This paper begins by demonstrating how the Florida Department of Transportation (FDOT) local scour equations take the ratio between grain size and structure size into account when computing equilibrium local scour depth and contrasts this with the well-known Colorado State University (CSU) equation that does not take sediment information into account. Then, a relatively recent empirical formulation from the J-L. Briaud research group for computing local equilibrium scour depth is presented that appears to take the structure size/grain size ratio into account indirectly. Next, a possible explanation for the dependency between local equilibrium scour depth and the structure/grain size ratio is presented that was originally developed by D. Max Sheppard in 2004. This explanation shows that superimposing the pressure gradient around a particle with the pressure gradient around a pile leads to the dependency between equilibrium scour depth and the grain size/structure size ratio. Finally, a new formulation for local equilibrium scour depth based upon turbulent energy spectrum decay is presented. This new formulation reduces the local scour problem to a problem whereby turbulent diffusivity must be better understood. However, this new formulation also appears to show a dependency between equilibrium scour depth and the grain size/structure size ratio. Overall, the analysis presented herein provides several reasons, explanations, and pieces of evidence to suggest that the grain/structure size ratio is an important parameter to consider when computing local equilibrium scour depth.