Analytical Solution to Cylindrical Cavity Expansion in Mohr–Coulomb Soils Subject to Biaxial Stress Condition

Abstract

In this paper, a semianalytical approach is presented to formulate an excavated cavity in Mohr–Coulomb soils subject to biaxial initial stresses. The response of cavity expansion within the plastic region was investigated by combining the Mohr–Coulomb criterion with the equilibrium equation. The elastic–plastic (EP) boundary was expressed by a new conformal mapping function with three unknown parameters, which were determined by the stress continuity condition at the EP boundary and the volume-conservation condition. In the elastic zone, the stress function was expanded into Fourier series for convenience of application and the coefficients of Fourier series were determined according to stresses at the EP boundary. An unassociated flow rule with a dilation angle of 0° was adopted in the plastic zone, and Hooke’s law governed the behavior of soil within the elastic zone. Comparisons between the proposed solution and Galin’s solution showed good agreements, which validates the proposed framework. Extensive parametric studies were also performed to explore the effects of the internal friction angle, cohesion, and coefficient of earth pressure at rest on responses of cavity expansion. The results suggested that an increase of the internal friction angle, cohesion, Young’s modulus of soil, and coefficient of earth pressure at rest all leads to a higher expansion pressure at the cavity wall, while the extent of the plastic region around the cavity shrinks with an increase of the aforementioned three parameters.