*2.3. Gas Diffusion Testing Procedures and Apparatus*

In the gas diffusion test, the effects of the attapulgite dosage, the diatomite dosage, and the ratio of dual-additives on the gas diffusion barrier performance of the amended compacted clay were conducted. Oxygen was used in this study, because when the gas dissolves easily in water or reacts with the components in the soil, the measured gas diffusion coefficient of the soil was low, resulting in the test error. The gas barrier performance of amended compacted clay was characterized by gas diffusion coefficient (*Dθ*) per the research results of Taylor et al. [39–41]. *D<sup>θ</sup>* was calculated based on the first Fick's law and the change rate of oxygen concentration in the diffusion chamber with time:

The first Fick's law is Equation (2):

$$\frac{d\mathbf{q}}{dt} = -D\_{\theta} \cdot \mathbf{A} \cdot \frac{\Delta \mathbf{C}\_{\mathbf{f}}}{\mathbf{h}\_{\mathbf{s}}} \tag{2}$$

where: *q* is the volume of gas diffusing into the chamber, cm3; *t* is the diffusion time, s; A is the diffusion area of specimens, 30 cm2 in this study; hs is the height of specimens, 2 cm in this study; *D<sup>θ</sup>* is the gas diffusion coefficient of specimens, cm2/s; Δ*Ct* is the gas concentration gradient of both ends of specimens, g/cm3.

The rate of gas diffusion volume into the chamber with time can be also presented as Equation (3):

$$\frac{\mathrm{d}q}{\mathrm{d}t} = \frac{\mathrm{d}(\Delta \mathcal{C}\_t)}{\mathrm{d}t} \cdot \mathrm{h}\_\emptyset \cdot \mathrm{A}' \tag{3}$$

where: hc is the height of the chamber, 15 cm in this study; A is the diffusion area of the chamber, 133 cm<sup>2</sup> in this study.

Then, Equation (4) is obtained by combining Equations (2) and (3).

$$-D\_{\theta} \cdot \mathbf{A} \cdot \frac{\Delta \mathbf{C}\_{\text{f}}}{\mathbf{h}\_{\text{g}}} = \frac{\mathbf{d}(\Delta \mathbf{C}\_{\text{f}})}{\mathbf{d}t} \cdot \mathbf{h}\_{\text{c}} \cdot \mathbf{A}' \tag{4}$$

At the initial time (*t* = 0), the oxygen concentration in the diffusion chamber is 0, in the atmosphere is C0, ΔC0 was the difference between the oxygen concentration in the atmosphere and the diffusion chamber before the test, ΔC0 = C0. With initial conditions *t* = 0, Δ*Ct* = ΔC0 = C0, Equation (4) is integrated from 0 to *t*, obtaining results as Equation (5):

$$\ln\left(\frac{\Delta\mathbf{C}\_{\rm t}}{\Delta\mathbf{C}\_{0}}\right) = -\frac{D\_{\theta}}{\mathbf{h}\_{\rm s} \cdot \mathbf{h}\_{\rm c}} \cdot \frac{\mathbf{A}}{\mathbf{A}'} \cdot \mathbf{t} \tag{5}$$

ΔC0, hs, hc, A, and A are the constants. Therefore, *D<sup>θ</sup>* can be calculated through the relationship of Δ*Ct* and *t.*

The optimal dosage and ratio of additives were determined through the orthogonal test. The test scheme of the gas diffusion test is shown in Table 3. The gas diffusion test was conducted as per the single chamber method recommended by Taylor et al. [39–41]. The testing schematic apparatus used for this study is shown in Figure 3. The apparatus consisted of a gas diffusion chamber, an oxygen transducer (KE-25, HELM AG., Hamburg, Germany), and a data acquisition (NL-115, HELM AG., Hamburg, Germany).

**Figure 3.** The chamber of soil gas diffusion test.

All experiments were conducted at a room temperature of 25 ± 1 ◦C and relative humidity of 64% ± 2% as per the following procedures: (1) The vacuum grease was applied to the inner wall of the cover (with 85% grids on the top) and outer wall of chamber top for lubrication and sealing. Then the prepared specimens were placed on the top of the chamber, and capped with the cover. (2) The inlet valve connected with the nitrogen cylinder and outlet valve was opened. It was deemed that the air in the chamber was discharged completely by nitrogen until oxygen concentration in the chamber decreased to 0.3–0.6%. Then, the inlet and outlet valves were closed after continuing to supply nitrogen for 10–15 s. (3) The data acquisition and oxygen transducer were used to automatically collect and record the oxygen concentration (*Ct*) in the chamber per 5 min until the oxygen concentration in the chamber was the same as the atmosphere (C0) and reached the stable state (*Ct* = C0). Combining the *Ct* and C0 obtained from the above, the gas diffusion coefficient *D<sup>θ</sup>* was calculated based on Equation (5).
