Analytical model for undrained residual shear strength of foam-conditioned coarse-grained soils in large deformation based on effective stress principle

Foam is usually used in soil conditioning of earth pressure balance shield tunnelling. The smooth muck discharge and chamber pressure transmission require foam-conditioned coarse-grained soils with suitable flowability to avoid face instability and excessive ground deformation. Inspired by undrained compression and shear mechanism, an analytical model is proposed for the undrained residual shear strength of foam-conditioned coarse-grained soils after large deformation under pressure. Firstly, the effective stress in one-dimensional undrained compression is obtained based on the ideal gas law and the hyperbolic equation for stress and strain. Then, the shear-induced excess pore pressure is calculated, and the relation between the residual shear strength and the vertical effective stress is derived. Furthermore, the analytical model for the residual shear strength dependent on shear rate is obtained. A series of undrained pressurized vane shear tests are performed to verify the analytical model. The average error between the analytical and experimental results is about 10%. It is proved that the analytical model is reliable in determining the residual shear strength under chamber pressure. Finally, the discussion of influencing factors manifests that the residual strength is raised by increasing the vertical total stress but reduced by increasing the foam injection ratio (FIR). It also revealed that the yield stress and plastic viscosity in the residual state are positively correlated with the vertical total stress but negatively correlated with FIR.