We describe a theory for the removal of volatile organic chemicals from an unsaturated soil stratum consisting of highly porous coarse sand layers sandwiching a thin and semipervious lens. Each soil layer is modelled as a periodic array of spherical aggregates formed by solid grains and immobile water trapped by surface tension. Volatile chemicals are vaporized in the mobile air in pores between aggregates, dissolved in the intra-aggregate water, and adsorbed on the surface of soil grains. Using the effective transport equations derived for the aggregated soils, we consider shallow layers with sharp contrast in physical properties. An asymptotic analysis is developed for an axisymmetric geometry, yielding quasi-one-dimensional governing equations for individual layers. At the leading order the flow and the vapour transport are horizontal in the coarse layers but vertical in the semipervious lens. Numerical results are presented for a simple example to demonstrate the significance of the lens permeability, diffusivity and retardation factor, and the aggregate diffusivity in the coarse layers, on the vapour transport during the stages of contamination and air-venting.