## 2 Materials and Methods
### Gas Diffusion Testing Procedures and Apparatus  
In the gas diffusion test, the effects of the attapulgite dosage, the diatomic 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 (\(D_{\theta}\)) per the research results of [PERSON] et al. [39; 40; 41]. \(D_{\theta}\) 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):  
\[\frac{\mathrm{d}q}{\mathrm{d}t}=-D_{\theta}\ \cdot\mathrm{A}\cdot\ \frac{\Delta C_{t}}{\mathrm{h_{s}}} \tag{2}\]  
where: \(q\) is the volume of gas diffusing into the chamber, cm\({}^{3}\); \(t\) is the diffusion time, s; A is the diffusion area of specimens, 30 cm\({}^{2}\) in this study; \(\mathrm{h_{s}}\) is the height of specimens, 2 cm in this study; \(D_{\theta}\) is the gas diffusion coefficient of specimens, cm\({}^{2}\)/s; \(\Delta C_{t}\) is the gas concentration gradient of both ends of specimens, g/cm\({}^{3}\). The rate of gas diffusion volume into the chamber with time can be also presented as Equation (3):  
\[\frac{\mathrm{d}q}{\mathrm{d}t}=\frac{\mathrm{d}(\Delta C_{t})}{\mathrm{d}t} \ \cdot\ \mathrm{h_{c}}\ \cdot\ \mathrm{A^{\prime}} \tag{3}\]  
where: \(\mathrm{h_{c}}\) is the height of the chamber, 15 cm in this study; \(\mathrm{A^{\prime}}\) is the diffusion area of the chamber, 133 cm\({}^{2}\) in this study. Then, Equation (4) is obtained by combining Equations (2) and (3). \[-D_{\theta}\ \cdot\ \mathrm{A}\cdot\ \frac{\Delta C_{t}}{\mathrm{h_{s}}}=\frac{ \mathrm{d}(\Delta C_{t})}{\mathrm{d}t}\ \cdot\ \mathrm{h_{c}}\ \cdot\ \mathrm{A^{\prime}} \tag{4}\]  
At the initial time (\(t\) = 0), the oxygen concentration in the diffusion chamber is 0, in the atmosphere is C\({}_{0}\), \(\Delta C_{0}\) was the difference between the oxygen concentration in the atmosphere and the diffusion chamber before the test, \(\Delta C_{0}\) = C\({}_{0}\). With initial conditions \(t=0\), \(\Delta C_{t}=\Delta C_{0}\) = C\({}_{0}\), Equation (4) is integrated from 0 to \(t\), obtaining results as Equation (5):  
\[\ln\left(\frac{\Delta C_{t}}{\Delta C_{0}}\right)=-\frac{D_{\theta}}{\text{h}_{ \text{s}}\cdot\text{h}_{\text{c}}}\ \cdot\ \frac{\text{A}}{\text{A}^{\prime}}\ \cdot\ t \tag{5}\]  
\(\Delta C_{0}\), \(\text{h}_{\text{s}}\), \(\text{h}_{\text{c}}\), \(\text{A}\), and \(\text{A}^{\prime}\) are the constants. Therefore, \(D_{\theta}\) can be calculated through the relationship of \(\Delta C_{t}\) 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 [PERSON] et al. [39; 40; 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). All experiments were conducted at a room temperature of 25 \(\pm\) 1 \({}^{\circ}\)C and relative humidity of 64% \(\pm\) 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%.