## 1 Introduction  
Currently, earth pressure balanced (EPB) technology has been widely used as the main construction method of urban subway tunnel construction. With the continuous advancements in technology and soil conditioner, the application scope of EPB construction encompasses almost all types of strata from clay to rock mass [1; 2]. When the tunnel is below the groundwater level, extreme water spewing will occur during the excavation in cohesionless soil that had loose structure and large permeability. To prevent groundwater spewing accidents in water-rich strata, the conditioned soil needs to have low permeability. Generally, when the conditioned soil permeability is less than \(10^{-5}\) m/s, the soil has reliable water resistance and can prevent the occurrence of water-spewing [3; 4].  
Foam stability has a large correlation with the permeability of foam-conditioned soils. The foam liquid half-life (\(T_{\text{hl}}\)) is the critical parameter of the foam stability. However, there is no uniform standard method to evaluate \(T_{\text{hl}}\). In the field of tunnel, most scholars tested the \(T_{\text{hl}}\) referencing the European Federation of National Associations Representing for Concrete (EFNARC) [5]. Some research shows that the \(T_{\text{hl}}\) is affected not only by the foam type, concentration, and FER, but also by the foam height, temperature, and atmospheric pressure [6; 7]. Therefore, to unify the test methods of \(T_{\text{hl}}\), it is necessary to specify the container (container diameter), foam height, foaming expansion ratio and laboratory temperature.  
Below the groundwater level in EPB TBMs, low permeability is the key to reducing the frequency of the water spewing phenomenon for the cohesionless soil layer with good flow plasticity and compressibility. To evaluate the foam properties of conditioned cohesionless soil, some scholars studied the influence of foam parameters (concentration, foaming ratio, injection ratio, etc.) on conditioned soil compression, slump, and permeability to meet the requirement of workability, plasticity (slump between 10-20 cm), and impermeability (permeability \(<\) 10\({}^{-5}\) m/s) [8,9]. Based on the results of slump and compressibility laboratory experiments, [PERSON] et al. (2009) [10] suggested that a higher FER (FER = 10-15) should be used in cohesionless soils. [PERSON] and [PERSON] (2010) [11] measured the permeability of foam-conditioned sandy soil (sand with a silt fraction equal to 5%) at FER = 12 and FER = 7.5 with, FIR = 60% and FIR = 40%. [PERSON] et al. (2018) [12] concluded that the increase in FIR (0%, 22%, 45%, and 67%) led to a decrease in permeability of the foam-conditioned weathered granite from 10\({}^{-3}\) to 10\({}^{-6}\) cm/s. However, most of the studies focused on the plasticity, compressive strength, and shear strength of foam-conditioned cohesionless soil, whereas systematic research on permeability was relatively limited.  
Cohesionless soil with a small amount of fine particles has a large porosity and permeability. When excavating below groundwater, it is easy to remove sand from the screw conveyor [13,14]. The higher the outlet pressure of the screw conveyor, the more obvious the water spewing phenomenon. [PERSON] et al. (2008) [15] found that soil pressure was linearly distributed with the screw conveyor length. When the groundwater pressure is high, it is not sufficient to rely on foam to improve the impermeability of cohesionless soils. Therefore, it is necessary to add a bentonite slurry or high-molecular-weight polymer materials to improve the impermeability of the cohesionless soils [16,17].  
To verify effect of foam parameters on cohesionless soil permeability and water spewing, this study explored the influence of \(T_{\text{hl}}\), FER and FIR on the sand permeability of foam-conditioned soils. Two aspects were included: (1) Determine the influence of the three factors on permeability and propose the optimal foam parameters; (2) Perform a case study to verify the optimum foam formation.