Decontamination and decommissioning at the Savannah River Site near Aiken, SC, have produced on-site disposals of low-level solid radioactive waste in the form of concrete rubble. In the case of a former tritium extraction facility, building demolition produced a significant volume of rubble containing tritium. The contaminated debris comprises a heterogeneous mixture of coarse aggregate sizes, shapes, and internal tritium distributions. The rubble was disposed in unlined earthen trenches that were subsequently backfilled and exposed to normal infiltration. To forecast tritium flux to the water table, an unsteady dual-porosity model was developed to describe vadose zone leaching and transport. Tritium release was assumed to be controlled by diffusion within concrete, while advective and diffusive transport occur in the surrounding backfill. Rubble size and shape variations were characterized through a combination of physical measurement and photographic image analysis. For simplicity, the characterization data were reduced to an approximately equivalent distribution of one-dimensional slab thicknesses for representation in the dual-porosity formulation. Tritium flux to the water table from concrete rubble was predicted to be roughly 40% of that from uniformly contaminated soil. The lower flux is a result of slow release to soil pore water and a reduced effective trench conductivity from the presence of impervious concrete. At early times, tritium release from concrete in the lower trench is depressed by downward migration of tritium from overlying material. The pattern reverses at later times, when tritium is largely exhausted in the upper trench but higher residuals occupy the lower trench.