MohrCoulomb Criterionbased Theoretical Solutions of Spherical Cavity Expansion Considering Seepage

Abstract:

An analysis was made of the cavity expansion based on the unified strength theory, seepage theory, strain compatibility equations in spherical coordinates and the associative flow rule. First, the excess pore water pressure formula was derived by the seepage theory in spherical coordinates and the basic formulas of stresses, strains, displacements in the elastic and plastic regions were obtained with the excess pore water pressure formula. Then the formula of displacements，boundary conditions of plastic zone were used to derive the theoretical relationship formula among the initial radius a0, expanded radius a and radius of plastic zone rp of the spherical bore. The solution method of the spherical cavity expansion considering seepage was obtained based on the abovementioned formula and some other relative formulas. The closedform solutions of stresses, strains, displacements in the elastic and plastic regions could be obtained in concrete problems of cavity expansion. In summary, the expansion pressure, stresses, strains, displacements in concrete problems could be directy obtained. Finally, a case study was made of the main parameters, the distributions of stresses, strains and displacements.

Key words:spherical cavity expansion theory; seepage theory; internal pressure; radius of plastic zone