].