Equation for determining cumulative particle size distribution using the pressure of a sedimenting suspension

Abstract

One of the basic properties of soil––its particle size distribution (PSD)––can be measured using several techniques, among which methods based on sedimentation have a prominent place. Many of these sedimentation methods use changes in the density of a suspension to produce a PSD curve. A certain group of these measure changes in suspension pressure during the ongoing sedimentation process. To date, conversion of the measured changes in suspension pressure to cumulative PSD (CPSD) has been performed using statistical methods and not a physical model of the phenomenon. Here, this gap is filled. Based on the assumptions similar to used at the Stokes equation, an equation was derived linking the CPSD function with the function describing the changes in suspension pressure and its derivative. The derived equation allows direct calculation of the CPSD function based on changes in the pressure of the suspension at a specific depth. In this work, it is shown that the calculation in the reverse direction––obtaining a function describing the pressure in the suspension at a certain depth, PL(D), depending on the soil CPSD function––is also possible, although it requires use of the finite-difference method. The use of the derived equation to interpret test results is shown through examples of six selected soils with different PSDs.