Relationship Between Log Permeability and Fraction of Finer Grains in Bimodal Sediment Mixtures

In sediment mixtures of two grain-size components, the mixture porosity (¿¿¿¿) and permeability (k) both vary non-linearly as a function of the grain size and the volume fraction of each component. A porosity minimum (¿¿¿¿min) occurs near the mixture fraction at which the volume of the finer grains equals the original pore volume of the coarser grains. An abrupt change in slope has been observed in the non-linear relationship between log(k) and the volume fraction of finer grains (rf). This slope change should occur at the rf where coarser pore pathways change from continuous to discontinuous. In this study, fine sand was mixed with coarse sand at different volume fractions, and the abrupt slope change was observed to occur at an rf near, but slightly above, the rf at which ¿¿¿¿min occurred. Among published experiments that used a variety of grain sizes, the change in slope was observed to occur at rf less than, equal to, or greater than the rf at which ¿¿¿¿min occurs, but commonly occurs at rf relatively close to that of ¿¿¿¿min.

For mixtures in which finer grains are approximately the size of coarser pores, unoccupied coarser pores will percolate (connect across the sample) if the fraction of occupied pores (¿¿¿¿¿) is below a percolation threshold (¿¿¿¿¿c), and not percolate if ¿¿¿¿¿ is greater than ¿¿¿¿¿c. An abrupt change in slope of the log(k) versus rf relationship should occur at the rf at which ¿¿¿¿¿ equals ¿¿¿¿¿c, which is less than the rf at which the ¿¿¿¿min occurs. The concepts from percolation theory apply to mixtures in which finer grains are equal to or larger than the size of coarser pores, and do not apply to mixtures in which finer grains are much smaller than the coarser pores. The literature contains three different methods for using the Kozeny-Carman equation to model the log(k) versus rf relationship based on ideas about the nature of the abrupt change in slope, and the rf at which the change occurs. The Kozeny-Carman equation is robust and represents the relationship well using any of these methods.