Comparison Between Equivalent Continuum and Discrete Crack Models of Transient Radon Transport at the Soil–Building Foundation Crack Interface Using TOUGH2/EOS7Rn

Abstract

In the framework of radon risk management in France, it is necessary to enhance knowledge on radon transfer from its source to exposure areas (e.g., buildings) by developing simple, accurate, numerical models for transient radon transport in three-dimensional (3D) unsaturated porous materials. The equivalent continuum model (ECM) of flow and transport at the interface between the soil and cracks (fissures) in a building foundation (e.g., slab on grade, basement) is attractive, since equivalent (effective) continuum properties assigned to model cells can represent the combined effect of individual cracks and solid matrix of the cracked concrete of the foundation (slab and blocks walls). Although the ECM approach based on the volume averaging method has been used to model flow and transport through cracks at the soil–building interface, it has never been verified numerically. Thus, the goal of the present work is to develop an ECM using this averaging method and to quantify its uncertainties based on its comparison to an accurate numerical discrete crack model (DCM) for flow and transport in the crack. As a first step, the DCM implemented in the TOUGH2/EOS7Rn module has been verified numerically through a comparison to a reference 3D steady-state numerical solution for radon transport into a house with basement under constant negative pressure. Then, 3D results of the DCM and ECM approaches were compared, under time-dependent indoor–outdoor pressure differentials conditions, for two crack line configurations in the basement slab floor and two different soil configurations with different soil permeability and radium \(^{226}\)Ra mass content values. Results of this comparison show that, for a homogeneous soil configuration, discrepancies between ECM and DCM simulated indoor radon activity concentrations decrease with the increase in soil permeability, regardless crack line configuration in the slab floor and soil radium mass content. However, ECM uncertainties were not within the range of absolute errors on measured radon concentration for the higher soil permeability \((1\times 10^{-9}, 1\times 10 ^{-8} \hbox { m}^{2})\) and the higher \(^{226}\hbox {Ra}\) mass content values (4500 \(\hbox {Bq\;kg}^{-1})\), especially for high radon pics induced by sudden increase in indoor air pressure drop. Regardless soil \(^{226}\hbox {Ra}\) mass content and crack line configuration in the slab floor, the ECM showed to be conservative for the two-layered soil configuration with the presence of aggregates beneath the slab foundation, generally practiced in buildings constructions.