Force chains, creep and acoustic reflection in marine sediments

Abstract

Marine sediments are water-saturated granular media. A feature of granular media is that the stress is not uniformly distributed but concentrated in force chains. Several force chains acting in parallel transmit external stresses through the medium. A force chain is a chain of particles through which the external stresses are concentrated and transmitted. Given that the contact stiffness between particles may be approximated as a Maxwell element, i.e. a spring in series with a damper, then the stiffness of any force chain may be modeled as several Maxwell elements in series. It is known that any number of springs and dampers in series may be reduced to just one spring and one damper in series, i.e., one equivalent Maxwell element. Therefore, several force chains in parallel may be modeled as parallel Maxwell elements. However, parallel Maxwell elements may not be reduced to one Maxwell element. The stiffness of a distribution of parallel Maxwell elements falls under the generalized creep model. This model is used to represent the skeletal frame of a larger porous medium model. The inversion of model parameters from the reflection coefficient is explored in the context of a muddy sediment. [Work supported by ONR, Ocean Acoustics Program.]