Predicting the porosity of sand-clay mixtures

Predicting porosity of sediments that contain a mix of coarse and fine components (i.e., binary mixture) can be of significant importance to many fields including earth sciences and engineering. Sand-clay mixture is one of the most significant sediment that is frequently encountered in hydrological, environmental and geophysical application, thus modelling the porosity of such mixture as function of clay content can be of great interest. An extensive literature has developed around the packing and porosity of binary mixtures, mostly from non-earth science disciplines. The literature presents a well-established model, named ideal packing model (IPM), to predicting the porosity of binary mixtures of spheres, although the applicability of such model for sand-clay mixture is not well understood. While some studies found that IPM could successfully reproduce the porosity data measured for sand-clay mixtures, other researchers reported significant underestimation of the measured porosity when using IPM. It remains unclear whether or not and under what conditions does IPM predict well the porosity of the sand-clay mixture. This suggests the need for a physical packing model that can be used to predict the porosity of sand-clay mixtures and account for the different packing conditions that may result in deviation from the existing theoretical model. Thus, the scope of this investigation is to compile the sparse data set reported for measured porosity of sand-clay mixtures in order to: a) specify and explain any different packing behavior of sand-clay mixtures that can explain deviation from IPM, and b) develop a model that can explain the packing behavior of sand-clay mixtures and predict their porosities, especially when IPM fails. For the later objective, we plan to examine and focus on a packing model developed originally in powder technology and chemical engineering fields for binary mixtures involving powders since packing of such material might be similar to that of clay. The utilization of such model was never carried out or applied in earth sciences related research or data set. The current study additionally proposes to modify the existing model and find the appropriate parameters for the case of sand-clay mixtures. The proposed modified model will be finally validated using extensive published data set for sand-clay mixtures highlighting any limitations. The outcomes of this study can be of great significance for applications in filter design optimization, civil and geotechnical engineering, and earth science.