Effective yield strength of a saturated porous medium with a spheroidal meso-pore and spherical micro-pores

A macroscopic yield criterion has been derived in the present work for a double saturated porous medium with a spheroidal pore at the mesocale and spherical pores at the microscale. These two types of pores are well separated at two different scales. The meso spheroidal pore saturated by a pore pressure which is different from the one in the micro spherical pores. A Drucker-Prager type criterion is adopted for the solid phase at the microscopic scale to describe its asymmetric behavior between tension and compression. The methodology to formulate this criterion is based on the limit analysis approach of a spheroidal volume containing a confocal spheroidal pore subjected to a uniform strain rate boundary conditions. The matrix at the mesoscopic scale obeys to a general elliptic yield criterion. Based on a two-step homogenization step, the influence of meso-pore shape (spherical, prolate or oblate), micro-porosity, meso-porosity and the effect of pore pressures at different scales are taken into account explicitly by this macroscopic yield criterion.