Results of novel theoretical approaches show a possible underestimation of building materials contribution to indoor radon levels

Solo-diffusive radon transport

In case of negligible driving pressure difference and/or low air permeability of the building structures, the radon exhalation rate from room’s building structures, as well as the resulting indoor radon activity concentration, may be estimated through the formulations 1.a or 1.b of Table 3, depending on the radon activity concentrations in the environments divided by the building structure itself. The simplified solution 1.b, that implicitly assumes the radon activity concentration to be the same on both building structure sides, was commonly adopted in the past even in scenarios not coherent with the assumption itself, mainly when the structure is a perimetral wall. The numerical difference due to the improper application of the simplified approach (1.b) instead of the exact one (1.a) has been evaluated by introducing \(\:{\Delta\:}{\text{E}}_{\text{\%},\:\text{d}\text{i}\text{f}\text{f}}\) and \(\:{{\Delta\:}\text{C}}_{\text{R}\text{n},\text{\%},\text{d}\text{i}\text{f}\text{f}}\).

where \(\:{C}_{\text{R}\text{n},1.b}\) and \(\:{C}_{\text{R}\text{n},1.a}\) are the radon activity concentrations in the reference room computed by considering the simplified approach (1.b) and of the exact one (1.a), respectively, \(\:{E}_{1.b}\) and \(\:{E}_{1.a}\) are the values of radon exhalation rate from the building structures computed by considering the simplified approach (1.b) and of the exact one (1.a), respectively.

The radon diffusion length

Figures 2 and 3 report \(\:{\Delta\:}{\text{E}}_{\text{\%},\:\text{d}\text{i}\text{f}\text{f}}\) and \(\:{{\Delta\:}\text{C}}_{\text{R}\text{n},\text{\%},\text{d}\text{i}\text{f}\text{f}}\) obtained by assuming the values reported in Table 2, and varying only the radon diffusion length of the building material the structures are made of, i.e., varying the material constituting the building structure. The radon diffusion length—defined as the square root of the ratio between the effective diffusion coefficient and the radon decay constant—may be defined as the ease with which radon atoms diffuse through the porous matrix of the building material.

Percentage difference of radon exhalation rate from building structures as a function of the building material radon diffusion length between the simplified approach (1.b) and the exact one (1.a). In black and in grey the results obtained at ground floor and upper floors, respectively. Next to the diffusion length axis, some typical building materials are reported (from the left to the right, bricks, Italian tuff, and aerated concrete) with the corresponding range of variability for radon diffusion length.

Percentage difference of indoor radon concentration established in the reference room as a function of the building material radon diffusion length between the simplified approach (1.b) and the exact one (1.a). In black and in grey the results obtained at ground floor and upper floors, respectively. Next to the diffusion length axis, some typical building materials are reported (from the left to the right, bricks, Italian tuff, and aerated concrete) with the corresponding range of variability for radon diffusion length.

Considering the simplified approach (1.b) instead of the exact one (1.a) always leads to an overestimation of both the radon exhalation rate and the resulting indoor activity concentration. Furthermore, the overestimation introduced is always higher at the ground floor—where the soil contribution exists as well—than at upper floors. The overestimation increases with increasing diffusion length of the building material. If the diffusion length is below about 5 m, e.g., as generally for bricks, adopting “simplified” approach implies an overestimation lower than 5% on indoor radon activity concentration; only for highly porous materials, such as Italian tuff and aerated concrete, such an overestimation may rise to about 15%.

The radon generation inside the porous material

Figures 4 and 5 report \(\:{\Delta\:}{\text{E}}_{\text{\%},\:\text{d}\text{i}\text{f}\text{f}}\) and \(\:{{\Delta\:}\text{C}}_{\text{R}\text{n},\text{\%},\text{d}\text{i}\text{f}\text{f}}\) obtained by assuming the values reported in Table 2, and varying the inner radon generation of the porous material constituting the building structure (G_v, in Appendix A). The radon diffusion length has been set to 10 m because the overestimation introduced by the simplified approach is more evident for highly porous, so greatly diffusing, materials.

Percentage difference of radon exhalation rate as a function of the building material radon production rate per unit pore volume between the simplified approach (1.b) and the exact one (1.a). In black and in grey the results obtained at ground floor and upper floors, respectively. The radon diffusion length is fixed to 10 m. The inner radon production rate per unit pore volume is normalized to the value computed considering the parameters in Table 2, i.e., 60 mBq m⁻³ s⁻¹. \(\:{C}_{\text{R}\text{a}-226},\rho\:,\:f\) are the radium-226 content, density, and emanation coefficient of the building material.

Percentage difference of indoor radon activity concentration established in the reference room as a function of the building material radon production rate per unit pore volume between the simplified approach (1.b) and the exact one (1.a). In black and in grey the results obtained at ground floor and upper floors, respectively. The radon diffusion length is fixed to 10 m. The radon production rate per unit pore volume is normalized to the value computed considering the parameters in Table 2, i.e., 60 mBq m⁻³ s⁻¹. \(\:{C}_{Ra226},\rho\:,\:f\) are the radium-226 content, density, and emanation coefficient of the building material.

As well as for the radon diffusion length, the simplified approach (1.b) always leads to an overestimation of both the radon exhalation rate and the resulting indoor activity concentration relative to the exact one (1.a).

