## 3 Soil Samples and Foam Agent Used in Experiments  
A mixed soil consisting of silty clay, fine-medium sand, and sandy gravel, with a volume proportion of 2:2:1 encountered in an EPBS tunneling projects in Beijing, was used in this study. The selected properties of the soil were tested based on GB/T 50123 [23] and are listed in Table 1. For silty clay, X-ray diffraction tests were performed to determine the mineral constituent, as shown in Table 2. Figure 4 shows the grain size distribution of the fine-medium sand and sandy gravel. Based on the liquid-plastic limit combined method [23], the plastic limit (\(W_{\text{P}}\)) and liquid limit (\(W_{\text{L}}\)) of the silty clay were 30% and 44%, respectively. For the natural silty clay with a water content of 25%, the plasticity index (I\({}_{\text{P}}\)) and liquidity index (I\({}_{\text{L}}\)) were 14% and -0.36, respectively. The gravel particles wrapped by silty clay and sand particles cohere the cutting tools on the cutterhead and it is hard to discharge the mixed soils via screw conveyor. The mechanical behavior of the mixed soil is not suitable for EPBS tunneling. Soil conditioning is needed to modify characteristics of the mixed soil to meet the requirement of EPBS machine. The natural water content of the mixed soil was approximately 25%, and the original water content was set to 25% for a group of soil sample test in this study. For foam agents, there are two performance indicators which are often used to characterize foaming behaviors and select a foam agent: Foambability and foam stability. Foambability means how many volumes of bubbles with stable structure and moderate size can be produced by a given amount of a foaming agent, which is quantified by the ratio between the resulting volume of the foam and the volume of foaming liquid (foaming agent + water), that is, the foam expansion ratio (FER). Foam stability (or drainage behavior) means how long the foam can remain and how long foamed soils can sustain the desirable properties or behaviors. The half-life period (\(T_{1/2}\)), representing the time for half volume of the liquid matrix flowing out of the foam, can be used to characterize the foam \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Soils**} & **Natural Bulk Density** & **Void Ratio** & **Cohesion** & **Internal Friction Angle** \\ \cline{2-5}  & \(\rho\) & \(\epsilon\) & \(\epsilon\) & \(\varphi\) \\ \cline{2-5}  & **(g/cm\({}^{3}\))** & & **(kPa)** & **(\({}^{*}\))** \\ \hline Silty clay & 1.96 & 0.77 & 25 & 10 \\ Fine to medium sand & 2.00 & 0.60 & 0 & 30 \\ Sandy gravel & 2.05 & 0.45 & 0 & 45 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geotechnical properties of tested soil. Figure 3: Friction coefficient test device. stability. There are several important conditioning parameters for foam agent, which are defined as follows [2,15]:  
\[C_{f}\ =\ \frac{V_{f}}{V_{L}}\times 100(\%) \tag{2}\]  
\[FER\ =\ \frac{V_{F}}{V_{L}} \tag{3}\]  
\[FIR\ =\ \frac{V_{FIR}}{V_{S}}\times 100(\%) \tag{4}\]  
where \(C_{f}\) is the concentration of the foaming agent (\(\%\)), \(FER\) is the foam expansion ratio (dimensionless), \(FIR\) is the foaming injection ratio (\(\%\)), \(V_{f}\) is the volume of foaming agent (mL), \(V_{F}\) is the volume of foam (mL), \(V_{L}\) is the volume of foaming agent and water (mL), and \(V_{S}\) is the volume of soil (mL). In order to obtain the foam during laboratory test, a commonly used method called the Waring-Blender method was used in this study. The procedure of foam production in the Waring-Blender test is as follows: (1) 100 mL foaming liquid (foaming agent + water) with different concentration of foaming agent (\(C_{f}\), _vol._%) was added into a mixer; (2) the foaming liquid was thoroughly mixed for 1 min at a rotational speed of 3000 rpm (revolutions per minute), as shown in Figure 5a. Then, the foamability (i.e., \(FER\)) and foam stability (i.e., \(T_{1/2}\)) of the generated foam were tested, as shown in Figure 5b.