Revisiting Undrained Cavity Expansion in Mohr–Coulomb Soils: Consideration of Limited Dilation

Abstract

The effective stresses are found to continually increase for undrained cavity expansion in Mohr–Coulomb soils with unlimited dilation. This paper revisits this problem and presents a new solution with further consideration of limited soil dilation. The soil is modelled as a non-associated Mohr–Coulomb model, and the limited dilation is controlled by the limited plastic volumetric strain, beyond which the soil dilation angle drops to zero. Both the auxiliary variable approach and total strain approach are leveraged for solution derivation, as the former helps to give more concise solutions while the latter is more efficient in calculating the stresses and deformation at a given time. A series of parametric studies is conducted based on the new solution, with highlighting on the influence of limited soil dilation. When dilation ceases for soils with limited dilation, it is found that the effective stresses remain steady instantly rather than keep increasing, and the excess water pressure and total inner cavity pressure gradually increase to steady states. The limit cavity pressure will be heavily overestimated if the limited soil dilation is neglected.