Analytical Models for 3-D Diffusion of Ions from Salt-Contaminated Aggregates

This article presents an analytical investigation of the mobility of salts from contaminated aggregates in concrete. Salt-contaminated aggregates may have varied effects on the mechanical properties and durability of concrete. These depend primarily on the mobility of salts within the concrete matrix. Existing diffusion-based models for the mobility of salts in concrete focus on their intrusion from external sources (e.g., chloride penetration from deicing salts and brines). Such problems are well described by the closed-form solution of Fick’s law for diffusion in one dimension from a continuous source. Salt-contaminated aggregates represent a case of diffusion from a finite internal source rather than intrusion from a continuous external source. When the source is internal—as in the case of salt-contaminated aggregates—diffusion occurs in three dimensions and the source is finite. The 1-D solution is ill conditioned to model this problem, so new diffusion models must be introduced. This article presents two models of varying complexity that are well conditioned to model diffusion of salts from contaminated aggregates. First, the problem is modeled using Fick’s law for the simplified case of 3-D diffusion from an instantaneous point source in an infinite medium. Contaminated aggregates are treated as infinitesimal slugs of diffusing material. The same problem is then modeled using Fick’s law for the more realistic case of 3-D diffusion from an instantaneous spherical source, where contaminated aggregates are treated as approximately spherical. The intent of this article is to present an academic discussion on how chloride ions might migrate within the concrete matrix if they are assumed to do so by diffusion alone.