Sample permeability characteristic
Based on the principles outlined in Eq. (1), the permeability coefficient for each specimen was determined. The results, illustrating how permeability varies under different covering layer thicknesses at moisture content levels of 5%, 10%, 15%, and 20%, were graphically represented in Fig. 6a–d. Upon examination of Fig. 6, it was evident that the permeability coefficient for each specimen declines with increasing pressure. This decline was initially steep, then levels off gradually. At pressures exceeding 0.35 MPa, the influence of pressure on permeability was markedly reduced, with the permeability curves tending to flatten and most values falling below 1 × 10− 11 m². Additionally, the variability in permeability among different covering layer specimens was minimal under these conditions. Conversely, when the pressure was below 0.35 MPa, the impact of pressure on permeability was more pronounced, as the curves exhibit a steeper gradient, showing a notable difference in permeability between specimens with varying covering layer thicknesses.
Gas permeability of covering layer specimens with different moisture contents. (a) 5% moisture content, (a) 5% moisture content, (c) 15% moisture content, (d) 20% moisture content.
The distribution range of gas permeability for each specimen was from 4.29 × 10− 12 m²~3.87 × 10− 11 m².The correlation between the permeability coefficient K(m2)and P(MPa) conformed to the mathematical model presented in Eq. (2), with most fitted R2 values exceeding 0.990.
$$K = \frac{1}{{a + bP}}$$
(2)
Where a represents the initial value of permeability; b reflects the degree to which pressure influences gas permeability.
The fitted model aligns well with the established model used for calculating the permeability coefficient. Variability was observed in the permeability characteristics of both the covering layer and tailings across the tests. This variability could be attributed to differences in the thickness of the covering layer and tailings in the test specimens, as well as inconsistencies in moisture content. These factors collectively contributed to the differences in coefficients a and b in the fitted models for each specimen.
Effect of covering layer thickness and moisture content on permeability
Figure 7 illustrated the average permeability of specimens with covering layer thicknesses of 0 cm, 5 cm, 10 cm, and 15 cm, while Fig. 8 depictd the average permeability of specimens with moisture content of 5%, 10%, 15%, and 20%. The difference in gas permeability between 0 cm and 15 cm covering layer thickness at 0.15 MPa(\(\Delta {K_{0.15}}\)) was 1.88 × 10− 11 m². In contrast, the difference at 0.55 MPa(\(\Delta {K_{0.55}}\)) was 2.40 × 10− 12 m², resulting in a total difference of 16.4 × 10− 12 m² between \(\Delta {K_{0.15}}\) and \(\Delta {K_{0.55}}\). Additionally, the difference in gas permeability between 5% and 20% water content at 0.15 MPa (\(\Delta {K_{0.15}}\)) was 5.59 × 10− 12 m². At 0.55 MPa (\(\Delta {K_{0.55}}\)), the difference was 1.51 × 10− 12 m², leading to a total difference of 4.08 × 10− 12 m². These results indicated that the effect of covering layer thickness on soil infiltration rates was significantly greater than that of soil water content, particularly under low-pressure conditions. Therefore, in the practical application of radon control using soil covers, increasing the thickness of the soil cover could more effectively reduce soil permeability and enhance its radon prevention performance. While increasing soil water content could also reduce permeability, its impact on radon prevention performance was comparatively limited.
Average permeability of specimens with different covering layer thicknesses.
Average permeability of specimens with different moisture content.
Samples of radon exhalation characteristic
Radon exhalation rate
The relationship between radon exhalation and cover thickness was often approximated using an empirical formula with the covering layer measurement method31. This relationship suggested that covering layer thickness was linearly correlated with the natural logarithm of the ratio of radon exhalation rates measured before and after the application of the cover. The equation representing this relationship was as follows:
$$X_{c} = B\ln \frac{{J_{0} }}{{J_{x} }} + A$$
(3)
where\(X_{c}\)is the thickness of the covering layer (cm); \(J_{0}\)is the radon exhalation rate when it is not covered (Bq·m− 2·s− 10);\(J_{x}\)is the radon exhalation rate of the covering layer layer after being covered (Bq·m− 2·s− 1); A reflects the degree to which the cover layer thickness affects the radon exhalation rate; B represents the initial value of the radon exhalation rate when there is no cover layer.
Substituting the covering layer thickness and the calculated radon exhalation rate into the above expression, the values of slope B and intercept A could be obtained after linear fitting, and the fitting results were shown in Fig. 9.
Fit of covering layer thickness to ln(J0/Jx).
The R² values of the linear fit depicted in Fig. 10 are 0.975, 0.903, 0.937, and 0.940, respectively, demonstrating a pronounced linear correlation. The results shown that the physical simulation test of radon control with soil covering layer conformed to the basic law of radon reduction. The coefficients A and B in the fitting model were.
Effect of covering layer thickness on radon exhalation rate.
different under different cover soil moisture content, and the fitting lines were obviously separated. It also shown that the moisture content had a significant effect on the radon exhalation rate.
Effect of covering layer thickness and moisture content on radon exhalation
The radon exhalation rates were calculated and categorized using cumulative radon concentrations based on varying cover thicknesses and moisture contents. This process facilitated the generation of graphs illustrating how the radon exhalation rate fluctuates with changes in cover thickness and moisture content, as shown in Fig. 11.
Covering layer properties for different covering layer thicknesses, a is the variation curve of radon exhalation rate and permeability coefficient under the covering layer thickness, and b is the variation curve of radon exhalation rate versus gas permeability.
