On the basis of the cylindrical cavity expansion theory

the concept of expansion velocity is introduced into the theory. The movement of the plastic boundary b is taken as the scale of “time” and the stress/strain of any point in the expansion body are described as the functions of the plastic boundary b and the current radius r. By using the spatially mobilized plane (SMP) theory of cohesionless soils in the plane strain condition

non-associated flow rule and considering cohesionless soils

shear dilation

the similarity solution of limit pressure is obtained. Meanwhile

the parametric study indicates that the influence of strength and shear dilation on the limit pressure and plastic zone radius is remarkable. With the increase of strength and shear dilation the limit pressure increases greatly while the plastic zone radius decreases. A comparative analysis shows that the limit pressure calculated from the SMP criterion which includes the effect of intermediate principal stress is obviously greater than that from the solutions based on Mohr-Coulomb criterion. The proposed solutions provide some theoretical bases for geotechnical engineering practices in cohesionless soils

such as cone penetration tests (CPT)

jacked piles

and so on.