Theoretical Solution for Cavity Expansion in Crushable Soil

Abstract

This paper proposed a theoretical solution for cavity expansion in crushable soils. The constitutive relations of the crushable soils were described by the breakage mechanics model that explains the grain crushing induced grain size redistribution. The governing partial differential equations (PDEs) for the cavity expansion issue were formulated through the equations of equilibrium, constitutive relations, continuity conditions, and drainage conditions. The similarity transformation method was utilized to transform the PDEs to first-order linear ordinary differential equations, for which the numerical solutions were then obtained through the Runge–Kutta method. The effective stress, breakage, and specific volume around cylindrical and spherical cavities were given. The limit expansion pressure was particularly discussed through parametric analyses. The results showed that the normalized limit expansion pressure increases as the normalized critical comminution pressure pc′/p0′ increases when pc′/p0′<10 and tends to a constant value when pc′/p0′>10. The increase of the normalized bulk modulus K/p0′ and critical state friction coefficient M led to the increase of limit expansion pressure, whereas the decrease of the ratio between bulk modulus and shear modulus δ, grading index ϑ, and coupling angle ω resulted in the increase of limit expansion pressure. Moreover, the limit expansion pressure was not sensitive to the initial specific volume υ0. The proposed solution could be used to interpret the issue of the pile end-bearing capacity in crushable soils.