Figure 10 demonstrated the significant influence of both moisture content and soil thickness on the radon exhalation rate. The data indicated a diminishing radon exhalation rate as soil thickness and moisture content increase, following a non-linear relationship. Specifically, with a moisture content of 15% and a soil thickness of 5 cm, the radon exhalation rate approaches zero. Additionally, at a soil thickness of 15 cm, the radon exhalation rate remains nearly minimal, indicating that the effect of moisture content on radon exhalation was minimal under these conditions.
As the cover layer thickens, the path for radon gas to travel becomes longer, increasing the distance over which it diffuses and reducing the permeability, which significantly lowers the radon exhalation rate. Meanwhile, higher water content improves the cover layer’s seal by filling the pores, further reducing radon gas release. However, when the cover layer is thicker, the effect of increasing water content on radon exhalation diminishes, illustrating the combined impact of thickness and moisture content working together.
Radon control law of covering layer
Upon examining Figs. 11 and 12, it becomed evident that radon exhalation in the surface of the covering layer shown a negative correlation with moisture content and covering layer thickness. Conversely, the radon exhalation rate shown a positive correlation with the permeability coefficient. The radon exhalation rates and infiltration coefficients, determined under varying moisture contents and thicknesses in this experiment and presented in Fig. 12b, conform to a natural exponential function model. These relationships were expressed by Eqs. (4) and (5), respectively.
$$y=17.84 – 9.36{e^{ – 19.07}}^{x}$$
(4)
$$y=13.98 – 7{e^{ – 63.42}}^{x}$$
(5)
Properties of covering layer with different moisture content, a is the curve of radon exhalation rate and permeability coefficient change with different moisture content, and b is the curve of radon exhalation rate versus gas permeability.
Figure 11a illustrated that both the gas permeability coefficient and the radon exhalation rate of the covering layer clay decrease as water content increases within the range of 5–20%. Notably, the radon exhalation rate decreased rapidly between 5% and 10% water content, while the reduction slows down in the range of 10–20%. The covering layer clay swells upon absorbing water, constricting the soil’s pore spaces. As water content increases, the free water further occupies these pore spaces32,33,34, leading to a decrease in the gas permeability of the soil. Consequently, the blocking effect of the covering layer on radon transport was enhanced, resulting in a reduced quantity of free radon in the tailings that can migrate through the covering layer’s pore space to the surface. This ultimately decreased the radon exhalation from the surface layer of the covering layer.
Figure 12a illustrated that both the permeability coefficient and the radon exhalation rate of the covering layer decrease as thickness increases from 0 cm to 15 cm. A linear relationship existed between gas permeability and covering layer thickness. The radon exhalation rate decreased rapidly in the interval from 0 cm to 5 cm, while the decline becomes more gradual from 5 cm to 15 cm. When free radon in tailings exhalants from the surface of the overlying layer, the migration path of radon in the overlying soil becomed longer with the increase of the thickness of the soil coverlying. At the same time, the gas permeability of soil overlying decreases, and the radon control performance of soil covering layer was enhanced20,35,36. This improvement in radon control properties was significantly influenced by the soil’s water absorption characteristics, covering layer thickness, and pore structure. Therefore, these parameters should be comprehensively considered when designing cover disposal strategies for UMTs to achieve a more economical and effective treatment solution.
In addition to gas permeability, diffusion coefficients played a critical role in understanding the migration of gases like radon through soil. The diffusion coefficient D describeed the rate at which a gas diffuses through a medium due to concentration gradients. According to Fick’s first law of diffusion, the diffusion flux J was directly proportional to the negative of the concentration gradient, as expressed by the Eq. (6):
$$J= – D\frac{{dC}}{{dx}}$$
(6)
Where J is the diffusion flux, Bq/(m2·s) ; D is the diffusion coefficient, (m2/s); is the concentration gradient, Bq/(m4).
For steady-state conditions, assuming a linear concentration gradient of radon C within the covering layer, the relationship between the radon exhalation rate J and the diffusion coefficient D could be described as Eq. (7):
$$D=\frac{{J \cdot h}}{{{C_0}}}$$
(7)
Where C0 is the radon concentration at the bottom of the covering layer, Bq/m³;h is the thickness of the covering layer, m;
The value of C0, the radon concentration at the bottom of the covering layer, was kept consistent across all experiments. This uniformity ensured that the observed variations in the diffusion coefficient and radon exhalation rate were primarily influenced by changes in the cover layer thickness and moisture conten, rather than by differences in initial radon concentration. By standardizing C0, the results could more accurately reflect the impact of the cover layer properties on radon diffusion and exhalation.
According to the results in Fig. 13, the diffusion coefficient decreased as the thickness of the cover layer increased, with a notable drop when the thickness reached 15 cm. This suggested that a thicker cover layer forced radon gas to travel a longer path, which increased flow resistance and reduced the diffusion rate. A positive correlation between gas permeability and the radon diffusion coefficient was observed, implying that higher permeability generally led to a higher diffusion coefficient. This could be attributed to diffusion being primarily driven by concentration gradients, with greater permeability facilitating gas flow and thereby enhancing radon diffusion. Furthermore, the diffusion coefficient decreased as soil moisture content, pressure, and thickness increased. This was due to higher moisture, pressure, and thickness increasing the resistance to gas migration, which ultimately reduced the diffusion coefficient.
Variation of radon diffusion coefficient with covering Layer thickness and moisture content.