Algebraic expressions for convective solute transport in a homogeneous soil below a surface barrier

Abstract Engineered surface barriers are expected to be used to cover sites containing buried waste radionuclides after site closure. Understanding the transport of contaminants in the soil below a surface barrier is of importance in order to protect the underlying groundwater. The travel velocity of these contaminants is dependent on numerous factors, such as the thickness, properties, the pre‐barrier hydrologic condition of the vadose zone, and the initial depths and properties of the contaminants. Although solute transport can be modeled with numerical modeling using site‐specific data, by nature a numerical method does not reveal the relationship between inputs and outputs. This work develops algebraic expressions of the velocities of convective solute transport in the vadose zone below a surface barrier, time lag, solute safe depth, zero‐protection depth of a surface barrier, and solute travel time to the groundwater. This development shows that solute convection in the soil with a surface barrier consists of up to three stages: constant high velocity, decreasing velocity, and constant low velocity. Solute transport based on the algebraic expressions was verified against numerical simulations. The algebraic expressions may be used to assess the expected impacts of a surface barrier to the convective transport of contaminants in the vadose zone.