A modified constitutive equation for characterizing the undrained mechanical behavior of foam-conditioned soil

Foam plays a crucial role in conditioning the mechanical properties of coarse-grained soil during earth pressure balance shield tunneling. Experimental findings have shown that an appropriate foam injection ratio improves the workability and compressibility of conditioned soil, while reducing its shear strength under undrained conditions. Understanding how foam operates in soil pores is essential for interpreting these phenomena. This study utilized a theoretical two-dimensional (2D) model to analyze the effects of gas saturation, gas-liquid interface, and gas dissolution on the undrained mechanical properties of foam-conditioned soil. Based on these analyses, a constitutive equation was developed, using the transition void ratio, compression index and contact coefficient as key parameters to describe the relationships among vertical stress σ v , void ratio e c , and shear strength τ . The undrained mechanical properties calculated by the 2D model align well with experimental observations, indicating that while foam enhances the bonding force between soil particles, both excessive and insufficient gas saturation, along with larger contact angles, notably undermine this enhancement, resulting in unsuitable workability. A gas saturation of 0.5–0.8 is recommended for soil conditioning. Under typical chamber pressures, the effects of gas-liquid interface and gas dissolution on compressibility and shear strength are negligible. The constitutive equation demonstrates excellent agreement with experimental data, and can well predict the variations in σ v - e c - τ . This study contributes to understanding the role of foam in soil pores, and the developed constitutive equation serves as a valuable reference for describing the undrained mechanical behavior of foam-conditioned coarse-grained soil.