The mechanism of mediated transport of copper (Cu) by humic acids (HA) in pore water was studied taking account of colloid filtration theory and by means of breakthrough experiments of HA in water-saturated columns filled with quartz sand. The influence of pH and Cu2+ concentration on Cu–HA binding and retention of Cu–HA complexes in the matrix were analysed with colloid-surface attachment models. Experiments were performed for differing Cu concentrations (0–20 mg l−1) and pH (5–7). Copper binding to HA increased with pH and Cu2+ addition, according to ion–humic complexation theory. The zeta potential of the HA became less negative with increasing amounts of Cu, which led to less electrostatic repulsion and an increase in the retention of the HA in the column. A kinetic colloid transport model with a random sequential adsorption (RSA) blocking function was well fitted to the experimental breakthrough curves (BTCs). The model accounted for heterogeneity in the adsorption sites in the quartz sand for all of the electrochemical conditions. For pH = 7, the transport of Cu was coupled with the HA, while at pH = 5, the transport occurred mostly as free Cu2+. Models of the influence of dissolved soil organic matter and electrochemical conditions on the fate of trace elements in the soil may contribute to a quantitative exploration of strategies for soil remediation and disposal of contaminated soil containing excessive amounts of trace elements.