The overestimation introduced by the simplified approach on the radon exhalation rate at ground floor reduces with increasing radon production rate per unit pore volume inside the building material (Figs. 4 and 5): it reaches a plateau at about 100% independently from the radon production rate. At the upper floors, the contribution from soil neglected, the overestimation is fairly constant at about 100%.

Referring to the indoor radon activity concentration, the increase of the radon production rate reflects on the increase of the overestimation due to the simplified approach up to about 40% for both ground and upper floors for building materials with high inner radon production rate.

Diffusive-advective radon transport

In case of not negligible driving pressure difference and/or low air permeability of the building structure, the radon exhalation rate from room’s building structures should be evaluated through the solution 2.a of Table 3 which considers both diffusive and advective radon transport. However, the ease of the formulation 1.b—mainly the lesser input parameters and the lower computational complexity—has supported, in the past, its adoption. The numerical difference due to the improper application of the simplified approach (1.b) instead of the exact one (2.a) has been evaluated by \(\:{\Delta\:}{\text{E}}_{\text{\%},\text{a}\text{d}\text{v}}\) and \(\:{{\Delta\:}\text{C}}_{\text{R}\text{n},\text{\%},\text{a}\text{d}\text{v}}\), defined as:

where \(\:{C}_{\text{R}\text{n},1.b}\) and \(\:{C}_{\text{R}\text{n},2.a}\) are the radon activity concentrations in the reference room computed by considering the simplified approach (1.b) and of the exact one (2.a), respectively, \(\:{E}_{1.b}\) and \(\:{E}_{2.a}\) are the values of radon exhalation rate from the building structure computed by considering the simplified approach (1.b) and of the exact one (2.a), respectively.

According to the mean value theorem, a uniform pressure gradient of 5 Pa along the building height was assumed. This value represents the average pressure difference between the indoor and outdoor environments observed in Fig. 1.

The air permeability

Figures 6 and 7 report \(\:{\Delta\:}{\text{E}}_{\text{\%},\text{a}\text{d}\text{v}}\) and \(\:{{\Delta\:}\text{C}}_{\text{R}\text{n},\text{\%},\text{a}\text{d}\text{v}}\) obtained by assuming the values reported in Table 2, and varying only the air permeability of the material constituting the building structure.

Percentage difference of radon exhalation rate from building structures as a function of the building material air permeability between the simplified approach (1.b) and the exact one (2.a). The figures also show the air permeability ranges of some building materials, i.e., bricks and ordinary concrete.

Percentage difference of radon indoor concentration established in the reference room as a function of the building material air permeability between the simplified approach (1.b) and the exact one (2.a). The figures also show the air permeability ranges of some building materials, i.e., bricks and ordinary concrete.

The results are about the same regardless the floor level. The simplified approach (1.b) always leads to an underestimation of both the radon exhalation rate and the resulting indoor activity concentration relative to the exact one (2.a).

The underestimation introduced is more severe for highly permeable building materials, whereas it reduces with decreasing air permeability. Thus, the application of the exact formulation for radon exhalation rate from building structures is critical when the building materials employed are highly porous, e.g., bricks, and sandstone³¹. When assessing the radon exhalation rate, and the resulting radon indoor concentration in case of building structures made of low permeable materials (e.g., ordinary concrete²⁹), the simplified formulation (1.b) is fully acceptable. This behaviour occurs because the low air permeability obstacles the advective flow, so the contribution of radon being transported down a pressure gradient gets negligible. The error introduced by considering the simplified approach is generally below 10% when the air permeability of the building materials constituting the structures is below 10^–12 m².

The evaluations reported have been conducted by assuming a uniform pressure gradient across the building structure of − 5 Pa (see § 2.1): if the pressure gradient is higher—various occurrences are documented in literature^33,34,35—the underestimation of both radon exhalation rate and radon indoor concentration may be even more severe.

The building structure thickness

Figures 8 and 9 report \(\:{\Delta\:}{\text{E}}_{\text{\%},\text{a}\text{d}\text{v}}\) and \(\:{{\Delta\:}\text{C}}_{\text{R}\text{n},\text{\%},\text{a}\text{d}\text{v}}\) obtained by assuming the values reported in Table 2, and varying only the wall thickness.

Percentage difference of radon exhalation rate from building structures as a function of the wall thickness between the simplified approach (1.b) and the exact one (2.a).

Percentage difference of radon indoor concentration established in the reference room as a function of the wall thickness between the simplified approach (1.b) and the exact one (2.a).

The results are about the same regardless the floor level. The simplified approach (1.b) always leads to an underestimation of both the radon exhalation rate and the resulting indoor activity concentration relative to the exact one (2.a), regardless the building structure thickness. The radon exhalation rate underestimation results roughly symmetrical relative to the wall thickness: this behaviour results from the mathematical formulation (see Appendix A) of the exhalation phenomenon in case of non-negligible advective flow (2.a).

The underestimation of the resulting indoor radon activity concentration gets roughly worse with increasing wall thickness. Thus, considering the simplified approach (1.b) leads to severe underestimation (up to around 50%) of the resulting indoor radon activity concentration especially in buildings characterized by thick structure, e.g., historical buildings. For buildings structures thicknesses up to 50 cm the radon activity concentration underestimation is constant at about 30%.