Network model for hydraulic conductivity of sand-bentonite mixtures

Abstract

A network formulation was used to model the hydraulic conductivity of sand–bentonite mixtures (SBMs) as a function of bentonite content. The sand particles were assumed to be spheres, and their arrangement was defined using a discrete element model simulating sand particle interactions. Pores between the spheres were approximated as a network of straight capillary tubes. The space defined by the spheres was divided into a collection of neighboring tetrahedrons, and the geometry of the tetrahedrons was used to define tube diameters and lengths in the network. Hydraulic heads throughout the network were computed by solving a system of equations describing flow through the tubes. Hydraulic conductivity of the network was calculated as the rate of flow per unit area for a given network of tubes driven by a one-dimensional hydraulic gradient. Bentonite was introduced into the network in several schemes to simulate SBMs. SBMs prepared with powdered bentonite were modeled as a packing of sand, where the sand particles are coated with bentonite (grain coating model and pipe blocking model), whereas SBMs prepared with granular bentonite were modeled as a packing of sand with bentonite occupying pores between the sand particles (junction blocking model). The relationship between hydraulic conductivity and bentonite content obtained from the grain coating model was similar to that measured on sand – powdered bentonite mixtures. A comparable relationship was also obtained for hydraulic conductivities predicted with the junction blocking model using a size-based filling approach and hydraulic conductivities measured on sand – granular bentonite mixtures.Key words: sand–bentonite mixtures, network models, hydraulic conductivity, degree of bentonation, bentonite distribution.