A Graphical Theoretical Framework for Cylindrical Cavity Expansion in Mohr-Coulomb Geomaterials

Abstract

This paper develops a complete analytical solution for the drained (or dry) cylindrical cavity expansion in non-associated Mohr-Coulomb soil, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single soil particle at the cavity wall). The novelty of the new solution lies not only in the relaxation of the strict intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but in the comprehensive consideration of arbitrary values of K_0, the coefficient of earth pressure at rest, as well. The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during drained expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K_0 being covered. Some selected results are presented for the calculated cavity expansion curve and limit cavity pressure through an example analysis.