A new theoretical treatment of compaction and the advective-diffusive processes in sediments: a reviewed basis for radiometric dating models

Classical treatment of mass conservation of solids in growing sediments states an advection-diffusion equation for the bulk sediment density. Thus, the diffusion coefficient has to account for elemental processes of exchange of solid particles by pore water or reciprocally. Nevertheless, in a gravity field, these exchanges are forced and cannot be treated as diffusion but as mass flow. A compaction potential energy is defined so that its spatial gradients force a mass flow involving a conductivity function. This leads to a more consistent definition of mass sedimentation rates and to a writing of the continuity equation for density involving only an advection term. Typical bulk density profiles show an asymptotic increase with depth. With the present formulation, this can be obtained as a steady-state solution under constant sedimentation rate and constant conductivity, while the classical formulation fails to do it. Alternatively, it can be found that under these conditions, the compaction potential is a linear function of the bulk density. The mass flow due to compaction and the compaction potential are found for several sediment cores from literature data. From this basis, the advection-diffusion equation for a particle-associated tracer is rewritten. In particular, when the mass flow term due to compaction is considered, the resulting sub-grid scale processes lead to a different formulation of the diffusive fluxes: they are proportional to the gradients of specific concentration in solids instead of the concentration per unit bulk volume. This new formulation is most suitable to find out analytical solutions for radiometric dating models involving mixing and compaction. Numerical solutions are found for the new and the classical treatment for some particular cases to illustrate differences.