In this study, contaminant leaching from three different secondary materials (demolition waste, municipal solid waste incineration ash, and blast furnace slag) to groundwater is assessed by numerical modeling. Reactive transport simulations for a noise protection dam and a road dam (a typical German autobahn), in which secondary materials are reused as base layers, were performed to predict the breakthrough of a conservative tracer (i.e., a salt) and sorbing contaminants (e.g., PAHs like naphthalene and phenanthrene or heavy metals) at the groundwater table. The dam constructions have a composite architecture with soil covers in inclined layers and distinct contrasts in the unsaturated hydraulic properties of the used materials. Capillary barrier effects result in strong spatial variabilities of flow and transport velocities. Contaminant breakthrough curves at the groundwater table show significant tailing due to slow sorption kinetics and a wide distribution of travel times. While conservative tracer breakthrough depends primarily on subsoil hydraulic properties, equilibrium distribution coefficients and sorption kinetics represent additional controlling factors for contaminant spreading. Hence, the three secondary materials show pronounced differences in the temporal development of leached contaminant concentrations with consequences for breakthrough times and peak concentrations at the groundwater table. Significant concentration reductions due to dispersion occur only if the source concentrations decrease significantly prior to the arrival of the contaminant at the groundwater table. Biodegradation causes significant reduction of breakthrough concentrations only if flow velocities are low.