||This study aims at determining the macroscopic strength of porous materials having a Drucker–Prager solid phase at microscale and two populations of saturated pores with different pressures at both micro and meso scales. To this end, and taking account of the available results by Maghous et al. (2009), we first derive a closed-form expression of approximate criterion for a dry porous medium whose matrix obeys to a general elliptic criterion. The methodology to formulate this criterion is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. The obtained results are then implemented in a two-step homogenization procedure, which interestingly delivers analytical expression of the macroscopic criterion for dry double porous media whose solid phase at microscale obeys to a Drucker–Prager criterion.
After a brief discussion of the results, we propose an extension to double porous saturated media, allowing therefore to quantify the simultaneous effects of the different pore pressures applied on each voids population. The results are discussed in terms of the existence or not of effective stresses. Finally, they are assessed by comparing them to recently available results.