A simple model incorporating foam rheology to quantify foam penetration behaviour in EPB shield tunnelling

Fulfilling the role of a soil conditioner, foam plays a pivotal role in Earth Pressure Balance (EPB) shield tunnelling by enhancing soil properties such as lowering permeability and increasing flowability. This study introduces a macro-model designed to quantify foam penetration behaviour in saturated sand, utilising rheological properties. To validate this model, experiments were conducted to replicate the foam penetration behaviour. Six sand beds characterised by varying particle sizes, along with foam having an expansion ratio of fifteen, were employed for penetration tests under different hydraulic conditions utilising a sand column device. The rheological profile of the foam is described by the power-law model, as also found by rheometer tests, although with different parameters. The flow behaviour of foam within the sand column conforms to the flow equation that governs power-law fluids in porous media. The developed model effectively predicts the foam penetration process under varying hydraulic conditions compared with the experimental results. Furthermore, the fitting results of the experimental data indicate that the flow behaviour index of the foam remains approximately 0.09 across all tests, regardless of the type of sand used. In contrast, the model-derived generalised permeability coefficient strongly correlates with the effective particle size (d₁₀) of the sand bed. Overall, the model effectively quantifies the foam penetration behaviour, accounting for changes in infiltration velocity and pore water pressure, which is essential for understanding the transfer of support pressure in EPB shield tunnelling.