## 2 Materials and Methods  
### Low-Gas-Pressure Supply Equipment for Soil Gas Permeability Measurement  
The apparatus for soil gas permeability measurement is improved by a triaxial cell connecting a low-gas-pressure supply equipment, as shown in Figure 1. The low-gas-pressure supply equipment contains two Mariotte bottles (Bottles I and II), a differential pressure transducer, and a three-way valve, as shown in Figure 2. The function of the Marriott bottle is to output the liquid under a constant water head regardless of the changing depth in the bottle. In order to guarantee the accurate measurement of gas output as the volume of water outflow, thereby ensuring gas compression stability, two Marriott Bottles are employed in the gas supply equipment. Bottle I stands upright, whereas Bottle II stands upside down. When Bottle I is relatively higher than Bottle II, the connection between the pipe and the Mariotte bottle ensures that the water pressure from Bottle I is balanced with the gas pressure from Bottle II. The establishment of this equilibrium leads to the compression of gas in Bottle II, resulting in a stable volume. Consequently, the gas pressure remains constant until all the liquid in Bottle I has been exhausted. Therefore, the gas pressure in Bottle II remains constant. In the study, the diameter of each bottle is 330 mm, whereas its height is 300 mm. In the two bottles, water is used to supply gas  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Air** & **Reference** & **Air** & **Pressure** & **Air Supply** & **Advantage** & **Disadvantage** \\  
pressure, and thus, Bottle I is \(\Delta h\) higher than Bottle II. According to the principle of Mariotte bottle for constant pressure, \(\Delta h\) is determined as follows:  
\[\Delta h=\frac{P_{s}}{\rho_{w}g} \tag{1}\]  
where \(P_{s}\) is the desired gas pressure for supplying the triaxial cell, \(g\) is gravitational acceleration, and \(\rho_{w}\) is water density. In the study, a forklift is used to provide \(\Delta h\), as shown in Figure 2. \(\Delta h\) is 2 m to supply the gas pressure of 20 kPa. Not only can these two bottles supply the constant gas pressure, but also the volume change and rate of the supplied gas can be measured. As the water flows from Bottle I to Bottle II, the total volume of the supplied gas, \(\Delta V_{a}\), equals the increased volume of the water in Bottle II, \(\Delta V_{w}\):  
\[\Delta V_{a}=\Delta V_{w} \tag{2}\]  
The gas flow rates can be calculated by the differentiation of the volume change with respect to time:  
\[v_{a}=\frac{d\Delta V_{a}}{dt} \tag{3}\]  
Figure 1: Schematic of apparatus for soil gas permeability using low-gas-pressure supply equipment. Figure 2: Photograph of low-gas-pressure supply equipment. where \(v_{a}\) is gas flow rate and \(t\) is time. Combining Equations (2) and (3), we obtain:  
\[v_{a}=\frac{d\Delta V_{w}}{dt} \tag{4}\]  
In the study, \(\Delta V_{w}\) is measured by a differential pressure transducer. Unlike traditional apparatus, it is not necessary that the gas outlet in the triaxial cell connects a series of bubble flow meters to measure gas flow rates [46; 47]. It is noted that a three-way valve is installed between Bottles I and II, which is designed to reuse these two Mariotte bottles. Before any test, all water should be stored in Bottle I. Valve I is opened, whereas valves II and III are closed. For the three-way valve, a is connected to c. In this condition, the two Mariotte bottles are able to supply the constant gas pressure. As the gas in Bottle II flows into the soil specimen, the water also flows from Bottle I to Bottle II. When all water is at Bottle II, the two Mariotte bottles cannot supply the gas anymore. In order to reuse these two Mariotte bottles, valve I is closed, whereas valves II and III are opened. Valve III is connected to the atmosphere, but valve II to a vacuum pump.