Unified Packing Model for Improved Prediction of Porosity and Hydraulic Conductivity of Binary Mixed Soils

Abstract

Binary mixed soils, containing coarse sand particles mixed with variable content of fines (fine sand, silt, or clay) are important for several environmental and engineering applications. The packing state (or porosity) of such sand-fines mixtures controls several important physical properties such as hydraulic conductivity. Therefore, developing an analytical packing model to predict porosity of binary mixed soils, based on properties of pure unmixed sand and fines (endmembers), can contribute to predicting hydraulic conductivity for the mixtures without the need for extensive laboratory measurements. Toward this goal, this study presents a unified packing model for the purpose of predicting the porosity and hydraulic conductivity of binary mixed soils as function of fines fraction. The current model modifies an existing packing model developed for coarse binary mixed soils to achieve three main improvements: (1) being inclusive of wide range of binary mixed soils covering the whole range particle sizes, (2) incorporating the impact of cohesive packing behavior of the fines on binary mixture porosity, and (3) accounting for the impact of clay swelling. The presented model is the first of its kind incorporating the combined impact of all three factors: particle size ratio, fines cohesive packing and swelling, on binary mixtures porosity. The predictions of the modified model are validated using experimental published data for the porosity of sand-fines mixtures from 24 different studies. The model shows significant improvement in predicting porosity compared to existing packing models that frequently underestimate the porosity. By using the predicted porosity as an input in Kozeny–Carman formulation, the absolute mean error in predicting hydraulic conductivity, as function of fines fraction for 16 different binary mixed soils, is reduced by 50% when compared to the use of the previous packing model. The current model provides insights about the endmembers properties (porosity, hydraulic conductivity, and grain size) and fines content required to achieve a certain target desirable porosity and hydraulic conductivity of the mixed soils. This can assist the optimization of soil mixing design for various applications.