###### Abstract  
Binary soil mixture, containing large silica particles (sand) mixed with variable content of very fine silt or clay, is an example of a functionally graded material that is important for several science and engineering applications. Predicting the porosity (or void ratio), which is a fundamental quantity that affects other physical properties, of such material as function of fines (clay or silt) fraction can be significant for sediment research and material design optimization. Existing analytical models for porosity prediction work well for binary mixed soils containing multi-sized non-cohesive particles with no clay, while such models frequently underestimate the porosity of sand-clay mixtures. This study aims to present an analytical model that accurately predicts the porosity of mixed granular materials or soils containing sand and very fine silt or clay (cohesive particles). It is demonstrated that accounting for the cohesive nature of very fine particles, which exists due to the effect of inter-particle forces, is a major missing aspect in existing packing models for mixed soils. Consequently, a previously developed linear packing model is modified so that it accounts for fines cohesive packing in sand-fines mixtures. The model prediction is validated using various experimental published data sets for the porosity of sand-fines mixtures. Improvement in the prediction of permeability and maximum packing dry density when incorporating cohesive packing behavior is discussed. The current model also provides important insights on the conditions under which, the lowest permeability and maximum packing state are expected. s 2020 xxxxxxxx-x 2020  
Developing an analytical model to predict the porosity of binary mixed soils, composed of large and fine particles, have been the focus of many studies [15; 32; 33; 34; 35], as it can reduce the need for extensive laboratory testing. [PERSON] and [PERSON] [28] and [PERSON] et al. [34] presented an analytical model that is based on the ideal case--the fines can effectively fill the space between the large sand particles without disturbing their packing. The ideal packing condition should be theoretically satisfied when the ratio of fines (clay or silt) particle size (\(d_{f}\)) to the large sand particle size (\(d_{l}\)), \(R=d_{f}/d_{l}\), is very small [28; 36; 37]. Although such ideal packing model provided reasonable estimates for porosity as suggested by few studies [25; 38], an increasing body of literature showed that such model underestimates the porosity for sand-clay and sand-silt mixtures (e.g., References [15; 20; 26; 32; 33]). Recent studies modified the ideal packing model by incorporating correction parameters that can be estimated based on \(R\) (e.g., References [15; 33; 35]) to account for deviation from ideal packing. The prediction of such models works well for coarse-grained mixtures (e.g., gravel-sand) mixtures but still predicts near-ideal packing case for sand-clay mixtures, as pointed out by [PERSON] et al. [35]. Mixed soils involving large sand and clay or fine silt should satisfy the low \(R\) condition, thus it remains unclear when and why the packing of such mixtures deviates from ideal packing. Packing of very fine cohesive particles (i.e., clay or fine silt) can be very different from larger non-cohesive particles (i.e., sand) due to the effect of inter-particle forces, such as van der Waals and electrostatic forces, whose impact on packing can become more important than gravity force for very fine particles [39; 40; 41]. Therefore, very fine particles such as clay or fine silt, tend to form aggregates that are larger than the actual particle size due to the cohesive nature of the particles. [PERSON] et al. [35], suggested that such cohesiveness can explain why the formulations developed for coarse-grained binary mixtures fail when applied to sand-clay mixtures. Nevertheless, the effect of fines cohesive packing behavior was never incorporated into the packing model for sand-clay or sand-silt mixtures.