A new yield criterion based constitutive model for porous materials

In the present work, a new explicit expression of macroscopic yield criterion is derived for porous materials, such as soil, rock and cement -based materials. To consider the asymmetric behavior between tensile and compression loading, the matrix is assumed to obey to a Drucker-Prager local criterion. The influence of porosity and the effect of matrix properties are well taken into account by this criterion. By using the stress variational approach with a suitable statically admissible stress field, a new more accurate estimation with a simple expression has been obtained for the case of purely deviatoric loading. The exact solutions can be retrieved by this criterion in the case of hydrostatic loading. It also resolves the problem of discontinuity between tension and compression. The weaknesses of the main existing criteria have been overcome by this new yield criterion. By comparing with the finite element numerical results with a wide range values of porosity and frictional parameter of the matrix, the proposed macroscopic yield criterion has a great accuracy and improves the existing ones. Based on this yield criterion, a complete constitutive model is constructed and implemented. This micro -mechanics based model is then applied to describe the mechanical behavior of porous sandstone, and validated by the comparisons with experimental results at different confining pressures.